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.
Dissertation defense 0227
The Integration of ProblemPosing in Teaching and Learningof MathematicsA Dissertation DefensebyRoslinda RosliTexas A&M University
Overview▪ Introduction▪ The effects of problem posing on student learning: A meta analysis▪ Middle grade preservice teachers’ mathematical problem solving andproblem posing▪ A mixed research study of elementary preservice teachers’knowledge and attitudes towards fractions▪ Summary and conclusions2
Why on problem posing? (Chapter 1)• Students of all ages, including those who subsequently becometeachers, have limited experience in problem posing (Crespo &Sinclair, 2008).• Preservice and inservice teachers posed many low qualitymathematical problems (Silver, Mamona-Downs, Leung, & Kenney,1996).3
Period Research Areas (Number of Studies) Research Methodologies1989-1994 Skills and abilities to pose problems (4) Descriptive statistics1995-2000 Relationship with problem solving (4)Creativity (2)Skills and abilities to pose problems (12)Mathematical Knowledge (2)Attitudes & Beliefs (1)Descriptive statistics, t-tests, WilcoxonMann Whitney testANOVA, correlation2001-2006 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, structuralequation modeling, ANCOVA, case study2007-2011 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,4Why on problem posing?
▪ Finding and knowing the possible benefits of using problem posingfor promoting student’s mathematics learning▪ To further the type of studies that can provide teachers with specificapproaches in developing and using problem posing activities5Why on problem posing?
Theoretical Framework• Constructivist learning theory (von Glasersfeld, 1989).• The openness feature of the problem posing tasks can reveal how an individuallearns mathematics (Kulm, 1994).6
The effects of problem posing on studentlearning: A meta analysis (Chapter 2)7
Chapter 3:Middle grade preservice teachers’mathematical problem solving and problem posing9•The results from previous studies were mixed suggesting a complexrelationship between problem solving and problem posing success (Cai &Hwang, 2002;Chen, Can Dooren,Qi, &Verschaffel, 2010).Research Questions1) How do select middle grade preservice teachers solve a block pattern task before or afterposing mathematical problems?2) How do select middle grade preservice teachers pose mathematical problems before orafter solving a block pattern task?3) What is the relationship between select middle grades preservice teachers’ problemsolving and problem posing?4) What are select middle grades preservice teachers’ perceptions and concerns whenposing 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 PatternProblem (Cai & Lester, 2005).▪ Additional data: Group presentation of the homework problems, two open-endedquestions 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 analysisMethod10Group A (n=25)Problem SolvingProblem PosingGroup B (n=26)Problem PosingProblem Solving
Results11• Solving the Block PatternTask• 70% of preservice teachers showed their understanding in finding the number ofblocks to build a staircase of 6 steps and 20 steps.
Chapter 4 : A mixed research study ofelementary preservice teachers’ knowledge andattitudes towards fractions12