Last year I wrote a post about what the PYP believes about how children learn math:
- Students construct their own meaning about math
- Students transfer their meaning into conventional symbols (vocabulary, notations, algorithms)
- Students apply their understanding to problems and real world contexts
I also shared some examples of how teachers at our school have been helping students to construct their own meaning about mathematical ideas and concepts. A lot of the teachers I work with are feeling confident about that first stage in the math cycle! However, they are still wondering how to bring all 3 of the stages together.
In an attempt to step back and see the big picture of how the stages fit together, our teaching teams generated a list of all the math strategies they use in their math programme.
Once the list was compiled, they asked these three questions:
What strategies give students the opportunity to construct their own meaning?
What strategies help students to transfer meaning into symbols?
What strategies provide students the chance to apply their understanding?
Then, they sorted each strategy into each phase of the math cycle. (Along with some amazing debates, disagreements, discoveries and many references to the PYP Math Scope and Sequence document!) We discovered that many strategies fit multiple stages in the math cycle depending on the question you ask or how you present it. We also spent a good chunk of time discussing how many of the strategies that allow students to construct their own meaning at the beginning of a new unit or new concept, would also be good at the end of the unit to allow students to apply their understanding using conventional symbolic representations.
It is interesting to note that no two teaching team’s chart looked the same. Another point for acknowledging that all learners construct their own meaning in their own way!
Here is the chart our Grade 3 team developed:
Now when we are planning a stand-alone math unit, we have an anchor chart that will help us purposefully select math strategies to support students as they to move through all three stages of the math cycle.
How do you bring the three stages of how children learn math together?
Making Good Humans 
I love the constructing their on meaning part. At ISKL we had really good training with a math program that focused on that. As a language acquisition teacher, this was really interesting and fun.
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I think this can be done with more than just math. Constructing meaning can and should be a meaningful part of every discipline.
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I like the last comment about constructing meaning is meaningful for every discipline. I remember the HoEnglish at an 11-18 school I taught in from 1973-85 would buy in a film, such as “Twelve angry men”which every year group would see. He and his colleagues then used the same stimuli as a resource for students to construct meaning across the entire age range. The same is true in mathematics. For example the Cuisenaire rod task of finding all possible two number partitions for 10 (the orange rod) can be extended into GCSE groups to explore the function x + y = 10 etc and extended further by considering products of the partitions to explore the function y = x(10 – x)
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You are absolutely right! All disciplines could take a lesson from this and allow learners – child and adult – to construct their own meaning about something before being given the convention symbol/algorithm/definition/understanding.
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