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Notice & Wonder can be found under classroom resources on the NCTM website. This particular classroom resource is broken down into four components: Overview, Digital Assets, Lesson Plans and Products.

I initially clicked on this resource because this type of activity is a familiar routine in Illustrative Math. Many of our warm ups are "Notice & Wonder" and so I thought this might be something I could immediately use in my classroom.

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When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas.

By asking "What do you notice? What do you wonder?" we help our students see problems in big-picture ways.

Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to discover multiple strategies for tackling a problem.

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Notice and Wonder - National Council of Teachers of Mathematics

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What is Notice and Wonder? When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas. By asking " What do you notice? What do you wonder?"

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How can "Notice & Wonder" resources be used in the classroom? 

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How can "Notice & Wonder" resources be used in the classroom? 

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By clicking on the lesson plans tab on the menu of options, one will find a breakdown of grade level resources for the "Notice & Wonder" lesson plans; prek-2, 3-5, 6-8, 9-12. Each lesson plan span has a few paragraph break down of the concepts and content students will engage with. From here, you can find many different "Problems to Ponder" that provide teachers with a lesson that goals along with some visual that inspires students to notice & wonder math around them.

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General: Members Only Page - National Council of Teachers of Mathematics

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When clicked, a lesson plan will download a pdf that outlines the various components of the lesson. The resources poses questions to ask, possible student responses and then follow up scenario and guiding questions. These activities could be used as a warm up, or to help deepen a students knowledge of a concept through utilizing it as a deep exploration of math around us.

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Position Statements can be found under standards & positions on the NCTM website. This particular resource identifies current problems, issues or needs in mathematics and seeks to address policy and action related to mathematics education.

As I browsed through the most recent position statements, this one caught my eye as I work in a school with a high percentage of multilingual learners and I hold a masters degree in multilingual education. We have done a lot of work around integrating SIOP components at our school and ensuring equitable learning environments for all students. Unfortunately, our newcomer students are still most often pulled from our math block and I thought that this resource might provide me with some ideas on how to continue to have complex conversations around pull out schedules and math education.

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A Position of the National Council of Teachers of Mathematics

Question: How do we transform practice and policies so that multilingual learners thrive in mathematics?

NCTM Position

For too long, our educational systems have privileged some students in the mathematics classroom while marginalizing others. Too often, we have dismissed the assets and strengths of multilingual students while prioritizing English-dominant or monolingual learners. Our policies and practices must be changed to ensure that multilingual learners thrive in the mathematics classroom.

Multilingual learners bring multiple assets to the mathematics classroom, including their dynamic and fluid identities, which consist of their race, language, culture, religion, class, sexual orientation, and status (NCSM and TODOS 2021). The use of natural language(s) and culture(s) is a human right, and in particular a linguistic human right (Skutnabb-Kangas 2000). Multilingual learners use more than one language to make meaning of mathematics (Ramirez and Celedón-Pattichis 2012; LópezLeiva, Torres, and Khisty 2013; Moschkovich 1999, 2015). Regardless of what language development stage multilingual learners are in, teachers can engage them in cognitively and meaningfully demanding tasks that not only leverage bilingualism as a tool to negotiate mathematical meaning, but also provide multiple entry points to represent solutions (Khisty 1995; LópezLeiva, Torres, and Khisty 2013; Moschkovich 1999; Turner and Celedón-Pattichis 2011). When mathematics teachers nurture environments in which students and teachers are respectful of one another, have high expectations, value collaborations, consider students' dynamic identity and agency, and position students as leaders, multilingual learners thrive by learning and developing mathematical proficiencies (Aguirre, Mayfield-Ingram, and Martin 2013; Chval et al. 2021; de Araujo et al. 2018; Ramirez and Celedón-Pattichis 2012).

Declarations

To design and enact educational spaces, learning opportunities, and curriculum with and for multilingual students, teachers, leaders, and administrators must invest in professional learning. These learning experiences should enhance participants' knowledge and competencies so they are equipped to effectively advocate for policies and practices that position multilingual learners as valued leaders and participants in the mathematics classroom. In particular, such experiences should do the following:

Work to build an understanding of deficit language in policies, practices, and resources regarding multilingual learners and their families and work to eradicate it (Civil et al. 2005; de Araujo and Smith 2022; Gutiérrez 2002). Such an understanding would also position the use of multiple languages as an asset that educators should encourage and draw upon in the classroom (Civil 2016; National Academies of Sciences, Engineering, and Medicine 2018).

Emphasize the importance of knowing and understanding students' individual assets in language, mathematics, and beyond. Multilingual students are not a homogenous group, and knowing their individual strengths is necessary to effectively devise instructional strategies to further their learning (Chval et al. 2021; National Academies of Sciences, Engineering, and Medicine 2018).

Aid participants in understanding intersections of race, language, gender, and other aspects of identity (Aguirre, Mayfield-Ingram, and Martin 2013; NCSM and TODOS 2021; TODOS 2020). Many multilingual students are also members of other historically marginalized groups. Understanding the history of marginalization and more equitable approaches to instruction are necessary to create the learning environments students deserve.

Center multiple modes of communication (e.g., speaking, writing, drawing, direct modeling) to simultaneously develop students' learning of both language and mathematics (Chval and Khisty 2009; de Araujo et al. 2018; Khisty 1995). Students' mathematics learning should not be put on hold as they learn English. Instead, teachers should build on students' strengths and work with support systems (e.g., language acquisition specialists) to help students gain access to mathematics while they develop language proficiency (National Academies of Sciences, Engineering, and Medicine 2018; Erath et al. 2021; Moshckovich 2015).

Multilingual learners deserve the right to thrive in mathematics education. Therefore, we need to learn and enact practices that center the brilliance of multilingual students and align with research. We must understand and interrogate long-standing policies that have served as roadblocks for multilingual learners (e.g., English-only schooling practices, biased mathematics assessments, tracking based on English proficiency). This will require our entire mathematics education community to build strong alliances to advocate for and enact policies, resources, and practices that will dismantle inequitable structures and racism that have hindered too many students for far too long.

References

Aguirre, Julia M., Karen Mayfield-Ingram, and Danny Bernard Martin. 2013. The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices. Reston, VA: National Council of Teachers of Mathematics.

Celedón-Pattichis, Sylvia, and Nora G. Ramirez. 2012. Beyond Good Teaching: Advancing Mathematics Education for ELLs. Reston, VA: National Council of Teachers of Mathematics.

Chval, Kathryn Bouchard, and Lena Licón Khisty. 2009. "Latino Students, Writing, and Mathematics: A Case Study of Successful Teaching and Learning." In Multilingualism in Mathematics Classrooms: Global Perspectives, edited by R. Barwell, pp. 128-44. Bristol, UK: Multilingual Matters.

Chval, Kathryn B., Erin Smith, Lina Trigos-Carrillo, and Rachel J. Pinnow. 2021. Teaching Math to Multilingual Students: Positioning English Learners for Success. Thousand Oaks, CA: Corwin.

Civil, Marta. 2016. STEM Learning Research through a Funds of Knowledge Lens. Cultural Studies of Science Education 11, no. 1 (March) : 41-59.

Civil, M., Bratton, J. & Quintos, B. (2005). Parents and mathematics education in a Latino community: Redefining parental participation. Multicultural Education, 13(2), 60-64.

de Araujo, Zandra, Sarah A. Roberts, Craig Willey, and William Zahner. 2018. "English Learners in K-12 Mathematics Education: A Review of the Literature." Review of Educational Research 88, no. 6 (December): 879-919.

de Araujo, Zandra, and Erin Smith. 2022. "Examining English Language Learners' Learning Needs through the Lens of Algebra Curriculum Materials." Educational Studies in Mathematics 109, no. 1 (January): 65-87.

Erath, Kirstin, Jenni Ingram, Judit Moschkovich, and Susanne Prediger. 2021. "Designing and Enacting Instruction That Enhances Language for Mathematics Learning: A Review of the State of Development and Research." ZDM-Mathematics Education 53, no. 2 (May): 245-62.

Gutiérrez, Rochelle. 2002). "Beyond Essentialism: The Complexity of Language in Teaching Mathematics to Latina/o Students." American Educational Research Journal 39, no. 4 (January): 1047-88. https://doi.org/10.3102/000283120390041047.

Khisty, Lena Licón. 1995. "Making Inequality: Issues of Language and Meanings in Mathematics Teaching with Hispanic Students." In New Directions for Equity in Mathematics Education, edited by W. G. Secada, E. Fennema, and L. B. Adajian, pp. 279-97. Cambridge: Cambridge University Press.

LópezLeiva, Carlos A., Zayoni Torres, and Lena Licón Khisty. 2013. "Acknowledging Spanish and English Resources during Mathematical Reasoning." Cultural Studies of Science Education 8, no. 4 (December): 919-34.

Moschkovich, Judit N. 2015. "Academic Literacy in Mathematics for English Learners." The Journal of Mathematical Behavior 40 (February): 43-62.

Moschkovich, Judit. 1999. "Supporting the Participation of English Language Learners in Mathematical Discussions." For the Learning of Mathematics 19, no. 1 (March): 11-19.

National Academies of Sciences, Engineering, and Medicine. 2018. English Learners in STEM Subjects: Transforming Classrooms, Schools, and Lives. Washington, DC: The National Academies Press. https://doi.org/10.17226/25182.

NCSM: Leadership in Mathematics in Education and TODOS: Mathematics for ALL. 2021. Positioning Multilingual Learners for Success in Mathematics. Joint position statement. Englewood, CO: NCSM; Tempe, AZ: TODOS.

Ramirez, Nora, and Sylvia Celedón-Pattichis. 2012. "Understanding Second Language Development and Implications for the Mathematics Classroom." In Beyond Good Teaching: Advancing Mathematics Education for ELLs, edited by Sylvia CeledónPattichis and Nora Ramirez, pp. 19-37. Reston, VA: National Council of Teachers of Mathematics.

Skutnabb-Kangas, Tove. 2000. Linguistic Genocide in Education or Worldwide Diversity and Human Rights? Mahwah, NJ: Lawrence Erlbaum Associates.

TODOS: Mathematics for All. 2020. The Mo(ve)ment to Prioritize Antiracist Mathematics: Planning for This and Every School Year. Tempe, AZ: TODOS. https://www.todos-math.org/statements.

Turner, Erin E., and Sylvia Celedón-Pattichis. 2011. "Mathematical Problem Solving among Latina/o Kindergartners: An Analysis of Opportunities to Learn." Journal of Latinos and Education 10, no. 2 (April): 146-69.

NCTM position statements define a particular problem, issue, or need and describe its relevance to mathematics education. Each statement defines the Council's position or answers a question central to the issue. The NCTM Board of Directors approves position statements.

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Transforming Practices and Policies So Multilingual Learners Thrive in Mathematics - National Council of Teachers of Mathematics

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For too long, our educational systems have privileged some students in the mathematics classroom while marginalizing others.

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How can "Position Statements" be used in the classroom? 

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How can "Position Statements" be used in the classroom? 

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I think that these position statements can be used to inform educators and then guide conversations around "hot button" items in education. A few of the most recent position statements include, artificial intelligence, large scale assessments and multilingual learners, all highly visible items in education at the moment.

As a reputable source, these NCTM position statements can be used to leverage viewpoints around policies both at the school level and at a broader scale (e.g., school boards, state leaders, federal level). Additionally, the references portion of each of the position statements opens up a wealth of resources for someone looking to learn more about these issues or needs in education.

When using this resource, an educator might ask themselves the following questions:

How does this apply to my current classroom?

What are my own beliefs on this position? How do these beliefs impact my practice?

What more do I need to learn about this topic?

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The Research Briefs & Clips resource can be found under the research tab on the NCTM website. This resource contains comprehensive information surrounding a variety of mathematical topics and teaching. Each topic identified contains a clip and a brief, the clip is a collection of more concise statements around the topic and the brief is a more comprehensive discussion of the topic. This resource is useful for teachers and other education professionals to dive deeper into current research in mathematics instruction.

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Research Briefs and Clips - National Council of Teachers of Mathematics

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Research Clips and Briefs provide a foundation for taking what the research says about mathematics teaching and learning to teachers, administrators, school boards and parents. Email research@nctm.org to recommend topics for additional Research Briefs and Clips.

Clips provide concise statements about classroom relevant research with companion Briefs that provide additional background and research references.

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How can "Research Briefs & Clips" be used in the classroom? 

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How can "Research Briefs & Clips" be used in the classroom? 

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I think that like the position statements, these research briefs and clips can be used to inform instruction as well as inform educators to be more of experts on particular components of mathematics instruction. The research brief and clip I selected to focus on was "Strategies for Discussion" which provided a comprehensive overview of conditions to meet in order to have productive discussions in the classroom. The research outlines nine important strategies and the research brief gives an in depth description of each strategy. I found the "examine and plan questions" discussion to be a particularly good reminder of the difference between closed and open questioning and how those will impact the discussion in the classroom. Additionally, the strategy "explore incorrect solutions" got me thinking more about this particular strategy and how it can be useful for students and teachers. I found the phrase in the brief "work in progress" as a way to refer to student work as a particularly insightful way to frame these. I often steer clear of addressing incorrect solutions publicly for fear of embarrassing students or causing them to shut down but I am wondering now about building this understanding and idea that all our work is just "in progress". Perhaps this might be a way to engage students in metacognition and build perseverance.

All in all, the research briefs and clips, while a bit lengthy, can be used as helpful tools for reflection and to inform instruction.

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Problems of the Week can be found under classroom resources on the NCTM website. This particular classroom resource is a comprehensive data base with math problems that range from K-12 math skills.

One of the great navigational tools this resource has is the ability to filter by grade level band. For example, as I primarily teach fourth grade students I was able to narrow my search to the 3rd-5th grade band, significantly decreasing the number of results shown. You can filter even further if you are looking for a specific content within a grade band such as "fractions" and the results will narrow to show 3rd-5th problems related to that content.

I explored this resource earlier in the semester when I was looking for some resources for a review day prior to giving a unit test.

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Problems of the Week - National Council of Teachers of Mathematics

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How can "Problems of the Week" be used in the classroom? 

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How can "Problems of the Week" be used in the classroom? 

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One of my biggest complaints about the IM curriculum is the lack of practice problems, each unit contains a few practice problems but I never feel like it is quite enough to target how much practice we need. This resource provides some great practice problems that engage students in deeper understanding of mathematical concepts.

I used some of the Problem of the Week questions for a review center prior to our fractions unit test.

While revisiting this resource to create this Padlet post I filtered by Place Value to see what problems exist as that is the unit we are currently working on.

I have found that the Problems of the Week tend to require students to think more in depth about the math and often, engage in multi-step problem solving. I see this being a great resource for me to continue to utilize when I am looking to extend our work in the classroom.

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Sample Problem of the Week: The Place Value Game

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Sample Problem of the Week: The Place Value Game

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One of the Problems I clicked on is definitely something I will be trying with students. The problem is titled "The Place Value Game" and targets NBT skills such as values of digits and number sense/reasoning.

Additionally, I could see extending this problem to turn it into our own classroom game following the structure presented in the problem.

All in all, the Problems of the Week provide a great resource for problems to present to students that ensure they will think deeply about the math and remove some of the pressure on the teacher to either create or find extra practice problems.

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The Place Value Game - National Council of Teachers of Mathematics

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Help Sylvia and Carina think about winning numbers in the Place Value Game.

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The NCTM Webinars can be found under the "Conferences & Professional Development" tab. One of the great features of the webinars is the ability to either tune in live to a webinar or to catch it on a future day. All webinars are uploaded to the site after they occur. I chose the second option and tuned in (after the fact) to the webinar titled "Implementing the 5 Factors of Belonging." Another great feature of the webinars is that when you click more info, there is a short description of the content that will be covered in the webinar so one can determine if it is the right fit for them. I personally wanted to learn more about belonging in the math classroom as I often focus on this sense of belonging in a more general way and thought it might be interesting to learn about how I can apply this specific to my math classroom/space.

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NCTM – Professional Development Webinars

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How can Webinars be used in the classroom? 

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How can Webinars be used in the classroom? 

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This is another resource that is certainly teacher specific. Participating in, or watching, a webinar can support teachers in bettering their math practices.

After watching this webinar on belonging in the math classroom, I was left considering how I could use the five factors of belonging to better support my students in our math classroom.

1. See each and every child

2. Stories: Allow them and tell them

3. Let them talk

4. Make space for multiple ways to show learning

5. Create counternarratives about math ability

I was able to gain some new ideas of how to support students in feeling like they belong in math. For example a "Me bag" specific to how do you use math at home, teacher/student journaling, my favorite mistake (one we've discussed previously), tell me/show me/teach me, who am I/what's my career.

This webinar was really thought provoking and has me considering how to continue to make space for my students to feel more like they belong in the classroom.

The webinar choices are endless and the particular one I listened to seemed it was interactive when it was live which makes me consider trying to tune into a live one in the future.

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The final resource I selected to highlight is the Figure This resource that can be found under the Classroom Resources tab on the NCTM website. This resource actually takes you to an external site (still within the NCTM domain) and is a great tool for connecting families to mathematical opportunity.

The primary goal of this resource is to help families engage in fun and high-quality math challenges and it was created by NCTM and a few other organizations.

There are many challenges within the Figure This site and the challenges primarily target middle-school math concepts. Each of the challenges include a variety of components such as a description of the math, a hint option, solutions, and fun facts.

The resource/site is comprehensive and has resources for both families and educators in supporting one another in the mathematical world.

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Figure This! Math Challenges for Families - Challenge Index

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Home · Take a Challenge · Challenge Index · Math Index · Contact Us · About Technical Requirements · Printing the Challenges · Family Corner · Teacher Corner PowerPoint Presentation · Contact Us!

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How can "Figure This!" be used in the math classroom?

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How can "Figure This!" be used in the math classroom?

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Figure This has its own guide on ways to use their site with students and families throughout the year. Some of the suggestions include sending Figure This! challenges home throughout the school year, giving our Figure This! challenges are parent-teacher nights and leading a Figure This! presentation (there is a powerpoint accessible on the website).

I personally see benefit in giving parents and families access to this site to explore with their students at home. I am not big on homework in my classroom but I often have families looking for ways to extend our learning from school to home and I think Figure This! is an awesome way to do this. While it may not be completely appropriate for my elementary age students, it is definitely a valuable resource, and I wonder if there are other sites like this that cater specifically to elementary age students.