From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving Across Mathematical Representations

2015 ◽  
Vol 33 (1) ◽  
pp. 46-87 ◽  
Author(s):  
Darrell Earnest
Keyword(s):  
Problem Solving ◽  
Coordinate Plane ◽  
Mathematical Representations ◽  
Number Lines

scholarly journals REPRESENTASI MATEMATIS SISWA DALAM PEMECAHAN MASALAH PERBANDINGAN TRIGONOMETRI PADA SEGITIGA SIKU-SIKU DITINJAU DARI KECERDASAN LOGIS MATEMATIS, LINGUISTIK DAN VISUAL SPASIAL

2020 ◽  
Vol 2 (1) ◽  
pp. 1-15
Author(s):  
Merlin Hitalessy ◽  
Wilmintjie Mataheru ◽  
Carolina Selfisina Ayal
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Quadratic Equation ◽  
Mathematical Representation ◽  
Vocational High School ◽  
School Students ◽  
Mathematical Representations ◽  
Quadratic Equations ◽  
Visual Spatial

One of the skills needed in learning mathematics is the ability to solve mathematical problems. In solving problems in mathematics learning, mathematical representation is needed by students in the problem solving process. Students tend to use mathematical representations, but sometimes they don't understand what they are doing. In general, mathematical representations also play an important role in improving mathematical competence. Beside the ability of representation, students also have intelligence, including mathematical logical intelligence, linguistics and visual spatial. This research is descriptive with qualitative approach that aimed to describe the complete mathematical representation of vocational high school students in solving a quadratic equation in terms. The research phase begins with the selection of research subjects were determined by gender and math skills test results were similar. Having chosen the subject and the continuation of the problem solving quadratic equations and interviews. The validity of the data using a triangulation of time that is giving the task of solving a quadratic equation are equal at different times. The results of this study as the mathematic description shows that vocational high school students in solving quadratic equations problem according to Polya step problem solving

Uncommon Partitions: Partitioning as a Problem-Solving Activity

2018 ◽  
Vol 24 (3) ◽  
pp. 164-171 ◽  
Author(s):  
Andrew Izsák ◽  
Sybilla Beckmann ◽  
Torrey Kulow
Keyword(s):  
Problem Solving ◽  
Teaching Practices ◽  
Common Factors ◽  
Success For All ◽  
The Third ◽  
Number Lines ◽  
Double Number ◽  
Mathematical Success

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series.

scholarly journals What Diagrams Are Considered Useful for Solving Mathematical Word Problems in Japan?

2021 ◽  
pp. 79-83
Author(s):  
Hiroaki Ayabe ◽  
Emmanuel Manalo ◽  
Mari Fukuda ◽  
Norihiro Sadato
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Crucial Role ◽  
Preliminary Investigation ◽  
School Level ◽  
Word Problem Solving ◽  
Textbook Series ◽  
Number Lines ◽  
Mathematical Word Problems

AbstractPrevious studies have shown that diagram use is effective in mathematical word problem solving. However, they have also revealed that students manifest many problems in using diagrams for such purposes. A possible reason is an inadequacy in students’ understanding of variations in types of problems and the corresponding kinds of diagrams appropriate to use. In the present study, a preliminary investigation was undertaken of how such correspondences between problem types and kinds of diagrams are represented in textbooks. One government-approved textbook series for elementary school level in Japan was examined for the types of mathematical word problems, and the kinds of diagrams presented with those problems. The analyses revealed significant differences in association between kinds of diagrams and types of problems. More concrete diagrams were included with problems involving change, combination, variation, and visualization of quantities; while number lines were more often used with comparison and variation problems. Tables and graphs corresponded to problems requiring organization of quantities; and more concrete diagrams and graphs to problems involving quantity visualization. These findings are considered in relation to the crucial role of textbooks and other teaching materials in facilitating strategy knowledge acquisition in students.

Toying with Math

2013 ◽  
Vol 20 (4) ◽  
pp. 226-227
Author(s):  
Lisa Englard
Keyword(s):  
Problem Solving ◽  
Coordinate Plane

A regular department of the journal that features collections of short activities focused on a monthly theme, Math by the Month articles aim for an inquiry or problem-solving orientation that includes at least four activities each for grade bands K—2, 3–4, and 5–6. This issue considers how children's toys and games offer many opportunities to count, compare numbers, look for patterns, explore the coordinate plane, and investigate fractions and ratios.

Hundred Chart Challenge

2015 ◽  
Vol 22 (2) ◽  
pp. 65-70
Author(s):  
J. Matt Switzer
Keyword(s):  
Problem Solving ◽  
Effective Teaching ◽  
Teaching Practices ◽  
Teaching And Learning ◽  
Success For All ◽  
Mathematical Representations ◽  
Mathematical Success ◽  
Effective Teaching And Learning

NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014) outlines eight teaching practices for effective teaching and learning of mathematics. One of them, Use and connect mathematical representations, involves engaging students in “making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving” (p. 10).

An application of the Patient-Oriented Problem-Solving (POPS) System

1991 ◽  
Vol 55 (5) ◽  
pp. 327-331 ◽  
Author(s):  
GT Chiodo ◽  
WW Bullock ◽  
HR Creamer ◽  
DI Rosenstein
Keyword(s):  
Problem Solving

Applying a Self-Regulating Private Speech Model to Classroom Settings

1982 ◽  
Vol 13 (2) ◽  
pp. 129-133
Author(s):  
A. D. Pellegrini
Keyword(s):  
Problem Solving ◽  
Private Speech ◽  
Speech Model

The paper explores the processes by which children use private speech to regulate their behaviors. The first part of the paper explores the ontological development of self-regulating private speech. The theories of Vygotsky and Luria are used to explain this development. The second part of the paper applies these theories to pedagogical settings. The process by which children are exposed to dialogue strategies that help them solve problems is outlined. The strategy has children posing and answering four questions: What is the problem? How will I solve it? Am I using the plan? How did it work? It is argued that this model helps children systematically mediate their problem solving processes.

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