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Assessing the Epistemic Analysis Competence of Prospective Primary School Teachers on Proportionality Tasks

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Abstract

Solving problems by different methods, identifying the knowledge put at stake in each case, and stating variants of the problems are fundamental aspects of the competence of analysis of mathematical knowledge for teaching. This paper reports on the design, implementation, and results of a formative intervention with primary education prospective teachers to promote developing this competence using tasks that involve proportional and algebraic reasoning. The experience has been carried out with a sample of 88 students (two class-groups), applying a didactic model that includes work in teams, institutionalization, and assessment of the individual learning achieved. Seventy three percent of students were successful in solving problems; however, only 27% of students managed to solve the four problems proposed by at least two different procedures. More than half of the students adequately identified the knowledge involved in each problem and the algebraization level was correctly assigned in more than half of the proposed solutions. Elaborating meaningful variants to the problems was only achieved in a suitable way by less than 20% of the students. It is concluded that developing the epistemic analysis competence of tasks bringing into play proportional and algebraic reasoning requires a greater attention in the teachers’ formative programs.

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Acknowledgments

Research carried out as part of the research project, PID2019-105601GB-I00 / AEI / 10.13039/501100011033 (Ministerio de Ciencia e Innovación) with support from the FQM-126 Research Group (Junta de Andalucía, Spain).

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Authors and Affiliations

  1. Universidad de Granada, Granada, Spain

    Maria Burgos & Juan D. Godino

Authors
  1. Maria Burgos
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  2. Juan D. Godino
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Correspondence to Maria Burgos.

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The manuscript is not previously published or simultaneously submitted elsewhere.

Appendix. Final assessment task

Appendix. Final assessment task

1. Solve the problems listed at the end (Annex, list of problems proposed), proper of primary education, by at least two different methods, considering those strategies that you think that your pupils would use to solve the problems.

2. Identify the knowledge put at stake in the solutions. For each solution, list the sequence of practices carried out to solve the problems and complete the table included below, adding the necessary rows.

Sequence of elementary practices to solve the problems

Objects referred to in the practices (concepts, propositions, procedures, arguments.)

3. Assign, in a justified manner, levels of algebraic reasoning to the different solutions that you have given in the previous point to the tasks, taking into account the previously identified objects and algebraic processes.

4. Enunciate related problems whose solution implies changes in the algebraization levels brought into play. Solve the problems you have proposed, justifying the assignment of the levels.

Annex (list of problems proposed)

Problem 1.

If a 22 g cereal bar contains 4 g of fat, how much fat is there in 100 g of the product?

Problem 2.

In my school, of the 60 students in the 6th grade, 15 read a book every day. Of the 40 students in the 5th grade, 12 read a book every day. In what grade the ratio of readers is greater? Explain your answer.

Problem 3.

Five friends want to make a birthday gift. Each one must pay 5.40 euros. Four other friends join to contribute to the gift. How many euros should each one pay now? Explain how you got it.

Problem 4.

Ana, María, and Luis are planting trees in a “Replanting” camp. Ana and María started at the same time, but María is faster. Luis goes at the same speed as Ana, but he started earlier. When Ana had planted 4 trees, María had planted 12 trees and Luis had planted 8 trees. When finishing, Ana has planted 20 trees.

  1. a)

    How many trees will Maria have planted? Explain your answer.

  2. b)

    How many trees will Luis have planted? Explain your answer.

  3. c)

    After a time, if you know the number of trees that Ana has planted, how would you know the number of trees Maria has planted? And the number of trees Luis has planted? Explain your answer.

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Burgos, M., Godino, J.D. Assessing the Epistemic Analysis Competence of Prospective Primary School Teachers on Proportionality Tasks. Int J of Sci and Math Educ 20, 367–389 (2022). https://doi.org/10.1007/s10763-020-10143-0

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  • DOI: https://doi.org/10.1007/s10763-020-10143-0

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