Connecting Research to Teaching: Affective Responses to Problem Solving

1993 ◽  
Vol 86 (9) ◽  
pp. 761-763 ◽  
Author(s):  
Douglas B. McLeod
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Affective Responses ◽  
School Mathematics ◽  
Affective Reactions ◽  
Reform Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Classrooms ◽  
The Future ◽  
Nonroutine Problems

The vision of the mathematics classroom that IS presented 1n the Natwnal Council of Teachers of Mathematics's Curriculum and Eualuation Standards for School Mathematics (1989) has inspired many of us to want to change the way in which we teach. We want to pose challenging problems, to see our students work cooperatively, and to have productive discussions with students about significant mathematical ideas. But as Ball and Schroeder have pointed out, that vision is “much more difficult to realize than to endorse” (1992, 69). We will encounter many difficulties as we move toward that ideal classroom of the future; getting students to respond positively to nonroutine problems or other tasks that require higher-orderthinking skills is one difficulty that teachers often face. Research suggests that students' affective reactions to nonroutine problems can be a source of both difficulty and support as we work to reform mathematics classrooms.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of problems.

How Does Your Mathematical Garden Grow?

2007 ◽  
Vol 13 (2) ◽  
pp. 68-76
Author(s):  
Shari A. Beck ◽  
Vanessa E. Huse ◽  
Brenda R. Reed
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Real Life ◽  
Middle School Mathematics ◽  
Content Standards ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Application Problem ◽  
Multiple Process ◽  
Problem Solving Process

Imagine a middle school mathematics classroom where students are actively engaged in a real-life application problem incorporating multiple Process and Content Standards as outlined by NCTM (2000). Sounds of mathematical communication arise as students use multiple representations to help connect mathematical ideas throughout the problem-solving process. Students apply various types of reasoning and explore alternate methods of proof while working attentively on applications that incorporate Number and Operations, Algebra, Geometry, and Measurement.

Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together

2002 ◽  
Vol 8 (8) ◽  
pp. 448-454
Author(s):  
Marilyn E. Strutchens
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Multicultural Literature ◽  
School Mathematics ◽  
Social Environments ◽  
Children And Parents ◽  
Learning School ◽  
Different Cultures ◽  
Mathematics Community ◽  
Learning Together

In recent years, the mathematics community has given more attention to the role that mathematics plays in our cultural society and the contributions of different cultures to mathematics (Bishop 1988; D'Ambrosio 1985; NCTM 1989; Frankenstein 1990; Joseph 1993). Teachers are encouraged to include culture in a variety of ways in the mathematics classroom. Students can be encouraged to use mathematics as a tool to examine their cultural and social environments, traditions, and artifacts. In addition, mathematics learned by students outside the classroom can be used as a bridge to learning school mathematics.

What Is in the Daily News? Problem-Solving Opportunities!

1999 ◽  
Vol 5 (7) ◽  
pp. 390-394
Author(s):  
Robyn Silbey
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Daily News ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
The Everyday ◽  
Everyday World ◽  
Real World Problems

In An Agenda for Action, the NCTM asserted that problem solving must be at the heart of school mathematics (1980). Almost ten years later, the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stated that the development of each student's ability to solve problems is essential if he or she is to be a productive citizen. The Standards assumed that the mathematics curriculum would emphasize applications of mathematics. If mathematics is to be viewed as a practical, useful subject, students must understand that it can be applied to various real-world problems, since most mathematical ideas arise from the everyday world. Furthermore, the mathematics curriculum should include a broad range of content and an interrelation of that content.

Expanding participation in problem solving in a diverse middle school mathematics classroom

2010 ◽  
Vol 22 (1) ◽  
pp. 91-118 ◽  
Author(s):  
Keith Weber ◽  
Iuliana Radu ◽  
Mary Mueller ◽  
Arthur Powell ◽  
Carolyn Maher
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Classroom ◽  
Middle School Mathematics ◽  
School Mathematics

scholarly journals Using Mindfulness/Contemplative Practices to Help Students Focus in Mathematics Classrooms

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Mary B. Walkins
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Deep Breathing ◽  
Contemplative Practices ◽  
Mathematics Classrooms ◽  
Class Time ◽  
Regular Class ◽  
Class Period ◽  
The One ◽  
Survey Responses

Can using mindfulness/contemplative practices help students become mindful, focused, and present in the mathematics classroom? In this study, mindfulness/contemplative practices were used in the mathematics classroom to determine if students were encouraged to be mindful, focused, and present or engaged in problem solving. During class time, students engaged in the following 2 contemplative practices: a “Mindful Minute of Deep Breathing” and “Beholding the Mathematics”. The one minute of mindful Deep Breathing took place usually at the beginning of class. Then, during a regular class period, students used Beholding to look more deeply at topics, probe questions, and investigate answers to questions. The survey responses indicated that the mindfulness/contemplative practices were very useful in the mathematics classroom to help students to be mindful (both inside and outside of the classroom), focus on the mathematics taught, and be present or engaged in the problem solving.   

scholarly journals Students’ Reflections on Dispositions in a Mathematics Classroom

2021 ◽  
Vol 6 (18) ◽  
pp. 61-78
Author(s):  
Teoh Sian Hoon ◽  
Parmjit Singh ◽  
Mazlini Adnan ◽  
Koo Ah Choo
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Publishing House ◽  
Mathematical Problem ◽  
Reflective Journal ◽  
Mathematics Classrooms ◽  
Mathematical Problems ◽  
International Publishing ◽  
Journal Entries ◽  
Open Access Article

This study investigated students' dispositions. It is a qualitative study that analyzes students' reflective journal entries. It captured students’ dispositions and described how the reflective activities influence their engagement mathematical problem-solving. The findings showed that the students considered the mathematical problems were challenging to them, but their positive dispositions kept them engaged in learning. Engagement through effort and thinking algebraically with teachers' guidance was the crucial first steps in problem-solving. Results from this study provide educators with a wealth of knowledge to develop learning dispositions that will encourage active thinking and engagement among students in mathematics classrooms.                                                                Keywords: reflection; disposition; mathematics; engagement eISSN 2514-7528 © 2021 The Authors. Published for AMER ABRA CE-Bs by E-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians / Africans / Arabians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/jabs.v6i18.384

Affective Issues in Mathematical Problem Solving: Some Theoretical Considerations

1988 ◽  
Vol 19 (2) ◽  
pp. 134-141 ◽  
Author(s):  
Douglas B. McLeod
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Affective Responses ◽  
Mathematical Problem Solving ◽  
Emotional States ◽  
Mathematics Students ◽  
Problem Solvers ◽  
Nonroutine Problems ◽  
Theoretical Considerations ◽  
Affective Issues

Mathematics students often report feelings of frustration or satisfaction when they work on nonroutine problems. These affective responses are an important factor in problem solving and deserve increased attention in research. Mandler's theory of emotion is suggested as a framework for investigating affective issues in problem solving. Several dimensions of the emotional states of problem solvers are specified, including the magnitude and direction of the emotions, their duration, and the students' level of awareness and level of control of the emotions. The implications of this framework for research on affective issues in problem solving are also discussed.

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