Influencing policy (training slides from Fast Track Impact)
Dissertation defense 0227
1. The Integration of Problem
Posing in Teaching and Learning
of Mathematics
A Dissertation Defense
by
Roslinda Rosli
Texas A&M University
2. 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
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3. 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).
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4. Period Research Areas (Number of Studies) Research Methodologies
1989-1994 Skills and abilities to pose problems (4) Descriptive statistics
1995-2000 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
2001-2006 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
2007-2011 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,
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Why on problem posing?
5. ▪ 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
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Why on problem posing?
6. 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).
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7. The effects of problem posing on student
learning: A meta analysis (Chapter 2)
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8.
9. Chapter 3:Middle grade preservice teachers’
mathematical problem solving and problem posing
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•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?
10. ▪ 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
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Group A (n=25)
Problem Solving
Problem Posing
Group B (n=26)
Problem Posing
Problem Solving
11. Results
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• Solving the Block PatternTask
• 70% of preservice teachers showed their understanding in finding the number of
blocks to build a staircase of 6 steps and 20 steps.
12. Chapter 4 : A mixed research study of
elementary preservice teachers’ knowledge and
attitudes towards fractions
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Many of these studies present positive outcome of problem posing on students’ knowledge, problem solving and problem posing skills, creativity, and disposition toward mathematics.
-knowledge is not passively received but actively built up by the cognizing subject; the function of cognition is adaptive and serves the organization of experiential world, not the discovery of ontological reality-students construct their own understanding while posing problems.
Hypotheses: Participants in group A (solved first) had a greater capacity to generate new problems. Group B (posed first) performed better on the problem solving task.
