Fostering Problem Solving : Singapore Math Success Story By Mark David C. Quitco

What is problem solving? A way to make sense of the environment and, in fact, control it (Britz, 1993). Application and integration of all basic and higher order thinking skills combined for one common objective (Quitco, 2009)

What is problem solving? An individual uses skills in object manipulation, metacognition, social interaction, and relationships (Britz, 1993) Math: Learning to solve problems is the principal reason for studying math (Wilson, 1993, as cited in NCSM, 1978)

Why foster problem solving? Lays the foundation for each child’s learning (Britz, 1993) Students will show success and enthusiasm in solving problems (Wilborn, 1994) Acquire skills that aid in school, the workplace and in everyday life (as cited in Millard, Oaks, and Sanders, 2002)

Singapore Math – Problem solving success story Has been ranked number one for the last three installments of the Third International Mathematics and Science Study (TIMSS). Beating countries like Japan, Taiwan, Korea and the U.S. The secret: modification of the curriculum to focus on Problem solving (Ginsburg, et. al., 2005)

Singapore Math Curriculum Basic Math problems Open – ended math problems

Less is more… Ministry of Education (1998): Reduction of Singapore’s curriculum content by up to 30% in most subjects Reason: to infuse thinking skills and integration of information technology

Less is more… Concepts or skills which rely on plains recall Overlaps with that taught at other levels in the same subject or with others. Content focused on technical details rather than conceptual understanding Irrelevant details to present Singaporean context; and Content which is too difficult or abstract for the intended level.

Less is more… Hogan (2004): describes Singapore’s math curriculum having the following:  High level of mathematical content  Builds strong number sense and higher level thinking skills

Major components in problem solving Polya’s model for problem solving (1957):  Understanding the problem  Devising a plan to solve it  Carrying out the plan  “Looking back” Still a dominant framework in the Philippine setting

Major components in problem solving Britz, problem solving model (1993): Problem solving by design  Identify the problem  Brainstorming for a variety of solutions  Choose one solution and try it out, and  Evaluating what happened

Major components in problem solving Capobiano and Tyrie (2009): Problem solving by design  Design challenges  Make a plan  Design, construct, and test  Improve your design  Lessons learned

Problem solving techniques Heuristic strategies or approaches  Multiple representations: charts, graphs, tables  Guess and check  Organize facts  Construct a picture  Abstraction  Analogy  Divide and conquer  Hypothesis testing

Problem solving techniques Heuristic strategies or approaches  Lateral thinking  Means - end analysis  Morphological analysis  Research  Root – cause analysis  Trial and error

Problem solving techniques Singapore math’s sample strategy: Model – drawing strategy  Ready made diagrams to help visualize problem  Translate problem in graphical form  Identify relationships between given

Fostering problem solving in the Classroom Identify the goals of problem solving  Navigate through school work and life in general  Improvement in terms of efficiency, precision, and accuracy  Singapore math: reduces use of trial and error by introducing visual representational skills as early as primary level

Fostering problem solving in the Classroom Teacher’s role in fostering problem solving (Fetrow, as cited in Jacobs and Ambrose, 2008)  Problems at suitable level  Promote reflection  Promote alternative approaches  Relevance of problems to setting Brahmer and Harmatys (2009): Cooperative learning encouraged effort in dealing with complex problems

Fostering problem solving in the classroom Hamza and Nash (1996): did not arrive at an ultimate process that fosters creative thinking and problem solving Was able to identify traits that should be considered:

Fostering problem solving in the classroom Considerations when preparing certain teaching methods:  Classroom climate  Teacher character traits  Classroom management  Teacher’s passion and attitude towards students, subject and teaching  Teaching style  Teacher’s knowledge  Teacher – student interaction  Student’s attitudes

Fostering problem solving in the classroom Parallels with Singapore Math teacher training program (Ginsberg, et. al., 2005):  Addresses a lot of the considerations noted  Teacher’s are superior in quality over U.S. Counterparts  Rigorous screening  Mentoring  Applicants are already pooled experts in math

Choosing good problems Goffin (1985): Criteria used for problem posing for children  Is the problem meaningful and interesting?  Can the problem be solved at a variety of levels?  Must a new decision be made?  Can the actions be evaluated?

Choosing good problems Singapore math in parallel with Goffin’s work:  Ministry of education: use of math for practical tasks, real life problems and within math itself  Criticism by Ginsberg (2005): Problems are not usually based on real world data