The Relationship between Elementary Teachers’ Beliefs and Teaching Mathematics through Problem Solving Misfer AlSalouli May 31, 2005

The purpose of the study: To understand the relationship between beliefs and teaching in a particular way. To understand the alignment between beliefs and practice.

Research Questions What specific beliefs do elementary teachers hold about teaching through problem solving? What is the relationship between teachers’ beliefs and their teaching practice ? What factors relate to teaching through problem solving?

Definition of Teaching Through Problem Solving “The teacher should work as a facilitator and strive to maximize opportunities for students to construct and understand concepts, and give fewer explanations, allow discussions, encourage students to find different ideas, ask leading questions, and assess understanding.”

Methods Setting Subjects Data collection Observations Field notes Post-observation discussion Interviews

Results Beliefs: Teaching practices: Teachers’ beliefs about teaching math Teachers’ beliefs about teaching through problem solving Teachers’ beliefs about factors related to teaching practice Teaching practices: Description of teaching practices Organization of a typical math lesson Two math lessons Scale of teaching practice

The scale of teaching practice PT M PN NT Approach to introducing observed lessons The nature of classroom tasks The nature of classroom work The nature of the teacher’s questions Encouraging for alternative methods The nature of classroom discourse The nature of classroom assessment The role of the teacher in classroom

Results continue … Beliefs about teaching problem solving vs. computation “They have got to get the basic skills first.” Beliefs about applying group work “I love it.” “It is very important that they are together” Beliefs about teacher’s role in teaching “I always try to go to the smallest, simplest level”

The scale of teaching practice PT M PN NT Approach to introducing observed lessons The nature of classroom tasks The nature of classroom work The nature of the teacher questions Encouraging for alternative methods The nature of classroom discourse The nature of classroom assessment The role of the teacher in classroom

Results continue … Beliefs about teaching problem solving vs. computation “I do not think you can separate them.” Beliefs about applying group work It is “the best thing possible to do”, “It gives them a little more confidence… they are more willing to argue with me.” Beliefs about teacher’s role in teaching “I like to make them struggle a little bit…I refuse to answer their questions.”

Q1. What specific beliefs do elementary teachers hold about teaching through problem solving? Four teachers believed that students should be taught computational skills in order to understand higher level of math. One teacher believed in a balance of both strategies: teaching through problem solving and computation skills One teacher believed that teaching through problem solving should be the focus of all instruction.

Q2. What is the relationship between teachers’ beliefs and their teaching practice? All the teachers believed in the importance of group work on students learning, but two teachers appeared to apply this strategy. All the teachers believed they focused on conceptual knowledge instruction, but only one teacher seemed to do so. Four teachers believed that memorization was a key tool to learn math, but two teachers thought about it beyond basic skills in that memorization should come after understanding.

Continued Five teachers believed that their role in classroom is to simplify math and make it easy for students. One teacher believed that students should struggle to figure out things for themselves.

Q3. What factors relate to teaching through problem solving? Four teachers believed that teachers should have strong content knowledge. Five teachers thought that pedagogical knowledge is the key factor in teaching math. Four teachers thought that class size influenced their teaching of math. All the six teachers believed that students’ ability level affected their teaching practice.

Some implications for teacher education Establishing sustained inservice training to expose teachers to different methods of teaching as well as to address the teachers’ role in the classroom. Teaching through problem solving needs time. Curriculum makers should design curricula that emphasize explorations of real world math. Preservice teachers need to be engaged in realistic applications for teaching through problem solving.

Questions!