scholarly journals Mathematics teachers’ knowledge for teaching problem solving

2015 ◽  
Vol 3 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Olive Chapman
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematical Problem ◽  
Research Literature ◽  
Mathematical Problem Solving ◽  
Knowledge For Teaching ◽  
General Ability ◽  
Mathematics Knowledge ◽  
Teaching Problem ◽  
Problem Solvers

In recent years, considerable attention has been given to the knowledge teachers ought to hold for teaching mathematics. Teachers need to hold knowledge of mathematical problem solving for themselves as problem solvers and to help students to become better problem solvers. Thus, a teacher’s knowledge of and for teaching problem solving must be broader than general ability in problem solving. In this article a category-based perspective is used to discuss the types of knowledge that should be included in mathematical problem-solving knowledge for teaching. In particular, what do teachers need to know to teach for problem-solving proficiency? This question is addressed based on a review of the research literature on problem solving in mathematics education. The article discusses the perspective of problem-solving proficiency that framed the review and the findings regarding six categories of knowledge that teachers ought to hold to support students’ development of problem-solving proficiency. It concludes that mathematics problem-solving knowledge for teaching is a complex network of interdependent knowledge. Understanding this interdependence is important to help teachers to hold mathematical problem-solving knowledge for teaching so that it is usable in a meaningful and effective way in supporting problem-solving proficiency in their teaching. The perspective of mathematical problem-solving knowledge for teaching presented in this article can be built on to provide a framework of key knowledge mathematics teachers ought to hold to inform practice-based investigation of it and the design and investigation of learning experiences to help teachers to understand and develop the mathematics knowledge they need to teach for problem-solving proficiency.

scholarly journals Mathematical knowledge for teaching: Adding to the description through a study of probability in practice

Pythagoras ◽  
2006 ◽  
Vol 0 (63) ◽  
Author(s):  
Mercy Kazima ◽  
Jill Adler
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
Mathematical Knowledge For Teaching ◽  
Mathematical Work ◽  
Mathematical Problem Solving ◽  
Knowledge For Teaching ◽  
Scaling Down ◽  
Multilingual Classroom ◽  
Everyday Knowledge

In their description of the mathematical work of teaching, Ball,  Bass & Hill (2004) describe the mathematical problem solving that teachers do as they go about their work. In this paper we add to this description through our study of teaching of probability in a grade 8 multilingual classroom in South Africa. We use instances of teaching to highlight the mathematical problem solving that teachers might face as they work with learners’ ideas, both expected and unexpected. We discuss  the restructuring of tasks as an inevitable feature of teachers’ work, and argue that in addition to scaling up or scaling down of the task as Ball et al. (2004) describe, restructuring can also entail shifting the mathematical outcomes from those intended. We also point out how well known issues in mathematics education, for example working with learners’ everyday knowledge, and the languages they bring to class, are highlighted by the context of probability, enabling additional insights into the mathematical work of teaching.

scholarly journals Teaching Strategies for Mathematical Problem-Solving through the Lens of Secondary School Teachers

TEM Journal ◽  
2021 ◽  
pp. 743-750
Author(s):  
Afiqah Hamizah Noor Ishak ◽  
Sharifah Osman ◽  
Chiang Kok Wei ◽  
Dian Kurniati
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Thematic Analysis ◽  
Teaching Strategies ◽  
Secondary School Teachers ◽  
Mathematical Problem ◽  
Structured Interview ◽  
Mathematical Problem Solving ◽  
School Teachers ◽  
Teaching Problem

Many studies have been conducted on problem-solving but only a small number of studies emphasized the strategies of teaching problem-solving. This paper explores the teaching strategies for mathematical problem-solving in a secondary school in Johor, Malaysia. It involves a qualitative study in which a semi-structured interview was conducted with mathematics teachers. Data were analyzed using a sixstep thematic analysis. The results can be viewed from three contexts of findings, namely the teaching strategies, the problems faced by teachers, and the solutions to overcome the problems. The findings revealed that there are teachers who have implemented personal teaching strategies, namely the Easy-Maths Model and the Cut-Stop-Solve Model to effectively teach mathematical problem-solving. The findings also explained some problems in teaching mathematical problem-solving, whereby students’ weaknesses in basic mathematics emerged as the main drawback. This study provides useful information to teachers on the different strategies for teaching mathematical problem-solving.

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.

Brief Reports: Some Factors That Impede or Enhance Performance in Mathematical Problem Solving

1993 ◽  
Vol 24 (2) ◽  
pp. 167-171
Author(s):  
Lynn C. Hart
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Average Ability ◽  
Complete Report ◽  
Average Students ◽  
Problem Solvers

Considerable emphasis in problem-solving research has been placed on studying the processes used by expert problem solvers or above-average students, often with the goal of identifying processes that might be taught to average-and below-average students (Dalton, 1974; Knippenberg, 1978; Simon, 1986). But, as Lesh (1981) points out, “the qualitatively different systems of thought used by gifted problem solvers may be … inaccessible to … average-ability children” (p. 239). Lesh's comments indicate that it may be important to identify factors that enhance or impede the problemsolving progress of average-ability students, rather than focusing attention on experts. Lester (1987) also calls for research in th is area. Identifying some of these factors was the goal of this study (a more complete report of which can be found in Hart, 1985).

Writing About the Problem Solving Process to Improve Problem Solving Performance

2003 ◽  
Vol 96 (3) ◽  
pp. 185-187 ◽  
Author(s):  
Kenneth M. Williams
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
National Council ◽  
Instructional Programs ◽  
Principles And Standards ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the most important components of mathematics. In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics emphasized that instructional programs should enable all students in all grades to “build new mathematical knowledge through problem solving, solve problems that arise in mathematics and in other contexts, apply and adapt a variety of appropriate strategies to solve problems, and monitor and reflect on the process of mathematical problem solving” (NCTM 2000, p. 52). But how do students become competent and confident mathematical problem solvers?

Documenting a Developing Vision of Teaching Mathematics with Technology

2016 ◽  
pp. 166-189 ◽  
Author(s):  
Dana C. Cox ◽  
Suzanne R. Harper
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Qualitative Data ◽  
Current Practice ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Teaching Mathematics ◽  
National Council ◽  
Teaching With Technology ◽  
Preservice Mathematics Teachers

This chapter reports on a study of 39 Preservice Mathematics Teachers (PSMTs) enrolled in a course on mathematical problem solving with technology. Qualitative data were collected with the purpose of examining the extent to which the course was supporting the development of a vision of teaching with technology amongst secondary preservice mathematics teachers. Two findings are discussed. First, PSMTs developed a vision aligned with the vision provided by the National Council of Teachers of Mathematics Technology Principle. Second, PSMTs drew heavily on instructional experiences gained in the course to illustrate that emergent vision. The voices in this study challenge key assumptions that may be prevalent in current practice in the preparation of PSMTs.

scholarly journals Upaya Peningkatan Kemampuan Pemecahan Masalah Matematis Siswa dengan Pendidikan Matematika Realistik Indonesia

2018 ◽  
Vol 5 (2) ◽  
pp. 85-92
Author(s):  
Reni Wahyuni
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Learning Process ◽  
Mathematical Problem ◽  
Learning Activities ◽  
Mathematical Problem Solving ◽  
Realistic Mathematics Education ◽  
Group Presentation ◽  
Realistic Mathematics ◽  
Working Together

ABSTRAKPenelitian ini merupakan suatu penelitian tindakan kelas yang berkolaborasi dengan guru matematika di sekolah sehingga tujuan penelitian adalah untuk memperbaiki proses pembelajaran sehingga memiliki dampak pada upaya peningkatan kemampuan pemecahan masalah matematis siswa kelas VIIc MTs Diniyah Puteri Pekanbaru. Secara teoritis dipilihlah suatu proses pembelajaran yang sesuai dengan masalah di kelas tersebut adalah Pendidikan Matematika Realistik Indonesia (PMRI) sebagai penerapannya. Pada penelitian ini didesain dengan menerapkan pendekatan PMRI berdasarkan karakteristik PMRI. Penelitian ini terdiri dari dua siklus untuk memperbaiki proses pembelajaran dan melihat kemampuan pemecahan masalah matematis siswa. Berdasarkan hasil analisis data dengan menggunakan lembar pengamatan pada siklus 1 dan siklus 2 maka terjadi perbaikan proses pembelajaran yang terlihat dari kegiatan aktifan siswa dalam belajar, bekerja sama, rasa ingin tahu , diskusi dan memberikan respon pada presentasi kelompok. Selanjutnya jika ditinjau tes kemampuan pemecahan masalah matematis siswa maka diperoleh rata-rata 63.15 dengan ketuntasan sebanyak 11 siswa sedangkan pada siklus II memperoleh rata-rata 70,70 dengan ketuntasan sebanyak 15 siswa. Secara klasikal terjadi peningkatan ketuntasan sebanyak 4 orang dari siklus 1 ke siklus 2 maka dapat disimpulkan bahwa pendekatan PMRI dapat memperbaiki proses pembelajaran dan meningkatkan kemampuan pemecahan masalah matematis siswa kelas VIIc MTs Diniyah Puteri Pekanbaru.ABSTRACTThis research is a classroom action research in collaboration with schools mathematics teachers so that the purpose of research is to improve the learning process so as to have an impact on improving the students' mathematical problem solving ability VIIc grade MTs Diniyah Puteri Pekanbaru. Theoretically chosen a learning process that is appropriate to the problem in the class is Indonesian Realistic Mathematics Education (PMRI) as its application. In this study was designed to implement an approach based on the characteristics PMRI. The study consisted of two cycles to improve the learning process and see the students' mathematical problem solving ability. Based on the analysis of data using observation sheet in cycle 1 and cycle 2, the improvements were visible learning process of the students in learning activities, working together, curiosity, discussion and responses to the group presentation. Furthermore, if the review test students' mathematical problem solving ability then gained an average of 63.15 with a mastery of as many as 11 students while in the second cycle obtain an average of 70.70 with a mastery of as many as 15 students. Traditionally an increase of completeness of 4 people from cycle 1 to cycle 2 it could be concluded that PMRI approach could improve the learning process and improve students' mathematical problem solving ability class VIIc MTs Diniyah Puteri Pekanbaru.

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