Mathematics teachers’ knowledge for teaching problem solving

Abstract

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.

Pre-Service Teacher’s Beliefs and Knowledge about Mathematics

“…Muhtarom, Juniati, & Siswono (2017b) explains that a large number of university pre-service students to become mathematics teachers who hold platonist views is due to their mathematics experience at school, and university courses have also strengthened these beliefs. Belief is an important thing that must be instilled in children early on as it can be the basis for disposition, the basis for action, the basis for change and the basis for learning (Chapman, 2015).…”

Problem posing ability among prospective mathematics teachers

“…In truth, the knowledge deals with problem-posing is one of the knowledge that is required to teach about mathematics problem-solving that should be mastered by mathematics teachers besides knowledge of problemsolving in mathematics itself. Knowledge of problem-posing needs to be mastered by mathematics teachers because through this knowledge, they are expected to have a capability in promoting problem-solving proficiency of their students by giving facilitation for students to construct the diverse and meaningful mathematics problems (Chapman, 2015). Moreover, Ellerton (2013) suggested that young teachers should be given a chance to acquire problem-posing skills and believe in their self-ability in posing mathematics problems as an effort to make themselves become capable in mathematics problem-posing and also to assist their students during the problemposing activity in mathematics learning.…”

“…More specifically, mathematics teachers need to master the knowledge of problem-solving for teaching mathematics because basically problem-solving itself is the core of teaching and learning mathematics. Such knowledge is required by mathematics teachers as problem solvers as well as to facilitate their students in attempting to be a better mathematics problem solver (Chapman, 2015). Furthermore, this knowledge is actually comprised of three classes, namely content knowledge of problem-solving, pedagogical knowledge of problemsolving, and beliefs and factors in the affective domain that may influence problem-solving.…”

Developing learning materials supporting teachersr understanding on mathematics problem-solving knowledge for teaching

“…While the focus has been given more on the students in the early years, a body of studies directly or indirectly offering recommendations of the knowledge teachers should hold to teach problem-solving is required to be developed. Therefore, in order to have a broader insight on the needs of teacher related to problemsolving, Chapman [1] has proposed the so called 'mathematics problem-solving knowledge for teaching' (MPSKT), i.e. the knowledge needed to effectively teach problem solving.…”

“…Chapman [1] describes the categories of problem solving knowledge into three main categories, namely problem solving content knowledge, pedagogical problem-solving knowledge, and knowledge of affective factors related to problem-solving teaching. Problem-solving content knowledge includes four things.…”