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Rubrics – Why use them in the math class? – SMathSmarts

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What are rubrics?
A rubric is an assessment tool that lists specific expectations for the solution to a problem, group/partner work, self-assessment or success with a specific task. The rubric should be clear, kid-friendly and concise. It’s even better when you create a rubric with your students so they have buy-in to the whole process. The feedback with the use of the rubric should be timely (within a concept) so students can learn from their misconceptions and adjust to show growth. Rubrics are also a great tool to use with goals setting and conferencing with students.

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Assessment Tools - Connected Mathematics Project

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CMP provides a variety of tools for student assessment. These assessments fall into the three broad categories of Checkpoints, Surveys of Knowledge, and Observations:

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The type of assessment in Inquiry Maths lessons is based on the chronological development of the inquiry: Assessment in inquiry Assessment as the end of inquiry Assessment after inquiry. Assessment in each phase becomes progressively more formal. Whatever the phase, however, all assessment in the

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Kath Murdoch's Inquiry Cycle is a model used to guide planning and teaching as an important step in the development of both teachers' and learners' understanding of inquiry. It is intended as a framework to support thinking and conversation. It is not a one-size-fits-all recipe or a prescriptive sequence. The elements listed in the model are components in an inquiry journey and generally happen in a cyclical or broadly sequential manner but it is expected that implementation is less 'ordered' than it appears on paper. No two inquiry journeys are the same.

The focus for an inquiry should be selected with a 'big picture' in mind. School and system level curriculum documents may assist. Foci (the centre of interest) will often be modified through negotiation with students or in conjunction with events or issues arising in the local or global community. The best inquiries are developed under the umbrella of overarching concepts or 'through-lines' - these might be expressed as big questions or essential statements. Sample big ideas might include: environmental sustainability, social responsibility, well-being and identity, the physical world, etc. At class, the inquiry is guided by a key question /s. These are most often developed by teachers but may be informed by or modified by students. The question should capture the essence of the problem/investigation/field of interest. This question has generative potential - it is open and often provocative. Simple, short, provocative questions to which there is no single answer are the best. The question acts as a large 'funnel' into which experience, thinking and understanding are gradually shifted.

Kath Murdoch's inquiry cycle consist of six. The very first stage in the inquiry cycle is "Tuning in,"an inquiry process about engagement and gathering prior knowledge and early thinking. Teachers design tasks that allow students to make their thinking visible. This is preparing the way for quality, formative assessment. Students use a variety of methods to show the thinking they already have in relation to the big idea. This will vary from very minimal to surprisingly comprehensive. Ask students: What theories do we have? How do already understand this? What connections can you already make? How could we find out more about this?Much of this happens early in the inquiry process but inquiry teachers constantly help their students connect the 'new' with the 'known' throughout.

Second process of an inquiry cycle is "Finding Out," students should experience the work of a researcher. They use various methodologies to gather information that help grow their thinking about the area of inquiry. These tasks should emphasize gathering data first hand and in a range of ways and should link to understanding goals. Data gathering may be through engaging with experts (using web 2 tools or in person), surveys, interviews, film, experiments, observations, emails, field work, etc).

Then, the third process is "Sorting Out." The 'sorting out' tasks are about MEANING MAKING. In an inquiry, students must be given opportunities to make sense of and present their refined thinking. This involves organizing, analyzing and communicating information gathered using a range of learning areas - eg: through maths, arts, English, drama, music, technology, etc. Importantly, this includes reflective thinking work - revising original theories and propositions. Reviewing the big question; What meaning can we make of this data? What are we learning? How is our thinking changing?

The fourth process is "Going Further." This element of inquiry is where students have opportunities to take more personalized learning pathways. This will depend very much on the content of the inquiry itself and the readiness of the student to work more independently. Going further means raising and revisiting questions, extending experiences and challenging assumptions. It is usually individually negotiated. May be students following personal inquiry into own questions - initiated earlier in the unit or raising new questions to investigate. This stage is characterized by differentiated programming. The emphasis here is on choice and differentiation. Here is where individuals and groups will take the inquiry into new and sometimes unexpected territory!

The fifth and sixth process is "Making Conclusion" and "Taking Action." Stating revised understandings - what do we think and know now? How do we feel? High level thinking about the topic. Identifying avenues for action and application. Generalizing (should be done throughout). While students have been encouraged to synthesize their thinking throughout the inquiry, now is the time to make that synthesis explicit. This may be through the use of metaphors, the formation of statements of generalization, etc. Connected to this is the importance of TRANSFER. Asking - what can we DO with this? What can I do now? How can I/we use this? Is there an action that seems important to undertake? These phases are most often woven throughout the unit. Explicit connections must be articulated. It is good to use some synthesis strategies here to help students clarify how their concepts have changed. Action may be shared or individual and may emerge as a result of the inquiry OR be embedded into the inquiry itself.

From Malaysia, 23 years old, completed Bachelor of Education at Unitar International University in 2019. Currently working with Fairview International School as a PYP Homeroom teacher. View all posts by ashiqinansari

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Kath Murdoch's Inquiry Cycle is a model used to guide planning and teaching as an important step in the development of both teachers' and learners' understanding of inquiry. It is intended as a framework to support thinking and conversation. It is not a one-size-fits-all recipe or a prescriptive sequence.

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Quizizz - The world's most engaging learning platform

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Find and create gamified quizzes, lessons, presentations, and flashcards for students, employees, and everyone else. Get started for free!

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PZ's Thinking Routines Toolbox | Project Zero

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The Toolbox organizes the Thinking Routines into categories that describe the types of thinking the routines help to facilitate. Some routines appear in more than one category, and some routines have different versions that offer modifications for specific age groups or more specific conceptual challenges.

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5. Good thinking utilizes a variety of resources and is facilitated by the use of external tools to "download" or "distribute" one's thinking. Papers, logs, computers, conversation, and various means of recording and keeping track of ideas and thoughts free the mind up to engage in new and deeper thinking and help ensure that our thinking doesn't get lost.

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Explore our collection of pedagogical tools, curated to equip you for adapting or designing tasks for your class.

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IB PYP Mathematics scope and sequence | Math Games & Worksheets

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IB PYP Mathematics scope and sequence | Math Games & Worksheets

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Math games & worksheets aligned to IB PYP Mathematics scope and sequence for K - 6. Learn math online today.

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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I'm often asked how I integrate maths into our IB PYP units of inquiry. I won't deny that depending on the unit, it can sometimes be easier said than done. However, I've found over the years, that it's best to keep it relaxed and, if necessary, simply focus on concepts in maths rather than content. Often, especially within the public IB schools in the USA, we are expected to meet certain maths standards by a certain time. This often results in a clash of math units and units of inquiry and a creative juggle ensues. But hey, who doesn't love a challenge? The rest of the IB world? You've got it luckier, I assure you! Anyway, a great resource for math in the beginning of the year is https://www.youcubed.org/. It encourages a maths mindset and is centred around collaborative thinking. It does require signing up for a free account but, once you're in, you can view the Week of Inspirational Math. This gives you a couple of days of lessons that demonstrate inquiry based thinking. It really has a ton of great information though.
Content vs Concepts
When in doubt as to how best to integrate maths, I will take the focus more to the conceptual level. For example: if we are learning about operations with decimals

and our UOI doesn't lend itself to this, then I'll look at the key concepts of CHANGE & CONNECTION. We can the see how those big ideas tie in with the different strategies needed to compute each operation- How is it changing? What is making the change? How do the equations connect with a different/the same answers? The children can make the connections and voila, we have succeeded in critical thinking and analysis of number and operations. ? You can link to a past blog post about the Key Concepts within the PYP here.
Content Based Inquiry
Another method to integrate maths, and this is my favourite, is to slightly stray from the central idea and work through a mini, project based learning opportunity.

This kills several birds with one stone: concepts, content, math conceptual reinforcement and inquiry. Not to mention the myriad of opportunity for developing the Approaches to Learning skills. Think COMMUNICATION, RESEARCH, THINKING, SELF MANAGEMENT etc. Love it! ( there is a great post all about developing those skills here)

The pictures show how I took a social studies unit about Human Rights, tossed in a great book about diversity in the world and used those together to come up with a differentiated maths based inquiry.

If the World Were A Village is a fabulous book to use by itself to look at the diversity amongst the people in the world. It uses large numbers ( in the millions and billions) as it shares how many people are of each nationality, religion, wealthy, educated, poor, starving, well fed etc. and how those large numbers would be shrunk if the world were only a small village. It's really an eye opener to see that the western civilisation is in the minority throughout the world when it comes to many aspects of life and exactly how diverse we are in some ways and yet wholly connected in many others. The numbers bring

an easy connection to maths and lends itself nicely to our UOI and it ties in so well with the Universal Declaration of Human Rights, with global citizenship, with civil rights and religion.

By incorporating the information from this book, I created a mini unit that had a huge emphasis on our math area of focus; measure, area & volume.

The kids made connections with the lines of inquiry in our unit, learned about the massive differences in the world's human rights and created their OWN 2 dimensional and 3D global villages using their math skills.

Such a hit with my fifth graders! The unit, found in my store, is differentiated and can be easily adapted for 3rd-6th, phases 3& 4, depending upon your IB World school.

You can find several more inquiry based math projects within my store:

Our School, The Thanksgiving Journey, The American Revolution, Tessellations All Around Us and of course, all of my complete units of inquiry packs contain integrated math lessons. Click here to keep in touch.

A few other great math resources that I love are linked here too.
Inquiry through authentic tasks from Dan Meyer and you can see Dan Meyer's famous TEDTalk here.

If you have other suggestions for integrating maths, please shout out. I'm always keen to learn from my peers. : )

Enjoy!

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Integrating Math into an IB PYP Unit of Inquiry

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I'm often asked how I integrate maths into our IB PYP units of inquiry. I won't deny that depending on the unit, it can sometimes be easier said than done. However, I've found over the years, that it's best to keep it relaxed and, if necessary, simply focus on concepts in maths rather than content.

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Think of the 5 coolest things you know in mathematics. Did you ever think about including them in your MLA course? You can, and perhaps should. "Cool things" are short "mini presentations or activities" about a mathematical topic that is exciting to us and usually different from the math content that we are currently working on in class.

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Unpacking the different phases in a cycle of inquiry and what makes these components effective.

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Inquiry-based learning is more than asking a student what he or she wants to know. It's about triggering curiosity. And activating a student's curiosity is, I would argue, a far more important and complex goal than mere information delivery.

Despite its complexity, inquiry-based learning can be easier on teachers, partly because it transfers some responsibilities from teachers to students, but mostly because releasing authority engages students.

Teachers who use inquiry-based learning combat the "dunno"-a chronic problem in student engagement.

When you ask a student something like, "What do you want to know about _____?" you're often met with a shrug or "dunno." Inquiry-based learning, if front-loaded well, generates such excitement in students that neurons begin to fire, curiosity is triggered, and they can't wait to become experts in answering their own questions.

What inquiry-based teachers do isn't easy at all; it's just hidden, and some people confuse the two. Teachers hide the strategies they use to encourage inquiry, and the students develop their own skills as content-area experts.

Learning Something New

Triggering inquiry is about learning something new, and triggering curiosity is no small feat. It takes modeling enthusiasm, and learning something new generates our own enthusiasm, even if it's something new about the content we've covered for years.

Let's say you're clicking through your Twitter or Facebook feed and you stumble on a link in your content area. You realize it's a new factoid, a new perspective on an age-old topic. Maybe it's a new TED talk or graph with statistics, something that makes a concept more concrete. Maybe it's an infographic or a photo, something that startles you and leads to furrow your brow and say, "Whaaa?!"

By the way, I think one of the reasons why the whole world seems to be losing its mind over the Broadway production of Hamilton is because it presents a fresh take on a story we've all heard before. The power of learning something new is undeniable.

You have to bring that "whaaa?!" into your classroom. You have to model your own curiosity quotient-that hunger to learn that defines how we advance our knowledge of the world. According to the Harvard Business Review, a higher curiosity quotient can indicate more flexibility and help build a greater ability to handle complexity.

So think about your content area. What is a new take on a topic that you can bring to your classroom? What new piece of information might help you trigger your own enthusiasm that can then trigger your students' curiosity?

The 4 Steps of Inquiry-Based Learning

So you've discovered something that generates your own inquiry, and you've recreated that moment for your students when your curiosity was triggered. So what comes next in inquiry-based learning? This can be answered in four basic steps that should represent the outline of a simple unit.

1. Students develop questions that they are hungry to answer. Have them develop a problem statement that requires them to pitch their question using a constructed response, further inquiry, and citation.

2. Research the topic using time in class. It's crucial to have some of this be classwork so students have access to the head researcher in the room-you. You aren't going to do the work for them, but you are going to guide them and model methods of researching reliably.

3. Have students present what they've learned. Students should create and present a culminating artifact. When I have my students present what they've learned, I use a rubric with "Able to Teach" as the acme of what to reach for. After all, many people can understand content, but can they communicate it? Students can develop a website using Weebly, or perhaps a slideshow using Google Slides.

4. Ask students to reflect on what worked about the process and what didn't. Reflection is key. And it isn't just about asking them to think back on their opinion of the topic. It's about reflecting on the process itself. That's where you can work in metacognition-thinking about thinking. Have students focus on how they learned in addition to whatthey learned.

In terms of your content area, imagine a classroom where different kids are presenting their findings on a single, simple aspect of the content. You'd have a classroom that, overall, learns deeper and wider than ever before.

In terms of student achievement, the power of their question should help drive the research, the writing, and the presentation. It should help motivate them to become experts in their self-described field. And the more often a student gets a taste of what it feels like to be an expert, in however small a concept, the more they will want that feeling later on in life.

It all starts with finding your own enthusiasm, your own excitement, and your own curiosity. Do that, and you'll be heading toward a classroom built on inquiry.

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What the Heck Is Inquiry-Based Learning?

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What the Heck Is Inquiry-Based Learning?

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What is it?

Inquiry-based learning is an education approach that focuses on investigation and problem-solving. Inquiry-based learning is different from traditional approaches because it reverses the order of learning. Instead of presenting information, or 'the answer', up-front, teachers start with a range of scenarios, questions and problems for students to navigate.

Inquiry-based learning prioritises problems that require critical and creative thinking so students can develop their abilities to ask questions, design investigations, interpret evidence, form explanations and arguments, and communicate findings.

How does it help?

Students learn key STEM and life skills through inquiry-based learning. Inquiry-based learning also promotes:

Social interaction. This helps attention span and develops reasoning skills. Social interaction encourages students to generate their own ideas and critique in group discussions. It develops agency, ownership and engagement with student learning.

Exploration. This allows students to investigate, design, imagine and explore, therefore developing curiosity, resilience and optimism.

Argumentation and reasoning. This creates a safe and supportive environment for students to engage in discussion and debate. It promotes engagement in scientific discussion and improves learning of scientific concepts. It encourages students to generate questions, formulate positions and make decisions.

Positive attitudes to failure. The iterative and evaluative nature of many STEM problems means failure is an important part of the problem-solving process. A healthy attitude to failure encourages reflection, resilience and continual improvement.

How do you do it?

UNESCO recommends a four-step process:

set a challenge for students

encourage active student investigations

make generalisations

reflect

For more information on inquiry-based learning and examples of classroom strategies. Griffith University has prepared a useful resource.

Want to know more?

Research reports

STEM Education: A review of the contribution of the disciplines of science, technology, engineering and mathematics - Science Education International Vol. 27, Issue 4, 2016, 530-569

Opening up pathways: Engagement in STEM across the Primary-Secondary school transition. A review of the literature concerning supports and barriers to Science, Technology, Engineering and Mathematics engagement at Primary- Secondary transition. Commissioned by the Australian Department of Education, Employment and Workplace Relations. June, 2008

Studies in Science Education - Volume 44, 2008 - Issue 1 - Students' questions: a potential resource for teaching and learning science

From concept to classroom Translating STEM education research into practice - Australian Council for Educational Research - June 2016

Case study: reSolve: Mathematics by Inquiry

reSolve: Mathematics by Inquiry is a national program to help teachers adopt inquiry-based methods when teaching primary and secondary mathematics. The reSolve approach encourages students to ask questions, test ideas, seek meaning and explain reasons. reSolve provides classroom resources, professional learning modules and a protocol that underpins excellent inquiry-based teaching and learning. It also trains 'reSolve Champions': teachers and leaders who take the messages and resources of reSolve into the wider mathematics teaching community. Approximately 300 teachers and leaders have either completed or are undertaking a 12-month professional learning program to become reSolve Champions. The reSolve program is funded by the Australian Government Department of Education Skills and Employment.

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The Department of Education works to ensure Australians can experience the wellbeing and economic benefits that quality education provides.

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Time capsule

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The Ministry is migrating nzmaths content to Tāhurangi. Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available.