### Abstract

This analysis illustrates the interdependency between developing mathematical understanding and using the specialized language unique to the discipline to express those understandings employing the mathematics register. Our focus is on Ariel, a 7th grade bilingual student from an urban district, over an 18-month period. He develops knowledge of both mathematics and the language (both oral and written) required for his successful problem solving and communication of this process. Three questions are addressed: (1) How does Ariel display his mathematical understanding during problem solving? (2) How does Ariel use the mathematics register while solving the problem? (3) What systems of representation, including language (oral and written), does Ariel bring to solving the problem? The findings show that initially, Ariel displays his mathematical understanding during his attempt to solve a specific algebraic problem; in this exploration of understanding algebraic ideas, he seeks to identify patterns. We follow his mathematical and language learning from this initial conjecture, to his reformulation and generalization of a rule. Eighteen months later, after studying algebra, Ariel attends to the systems of representation, including both the oral and written expression of the mathematics register. The findings underscore the assertion that students may not be in full command-for production and comprehension-of the mathematics register until they understand the underlying mathematics. Teachers should be encouraged to create situations in which students deploy all of their diverse repertories of mathematics knowledge and skills to the instructional tasks at hand, and to refine their use of the mathematics register.

Original language | English (US) |
---|---|

Pages (from-to) | 75-87 |

Number of pages | 13 |

Journal | Journal of Mathematical Behavior |

Volume | 40 |

DOIs | |

State | Published - 2015 |

### Fingerprint

### Keywords

- Communication
- Discourse
- Language
- Mathematics register
- Oral and written
- Problem solving

### ASJC Scopus subject areas

- Applied Mathematics
- Applied Psychology
- Education

### Cite this

**Ariel's cycles of problem solving : An adolescent acquires the mathematics register.** / Sigley, Robert; Wilkinson, Louise C.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Ariel's cycles of problem solving

T2 - An adolescent acquires the mathematics register

AU - Sigley, Robert

AU - Wilkinson, Louise C

PY - 2015

Y1 - 2015

N2 - This analysis illustrates the interdependency between developing mathematical understanding and using the specialized language unique to the discipline to express those understandings employing the mathematics register. Our focus is on Ariel, a 7th grade bilingual student from an urban district, over an 18-month period. He develops knowledge of both mathematics and the language (both oral and written) required for his successful problem solving and communication of this process. Three questions are addressed: (1) How does Ariel display his mathematical understanding during problem solving? (2) How does Ariel use the mathematics register while solving the problem? (3) What systems of representation, including language (oral and written), does Ariel bring to solving the problem? The findings show that initially, Ariel displays his mathematical understanding during his attempt to solve a specific algebraic problem; in this exploration of understanding algebraic ideas, he seeks to identify patterns. We follow his mathematical and language learning from this initial conjecture, to his reformulation and generalization of a rule. Eighteen months later, after studying algebra, Ariel attends to the systems of representation, including both the oral and written expression of the mathematics register. The findings underscore the assertion that students may not be in full command-for production and comprehension-of the mathematics register until they understand the underlying mathematics. Teachers should be encouraged to create situations in which students deploy all of their diverse repertories of mathematics knowledge and skills to the instructional tasks at hand, and to refine their use of the mathematics register.

AB - This analysis illustrates the interdependency between developing mathematical understanding and using the specialized language unique to the discipline to express those understandings employing the mathematics register. Our focus is on Ariel, a 7th grade bilingual student from an urban district, over an 18-month period. He develops knowledge of both mathematics and the language (both oral and written) required for his successful problem solving and communication of this process. Three questions are addressed: (1) How does Ariel display his mathematical understanding during problem solving? (2) How does Ariel use the mathematics register while solving the problem? (3) What systems of representation, including language (oral and written), does Ariel bring to solving the problem? The findings show that initially, Ariel displays his mathematical understanding during his attempt to solve a specific algebraic problem; in this exploration of understanding algebraic ideas, he seeks to identify patterns. We follow his mathematical and language learning from this initial conjecture, to his reformulation and generalization of a rule. Eighteen months later, after studying algebra, Ariel attends to the systems of representation, including both the oral and written expression of the mathematics register. The findings underscore the assertion that students may not be in full command-for production and comprehension-of the mathematics register until they understand the underlying mathematics. Teachers should be encouraged to create situations in which students deploy all of their diverse repertories of mathematics knowledge and skills to the instructional tasks at hand, and to refine their use of the mathematics register.

KW - Communication

KW - Discourse

KW - Language

KW - Mathematics register

KW - Oral and written

KW - Problem solving

UR - http://www.scopus.com/inward/record.url?scp=84957427349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957427349&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2015.03.001

DO - 10.1016/j.jmathb.2015.03.001

M3 - Article

AN - SCOPUS:84957427349

VL - 40

SP - 75

EP - 87

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

ER -