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"Old": The 'power' of national curricula and international tests, and few opportunities for teacher agency for integrating social and ecological problems (especially in my reading of the Indonesian and Nepalese cases) resonates strongly with the ME situation in my country.

"New": I learnt for the first time about the cultural and linguistic diversity of the countries represented in the paper - suggesting potential for important socio-ecological ME? The notion of Ethno-Realistic Mathematics Education is new to me.

"Wonderings": I am interested in how language diversity has/can be used as a resource in the socio-ecological ME. I wonder if the tensions identified in the final discussion can be 'resolved' - are these not unavoidable tensions of scale and place that need to be navigated productively?

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"Old": The extent of the (educational) inequality, as it pertains to socio-economic context of communities and educational provision by school authorities.

"New": While, as noted above, the inequality resonates with my context on a different continent, the term 'educational poverty' is new and I think pertinent for my context. (I wondered if this notion is theorised?). The productive use of the notion on 'scales' (and 'multiple scales of socio-ecological encounters' as described in the paper) - scales of education (such as the classroom, research, out of school activities); and scales of the ecological in terms of studying the pond.

"Wonderings": As I read the paper, the drive for the education change/initiative emerged in the fact that a physical building had fallen into disuse? But the response itself was a complex and rich 'socio-ecological gesture'. Do the authors have thoughts on what can prompt such gestures? Also I am interested in how the authors are specifically using the 3 socio-ecological gestures proposed by Coles et al., (2024). The notion of mother tongue language is mentioned in the introduction. I am interested in how the innovation might have used language as a resource.

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"Old": I am familiar with the theoretical concepts - Wagner's community of practice and Valero's network of mathematics education practices.

"New": However, I was inspired by their richness for thinking about the complexity of a social, political, ecological and economic phenomenon such as peatlands. Also, the term 'peatlands' is new to me, as we refer to these as 'wetlands' in my context.

"Wonderings": Valero's network was developed in the turn towards the socio-political dimensions of mathematics education. I had certainly not thought of it was way to think about scales in the socio-ecological, and I am interested in the way Lisa has used their empirical work to add practices to the network in Figure 1. But given the history of the thinking, I wonder if it is still a human-centric model of the world? I am interested in how we might re-imagine this network (and its representation) for the socio-ecological world.

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Old: The collaborative project in the Philippines brings to mind the work of the Dakota/Lakota Math Connections project (Luecke and Sanders).

New: I was not aware of the PMRI adaptation of Realistic Mathematics Education in Indonesia or the Indigenous Peoples Education Curriculum Framework in the Philippines. I am interested in learning more about each of these initiatives.

Wondering: Does/could RME or the IPEd have a framework to facilitate incorporation of the values of multiple stakeholders, as well as mathematics in specific contexts? If not, could a framework be developed that is adaptable in different settings to spread decision-making into different scales? What are the essential characteristics that could be/must be adapted in different cultural settings (mastery of mathematics skills, values, personal development, …)?

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Old and New: This is one of the first papers I have read to mention the specific feelings of intimidation or threat for educators as they seek to empower their own students in the classroom. In my experience with secondary teachers, these challenges in role/identity shake the confidence and truly limit educators’ willingness to try new things. These feelings seem like important factors with which to engage through the training of a transdisciplinary approach.

Wondering: As the specific work of understanding the narrative continues, I wonder how one might address the challenges at all different scales of the local educational identity. How might an educational system (at a national level?) decide to incorporate or emphasize a transdisciplinary approach? How might those in power be convinced to disrupt said power? Are educators the point at which these conflicts come to pressure?

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"Old": The marginalisation of Indigenous knowledge in mathematics education - in my context this takes on the form of tokenism. In your description of the communitarian values, and the notion of 'fono' in Pacific communities, I am struck once again by the resonances with the values in other Indigenous communities, e.g. the notion of 'ubuntu'.

"New": The notion of MWB, which I would like to explore for use with undergraduate mathematics students (and then the links to other forms of wellbeing).

"Wonderings": Noting the 'local' scale of much of this work, I'm toying with what aspects might 'travel' - Is it the nature of the values? The nature of the mathematics? Regarding the former, I am reminded of comments by a colleague in my context who has noted the difficulties of teaching these values to those who have been raised in different value systems. Regarding the latter, I'm interested in whether the mathematical activity you propose is 'traditional' curriculum mathematics, or whether these knowledges need to change.

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Old: A colleague(Jessi Lajos)  introduced me to embodiment in mathematics. Since then, I have become more aware of how I use gestures in (at least) part of my mathematical conception-building and communicating. This colleague (and mentor) asks students to create metaphors to demonstrate conceptual understanding of abstract algebraic concepts. Asking students to visualize their understanding also connected me to Boaler’s work in Mathematical Mindset. I was also reminded how much valuable insight we receive through even short conversations with students.

New: It was interesting to analyze responses to a creative drawing prompt for the entanglements of mathematics and socio-ecological understandings, rather than strictly for evidence of student mathematical understanding.

Wondering: As the author mentions, I wonder if a more specific prompt would encourage additional students to bring their socio-ecological experiences into the mathematical conceptions they create. How might a similar task be extended to older students? How might presentations/conversations develop from these tasks in a classroom?

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"Old": I am familiar with Louie and Zahn's socio-ecological framework, as well as Coles et al.'s discussion thereof.

"New": I was inspired by the collaborations across scales described in the paper - shows potential to achieve this. Thinking about the link between culturally response mathematics education (which has the potential to invite knowledges and ways of knowing not recognised in traditionally dominant mathematics curricula) and mathematical modeling and data science. When the latter two are used, the nature of the mathematics itself is commonly not challenged. Although the work of Anania and Stiglitz is an exciting exception that I am aware of.

"Wonderings": As noted, the multi-scaled relations that were achieved in the two projects described are inspiring. I wonder if there are enabling conditions for this? This is useful for us to think about 'travel' across sites. The Louie and Zahn framework is developed in ME from the work of Bronfenbrenner. Coles at al. (2024) critique this for its human-centric approach - it focuses on social relations at different scales. I am interested in the authors' ideas on this in relation to Coles et al.'s prompt to ME to think about the the social and ecological as entangled, and to work against the culture/nature divide. So how do the authors see the ecological (in this sense 'natures') at these different scales. There is extensive mention in the paper of "community, culture and place", attention to Indigenous knowledges, and also an example involving oil companies, and I wonder how this might engage the ecological as well?

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"Old": I am familiar with the Atoyac River project, in particular the Museum aspect, from previous writings. Also various community mapping approaches. "Territory" as a network of multiple relations.

"New": The mapping aspects from the Atoyac River project. "Territory" as it pertains to spatial knowledge (possibly similar to scientific cartography as in le Roux & Motala?). How the mappings engaged different knowledge scales.

"Wonderings": The authors identify how the students were using spatial concepts in their mappings. I'm interested in what/how space and measurement - particularly in mapping - is prescribed in the mathematics curriculum and how it is taught, and whether the authors have any insights into how the community mappings and the curricula mappings might be related going forward. I am also interested in how the community mappings show the limits of traditional approaches to teaching space and measurement - for example, in my context finding/mapping the shorted distance from, for example, home and school, is not realistic. Students who walk often long distances to school have to consider personal safety, but also flooded rivers.

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Old: I've read about empowerment, critical citizenship, and post-human theories. I think empowerment and critical theories worked well in this text as it shows the connection to students and their work in the context of studying the water in their locality.

Wondering about: There was an implicit mention of post-human theories, and I wonder if this could be useful as another or next direction of this paper? In this sense, to explain how humans and non-humans collaborate and interact in the context of the study, that is water in this case.

New: The theory of Critical Stochastic Modelling Scenario is new to me. I think this theory explained clearly how statistical/math literacy is in connection with socio-ecological issues. By using this, it opens up how mathematics or mathematics education can be related or connected to other areas or other disciplines, which as also mentioned in the text, do not fit in 'mathematics category'. I think through research like this, we can show how mathematics and mathematics education are not limited to certain aspects.

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Old: The disconnection between indigenous ways of being and knowing, and mathematics. I am also grappling with the tension between school mathematics and indigenous knowledge (mathematics), how to bridge the two, and how to recognize indigenous knowledge systems. This problem is not only in indigenous communities but also in societies that were formerly colonized, and also in societies with immigrant population.

New and Wondering: the notion of Mathematical Wellbeing and the concepts of relationships and collectivism. I am trying to understand the roles of contextualization and cultures in different contexts; on how certain communities have different values and beliefs which are carried in the educational system (classrooms). But by reading this text, I am now wondering about how the concept of collectivism can also be used or can be 'other' option in other contexts, cultures, and educational systems.

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Old: The perspectives of family resemblances. I have read, albeit briefly, about those concepts; and how indigenous people have been marginalized through these perspectives.

Old and new: The concept of walking through the territory in the company of Elders, and/ or walking the word, that is, to have a dialogue with the elders. These concepts remind me of different indigenous communities that are consulting their elders to develop indigenous curriculums and reclaim their heritage, cultures, and languages. I like the idea of walking in the territory with the elders because it shows not only the personal connection of people to their lands, which is not part of school (mathematics) curriculum, but also the value being given to the knowledge, perspectives, and stories of elders who are otherwise ignored in school curriculum. These also show how mathematics is connected not only to people, their experiences, but also to their territories.

Wondering: The discussion on how ethno-educational knowledge ends up with evaluation using standardized model; and how an ethical-political perspective situated in territory and not on disciplines can be a solution to the socio-ecological disharmonies brought by development and civilization, and also for territorial autonomy. It made me think about the disparities between indigenous knowledge and school knowledge, and how to navigate between the two. I am thinking of it in the current society where we need indigenous knowledge to protect our culture and territories/lands; but we also cannot ignore that 'development' is also now part of our societies. With this, I am thinking how with the history of colonization/civilization, and now reclamation of indigenous knowledge, we now have a society where these two are intertwined and in the same space. We can have 'other' options, as what decoloniality is saying, but I am thinking about how these multitude of options can exist together.

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Old: Bringing socio-ecological issues in the classroom, and educational poverty. I think we've been tackling these issues recently and different disciplines.

New: The bottom-up approach of bringing the knowledge from the communities to the classrooms. Recent research, particularly those that involve indigenous communities, have been implementing this approach. However, the idea of promoting and using non-traditional approach to teaching math and science, instead of doing the opposite is new and interesting. By this, I mean that it has always been the opposite but this approach shows the acknowledgement of the values and knowledge of the communities, which are often positioned as below academic approaches. This approach does not only recognize indigenous/local knowledges, but also shifts the discourses surrounding the knowledge of local communities. And I think that this is very important, not only in learning but also in the preservation and maintenance of different cultures.

Wondering: Through the use of non-traditional approach to teaching math and science, I wonder how the discourses on standardization and academic language/disciplines will change.

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Old: The tension between school (formal math curriculum) and community (non-formal curriculum). This is not only evident in indigenous population, but also in countries that have curriculums that are not adapted to their contexts.

Old and New: The concept of learning with indigenous communities. This concept reminds of indigenous communities that consult their elders in developing indigenous curriculums to reclaim their heritage, cultures, and languages. I like this idea of bringing the communities to schools and recognizing their importance in learning mathematics and in the preservation of local cultures.

Wondering: Instead of integrating indigenous knowledges in school curriculums, what other things can be done? I am thinking that the concept of integration by placing indigenous knowledges in school curriculum, perpetuates the hegemony or dominance of school or formal curriculum. I understand the importance of formal curriculum but the shift in the discourses regarding the importance of indigenous knowledges can also help in the transformation of education systems. I understand that different countries have different policies regarding their education systems, but I am thinking that maybe, questioning this could eventually help in the transformation of education systems.

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OLD: Most mathematics educators have had limited success in influencing policy in many education systems. Similarly, many scholars and researchers are not in national leadership positions. Also, I agree with Geiger et al.'s (2023) report that mathematics educators’ goals and initiatives may start with different concerns than central and often top-down policy directions.

NEW: I was introduced to new concepts such as the political economy of climate change and climate justice. It was fascinating to learn that sustainability can be interpreted in multiple ways. The various understandings of sustainability stood out to me the most, particularly the distinctions between education about sustainability—accommodation, education about sustainability—reformation, and education as sustainability—transformation.

I was surprised to discover that climate change is often marginalized in educational curricula. According to the report, “only just over half (53%) of national curriculum frameworks include climate change, and usually, the depth of that inclusion is minimal.” Furthermore, only a small number of countries—just four out of a hundred—illustrate how mathematics contributes to their curricula addressing socio-ecological issues. As a result, mathematics seems to play a marginal role in discussions about environmental education, climate change, and sustainability.

WONDERING: The discussion focuses on the roadmap for enhancing educational practices, particularly in mathematics education, within the context of climate change. I wonder how different countries, especially those prioritizing climate change mitigation, address the gap between the necessary social actions and current educational methods. Also, I am curious about those countries that view adaptation with equal or greater urgency than mitigation. Furthermore, it is interesting to know how countries with centralized national curricula, which are common in many Asian countries, adopt a multifaceted approach in policy development, similar to multiple streams analysis.

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Something old: The role of norms and power structures in influencing what is valued and seen as the ‘right’ (privileged) ways of knowing is an aspect of mathematics education that I am familiar with both in relation to teaching and learning in a colonised country, and within research and publishing - whose and what perspectives are valued by reviewers and editors. This includes consideration of how this can be disrupted. I have also noted issues with authority when dynamics are changed within the classroom.

Something new: the conception of a transdisciplinary narrative in mathematics education and how this can extend ideas and disruption further. Also I have limited knowledge of the context of Egypt so both the history and types of governance structures were new to me.

Wondering: What would a transdisciplinary approach in mathematics education look like in action with students at different levels of schooling?

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Something old: Colonisation and the impact of this on the education system including the exclusion of Indigenous knowledge and ways of being and the domination of English language through schooling. Community mathematics practices could also be linked to the theory of funds of knowledge.

Something new: commonality of community and local knowledge and practices between Pacific nations and people that illustrated in this paper of Filipino peoples in relation to measurement.

Wonder: how can we support teachers to connect to and value community mathematics practices? Another idea that I grapple with both from this paper and my work is how decolonisation could be achieved in schooling when our school systems are inherently colonising?

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Something old: I am familiar with the socio-ecological framing used by Louie and Zhan (2022) to examine approaches to equity and also the use of mathematical modelling and data science to connect to student experiences and knowledge.

Something new: The launch years initiative and the scale of this and ways in which

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Old: I appreciate the use of Skovmose’s concepts of empowerment to gauge student development throughout this process. To me, student empowerment is a primary goal of mathematics education. The Critical Stochastic Modeling Scenario, while new to me, captures a familiar math modeling cycle paired with a familiar critical approach to mathematics. I am reminded of the Modules project in the U.S., math modeling curriculum with a social justice aim.

New: The length of this project was a surprise to me.  I am not familiar with the use of a long-term, engaging project with the same group of students over multiple years.

Wondering: I am wondering more about the teachers who perceived themselves as in crisis. I recognize that there exists a nearly constant tension between the mathematics of what is expected of teachers and what teachers value. Could you elaborate a bit more on the tension in this context?

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Continued from above: the voices of multiple contributors were drawn upon to gather the feedback and develop recommendations.

Wondering: the process used to build on the voices of multiple stakeholders in the initiative? How do you ensure voices of those typically marginalised are given status?

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Something old: The ideas of re-storying mathematics, ethno-mathematics and connecting to Indigenous knowledge and ways of being and storytelling.

Something new: The history of Kanaka Maoli and the colonisation of this area. This highlights to issue of food insecurity which is a common across the Pacific due to colonisation coupled with the importation and flooding of markets with cheap processed food.

Wondering: The connections between cultural values and mathematics across different cultures. How to harness the power of collectivism to shift to changes such as advocated in this paper. How do we move beyond cases which we individually recognise and analyse to wide spread models of change?

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Something old: The Atoyac river project, connections between mapping and spatial activities and environmental contexts. Ethnomathematics and critical mathematics framings.

Something new: The theoretical framework of territory and the broader definition of mapping used in connection with territory.

Wondering: the framing in this work is similar to my own where the connections and synergy between classical mathematics (represented in curriculum) and environmental contexts are connected. I wonder does this relate to student age - working with primary/elementary students - constraints of funding - what is possible in regards to disruption in the constraints of schooling?

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OLD: I am familiar with the concepts of power relations, such as the prominence of English as a language of power and prestige, as well as coloniality and the Bilingual Education Policy, which designates English as the main language of instruction in school mathematics while the mother tongue serves as an auxiliary language. In many Southeast Asian countries, school mathematics curricula are inherited from their colonial rulers. The Philippines shares many similarities with the Americans, especially regarding curricular content, the sequencing of topics, and teaching approaches (Vistro-Yu and Toh, 2019).

NEW: I was really excited to learn about the "locus of enunciation" concept, which highlights how some voices are heard in school math while others are ignored. It essentially points out that the individuals who represent math in schools often overlook the knowledge and experiences from local communities. Traditional and everyday ways of doing math in those communities are typically seen as less significant than what is taught in schools, as noted by Estrella, Valero, and Steenbrugge (2024). On a different note, the decolonial movement encourages us to rethink Eurocentrism and challenges us to reconsider Western educational ideas. This approach could serve as a fresh area to explore in mathematics education in the Philippines.

WONDERING: Based on the classroom observations and field notes from a Grade 5 mathematics class, as well as an interview with a fruit vendor, I think the disparity cited between school and community mathematics is similar to our study. This study identifies the tension that exists between the formal mathematics curriculum in school and the non-formal curriculum in the community. It is important to consider Bishop’s (1994) assumptions that “all formal mathematics education is a process of cultural interactions, and every child experiences some degree of cultural conflict in the process.” Hence, schools differ from social institutions like home or community.

I believe that the Indigenization of STEM education in the Philippines—whether as a collaborative project or through independent efforts by teachers and researchers—represents one concrete way to address the disparity between school and community mathematics. I wonder what other strategies we can implement to resolve this disparity. Also, I wonder whether the disparities in mathematics language are limited to spoken (verbal) or written forms. What about non-verbal mathematics languages?

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OLD: Concepts of restor(y)ing to rewrite histories with Indigenous timescales and cartography as a method (used both dominantly and in forms of resistance/activism).

NEW: Motala's notion of maps as characters in the case of Cape Town. That was fascinating approach

WONDERING: What do these "dynamic three dimensional maps that transcend multiple scales of space, time, and beings" look like? You mention activism. How do these maps help local communities with their territories?

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OLD: I am familiar with Foucauldian notion of power and the idea that mathematics as a discipline creates hierarchies and "others" Indigenous peoples. Also, the Embera perspective is similar to many Indigenous perspectives about the body/mind/spirit and a focus on oral knowledge, and the use of boarding schools by settlers who attempted to erase the knowledges/languages/practices of Indigenous peoples.

NEW: I learned the phrase "walk the word" and its use in context Sabaleta.

WONDERING: I wonder how the case of the Sabaleta who resisted an "Ethno education" can shine light on the longings/desires of the Embera Chami people and what might mathematics (and assessment) look like for them in a world where their ways of life were respected and there was a focus on healing (which relates to my work as well!)? How would that tie to scales?

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OLD: I am familiar with a collectivist lens used by other Indigenous peoples, focusing on student/community voice to drive change and make education meaningful, wellbeing in connection with mathematics

NEW: Talanoa as a form of methodology (similar to "talk story" in Hawaii)

WONDERING: I wonder if the social justice mathematics lessons based on modeling that are proposed could inadvertently reinscribe dominant forms of mathematical thought. Is there room for the MWB to change what we even count as mathematics? Or is it primarily about helping Indigenous students to use dominant mathematics to "address socio-ecological challenges of our time" by modeling data and making predictions? I'm intrigued by your work

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OLD: The Atoyac River project

NEW: Territory as a web of relationships between people and their environment.

WONDERING: I am wondering how the students' gestures might also be documented in terms of mathematics. I also wonder if there is any way to highlight the "privileged" perspective of knowing/sighting certain animals (e.g., eagles) and if that can be shown in their maps, or if they can be asked about how ratios relate to what is important (valued) on their maps (not just about distance).

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Old

I’ve experimented with collaboration across scales in two projects to tackle educational poverty. I know the fundamental importance of working on multiple scales, but at the same time, I experienced the enormous difficulty of having control that each stakeholder made work responsibility.

New

This is a new but old (vintage) aspect regarding learning communities. Data science classes include a higher percentage of students from underrepresented groups. I’m interested in discussing the idea that “cultural exchange opportunities with relevant modelling contexts correspond with a strong sense of belonging.”

Wondering

We are keen to gather insights from cultural experiences and integrate them into mathematical modelling.

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OLD: I am familiar with the concept of Wenger's Communities of Practice and also various researchers using socio-ecological issues to engage students in mathematics learning.

NEW: I have seen many social justice projects that use outside sources to inform students and their learning. But I do not find it common to see the students' findings/measurements to question the practices of others in society. I like the way your community of practice extended to engage multiple people (e.g,. landowner, representative from Naturvernforbundet) and how that led to a questioning of the measurement of carbon.

WONDERING: It seems one underlying goal of this project is for students to use mathematics as a "tool" to "read the world" (ala Gutstein, Coles, and others). As you proceed to analyze student work in greater detail, I wonder what opportunities are there for students to rethink mathematics as a discipline? What evidence is in their work that they have had opportunities to rethink what counts as mathematics, or mathematical terms/practices. I look forward to following more of your work

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Old

Oversimplification and the lack of authenticity in mathematics textbooks are well-known problems. A nontraditional approach to teaching mathematics could be beneficial. Students must take a direct role in constructing mathematical theories, observing, manipulating, and discussing artefacts.

New

Although we practised action research, we are unfamiliar with the photovoice method (Liebenberg, 2018). We also found the data analysis to be new.

Wondering

The authors observe shifts in Nadin's behaviour that enhance her confidence in mathematics. Do the authors note an increase in her study and knowledge of mathematical content?

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Old

We have direct experience with the community of practice (Wenger,1998). Over the years, we’ve worked to form a broad CoP, including teachers of all grades, educators, secondary students and researchers who reflect on innovative and non-traditional practices for teaching mathematics.

New

The role played by mathematics knowledge to protect and study the peatlands and their complex ecosystems.

Wondering

The author discusses forming a community of practice made up of only teachers/educators who collaborated with many experts. We wondered why we don’t include experts in the community of practice team.

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Something Old = Offer comments about how the paper raises issues that are already familiar to you (e.g., other literature you know, your context, things you’ve learned/experienced personally)

In the field of mathematics education, the recognition of the injustices caused by past and present colonization processes is deeply rooted in the so-called “enterprise of decolonization” initiated by the Ethnomathematics group led by Ubiratan D’Ambrosio. This pivotal perspective has evolved in various directions, particularly emphasizing the role of language, as explored in Bill Barton's book The Language of Mathematics and further developed in psychanalytic direction by Tony Brown.

The vignette described in the paper about the importance of “mango shape” reminds me of another example from Tony Brown's book Mathematics Education and Subjectivity. It recounts an experiment conducted by an English teacher, Krista Bradford, at a school in Uganda, which highlighted how the Runyankore language lacks terms for geometric shapes, particularly for the sphere.

Something New = Offer comments about how the paper raises issues that are new for you (e.g., new language/terms, new issues, new angles on the work, something you hadn’t thought about)

The focus on the specific context of Philippine allowed us to reflect about the double colonization processes happened in this country, the Spanish and the USA ones, open reflections to how transform this particular condition in opportunity also for mathematics education of these schools.

Something Wondering = Offer things you are wondering about (e.g., Are there connections/ resources/citations you see that you think might be useful? Are there other angles on the work that could extend it? Are there things that could be misconstrued by others that would

As Italians, we find strong resonances between these reflections and Gramsci’s profound discourses on subordination (or "subalternità" in Italian). Additionally, the authors' call to “By addressing the disconnections between school and community mathematics, it encourages a shift toward educational practices that honor local knowledge and empower communities, ultimately contributing to a more equitable and sustainable future” aligns closely with D’Ambrosio’s vision of equity, understood as the complete absence of exclusion.

We believe it would be valuable to further explore the comments on the vignette, particularly the significance of the mango shape. Delving deeper into the mathematical aspects related to it, such as a discussion on models like the geoid or ellipsoids and their eccentricity, could prove particularly insightful.

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Something Old = Offer comments about how the paper raises issues that are already familiar to you (e.g., other literature you know, your context, things you’ve learned/experienced personally)

The author was inspired by the study presented in Solares-Rojas et al. (2022) developed mathematical activities to foster students' ecological awareness by highlighting the historical and environmental significance of a polluted river in Mexico. This project included creating a museum to connect community members with the river's past, present, and future. This initiative linked mathematics, education, and sustainability. From this experience the author develop something completely new.

Something New = Offer comments about how the paper raises issues that are new for you (e.g., new language/terms, new issues, new angles on the work, something you hadn’t thought about)

The research draws on the theoretical framework of socio-ecological entanglement, which views social and ecological dimensions as inseparable. Socio-ecological gestures, as defined by Coles et al. (2024), involve practices that make visible the interconnectedness of ecological and mathematical concepts in teaching and learning. The study aims to investigate how students incorporate socio-ecological ideas into their mathematical thinking, specifically through their drawings.

Something Wondering = Offer things you are wondering about (e.g., Are there connections/ resources/citations you see that you think might be useful? Are there other angles on the work that could extend it? Are there things that could be misconstrued by others that would

The study emphasizes the transformative potential of integrating socio-ecological perspectives into mathematics education, showcasing how such approaches can enrich learning and foster sustainability. In an Italian interdisciplinary project connecting Dante Alighieri’s Inferno with mathematics, in which the students were invited to draw many times, one student suggested adding a new infernal circle for ecological crimes, this can be seen as socio-ecological gestures. This highlights the power of interdisciplinary approaches in fostering students’ ecological awareness and creative expression. A relevant theoretical framework for discussing this phenomenon could be Nemirovsky’s construct of Emergent Learning (2018).

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OLD: I am familiar with using mathematical modeling approaches to address critical social issues, local issues, and environmental issues. The investigation described in this chapter involves all three purposes.

NEW: The CSM framework (2021) was new to me, as was the regional context for the investigation. It was also new that this class project was spread out in time and space, and that the validation involved meeting with municipal officials.

WONDERING: How did the sampling points play into the students analysis of the water contamination? Were there spatial and dynamic aspects of the sources and dissipation of contaminants in the river and tributaries?

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OLD: Engaging families, parents with their children in hands on scientific investigations is familiar. We host a series of public lectures that are followed by a fair-like event in which university students run hands-on learning activities for children and parents.

NEW: I was intrigued by the construction of the pond, and the learning activities that were designed at the different scales. I particularly thought that the drop of water volume estimation would be engaging mathematically and easy to implement even with minimal equipment. Much of the plant life and microorganisms in this article were new to me.

WONDERING: How were the activities specifically organized? Were the teachers at the school primarily the leaders, and was it necessary to break the audience into smaller groups with multiple facilitators?

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OLD: Reading this I was reminded of learning about various ways of describing/knowing spatial orientation when I was visiting New Zealand. Maori and perhaps other Pacific Islanders would often describe locations based on story and reference points, like a volcano at the center of the island, rather than western traditional structures like a Cartesian grid. Here’s a reference to something like what I had heard of before — https://www.redalyc.org/journal/2740/274041586021/html/

NEW: So much!

WONDERING: Would love to see examples of the documents that emerge when groups engage in cartography 2 based creative activities.

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OLD: I am familiar with cartography as an objective mathematical science—a visual display characterized by a system that links numeric calculations with data measurements of land and time, similar to the maps typically used in school mathematics.

NEW: I like the line of thinking on critical posthuman cartography and the possibility of (re)storying through participatory. “counter-mapping” practices that challenge interactions that reproduce injustices and deal with other socio-ecological issues. I get to learn new terms like contemporary dot destiny map, vulnerability map, and choropleth map. I learned that maps can be used to tell stories about power relations, inequalities, and other socio-ecological interactions. Maps can be used to teach spatial justice and even (re)produce hierarchical scales of knowledge and knowers. Thus, it made me realize how maps can/have been used in interactions between school mathematics and space.

WONDERING: I wonder what other tools/activities can be used to (re)story mathematics education’s interactions at varied scales (past and present) that tackle socio-ecological issues.

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OLD:

I understand how different government structures impact the power dynamics of education and the dissemination of knowledge. This is often evident in colonized countries like the Philippines, where bureaucratic processes govern educational decision-making. I also connect with the concept that local narratives play a significant role in shaping the evolution and development of communities. Additionally, I recognize the importance of educational narratives in how they are communicated, transported, and orchestrated.

NEW:

I was thrilled to discover new terms such as transdisciplinary narrative, socially populated narrative, culturally populated narrative, and disruptive narrative. The comparison between traditional mathematics education and transdisciplinary mathematics education, as adapted from the International Society of Transdisciplinary Engineering (ISTE), is quite informative. I found it fascinating to learn that Egypt has three main types of schools: national public schools, national private schools, and international schools. However, transdisciplinary mathematics education is only experienced by a small minority of learners. The mathematical educational landscape in Egypt is deeply influenced by its social structures and cultural context.

WONDERING:

I wonder what classroom strategies and activities can be adopted or explored by teachers in the transdisciplinary integration of the socio-ecological into the mathematics classroom.

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Old: I am familiar with Gutstein’s work with secondary students in reading and writing the world with mathematics, in close connection with their community. While inspiring, I found it difficult (as a secondary teacher) to find practical ways to implement in a classroom with a fairly rigid math education system and curriculum.

New: I had not yet thought about how the content in this work was limited to using classical mathematics to read and write the world.

Wondering: The case of the kalo farmers is a specific example of incorporating multiple ways of knowing/doing/valuing within a colonized system and realizing change. I wonder how the lessons from this example could flow into a university and secondary math education program to realize systemic change. I think there is a tendency to collect specific challenges/problems from different contexts and present them to students as “projects” within an existing set of standards/curricula. Is there a bridge between the coordination of patterns, structures, and logics to read, restore, restory the world and the learning to do so?

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Old: I think this work connects to my paper. Instead of photovoice, the author used drawing. Do they use mathematics to connect to socio-ecological issues, or do they express socio-ecological issues through mathematics? For me, there seems to be a distinction between describing the socio-ecological, expressing the socio-ecological, and describing the mathematics with socio-ecological with.

I also perceive the connection of students' gestures from an embodied perspective, linking it to their ecological contexts.

New: I haven't thought about the difference between drawing and photovoice in terms of their embodied ways of knowing. It made me consider whether photovoice is also embodied, and in which ways. I think it might be. Another new thing – the term "Fraction Land." Does the word "land" also mean space? In that respect, it would make sense (to me). It seems like an interesting example where the mathematical phrase might have a double meaning with socio-ecological meaning inherent in it. I wonder if there are additional words like that. I am also amazed by the issues the kids draw in connection to fractions.

Wondering: Regarding sustainable mathematics education, which argues that mathematics education needs to connect mathematical concepts with the environment (e.g., interpreting large numbers as ecological quantities) – I feel that there are also other ways to interpret this. Is it the mathematics that's sustainable, the education, or the environment? For me, there is a tension between how I read the example and how I read the definition.

How do socio-ecological gestures and embodied perspective relate to one another? I wonder about the student's words: "flood" and "flood preservation." I would imagine that this is context-dependent (what she uses and thinks about). I wonder whether the phrase "Fraction Land" provoked this drawing? And if so, what could this apply to, or can we see this phenomenon in other mathematical topics?

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Old: It seems that poor achievement is a vehicle for many curriculum reforms.

New: I found it interesting that one possible reason for the contradiction between the positive feedback on the new curriculum and the low PISA results is a lack of balance between RME and the Indonesian educational context. I think other places could find this informative as well (thinking, of course, about their own context).

Wondering: I would love to learn more about the Kampung Naga Indigenous community in West Java and how they use geometry in an intuitive way in their everyday life. Do the other indigenous communities in the Napal and the Philippines have similar everyday situations which they address using mathematics in an intuitive way?

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Old: The concept and theories on embodiment and spaces. I have learned about how spaces and also tools influence the learning and behavior of students. De Freitas' research on school spaces show this.

New: The use of drawing to show ecological gestures is new to me. I think that drawings or illustrations can evoke and produce different feelings and ways of thinking, and in this text, the students produced drawings that connect mathematics and socio-ecological issues.

Wondering: In terms of connecting mathematics and socio-ecological issues, I am wondering how the two students came up with the idea of fractions and connect it to socio-ecological issues. I wonder what prompted then to make these drawings, as opposed to others who didn't. I also wonder what the other students drew.

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Old: The perspective that math has a marginal role in environmental, climate change, and sustainability education. With the shift towards the connection and entanglement of mathematics in different areas, the narrative that math is neutral, absolute, and abstract still remains. Additional, the limited influence of teachers in curriculum policies. This is the case in most countries because policies follow top-down approach.

New: The proposal to adopt a socio-ecological discourse in the math curriculum. Although this has been a topic of research recently, I think adopting a socio-ecological discourse in math curriculum will help frame mathematics as connected in different areas and disciplines, thereby changing the discourse and narratives towards mathematics.

Wondering: I think that we are moving towards changing the perspectives regarding mathematics and how mathematics education has an important role in this. However, this is challenging especially in countries where curriculums and policies are difficult to change. I wonder what possibilities are there in those contexts.

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Old: The paper sort of reassured what I felt before, that connecting socio-ecological issues to mathematics is easier in a voluntary after-school program, with issues that are out-side the formal curriculum.

New: I have not heard about the term “educational poverty” before. Additional, this is the first time I see that the mathematics is used not only to explore the socio-ecological issue, but rather as way to take an activist action, which is something that I aspire to do through connecting socio-ecological, but was not able to do so far.

Wonder: I wonder what lessons can be learned if we want to scale up this type of activism. I also wonder how it can be more explicitly connected to school mathematics? Or do these two aspects of mathematics are parallel (for being an activist in the socio-ecological space, and working on socio-ecological issues emerging from the “traditional” curriculum)?

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"Old": How the law was a central tool of coloniality, and how it harnessed science (e.g. cartography) to set up boundaries that destroyed relations, between humans and other than humans, including food systems. So law, science, education, etc., are all part of the colonial matrix of power. Also familiar with the concepts of restor(y)ing, mathematx, Lak'ech, nepantla. The paper gives an example of how disrupting systems can require using those dominant structures (e.g. formal legal system). i know of similar examples in my context where a colonial language is put to use for disrupting thinking about language.

"New": The case itself.

"Wonderings": Interested in research positionality in this case. And implications of this case knowledge for knowledge building across contexts.

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Old: It seems that having multiple stakeholders in beneficial for this type of project (this connect to other papers I read in this theme). I think that paper connect to Castilla et al.’s paper (discussing the challenges of RME in Indonesia) by presenting an example of how the local context can be used when working around RME.

New: I learned about PEATLANDS for the first time. I also found that the use of community of practice to be an interesting use in this case of multiple collaborators. Another interesting point was the engagement of different stakeholders, such as a public representative as part of the community. This made the students work to be of something of real and actual problem-solving and not only pretend problem-solving that students do to please their teachers.

Wonder: I wonder whether and how we can scale up this use of community of practice when addressing initiatives to promote socio-ecological issues in mathematics education?
Maybe like we have inquiry-based-learning, and project-based-learning where we refer to students learning through engagement around a topic, we can frame something like “socio-ecological action-based-learning 😊

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Old: I recognized the Atoyac River Memorial Museum school project from which this paper stems. The student narratives are especially powerful in bringing family history and community hopes to light.

New: I really appreciate using this concept of territory, as it can encompass a complex web of relationship. Incorporated in a mapping project, I can see how students are empowered mathematically and culturally.

Wondering: I am curious about the tension between these young students’ notion of territory and the concept of scale. Traditionally, the concept of scale is used as a way to make sense of a physical situation by applying common metrics, but I wonder if these younger students establish a concept of scale based on their values and their perceptions of importance. I also wonder whether the age of the students is a factor in the creativity and the details shared. Would older students, perhaps “well-schooled” in the concept of scale, be willing to challenge or adjust their territorial map based on their own experiences?

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Old: Professor Jhon’s Walking the Word reminds me of Freire’s Reading the World, but perhaps more broadly defining this reading or communication. (Being realistic about the human condition, but also recognizing the condition of the non-human and the connections that exist between). I was also reminded of similar conditions/goals of boarding schools in North America, to disconnect children from their families, language, culture.

New: The combined perspective of the “family resemblances” was new to me.

Wondering: I am curious about the reframing of the educational system from the development project to the care and protection of the Indigenous territories. In this paper, and others in this collection, there seems to be a need to know and work within the current, economic focused education structure in order to transform. For example, Professor Efraín states both an acceptance of the ICFES exam and a desire to improve/transform. Was that a common perspective with the Indigenous Embera Chamí teachers and the community at large?

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Old: I was reminded of the participatory design projects that Gutstein incorporates in his Chicago neighborhood school. With close community ties, authentic needs arise and can certainly stimulate engagement by students and adults alike.

New: I was struck by the comment that the pond discussion began with “every living being represents a point of view”. How was that theme carried throughout the project?

Wondering: I was wondering about the timing/planning of these family activities centered on the pond.  The headmistress mentioned a reframing of the discussion plane with parents, but I am curious how the parents were actually engaged in the conversation and the project.  Is it common for parents to be available during the school day for these partnerships or were they “after school” community activities?

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Old: As with mathematics knowledge, it is interesting to consider the transitioning view of cartography from artform to scientific and therefore “neutral” form. I am reminded of school lessons that analyze the “Mercator misconceptions” as, at least, starting points to questioning the neutrality of these works.

New: An idea that I am still thinking about: stories as both analytic and creative. The re-storying of cartography by the authors is a new idea for me, stimulating ideas for classroom experiences.

Wondering: As referenced in the paper, the mapping project for students in the Atoyac River valley seems to stimulate the re-storying of the local cartography. I’m wondering how to expand a project like this one for young students, to a project for secondary or university students, with the theoretical lens presented in this paper. Illustrating personal or community values using different scales, highlighting these values over time, thinking of boundaries, not as barriers or separators, but as zones of interaction and sharing.

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Old: Based on my experience in the US, and in the state of Utah in particular, the findings of this study do not surprise me. Locally, there is certainly a reticence, if not clear unwillingness, to include socio-ecological concerns in educational policy The predominant view is of mathematics as a neutral subject, with no room for social, environmental, or political concerns.

New: It was interesting to see which “vulnerable” countries incorporated mitigation and adaptation in their curriculum.

Wondering: I am curious about the multiple streams analysis in practice. Could you share a particular example of an innovation being used, through alignment, to transform policy?

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New: That in the Filipinas English is used as the language taught in school. And thinking  colonization and decolonization through language and mathematics.

Old: The disparities between school mathematics and community mathematics is a known phenomenon. I think this a particular case where there are tensions between the everyday local language and the language taught in school (English). For me it resonated other countries where math is taught in English (or half and half, some local language and some English). See for example: Morris, N. (2021). Learning probability in the Kingdom of Tonga: The influence of language and culture. Educational Studies in Mathematics, 107(1), 111-134.‏

Wonder: Following the citation above, I wonder if looking at the vignettes with other theoretical perspective will allow to view learning and teaching in a different way (so for example using commognition). Could it be that some mathematical concepts don’t have words of meaning in the local indigenous language? Like in the Tonga case?

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Old: It feels that the disconnection and sometimes even tension between school/western mathematics and Indigenous ways of knowing and doing is an emerging theme, which I read about in many papers in this theme.

New: I have learned a new definition for wellbeing and its connection to and use with thinking about mathematics education in the context of Indigenous ways of knowing and doing.

Wonder: I wonder how we can connect the two things, bringing the students and the community's voices to the center of the discussion, acknowledging the communities ways of knowing and doing, maintaining integrity to western mathematics while also being more explicit about differences that causing this gap (such as in the Morris, 2021).

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Old: I am familiar with the approach of authentic problem-solving as a way to integrate socio-ecological issues in mathematics education. Also building a strong partnership with stakeholders from different arenas seems to be a force enabling reimagining how mathematics can take new forms of knowing and doing.

New: The idea of collaboration across scale.

Wonder: Since building a strong partnership seems like an important aspect in shifting mathematics to include socio-ecological issues, I wonder how we can achieve that, and whether that should be on of the next emerging goals in the field.

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Old: Different mathematics such as ethnomathematics and social justice mathematics. I am a bit familiar with the different shifts and perspectives in mathematics education.

New: I find the concept of restor(y)ing mathematics very interesting - that we can restore, restory, and therefore change the dominant and current logics and ways of doing things. The notion of relationality reminds me of Tsing's The Mushroom at the End of the World, and how we, humans and non-humans are connected and entangled with each other. In the text, the Maoli farmers put kalo at the center in arguing for their needs - kalo, lands, farmers, and show how a simple mathematical equation can't solve their problems because the relationships between them are more complicated.

Wonder: This is the case of indigenous people and their relationship with their lands. I wonder, how it will be in the case of non-indigenous people? I am thinking that indigenous people have this sacred and close relationship with their lands and other humans. However, non-indigenous people do not have the same degree of relationship with their non-human counterparts. But this does not mean that they don't deal with the same problems.

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Old: The use of abstract and non-realistic examples and situations in mathematics classes.

New: The concept of authenticity in mathematical content. This somehow reminds me of contextualization and localization of mathematics content, but this text discussed authenticity in on the side of the pre-service teacher.

Wondering: I find the transition from the use of the image of Tom and Jerry to Ramadan interesting as it helps the pre-service teacher move from something that she thinks will spark interest towards something related to her. I wonder how we can apply this method to not just teach or learn math content, but also to learn the context in which the math content is situated, as in this text, religious practices.

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Old: The relationship between human and non-humans; and the connection of people to their land/territory.

New: The use of maps to understand how children construct meanings about their territory. I find it interesting that the activity opens up a space for students to talk about their culture and heritage from the stories of their family, and to share their experiences without being limited to questions or tasks that focus on math content. In this approach, the researchers are the ones identifying the math content in the conversations and maps of the students.

Wonder: The study showed how notions of space, scale, and proximity can be connected to socio-ecological issues and experiences/stories of the students. I am thinking about how there are notions in people's experiences or cultures that are not explicitly mathematics, in terms of school mathematics, and with this, how can we identify which are mathematics and not?

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OLD

I am aware that many countries incorporate authentic real-life problems into mathematics classrooms.

NEW

It was interesting to explore the interplay between authenticity, mathematical content, and socio-ecological issues through the “Designing-Teaching-Reflecting Cycle.” I learned about the Bedouin community, which is marginalized in Israel, and discovered that there is only one scholarly article related to mathematics education in this community. I was particularly struck by how the “photovoice” method was used as a tool in the mathematics classroom.

I appreciate the concept of “chunked protocols,” as well as the definitions of authenticity (relevance, appeal, and student motivation) and mathematical content (diversity, generalization, and precision). Additionally, I found Stillmen’s (1998) description of “wrapper tasks” to be insightful.

WONDERING

I wonder how tensions between authenticity and mathematical content are resolved in the mathematics classrooms of other marginalized communities that utilize the “photovoice” method and adopt the “Designing-Teaching-Reflecting Cycle

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Old:

The use of mapping activities is reminiscent of those developed in the kindergarten schools of Reggio Emilia or in schools inspired by the pedagogy of Celestin Freinet. Furthermore, the way children incorporate local knowledge, historical narratives, and environmental changes into their maps evokes the fundamental concept of Paulo Freire’s game of the people, emphasizing education as a process rooted in lived experiences and collective understanding.

New:

The idea of involving different schools from the same area, each experiencing different aspects of the river—some more preserved and others more polluted—is highly engaging and meaningful. It not only raises awareness of the harm already done but also fosters hope for preserving what remains unspoiled. Additionally, combining this with mathematics education and ecological studies makes it a rich and impactful initiative.

Wondering:

The future goals of the study include designing educational activities that enhance both spatial awareness and ecological responsibility, empowering children to advocate for their environment. However, I believe the mathematical learning outcomes developed by the children during these activities should be more explicitly addressed. Additionally, it is unclear what specific actions were taken during the project: Were there teacher training activities conducted for the educators involved from the different schools? If so, what were they? Providing more details about the activities carried out with the students would also be beneficial. For example, did students from the different schools have the opportunity to interact or collaborate in any way?

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Old

In this study mathematics education is reimagined to incorporate community-relevant problem-solving, replacing traditional, isolated approaches and this approach makes us think to the work of Eric Gutstein (cfr. Reading and writing the world with mathematics: Toward a pedagogy for social justice (2006))

New

The DRUMM project’s focus on empowering secondary students and teachers in rural and Native American communities through culturally responsive mathematics and data science curricula is highly impactful. The study’s identification of key obstacles—such as resistance to change, systemic inertia, and the need for sustained funding and support—highlights challenges that must be addressed for meaningful transformation. These barriers are not only practical concerns but also critical considerations from a research perspective if the mathematics education community aims to create a tangible impact. Promoting collaboration among teachers, university faculty, and policymakers to align curriculum reforms with the specific needs of these communities is a pivotal step toward achieving this goal.

Wondering

Nothing to declare ;)

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old

I agree with the main structure of the article: "The very heart of mathematics education is its people and their needs." I refer to a framework rooted in Vygotsky and socio-constructivist theory, which posits that learning and teaching processes are generated partly by internal representations of reality and partly by external cultural constructions. The researchers' role is to bridge the gap between these two representations, remain in the field and assist students and teachers in their mathematical modelling processes.

new

The utilisation of critical theory as a lens to construct a curriculum from a multicultural perspective.

wondering

Are critical theory elements suitable for discussing cognitive processes in learning and teaching? Do you think a model of cognitive dynamics is necessary to support students and teachers in their daily practice?

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OLD:  The following things were familiar to me: the framework of RME from Freudenthal supporting innovative ways of students learning mathematics; Ethnomathematics, the work of Coles et al about using community and climate contexts to explore mathematics, and the inappropriate nature of one-size-fits-all, top-down curricula, and piece-meal approaches especially when considering Indigenous communities.

NEW:  Latest developments in mathematics education reforms in Indonesia, Nepal, and Philippines.These were very interesting to learn!

WONDERING:  I'm wondering if the authors from Indonesia feel a tension between focusing on PISA data and wanting to talk about socioecological perspectives which tend to take up critique of mainstream views about mathematics and achievement, especially as it impacts Indigenous communities. Overall, is the goal of these three collaborating sites to use dominant mathematics (as a tool) alongside of or in association with community values/perspectives/wisdom? Or is there also a goal of wanting to challenge what counts as mathematics?

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OLD:  I’m familiar with and agree with the perspective that mathematical modeling and data science can serve as a means to engage students to learn STEM.

NEW:  Louie and Zhan’s socio-ecological framework.  Seeing the particular way the mathematicians, mathematics educators, and policy makers across layers of social and ecological activity was refreshing. I also liked seeing how you fleshed out Louie and Zhan’s framework with specific examples from your setting in Utah (Table 2)—the closing of the coal mine, etc. and the roles that different people would play at different levels.
WONDERING: Given the goal of using socio-ecological to not just mean the ecology of mathematics education (at this conference), I’m wondering how you see your work connecting with that of people who have theorized about mathematics in connection with Indigenous perspectives of lands, waters, etc. I’d like to learn more about how you see the closing of the coal mines relating to issues of territory, voice, time, etc.

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OLD: The need for a close proximity to the school if one is going to design a research project that involves students learning from ecology.

NEW: I appreciated learning about the specific case of a 3-year participatory design related to a pond and surrounding environment (EduCare Project) in Naples. The more we collect these specific cases (and with significant investment in these communities over time), the more we will be able to start thinking about similarities and differences across scales of place, time, peoples/nature, etc. I thought the cycle of integrating findings to inform teacher education and parent workshops was especially useful.  Seeing photos was really helpful for getting a broader and deeper sense of the project. I also liked the agency that was given to water.

WONDERING:  There is so much rich data in this project. At times, I felt like it had more of a science focus than a mathematics one.  I wonder what kinds of things students, teachers, and parents would say they learned that facilitated their mathematical understanding of this pond. Is it primarily about scale (macroscopic to microscopic)? If so, what does this help them understand about ratios or other concepts?

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OLD: I was familiar with Mignolo’s frame of coloniality of power; oppression of Indigenous people’s from their cultures/languages/world views through English language and Western views of mathematics and the world; and Coles et al framework.

NEW: The example of the different shapes of mangos and how students hold that as valuable community knowledge.

WONDERING:  The focus of the paper seems to be on how coloniality is maintained in the Philippines.  Yet, Mignolo (and others) talk about the ways people resist the Western codes and maintain/center their own perspectives.  I wonder if you also collected data that supports his claim or if you have thoughts about it?  In addition, I wonder about your use of the term “community mathematics” as opposed to “ethnomathematics.”  For example, with respect to using the body and nature as forms of measurement, what do you see is the distinction between the two terms?

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"Old": How local narratives are invisiblised in 'global' curriculum and mathematics education research discourses. This is a problem in mathematics education in generally, but will have particular manifestations for topics such as interdisciplinarity and socio-ecological.

"New': This short, working-in-progress paper gave me sense of the power of the notion of scales (a) within the 'local', e.g. difference schooling systems; (b) as historical, cultural, and socio-political; and (c) as classroom, teacher, schooling system.

"Wonderings": I thought about adapting a framework (the ISTE) from engineering, given the role of maths in that disicpline. So maths, like physics, chemistry, computer science, are commonly considered foundational knowledge that is put to work in engineering for human-centred design. Whereas maths as a sucject has different aims?

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"Old": How only some (and a very limited scope) of stories get told in maths problems.

"New": While I am familair with the type of problem, I have not heard it called a 'wrapper' problem before. Very apt! The Marco and Palatnik framework for task design. Using photovoice in thie way to generate thinking in task design.

"Wonderings": As I read, I wondered if Marco and Palatnik set up binaries between content and authenticity? and can maths be authentic, appealing and motivating? It certainly needs to be in higher maths. I wondered how local and global are defined. I read Tom and Jerry as being part of the teacher's experience? We get a powerful sense of this teacher's shifts over time. I wondered if the authors have have explore why they think this happened, given the design process used in the course?

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Old & New

I have read something about cartographies and their dystopian uses, and I admire the art of Sabine Réthoré, particularly the "Mediterranean without Borders". This article has opened my mind to numerous new ideas, including new words, concepts, references, and perspectives on mathematics and its power in education. Many thanks

Wondering

I reread the work and need to read it once or twice more to consolidate the new concepts and understand the potential for restoring scales in territories of socio-ecological interactions in mathematics education. I wonder if I may be lacking some theoretical arguments and literature references to grasp the message of this article entirely. Even though the work provided consistent examples, I need some more.

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(Relatively) OLD: Tensions between authenticity and mathematical content, as well as between real-life socio-ecological issues and mathematical content, are crucial for research in mathematics education.

NEW: I am excited to learn about the authors' introduction of the sacred into the mathematics classroom as a tension of scales. I agree with the authors that the sacred can offer a "potential route into mathematics that does not alienate learners from the living world." This perspective reminds me of the Baroque period's relationship between mathematics and the sacred.

WONDER: Could you provide a more explicit discussion of your understanding of socio-ecological issues and scales?

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OLD: The theoretical framework of Communities of Practice (Wenger, 1998) to address social participation processes. The author combines this theoretical tool with the concept of a network of mathematics education practices (Valero, 2010).

NEW: The author's perspective emphasizes the dialectical, multilayered, and multidirectional nature of the interactions among the actors involved.

WONDER: I would like the author to provide a more explicit discussion on the relationship between different scales and the network of mathematics education practices.

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OLD: The importance of meaningfully connecting mathematics with students’ real experiences and collective values.

NEW: The concrete examples of listening to the voices of young Pacific people highlight the opportunities for mathematics education to connect to social justice and socio-ecological issues by building on family and community experiences and values related to mathematical wellbeing (MWB).

WONDER: How do the authors visualise the connections between the identified experiences and values to teach mathematics? For instance, what specific modelling tasks could educators design to explore the impact of climate change on Indigenous food systems?

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(Relatively ) OLD: The meaningful dialectical connection between using socio-ecological issues as resources for mathematical thinking while simultaneously shaping the socio-ecological understanding through mathematical insights.

NEW: Ahn's perspective to understand the cultural contexts embedded in students' drawings and the interpretive nature of knowing situated in contexts, understanding students' drawings as embodied acts that bring forth their understanding of concepts.

WONDER: 1) Could you elaborate on Dami's interpretation of fractions in relation to her kingdom metaphor? 2) How can fractions be integrated into new tasks to provide meaningful insights into socio-ecological issues as depicted in the drawings?

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OLD: Layers of a socio-ecological framework (Louie & Zhan, 2022)

NEW: The authors offer a perspective on transforming mathematical learning environments for students through flexible mathematical modelling and data science processes to develop mathematics education rooted in community, culture, and place.

WONDER: Could you elaborate on the role of socio-ecological issues in the case of population change tasks, such as the influx of people to support the oil industry and population loss due to the closing of the coal mine?

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Old:

The definition of relational theory shares numerous points with the framework we adopt: the resonance model (Guidoni & Tortora, 2005a). It is asserted that teaching and learning are processes governed by a continuous interaction between individuals' internal pre-representations and the external representations of reality framed by cultural contexts.

New:

The restor(y)ing mathematics is a new concept, and I want to know more.

Wondering:

Does the restoring of a valid mathematics framework allow for a review of mathematics teaching for individuals (students and teachers) who live far from natural contexts (for example, in a concrete jungle)?

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Old: “There are some countries where there are links to recent mathematics educators’

attempts to rethink human-nature relationships (Barwell et al., 2022; Boylan, 2017; Coles 2023) and

embrace Indigenous perspectives (Coles et al., 2024; Guiterrez, 2017).“ The embrace of human-nature relationships and Indigenous perspectives in Canada and New Zealand is something I experienced while my children attended school in those countries.

New: .“Countries more vulnerable to climate change are more likely to include climate change in the

curriculum (UNESCO, 2021). Considering the case studies, there is a distinction between a focus on

mitigation and adaptation. Countries that have greater responsibility tending to focus on mitigation,

and within that on individual responses and actions. Those that are more vulnerable tend to either

include both mitigation and adaptation or make adaptation more prominent.” Firstly, I wasn’t aware of the UNESCO analysis of national curricula with respect to the climate crisis. Secondly, while not surprising, I was struck to learn that individual responses and actions were emphasized in countries that have greater responsibility for the global crisis. And finally, I found the author’s discussion of mitigation and adaptation new and interesting, and the article as a whole directed my thinking towards the role that mathematics education might have in the policy making.

Wondering: I’m trying to understand in what sense the relational approach to the socio-ecological is meant by the author in “the philosophy of mathematics education.” I wonder how human (and non-human) flourishing relates to the philosophy of mathematics education.

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Old: The project approaches to blending ecology with mathematics education. The collaborative engagement among teachers, students, and researchers highlights socio-ecological entanglements in the local context.

New: The inclusion of scientific exploration with natural elements like water and soil is exciting. Extending the traditional boundaries of laboratory learning into ecology contexts helps bridge mathematical scientific concepts with students’ lived experiences.

Wonder: For me, the discussion on the role of adults (researchers, family members, and teachers) raises important questions. Are adults primarily seen as facilitators, role models, or co-learners in this context? Additionally, I wonder about how sustainable this project is.

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Old: Connecting socio-ecology to community through collaboration among mathematicians, educators, and policymakers. These partnerships have consistently shown potential to align mathematical learning with socio-ecology education.

New: The establishment of a socio-ecological framework for mathematics courses integrates students’ collaborative experiences and highlights their interdependent relationships.

Wonder: Are there any differences between the two similar projects the authors engaged in?

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Old: The analysis of national curricula across various countries to highlight the need for a socio-ecological approach in mathematics education is a critical and familiar theme.

New: Revisiting and redefining socio-ecological terms in curriculum and pedagogy offers me with a fresh perspective.

Wondering: I want to hear more about the interpretations of the socio-ecological terms. And how climate change is addressed in the curricula of the four countries dealing with socio-ecology. How do these examples differ across countries?

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Old: Curriculum innovation that interconnects cultural contexts with mathematics. Recognising the interplay between cultures and curriculum has consistently proven effective in making mathematics more meaningful and relevant to learners’ lived experiences.

New: The synthesising scale across three countries is interesting.

Wondering: Has there been a noticeable shift in its mathematics curriculum to enact with socio-ecology? Are there unique challenges that emerge from their diverse cultural and educational contexts?

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“Old”: The place where I currently live in Chocó (Colombia), usually has the same problem: during the rainy season the rivers are at risk of overflowing. Another aspect that is similar with Colombia is that socio-ecological issues are not explicitly addressed in mathematics curriculum policies.

“New”: the concept of “embodied cognition” is new to me, in the perspective from which you approach it. In the Wittgensteinian perspective, which is the one I work with, thinking is also bodily actions themselves. In fact, from this perspective, mathematics is a set of “language games” that follow sociocultural rules. In this way, it can be understood that mathematics is practiced with the whole body, and not just with the mind.

“Wondering”: I keep thinking about the importance of connecting socioecological issues with mathematics, just as you propose. However, I wonder if students understand the socio-ecological issues through mathematics, or the socio-ecological issues and mathematics are intertwined.

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OLD: Although school mathematics offers students more opportunities and supports their development, it also contributes to the continuation and reproduction of coloniality. This occurs by promoting a Eurocentric notion of progress, which overlooks and disregards local community mathematical knowledge.

NEW: Making explicit the connections between the colonialist role of school mathematics and its impact on industrialization, urbanization, and economic development.

WONDER: Regarding the mango shape scenario, could you elaborate on students' and teachers' reactions to the disconnect between real, situated experiences and the official curriculum? Additionally, could you provide more detail on the specific socio-ecological crises faced by local communities in the Philippines that are perpetuated through coloniality in school mathematics practices?

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(Relatively) OLD: The discussion of how maps can/have been used in interactions between school mathematics and space, and its possibilities to detonate critical understandings of socio-ecological local issues.

NEW: The proposed theoretical perspective of using mathematical, cartographic science and critical posthuman cartography together (re)story mathematics education’s interactions towards socio-ecological justice.

WONDER: I would like the authors to elaborate their theoretical understandings of the relations and differences between the following related notions:

1. territory, territories of interactions, and complex territories of socio-ecological interactions

2. Deterritorialisation,  reterritorialise, and to territorialisation.

3. Cartographies and maps

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OLD: Thank you for sharing the struggles of the Kānaka Maoli people. Highlighting how different communities defend their territories can inspire others to explore their own methods of resistance and restoration.

NEW: This paper introduces me to many new concepts, yet they also resonate with my personal experiences and stories. For example, the unique ways the Kānaka Maoli people restore and restory mathematics to defend their narratives and territories, along with the living mathematx perspective, are particularly striking.

WONDERING: Are you planning to connect this work to school mathematics? If so, how will you do it? What voices will you include in this dialogue? Additionally, how will you address the traditional mathematics curriculum?

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Old: “Indigenization addresses socio-ecological issues by enriching mathematical understanding and cultivating responsible and culturally aware future citizens.” The authors’ examples of curriculum innovations were considered “small-scale” yet surely powerful for the teachers, students, and communities involved.

New: “One lesson plan developed under the study integrated the Bago’s ‘panagrama’ fishing method into

probability lessons, later expanding to include geometry concepts.” I’d love to know more about the ‘panagrama’ method. Very intriguing and fascinating, the alternate dynamite sounds horribly destructive. Fishing interestingly simultaneously requires very local expertise and rich opportunities for mathematical investigation.

Wondering: When teachers come from the communities in which they are teaching, that can surely diminish the issue that “the learners encounter dissonance between out-of-school and in-school cultural norms.” But what successful models are there to develop mathematics teachers with Indigenous heritage? Are there tensions that must be addressed in prevailing power structures? How?

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Something old: I am familiar with work focused on Indigenous knowledge and spatial reasoning. This has a strong connection with my own heritage from the Pacific region and our traditions of wayfaring and navigation through use of the natural world.

Something new: The conception and analysis of cartography through a critical lens and the transition of the positioning of cartography and the potential of new ways to think and use cartography which align with Indigenous ways of knowing.

Wondering: How do we leverage this type of work and understandings to challenge the hierarchy of ‘science’ and ‘mathematics’ and dominant narratives?

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“Old”: I am somewhat familiar with this type of projects that involve different actors at multiple scales, applied to contexts of poverty. Besides, I have worked on mathematical modeling (MM) and data science (DS).

“New”: Maybe, something new for me is working together with mathematical modeling (MM) and data science (DS) “as means for centering education on authentic problem solving that makes meaningful impact in communities” (p. 166).

“Wondering”: In that sense, I consider it a great challenge to be able to work on multiple scales combining these perspectives. As you point out, it requires active participation from different actors in multiple scales. I wonder what the negotiation processes would be like with each of these social groups.

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Something old: I am familiar with communities of practice and how this can be used to develop innovations and change in education. I am also familiar with the use of environmental tasks and mathematics.

Something new: I enjoyed the rich description of the peat lands and the ways in which these are managed and the environmental importance of these. Although not new as such, I really enjoyed the in depth description of how the community of practice was enacted in this study and the varying roles that were taken.

Wondering: How do we leverage rich interdisciplinary opportunities for learning such as exemplified in this example in schooling systems which continue to separate curriculum subjects and position teachers in silos?

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OLD: The idea of integrating socio-ecological issues within mathematics education reminds me of interdisciplinary teaching approaches which I have come across in previous literature. Educators often advocate for teaching strategies that bridge gaps between subjects to foster a deeper understanding of how different fields interact in real life. This paper seems to echo that sentiment by highlighting the importance of embedding ecological issues within the mathematics curriculum to enrich learning experiences.

NEW:. The paper introduces an innovative angle by focusing on how students' drawings on fraction concepts can reflect their awareness of social and ecological issues, in particular, to the concept of ‘socio-ecological gestures’. It is interesting to see how the creative act of drawing can serve as a medium for students to express their understanding and concerns about real-world problems while engaging with mathematical concepts.

WONDERING: I liked the questions the author posed in the end. I started to wondering about how the author, imagining going back – with the intention to dwell on the “new prompt”, what she would do and act in the classroom with the students? I am also wondering about the broader applicability of this approach beyond the specific context of sixth-grade Korean students. For instance, could similar drawing tasks yield comparable results in diverse cultural and educational settings? Additionally, it would be interesting to explore how this methodology can be expanded to other areas of mathematics education and whether it can help in addressing other pressing socio-ecological issues. The potential for such interdisciplinary studies raises questions about the long-term impacts on students' overall awareness and problem-solving skills.

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OLD: The discussion around educational poverty and its link to socioeconomic factors such as gender, ethnicity, disability, geographic location, and economic status resonates with existing literature on educational inequality. For instance, reports and studies by UNESCO and OECD often highlight these disparities, underscoring their global impact. My personal experiences is rather scarce when it comes to diverse educational settings but I can imagine how these factors manifest in different contexts, reinforcing the critical need for inclusive education strategies.

NEW: The authors introduce an interesting approach by advocating for an action research approach to address educational poverty. The participatory design project to create a pond in underprivileged areas adds a practical, community-driven aspect to the discussion, which is relatively novel compared to traditional policy-driven initiatives. Additionally, emphasizing the role of adults in fostering a scientific culture to combat educational poverty, rather than focusing solely on children or institutional changes, presents a new perspective that broadens the scope of potential interventions.

WONDERING: I am curious about the specific methodologies used in the action research approach mentioned in the paper. How were the school children (and other community members) engaged in the design and implementation process, and what measures are in place to ensure their active participation and ownership? Additionally, considering the goal of promoting scientific literacy and reducing educational poverty, how will the impact of this project be measured? It would be helpful to have more details on the evaluation criteria and long-term sustainability of such initiatives to understand how they might be replicated or scaled up in other contexts.

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OLD: The idea that engagement with policy is crucial for addressing socio-ecological issues in education is familiar territory. In my experience, similar themes have been explored in other educational research, particularly within the contexts of science education and environmental studies. The notion that mathematics education often finds itself on the peripheries of curriculum policy also resonates with existing literature that discusses the marginalization of certain subject areas in broader educational reforms.

NEW:  The discussion on how the fluid meanings of terms used in educational policy can influence the alignment (or lack thereof) between mathematics curricula and socio-ecological issues introduced a fresh perspective. Additionally, the specific mention of a gap between the concerns of mathematics educators and curriculum policy, using an analysis of 80 countries, provided new, concrete insights into the global dimensions of this issue.

WONDERING: I am curious about the specific methodologies used to analyze the curriculum policies of 80 countries. How were the data collected and what criteria were used to assess the extent of socio-ecological integration within mathematics curricula? Also, I wonder if there are any successful case studies where mathematics educators have managed to significantly influence policy, which could serve as models for other countries. It would be interesting to explore further how collaborative efforts between stakeholders—educators, policymakers, and environmental scientists—could be structured to bridge the identified gaps more effectively.

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OLD: The authors touch on the interdisciplinary nature of mathematics education, especially in its application to socio-ecological issues. This is related to various academic discussions I've encountered, where mathematics is increasingly being integrated with social sciences to address complex real-world problems. The use of mathematics to map socio-ecological territories brings to mind the broader discussions within the STEM field about the importance of cross-disciplinary approaches to education and research.

NEW:  The introduction of "critical posthuman cartography" as a framework is entirely new to me. This concept challenges traditional boundaries and emphasizes interconnected ways of knowing and being, which is a refreshing angle in mathematical discourse. The paper’s method of exploring mathematical practices in the context of socio-ecological activism in South Africa also provides a novel perspective, combining activism with education in a highly localized, context-sensitive manner.

WONDERING: Being fond of practical and hands-on examples, I wondered how these maps would look like (as actual drawings/maps). I also wonder about the practical implications of applying these theoretical cartographic practices in a real-world classroom setting. How might educators be trained to incorporate critical posthuman cartography in their teaching? Additionally, are there specific case studies or examples where this approach has successfully led to socio-ecological justice? Exploring these aspects further could provide a more comprehensive understanding of the tangible impacts of this theoretical framework in mathematics education.

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OLD: The authors emphasis on the socio-political and ecological interventions within the education framework brings to mind similar discussions found in critical pedagogy literature, such as the works of Paulo Freire and bell hooks. Their perspectives often stress the importance of addressing educational practices within broader societal contexts, resonating with the idea of educational efforts extending beyond the school's boundaries that the authors highlight. This alignment with established critical theories provides a familiar foundation for understanding the action research's objectives and outcomes.

NEW: New to me is the way of teaching in such a phase-based approach. Also, I had not previously read so much about the integration of a "critical stochastic modeling scenario" into the socio-ecological perspective. The concept of stochastic modeling applied to educational interventions is interesting. It introduces a new dimension to how we think about variability and uncertainty in educational contexts, particularly in analyzing the dynamic interactions between different actors and the environment.

WONDERING: One aspect that I am curious about is the specific methods used to incorporate stochastic modeling into the action research—how were the models constructed, and what specific variables were considered? Additionally, I wonder about the potential scalability of this approach: Could these methods be applied to other educational contexts beyond Córdoba? Or are they uniquely tailored to the local environment and socio-political conditions?

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OLD: The author's exploration of the significance of local narratives in education reminds me of several pieces of literature that emphasize culturally responsive teaching. For instance, work on culturally relevant pedagogy highlighting the importance of drawing on students' cultural contexts to make learning more meaningful and effective, and having an understanding of the broader socioecological factors influencing education.

NEW: While I am familiar with interdisciplinary approaches in education, and the concept of transdisciplinary, I was not familiar with the definition provided. The author emphasis on the localized Egyptian narrative to create a more relevant mathematics education experience is an interesting new angle that challenges the conventional dominance of universalized educational practices.

WONDERING: I am curious about how the integration of socio-ecological factors into the mathematics curriculum would be practically implemented in Egyptian classrooms. Are there specific examples or case studies that have already explored this integration successfully? Additionally, I wonder about potential challenges educators might face when balancing the localized context with standardized curricula and assessment methods. Would this approach require extensive teacher training or curriculum development, and are there resources or existing frameworks that could support such an integration? Also, I was wondering about the current political situation in Egypt. How would that influence the socio-ecological aspects?

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OLD: The authors highlights the importance of equity in mathematics education, a subject which is familiar to me as it resonates with the broader field of educational reform and social justice. The connection to Indigenous and minority communities echoes themes present in critical pedagogy, which emphasizes the need to incorporate students' cultural backgrounds and lived experiences into the learning process to enhance engagement and understanding.

NEW: I found it particularly interesting how the authors introduces the concept of "mathematical wellbeing" (MWB), linking it directly to social justice and ecological issues within Indigenous and minority communities. This integration of MWB within the context of cultural values and community practices is a fresh perspective that I had not previously considered, and it adds a valuable dimension to understanding how mathematics education can be more inclusive and relevant. Also, relatively new to me, is the method of photo-elicitation (pictures and interviews), so that was rather interesting to read about.

WONDERING: I am wondering about how the MWB would “turn out” in my own community (not indigenous). Also, I am curious about how the findings from this research can be practically implemented in diverse educational settings with varying resources and teacher preparedness. Additionally, I wonder if there are specific professional development programs or curricular frameworks that could support educators in making these connections between cultural knowledge systems and mathematics. Finally, it would be interesting to explore how students' mathematical wellbeing is assessed and measured in the context of these culturally responsive approaches.

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OLD: The idea of ethnomathematics is one that I have encountered in various readings within the field of educational research. Ethnomathematics, which deals with the way different cultures understand and conceptualize mathematics, aligns closely with the discussions in the paper about relating mathematics to Indigenous storytelling and patterns in nature. This paper's focus on mathematical practices in Kanaka Maoli taro farming beautifully extends this discourse and provides practical examples that underscore the wider relevance of culturally grounded mathematical practices.

NEW: : (relatively) new to me, is the concept of "restor(y)ing mathematics". This term emphasizes the power of storytelling in rebuilding and recontextualizing mathematical knowledge through an Indigenous lens. It challenges the traditional, often Eurocentric, perspectives on mathematics by introducing a narrative that is more holistic and interconnected with the natural world, which broadens the scope and approach to teaching and understanding mathematics.

WONDERING: I am curious about how the principles of restor(y)ing mathematics can be practically implemented in mathematics classroom, and educational curriculums. Are there specific pedagogical strategies or resources that can be adapted? Additionally, I wonder how the integration of Indigenous knowledge systems and practices, like those of the Kanaka Maoli taro farmers, can influence policy-making in education to ensure a more inclusive and diverse mathematical curriculum. It would also be important to explore potential resistance from traditional education systems and how these can be mitigated.

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Something old: The use of drawing and visual imagery to provide understanding into student perceptions and conceptions of different mathematical aspects. The use of gestures in the mathematics classroom.

Something new: The conception of socio-ecological gestures with drawings and the idea of drawing as embodiment as I have always thought of gesture more literally as physical body actions.

Wondering: This has challenged my own narrow conception of gesture and I am interested in the idea of a physical action as embodiment and wondering about the boundaries of this - for example, can we consider other visual methods such as photo voice or creating diorama also as socio ecological gesture?

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OLD: The focus on authenticity and mathematical content in teaching tasks is recognisable from previously, and emphasize the importance of relating educational content to such as students' cultural contexts, which enhances engagement and learning. Also, it is similar to projects that aim to incorporate real-life issues into educational settings to make learning more relevant and impactful for students from diverse backgrounds.

NEW: One of the new aspects introduced in this paper is the specific process the prospective teacher, Nadin, follows: taking a photo of an issue, making collaborative decisions, and designing and teaching a task. This structured approach is innovative to me, as it systematically integrates real-life issues into the curriculum while also fostering collaboration and reflection among teachers. Additionally, the emphasis on using photography as a starting point for discussion and task design is a fresh idea I haven't encountered before.

WONDERING: The paper makes me wonder about the scalability of the approach described. Could this model be effectively implemented in various educational settings, particularly in communities that face different kinds of marginalization? Or to my own educational situation? I also wonder about the long-term impacts on both teachers and students—does this increased authenticity in learning lead to sustained improvements in engagement and mathematical understanding? Further, it would be interesting to see how the peer-assessment aspect influences the quality and creativity of the tasks designed by the prospective teachers. Also, how do we move beyond “wrapper tasks”?

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OLD:  The examination of children's spatial awareness and their ability to construct meanings about their territory is reminiscent of classic studies in cognitive development (e.g., Piaget and spatial representation in children). Additionally, the use of map-making as a pedagogical tool aligns well with previous research where students are encouraged to engage actively with their environment to enhance their spatial reasoning skills.

NEW: The authors introduces an innovative perspective by connecting children's spatial knowledge with socio-ecological issues, a combination that is less commonly addressed in traditional educational research. It provides fresh insights into the interdisciplinary connections between environmental education, cognitive development, and social issues. The specific focus on the Atoyac River basin and the impact of socio-ecological devastation on the children's learning process is particularly novel and adds a localized context to the research.

WONDERING: This research prompts several interesting and relevant questions: How do children’s emotional responses to socio-ecological devastation influence their map-making and spatial understanding? Are there longitudinal studies capturing how these mapping activities might influence children's perception of their environment over time? Additionally, how can the findings be generalized to other regions experiencing different forms of socio-ecological challenges?

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Something old: the impact of colonisation on Indigenous people and the use of separation of young people from their families in the guise of education. There is a history of the use of boarding schools across countries to separate children from their culture and traditions.

Something new: I am familiar with the different theoretical framings used in the paper but it was new in regards to how the author/s teased out the different threads and connections to aspects of their work.

Wondering: The authors raise an issue which I also grapple with in relation to the use of national and international testing as a means of maintaining the status quo and further perpetuating marginalisation.

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Something old: I am familiar with mathematical modelling and the use of this to explore issues related to social justice and the environment and also the types of modelling cycles used within these.

Something new: The use of the stochastic modelling cycle which is aligned but extends mathematical modelling cycles that I am familiar with. The paper provides a rich exemplar of a stochastic modelling cycle.

Wondering: I was interested in the reasons as to why the connections between statistics and mathematics were not recognised in the mathematical category of the science fair?