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Moving beyond a traditional algorithm in whole number subtraction: Preservice teachers’ responses to a student’s invented strategy

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Abstract

Although students’ invented strategies typically prove to be meaningful and effective in improving the students’ mathematical understanding, much remains unexplored in the current literature. This study examined, through a teaching-scenario task, the nature of 80 preservice teachers’ reasoning and responses to students’ informal and formal strategies for whole number subtraction. This study also examined challenges reported by preservice teachers attempting to connect students’ informal strategies to a traditional method. The broader implications of this study for the international community are discussed, and recommendations for teacher education programs are presented in accordance with the findings of the study.

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Authors and Affiliations

  1. Department of Learning and Instruction, Graduate School of Education, University at Buffalo – The State University of New York, 569 Baldy Hall, Buffalo, NY, 14260-1000, USA

    Ji-Won Son

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Correspondence to Ji-Won Son.

Appendices

Appendix 1 Teaching approaches in connecting Tommy’s and Dan’s method

figure c

Appendix 2 Examples of teacher-focused and student-focused response to Sally

Teacher-focused: “I would tell Sally that although her strategy was a good idea, it will not work for subtraction problems. When you find that there is a smaller number on top in the ones place than the number in the ones place in the 2nd number, you can’t just put 3. You have to borrow from the tens place so you have a larger number to subtract 5 from (i.e., 12−5 instead of just 3)” (Category 3).

Student-focused: “I would ask Sally to compare her answer to Tommy’s and Dan’s and see if she could figure out where she went wrong. I would point out the ones place and ask her if those numbers subtracted from each other. When she said yes, I would have her compare two problems 5−2 = and 2−5 = and use manipulatives. Then she would hopefully understand her error and how to correct it in relation to Tommy’s or Dan’s strategy” (Category 10).

Appendix 3

Table 9 Distribution of the rationale for the need of a traditional method
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Son, JW. Moving beyond a traditional algorithm in whole number subtraction: Preservice teachers’ responses to a student’s invented strategy. Educ Stud Math 93, 105–129 (2016). https://doi.org/10.1007/s10649-016-9693-8

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