The Integration of Problem Posing in Teaching and Learning of Mathematics A Dissertation Defense by Roslinda Rosli Texas A&M University

Overview ▪ Introduction ▪ The effects of problem posing on student learning: A meta analysis ▪ Middle grade preservice teachers’ mathematical problem solving and problem posing ▪ A mixed research study of elementary preservice teachers’ knowledge and attitudes towards fractions ▪ Summary and conclusions 2

Why on problem posing? (Chapter 1) Students of all ages, including those who subsequently become teachers, have limited experience in problem posing (Crespo & Sinclair, 2008). Preservice and inservice teachers posed many low quality mathematical problems (Silver, Mamona-Downs, Leung, & Kenney, 1996). 3

PeriodResearch Areas (Number of Studies)Research Methodologies Skills and abilities to pose problems (4) Descriptive statistics Relationship with problem solving (4) Creativity (2) Skills and abilities to pose problems (12) Mathematical Knowledge (2) Attitudes & Beliefs (1) Descriptive statistics, t-tests, Wilcoxon Mann Whitney test ANOVA, correlation Relationship with problem solving (4) Skills and abilities to pose problems (17) Mathematical Knowledge (1) Attitudes & Beliefs (3) Descriptive t-tests, chi-square, confirmatory factor analysis, structural equation modeling, ANCOVA, case study Relationship with problem solving (5) Creativity (2) Skills and abilities to pose problems (12) Mathematical Knowledge (2) Attitudes & Beliefs (2) Descriptive statistics, t-tests, chi-square, correlation, ANCOVA, qualitative analysis- observation, 4 Why on problem posing?

▪ Finding and knowing the possible benefits of using problem posing for promoting student’s mathematics learning ▪ To further the type of studies that can provide teachers with specific approaches in developing and using problem posing activities 5 Why on problem posing?

Theoretical Framework Constructivist learning theory (von Glasersfeld, 1989). The openness feature of the problem posing tasks can reveal how an individual learns mathematics (Kulm, 1994). 6

The effects of problem posing on student learning: A meta analysis (Chapter 2) 7

Two Content Layout with SmartArt Group A Task 1 Task 2 Group B Task 1 Task 2 Group C Task 1 ▪ First bullet point here ▪ Second bullet point here ▪ Third bullet point here 8

Chapter 3:Middle grade preservice teachers’ mathematical problem solving and problem posing 9 The results from previous studies were mixed suggesting a complex relationship between problem solving and problem posing success (Cai & Hwang, 2002; Chen, Can Dooren, Qi, & Verschaffel, 2010). Research Questions 1)How do select middle grade preservice teachers solve a block pattern task before or after posing mathematical problems? 2)How do select middle grade preservice teachers pose mathematical problems before or after solving a block pattern task? 3)What is the relationship between select middle grades preservice teachers’ problem solving and problem posing? 4)What are select middle grades preservice teachers’ perceptions and concerns when posing mathematical problems?

▪ Participants: 51 middle school preservice teachers in a problem solving course. ▪ Instrument: A pair of problem solving and problem posing task - The Block Pattern Problem (Cai & Lester, 2005). ▪ Additional data: Group presentation of the homework problems, two open-ended questions on problem posing task. ▪ Procedures: ▪ Data analysis: – Rubrics according to performance indicators 1 (unsatisfactory) through 4 points (extended). – Inter-rater agreement: 73-87% – Descriptive statistics, Mann-Whitney test, Spearman’s Rho, constant comparison analysis Method 10 Group A (n=25) Problem Solving Problem Posing Group B (n=26) Problem Posing Problem Solving

Results 11 Solving the Block Pattern Task 70% of preservice teachers showed their understanding in finding the number of blocks to build a staircase of 6 steps and 20 steps.

Chapter 4 : A mixed research study of elementary preservice teachers’ knowledge and attitudes towards fractions 12

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Summary and conclusions (Chapter 5) 21