scholarly journals Components of Mathematical Problem Solving Competence and Mediation Effects of Instructional Strategies for Mathematical Modeling

2020 ◽  
Author(s):  
Sunyoung Han ◽  
Hye Mi Kim
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Instructional Strategies ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mediation Effects

Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework

2020 ◽  
Vol 13 (2) ◽  
pp. 130-151
Author(s):  
Kadek Adi Wibawa ◽  
I Putu Ade Andre Payadnya ◽  
I Made Dharma Atmaja ◽  
Marius Derick Simons
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Undergraduate Students ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Graph Representations ◽  
Symbolic Representations ◽  
Mathematics Educators ◽  
Three Stages ◽  
Algebraic Forms

 [English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations. The problem-solving involving modeling problems requires translational thinking, changing from source representations to targeted representations. This research aimed to formulate undergraduate students’ effort in restructuring their fragmented translational thinking (defragmentation of translational thinking structure). The defragmentation was mapped through the CRA framework (checking, repairing, ascertaining). The subjects were three of eighty-five 4th and 6th-semester students. Data were analyzed through three stages; categorization, reduction, and conclusion. The analysis resulted in three types of defragmentation of translational thinking structure: from verbal representations to graph representations, from graph representations to symbolic representations (algebraic forms), and from the graph and symbolic representations to mathematical models. The finding shows that it is essential for mathematics educators to allow students to manage their thinking structures while experiencing difficulties and errors in mathematical problem-solving. Keywords: Thinking structure, Fragmentation, Defragmentation, Translational thinking, CRA framework  [Bahasa]: Fragmentasi struktur berpikir merupakan kegagalan konstruksi yang terjadi di dalam memori akibat dari konsep-konsep yang dipelajari tidak terkoneksi dengan baik. Hal ini membuat mahasiswa sering mengalami kesulitan dan kesalahan dalam memecahkan masalah pemodelan matematika. Untuk itu, perlu dilakukan upaya agar tidak terjadi fragmentasi struktur berpikir yang permanen. Dalam memecahkan masalah pemodelan matematika, mahasiswa perlu melakukan berpikir translasi, yaitu mengubah representasi sumber menjadi representasi yang ditargetkan. Penelitian ini bertujuan untuk merumuskan upaya mahasiswa dalam melakukan penataan fragmentasi struktur berpikir translasi yang terjadi (defragmentasi struktur berpikir translasi) dalam memecahkan masalah pemodelan matematika. Defragmentasi yang dilakukan mahasiswa dipetakan melalui kerangka CRA (checking, repairing, dan ascertaining). Subjek penelitian adalah mahasiswa semester 4 dan 6 yang terdiri dari 3 orang dipilih dari 85 mahasiswa. Analisis data dilakukan melalui tiga tahap, yaitu pengategorian data, reduksi data, dan penarikan kesimpulan. Penelitian ini menemukan tiga jenis defragmentasi struktur berpikir translasi: defragmentasi dari representasi verbal ke grafik, dari representasi grafik ke simbol (bentuk aljabar), dan representasi grafik dan simbol (bentuk aljabar) ke model matematika. Penelitian ini menunjukkan pentingnya pengajar matematika memberikan kesempatan kepada mahasiswa dalam menata struktur berpikirnya ketika mengalami kesulitan dan kesalahan dalam memecahkan masalah matematika. Kata kunci: Struktur berpikir, Fragmentasi, Defragmentasi, Berpikir translasi, Kerangka CRA

A Visual Approach to Solving Mixture Problems

1996 ◽  
Vol 89 (2) ◽  
pp. 108-111
Author(s):  
Albert B. Bennett ◽  
Eugene Maier
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Mathematical Problem ◽  
Multiple Representations ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Conceptual Understandings ◽  
Visual Approach

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), the 9–12 standards call for a shift from a curriculum dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. One approach that affords opportunities for achieving these objectives is the use of diagrams and drawings. The familiar saying “A picture is worth a thousand words” could well be modified for mathematics to “A picture is worth a thousand numbers.” As an example of visual approaches in algebra, this article uses diagrams to solve mixture problems.

Classroom characters coach students to success

2010 ◽  
Vol 16 (6) ◽  
pp. 342-349
Author(s):  
Sharon A. Edwards ◽  
Robert W. Maloy ◽  
Gordon Anderson
Keyword(s):  
Problem Solving ◽  
Instructional Strategies ◽  
Mathematical Problem ◽  
Mathematical Problem Solving

Learning mathematical problem solving is as easy as 1, 2, 3 when teachers use flexible instructional strategies.

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