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Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions

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Abstract

This article describes sixth-grade students’ engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students were also able to generalize the fraction model and transfer it to a new situation. Analysis of the students’ work demonstrates that they made use of four fraction constructs—part-whole, operator, quotients, and ratio. The activities also revealed difficulties in the students’ knowledge of fractions, some of which were overcome in the process of organizing and mathematizing the problem.

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Authors and Affiliations

  1. University of Haifa, Haifa, Israel

    Juhaina Awawdeh Shahbari & Irit Peled

  2. Al-Qasemi Academy - Academic College of Education, Baqa al-Gharbiyye, Israel

    Juhaina Awawdeh Shahbari

  3. The College of Sakhnin, Sakhnin, Israel

    Juhaina Awawdeh Shahbari

Authors
  1. Juhaina Awawdeh Shahbari
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  2. Irit Peled
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Correspondence to Juhaina Awawdeh Shahbari.

Appendices

Appendix A: The Garage Set Activity

In a toy shop, customers wish to purchase individual items of a garage set which only comes in sets of five items. While the sets all contain the same items, they differ in some respects and so are priced differently. The shop owner decides to break up the sets in order to sell each item separately. The owner decides that the sum of the individual items in each set must equal the price of the whole set. He asks his employees to price the individual items in two sets selling at $50 and $60. The prices of each item must be comparable between the two sets.

Students, you are employees of the toy shop, so the decomposition and pricing task is your responsibility.

[After they finish coping with the activity and constructing the mathematical model, students are presented with a final task.]

Final task: The shop owner found another garage set in the store that costs $140. You are responsible for pricing the individual items in the new set.

Appendix B: The Snow White and the Seven Dwarves Set Activity

A toy shop has a lot of unsold “Snow White and the Seven Dwarves” sets consisting of 20 items. All the sets have similar composition, and are priced based on the material they are made of—canvas, plastic, wood, cardboard, etc. The owner decides they will sell better if each item is sold separately, but decides that the sum of all the items must equal the price of the whole.

Students, as employees of the toy shop, you are responsible for the decomposition and pricing tasks. The sets are priced at $90, $120, and $240. The price of each item must be comparable between the three sets.

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Shahbari, J.A., Peled, I. Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions. Int J of Sci and Math Educ 15, 371–391 (2017). https://doi.org/10.1007/s10763-015-9702-x

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  • DOI: https://doi.org/10.1007/s10763-015-9702-x

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