# Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

Posted by Bang Qohar

**Introduction**

Research on discussing the relationship between teacher’s belief and practice within mathematics instruction have been addressed by many scholars with a variety of purposes. Some tried to conceptualize models on such relationship [1,2,3,4], while others reported how such relationship was confirmed into practical interest [5,6]. Either the models or the reports were identified to have several associated key variables which emphasize on explaining to what extend one variable influence another variable. Such key variables such as past school experience and immediate classroom situation, for instance, respectively have a strong influence on teachers’ mathematics beliefs and teacher’s teaching practice [1]. Another important variable, teacher’s knowledge, is scrutinized to have a strong interaction with beliefs in shaping teachers’ teaching practice with varying degree being given to particular types of knowledge or beliefs in different situations [5]. Fennema et al [3] added that besides students’ behaviors, such interaction will directly affect teacher’s decisions in planning classroom instructional activity. Hence, more recent studies reported how such interaction influence teachers’ teaching practice. Bray’s study results [6] argued that teacher’s beliefs seemed most likely influence on how teacher structure class discussion whereas teacher’s knowledge appeared to drive quality of teachers’ responses within classroom discussion. On the other hand, Anderson et al [1] summarized the knowledge component includes mathematical content and plans, professional development, teachers’ knowledge and decisions, important mathematics and assessment procedures, use of mathematics texts, and teacher education program.

While such scholars above discussed general knowledge needed by teachers regarding mathematics instruction, in particular on problem-solving, what knowledge do teachers need to hold? Some describe in a pedagogical context, while others revealed in the context of content. Pedagogically, Franke, Kazemi, & Battey [7] explained that teachers need to orchestrate class discussion so that students share multiple problem-solving strategies, analyze relations among strategies, and explore contradictions in students’ ideas to provide greater insight into the mathematical focus. In brief, Chapman [8] summarised three types of knowledge for teaching problem solving: problem solving content knowledge consisting of knowledge of mathematical problems, problem-solving proficiency, and problem posing, as well as pedagogical problem solving knowledge consisting of knowledge of students as problem-solvers, and instructional practices for problem-solving, and affective factors and beliefs.

Regarding types of mathematics-related beliefs which might be held by teachers in teaching problem solving, several authors proposed some categories, such as Ernest [9] with his prominent categories: instrumental, platonist, and problem-solving. Table 1 summarizes several authors’ view on how such three beliefs are characterized [10].

Table 1. Summary of beliefs about mathematics, mathematics teaching, and mathematics learning

Beliefs about the nature of mathematics | Beliefs about mathematics teaching | Beliefs about mathematics learning |

Instrumentalist | Content focussed with an emphasis on performance | Skill mastery, passive reception of knowledge |

Platonist | Content focussed with an emphasis on understanding | Active construction of understanding |

Problem-solving | Learner focussed | Autonomous exploration of own interests |

Our study aims to describe teachers’ mathematics-related belief and knowledge about mathematical problem solving as well as search for possible interaction between such two variables emerging in our teacher participants.

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## About Bang Qohar

I'm Wachid. I'm Indonesian. I'm interested in educating children, especially in mathematics learning. I believe that mathematics could be well built to children for better life. I graduated from Mathematics Education of State University of Surabaya. I am studying Mathematics Education for my magister degree focusing on Realistics Mathematics Education.Posted on April 1, 2017, in Articles, For Teachers, Math Articles, Problem Solving, Research in Mathematics Education, Uncategorized and tagged instrumental, mathematics teacher, mathematics-related beliefs, Platonist, Problem Solving, teacher beliefs. Bookmark the permalink. Leave a comment.

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