### Abstract

Mathematicians and mathematics educators have been curious about the processes and attributes of problem solving for over 50 years. As mathematics teachers at any level of education, we want to know what teaching practices we can employ to help our students develop effective problem solving abilities. This curiosity has led to numerous investigations of the attributes and processes of problem solving. In this chapter, we describe insights from a study we conducted of the mathematical practices of 12 research mathematicians. We believe these insights are useful to teachers striving to promote mathematical practices in students at all levels–from first-grade mathematics to beginning algebra, calculus, and abstract algebra. Our chapter begins by inviting you to work a problem that our research study posed to 12 mathematicians and to reflect, as they did, on your own problem solving behavior as you attempt to solve this problem. In inviting you to work this problem, our intent is to raise your awareness of the processes, emotions, knowledge, heuristics, and reasoning patterns that you use when working a novel problem. Our research suggests that by reflecting on our own mathematical practices, instructors can become more attentive to the development of problem solving attributes in students (Bloom, 2004). This exercise should make the remaining sections of our chapter more meaningful. In particular, it is our hope that our description of the Multidimensional Problem Solving Framework is more accessible.

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

Title of host publication | Making the Connection: Research and Teaching in Undergraduate Mathematics Education |

Publisher | Mathematical Association of America |

Pages | 275-288 |

Number of pages | 14 |

ISBN (Print) | 9780883859759, 9780883851838 |

DOIs | |

State | Published - Jan 1 2008 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Making the Connection: Research and Teaching in Undergraduate Mathematics Education*(pp. 275-288). Mathematical Association of America. https://doi.org/10.5948/UPO9780883859759.022

**Promoting effective mathematical practices in students : Insights from problem solving research.** / Carlson, Marilyn; Bloom, Irene; Glick, Peggy.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Making the Connection: Research and Teaching in Undergraduate Mathematics Education.*Mathematical Association of America, pp. 275-288. https://doi.org/10.5948/UPO9780883859759.022

}

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T1 - Promoting effective mathematical practices in students

T2 - Insights from problem solving research

AU - Carlson, Marilyn

AU - Bloom, Irene

AU - Glick, Peggy

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Mathematicians and mathematics educators have been curious about the processes and attributes of problem solving for over 50 years. As mathematics teachers at any level of education, we want to know what teaching practices we can employ to help our students develop effective problem solving abilities. This curiosity has led to numerous investigations of the attributes and processes of problem solving. In this chapter, we describe insights from a study we conducted of the mathematical practices of 12 research mathematicians. We believe these insights are useful to teachers striving to promote mathematical practices in students at all levels–from first-grade mathematics to beginning algebra, calculus, and abstract algebra. Our chapter begins by inviting you to work a problem that our research study posed to 12 mathematicians and to reflect, as they did, on your own problem solving behavior as you attempt to solve this problem. In inviting you to work this problem, our intent is to raise your awareness of the processes, emotions, knowledge, heuristics, and reasoning patterns that you use when working a novel problem. Our research suggests that by reflecting on our own mathematical practices, instructors can become more attentive to the development of problem solving attributes in students (Bloom, 2004). This exercise should make the remaining sections of our chapter more meaningful. In particular, it is our hope that our description of the Multidimensional Problem Solving Framework is more accessible.

AB - Mathematicians and mathematics educators have been curious about the processes and attributes of problem solving for over 50 years. As mathematics teachers at any level of education, we want to know what teaching practices we can employ to help our students develop effective problem solving abilities. This curiosity has led to numerous investigations of the attributes and processes of problem solving. In this chapter, we describe insights from a study we conducted of the mathematical practices of 12 research mathematicians. We believe these insights are useful to teachers striving to promote mathematical practices in students at all levels–from first-grade mathematics to beginning algebra, calculus, and abstract algebra. Our chapter begins by inviting you to work a problem that our research study posed to 12 mathematicians and to reflect, as they did, on your own problem solving behavior as you attempt to solve this problem. In inviting you to work this problem, our intent is to raise your awareness of the processes, emotions, knowledge, heuristics, and reasoning patterns that you use when working a novel problem. Our research suggests that by reflecting on our own mathematical practices, instructors can become more attentive to the development of problem solving attributes in students (Bloom, 2004). This exercise should make the remaining sections of our chapter more meaningful. In particular, it is our hope that our description of the Multidimensional Problem Solving Framework is more accessible.

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