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Mathematical conceptual understanding in the PYP: Part 1

Carla Marschall

Carla Marschall, PYP coordinator and Middle School curriculum coordinator at Zurich International School

In this two-part series a PYP coordinator describes a process to develop conceptual understanding in mathematics.

Although the unit of inquiry is where a lot of talk occurs about conceptual understanding in the PYP, the development of big ideas should permeate all other areas of the programme in order to provide a holistic concept-driven curriculum. Developing conceptual thinkers means consistently activating the conceptual mind during learning engagements. What are the implications of this within mathematics teaching and learning?

The development of big ideas should permeate all other areas of the programme in order to provide a holistic concept-driven curriculum.

Plan for teaching and learning using mathematical conceptual understandings

Planning in mathematics using big ideas ensures that student learning engagements are more than a series of activities.

Let’s say a Kindergarten pattern unit has the following sample learning outcomes:

  • Describe pattern using simple language, e.g. pattern, over and over, repeat, again.
  • Record and describe patterns in a variety of ways, e.g. colors, letters, symbols, words.
  • Sort and classify patterns into like groups, e.g. all ABAB patterns together, all ABCABC patterns together.

Identify a list of related concepts based on these learning outcomes. In this case they could be pattern, sequence, symbol, repetition, representation, sorting, and classification. Lynn Erickson suggests the following attributes for concepts: concepts are nouns, universal, timeless, abstract and usually represented by 1-2 words.

Use two or more of these related concepts to write a statement of understanding. The PYP key concepts can be used to supplement the big idea.

By the end of the unit students will understand that people can describe patterns by representing these using symbols and visual representations.

Develop students’ understanding of mathematical concepts

When we develop conceptual understanding, we are able to take knowledge gained in the form of facts and topics and generalize about it using concepts. In this process we make meaning, summarizing swaths of information by creating statements of understanding.

In mathematics, students work conceptually from the very beginning because of the nature of the subject. Think about the mathematics ‘topics’ we might teach. Each of the ideas of pattern, fractions, addition, multiplications is actually a concept. Students should be invited to investigate the concepts through many materials or modes in order to have a concrete and contextual understanding of these mathematical concepts.

Here are some strategies for supporting the development of big ideas using materials and methods:

  • After students become confident with one material, ask them to transfer their knowledge to another material, for example if using fraction circles for a fractions unit, ask students how they could show the same ideas using Unifix cubes.
  • Provide unconventional materials and let students create models of concepts with them, for example, provide dice, toothpicks and beans and ask students to pick a material and show their understanding of division.
  • Use manipulatives with all grade levels, not just with the lower years. Materials help the conceptual mind express and revisit concepts through visual and tactile modes.

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Carla Marschall, PYP coordinator and Middle School curriculum coordinator at Zurich International School, Baden Campus, Switzerland. Carla previously worked in Hong Kong at Quarry Bay School (English Schools Foundation) as well as in Berlin, Germany as PYP coordinator. Carla is a PYP workshop leader and field representative and a Lynn Erickson concept-based curriculum and instruction trainer. She is especially interested in the role of the curriculum to help students develop critical and creative thinking. She tweets as @carlamarschall.

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