Changes in mathematics teachers’ self-reported beliefs and practices over the course of a blended continuing professional development programme

Abstract

The interplay between mathematics teachers’ beliefs and practices has been widely investigated and research has examined how teachers’ beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers’ self-reported beliefs and practice changes as they participate in a 1-year CPD programme intended to support them in learning to teach mathematics through inquiry (LTMI). LTMI is a blended programme that integrates two phases: summer workshops and monthly follow-up meetings held during the scholastic year. Using a case-study design, data focusing on self-reported beliefs and practices were collected, using questionnaires and interviews, from three teachers at different stages: before, during and at the end of the CPD. Results show that, following teachers’ participation in summer workshops, they reported stronger connectionist beliefs. However, by the end of the CPD, while their connectionist beliefs remained strong, teachers reported increased discovery beliefs. Discovery beliefs were consistent with their reported changes in teaching practices. It appears that, in changing from transmission to inquiry teaching, these teachers adopted a non-interventionist and non-interactionist discovery teaching approach. This finding has implications for the design of CPD and, hence, the need to offer a supportive structure that helps teachers to recognise and address the limitations of their practices, along their journey to change towards more inquiry teaching.

Appendices

Appendix 1. Belief statements

You are presented with three statements about mathematics, learning and teaching.

For each statement, give a percentage (%), so that the three percentages in each section add up to a 100.

Appendix 2. Sample pen portrait

Chris: Pen portrait prior to his participation in CPD

His self-reported practices and beliefs

My explanations are clearly delivered and include questions directed at individual students. I keep introductions short and do not waste much time on ideas that are ‘out’ of the syllabus. I only ask a few questions and then provide extended periods where students work on exercises from the textbook or a worksheet. The exercises I assign start with a few easy questions and then gradually move to harder examples. I set students working and deal with student difficulties individually while I go around the class. When students are working, I prefer to tell students where they have gone wrong and show them where and how to correct mistakes. I stop the class from time to time to clarify questions that I identify as particularly difficult because it is useful to discuss errors and alternative methods.

I have a formal, yet cheerful and positive relationship with students. I make sure to get to know my students and try to establish a relationship with them first. I feel that the students in my class need to be motivated and prompted all the time. I am not too hard on them. My students seem to like to be organised and prefer to be told what to do. Students have the idea that mathematics is about working lots of problems from the textbook and trying to get as many of them correct as possible.

I believe that students learn best when their own ideas are discussed and investigated, but there is little evidence of this in my classroom. Although I believe that it is more important for students to develop conceptual understanding rather than computational skills, I find it very difficult to do because of many constraints. I feel much pressure to ‘cover’ the syllabus and I want to make sure that students do well in their exams. I feel constrained and frustrated by the scheme of work. I also claim that overloaded syllabi, high-stakes examinations and pressure from parents are constraints that I find hard to overcome.

His typical sequence of classroom actions

• 1. Provide notes

• 2. Give an explanation

• 3. Pose oral questions to the students

• 4. Devote time for student questioning

• 5. Give an easy question

• 6. Demonstrate examples

• 7. Give a challenging question

• 8. Assign work to be done individually

Mean percentage weighting on his beliefs statements

Transmission—42%

Discovery—33%

Connectionist—25%