Encouraging Mathematical Thinking

1997 ◽  
Vol 3 (1) ◽  
pp. 66-72
Author(s):  
Julianne C. Turner ◽  
Karen Rossman Styers ◽  
Debra G. Daggs
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
Challenging Problem ◽  
The Past ◽  
Past Experiences ◽  
Constructing Meaning

With these words, the NCTM (1989, 65) portrays a dilemma familiar to many middle-grades teachers. Although many teachers strive to involve their students in active and challenging problem-solving activities, students' past experiences may have instilled preconceptions that mathematics is mechanical, uninteresting, or unattainable. In addition, many teachers lack models and examples of how to design mathematics instruction so that it fosters students' engagement. Because the middle grades are crucial years for developing students' future interest in mathematics, middle-grades teachers must take seriously the challenge of presenting mathematics as an exciting discipline that is relevant and accessible to all students. For the past two year, we have been experimenting with approaches that will inte rest students in challenging mathematics while supporting them in constructing meaning.

Problem Solving and Risk Management Methodology

2021 ◽  
pp. 378-395
Author(s):  
Esmeralda Andrade Hernández ◽  
Gregorio Fernández-Lambert ◽  
David Lara Alabazares ◽  
Yesica Mayett Moreno ◽  
Laurent Geneste
Keyword(s):  
Risk Management ◽  
Problem Solving ◽  
Knowledge Base ◽  
Continuous Improvement ◽  
Management Problem ◽  
Current Event ◽  
The Past ◽  
Risk Management Methodology ◽  
Past Experiences ◽  
A Current

Intending to lead organizations to continuous improvement, this chapter proposes a methodology that involves three axes: risk management, problem- solving, and feedback experience. This methodology allows organizations to characterize the experiences they have already confronted, as well as new experiences (which can be risks or problems) with the use of taxonomies established by the organization. It also enables them to capitalize and exploit their knowledge base. This work proposes a best-use approach of the past experiences that are similar to a current event and facilitate their treatment and provide solutions. The authors take the feedback as a point of articulation between the two methodologies because it is a mechanism that offers knowledge where it can be found that the organizations must avoid and take advantage of.

Invented Strategies Can Develop Meaningful Mathematical Procedures

1997 ◽  
Vol 3 (7) ◽  
pp. 370-374
Author(s):  
William M. Carroll ◽  
Denise Porter
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Mathematics Instruction ◽  
The Past ◽  
Reasoning Problem

Over the past decade, a growitig consensus among educators favors a shift in mathematics instruction from a curriculum in which children learn and practice the standard school algorithms to one in which reasoning, problem solving, and conceptual understanding play a major role.

Teaching Toward the Big Ideas of Algebra

2000 ◽  
Vol 6 (4) ◽  
pp. 226-231
Author(s):  
Sonia Woodbury
Keyword(s):  
Problem Solving ◽  
Conceptual Knowledge ◽  
Middle Grades ◽  
Procedural Knowledge ◽  
Conceptual Structure ◽  
Algebraic Manipulation ◽  
Relational Understanding ◽  
The Past ◽  
Starting Point ◽  
Big Ideas

IN WHAT WAYS DO WE WANT MIDDLE-GRADES STUDENTS TO UNDERSTAND ALGEBRA? Hiebert and Carpenter (1992) describe the need for students to gain both procedural knowledge and broadly connected conceptual knowledge to understand mathematics. A knowledge of rules and procedures provides students with tools for efficient problem solving. However, in learning the procedures of algebraic manipulation, for example, students often develop what Skemp (1978) calls an “instrumental understanding” of algebra. He explains, “It is what I have in the past described as ‘rules without reasons,’ without realizing that for many pupils… the possession of such a rule, and the ability to use it, was what they meant by ‘understanding’ ” (p. 9). Skemp contrasts instrumental understanding with “relational understanding,” which “consists of building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (p. 14).

Calculators in the Classroom: How Can We Make It Happen?

1987 ◽  
Vol 34 (6) ◽  
pp. 12-14
Author(s):  
Barbara J. Reys ◽  
Robert E. Reys
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Teaching Method ◽  
Vast Amount ◽  
The Past ◽  
Young Students ◽  
Problem Solving Process

Although curriculum and teaching method change slowly, we have witnessed some major changes in mathematics instruction over the last ten years, most notably the emphasis placed on the problem-solving process. We've also observed vast amount of resources funneled into microcomputer equipment for young students. In part because of this interest in microcomputer technology, we may have overlooked a technological device that has even more potential for revitalizing and enhancing mathematics instruction for children. Simple four-function calculators have been hoved to the back burner (or rear shelf of the school storeroom) in the past few years, but interest in them is reviving as evidenced by this focus issue.

scholarly journals Remembering the past and imagining the future: Identifying and enhancing the contribution of episodic memory

2016 ◽  
Vol 9 (3) ◽  
pp. 245-255 ◽  
Author(s):  
Daniel L Schacter ◽  
Kevin P Madore
Keyword(s):  
Problem Solving ◽  
Episodic Memory ◽  
Creative Thinking ◽  
The Past ◽  
Brief Training ◽  
Episodic Simulation ◽  
Neural Processes ◽  
The Future ◽  
Future Events ◽  
Past Experiences

Recent studies have shown that imagining or simulating future events relies on many of the same cognitive and neural processes as remembering past events. According to the constructive episodic simulation hypothesis, such overlap indicates that both remembered past and imagined future events rely heavily on episodic memory: future simulations are built on retrieved details of specific past experiences that are recombined into novel events. An alternative possibility is that commonalities between remembering and imagining reflect the influence of more general, non-episodic factors such as narrative style or communicative goals that shape the expression of both memory and imagination. We consider recent studies that distinguish the contributions of episodic and non-episodic processes in remembering the past and imagining the future by using an episodic specificity induction—brief training in recollecting the details of a past experience—and also extend this approach to the domains of problem solving and creative thinking. We conclude by suggesting that the specificity induction may target a process of event or scene construction that contributes to episodic memory as well as to imagination, problem solving, and creative thinking.

Innovation in Curriculum: Fostering Student Discourse: Don't Ask Me! I'm Just the Teacher!

2001 ◽  
Vol 7 (4) ◽  
pp. 218-221
Author(s):  
Jeffrey A. Frykholm ◽  
Mary E. Pittman
Keyword(s):  
Critical Thinking ◽  
Problem Solving ◽  
Middle Grades ◽  
Learning Theories ◽  
Significant Shift ◽  
Mathematical Communication ◽  
The Past ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
Mathematics Curricula

Throughout the past several years, middle-grades mathematics curricula have undergone a significant shift. Recently developed curriculum programs based on both recommendations of the NCTM and contemporary learning theories now emphasize problem solving, critical thinking, mathematical connections, and mathematical communication in ways that they did not before. As these powerful curriculum programs continue to find a stronghold in our middle schools, new implications and roles for both teachers and students are becoming clear.

Review of Mathematical Thinking and Problem Solving.

1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking

Truth Matters: Cognitive Integrity as an Intervention for Self-Deception

2017 ◽  
Author(s):  
Eugenia Isabel Gorlin ◽  
Michael W. Otto
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Autonomous Agents ◽  
Therapeutic Interventions ◽  
Empirical Validation ◽  
The Past ◽  
Adaptive Problem

To live well in the present, we take direction from the past. Yet, individuals may engage in a variety of behaviors that distort their past and current circumstances, reducing the likelihood of adaptive problem solving and decision making. In this article, we attend to self-deception as one such class of behaviors. Drawing upon research showing both the maladaptive consequences and self-perpetuating nature of self-deception, we propose that self-deception is an understudied risk and maintaining factor for psychopathology, and we introduce a “cognitive-integrity”-based approach that may hold promise for increasing the reach and effectiveness of our existing therapeutic interventions. Pending empirical validation of this theoretically-informed approach, we posit that patients may become more informed and autonomous agents in their own therapeutic growth by becoming more honest with themselves.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

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