### Abstract

Tasks that are descriptive of a goal state and not prescriptive of the paths students must take to reach it inevitably generate spaces of possible interpretations of givens and goals, as well as possible paths from givens to goals, each featuring elements of a bounded space of mathematical concepts. When a sample comprised of students at elementary and post-baccalaureate levels of schooling was given one of these tasks, the solutions expressed rich and deep understandings of mathematical concepts that were common among groups at both levels of schooling. These findings are less supportive of the foundational metaphor of curriculum in which understandings serve to support the acquisition of more formal mathematics, and more supportive of the notion of a curriculum that "spirals" around central ideas that are revisited at multiple levels of schooling in order to provide learners with greater access to powerful ways of understanding mathematics.

Original language | English |
---|---|

Title of host publication | Modeling Students' Mathematical Modeling Competencies |

Subtitle of host publication | ICTMA 13 |

Publisher | Springer US |

Pages | 245-254 |

Number of pages | 10 |

ISBN (Print) | 9781441905604 |

DOIs | |

State | Published - 1 Dec 2010 |

### Fingerprint

### Keywords

- Assessment
- Concept/Conceptual system
- Definition of mathematical modeling
- Games
- Generative activities
- Mathematics curriculum
- Model eliciting activity
- Models and modeling perspectives

### Cite this

*Modeling Students' Mathematical Modeling Competencies: ICTMA 13*(pp. 245-254). Springer US. https://doi.org/10.1007/978-1-4419-0561-1_21

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*Modeling Students' Mathematical Modeling Competencies: ICTMA 13.*Springer US, pp. 245-254. https://doi.org/10.1007/978-1-4419-0561-1_21

**Investigating the relationship between the problem and the solver : Who decides what math gets used?** / Carmona, Guadalupe; Greenstein, Steven.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

TY - CHAP

T1 - Investigating the relationship between the problem and the solver

T2 - Who decides what math gets used?

AU - Carmona, Guadalupe

AU - Greenstein, Steven

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Tasks that are descriptive of a goal state and not prescriptive of the paths students must take to reach it inevitably generate spaces of possible interpretations of givens and goals, as well as possible paths from givens to goals, each featuring elements of a bounded space of mathematical concepts. When a sample comprised of students at elementary and post-baccalaureate levels of schooling was given one of these tasks, the solutions expressed rich and deep understandings of mathematical concepts that were common among groups at both levels of schooling. These findings are less supportive of the foundational metaphor of curriculum in which understandings serve to support the acquisition of more formal mathematics, and more supportive of the notion of a curriculum that "spirals" around central ideas that are revisited at multiple levels of schooling in order to provide learners with greater access to powerful ways of understanding mathematics.

AB - Tasks that are descriptive of a goal state and not prescriptive of the paths students must take to reach it inevitably generate spaces of possible interpretations of givens and goals, as well as possible paths from givens to goals, each featuring elements of a bounded space of mathematical concepts. When a sample comprised of students at elementary and post-baccalaureate levels of schooling was given one of these tasks, the solutions expressed rich and deep understandings of mathematical concepts that were common among groups at both levels of schooling. These findings are less supportive of the foundational metaphor of curriculum in which understandings serve to support the acquisition of more formal mathematics, and more supportive of the notion of a curriculum that "spirals" around central ideas that are revisited at multiple levels of schooling in order to provide learners with greater access to powerful ways of understanding mathematics.

KW - Assessment

KW - Concept/Conceptual system

KW - Definition of mathematical modeling

KW - Games

KW - Generative activities

KW - Mathematics curriculum

KW - Model eliciting activity

KW - Models and modeling perspectives

UR - http://www.scopus.com/inward/record.url?scp=84884629759&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-0561-1_21

DO - 10.1007/978-1-4419-0561-1_21

M3 - Chapter

SN - 9781441905604

SP - 245

EP - 254

BT - Modeling Students' Mathematical Modeling Competencies

PB - Springer US

ER -