Journey toward Teaching Mathematics through Problem Solving

Abstract

Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving? A group of teachers began the journey of learning to teach through problem solving while taking a Teaching Elementary School Mathematics graduate course. This course was designed to engage teachers in problem solving during class meetings and required them to do problem solving action research in their classrooms. Although challenged by the course problem solving work, teachers became more comfortable with the mathematics and recognized the importance of group work while problem solving. As they worked with their students, teachers were more confident in their students' abilities to be successful problem solvers. For some teachers, a strong problem solving foundation was established. For others, the foundation was more tentative.

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

“…The results echo the findings of Sakshaug and Wohlhuter () and Kersaint and Chappell () among elementary teachers. Furthermore, in answer to Sakshaug and Wohlhuter's concern about elementary teachers' lack of experience with a student‐centered, problem‐solving approach to teaching, many of our teachers responded strongly to their experience in math circles.…”

“…Cai also states that there is little research on how teachers learn to use problem solving in their classrooms. However, Sakshaug and Wohlhuter () provided evidence that teachers can change from a traditional style of teaching to teaching through problem solving. They studied a group of 41 teachers who were taking an elementary mathematics methods graduate course that was designed to help the teachers become better problem solvers and encourage them to teach mathematics through problem solving.…”

“…There is a growing body of literature designed to help elementary teachers, in particular, to engage their students in problem solving to learn mathematics (Foote, Earnest, Mukhopadhyay, & Curcio, ; Lester, ; O'Donnell, ; Schwartz & Curcio, ; Wilburne, ). However, according to Sakshaug and Wohlhuter ():

Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving?

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Effectiveness of the Metacognitive – Based Algebra Learning Model

“…Some other students, who can understand the problems, may make plans as their solution steps, but they possess less knowledge and skills in solving problems. Most problems, if considered from the process of solving them, lie at the aspects of the review of the obtained results (Lai et al, 2015;Phonapichat et al, 2014;Sakshaug & Wohlhuter, 2010). Those with high capability do not make some reviews since they are sure that their solutions are correct.…”

Students’ and Teachers’ Conceptual Metaphors for Mathematical Problem Solving

“…Secondary school teachers have significant influence over students’ perception of problem solving (Pólya, ; Schoenfeld, ). To communicate in a language that is meaningful to the student, it has been suggested that a teacher could start with the student's contextualization of problem solving rather than assuming the student shares the teacher's meaning of mathematical problem solving (Sakshaug & Wohlhuter, ). However, current research lacks a means to tap into students’ experiences that generate students’ contextualization of problem solving.…”