Mathematics Problem Solving  
                and Problem-Based Learning  
                      for Joyful Learning  
           in Primary Mathematics Instruction 
                                   
                                   
                                Sahid 
                          sahidyk@gmail.com  
                   Department of Mathematics Education 
                       Yogyakarta State University 
                                   
                                   
                   SEAMEO QITEP IN MATHEMATICS 
                      YOGYAKARTA, INDONESIA 
                                2011 
                                   
         
                                                                                          Table of Contents 
                             
                               A.  Introduction ............................................................................................................................... 1 
                               B.  Problem Solving in School Mathematics Curricula ....................................................................... 1 
                               C.  Classification for Mathematical Problems ................................................................................... 3 
                               D.  Heuristic and Strategies for Mathematics Problem Solving ......................................................... 5 
                                     1.  Giving a Representation to the Problem ..........................................................................................7 
                                          a.  Drawing a Diagram ......................................................................................................................7 
                                          b.  Making a Systematics List ...........................................................................................................8 
                                     2.  Making a Calculated Guess ..............................................................................................................9 
                                          c.  Guessing and Checking ...............................................................................................................9 
                                          d.  Looking for Patterns ....................................................................................................................9 
                                          e.  Making Suppositions ................................................................................................................ 11 
                                     3.  Going through the Process ............................................................................................................ 12 
                                          f.  Acting it Out ............................................................................................................................. 12 
                                          g.  Working Backwards ................................................................................................................. 13 
                                          h.  Model Methods (Part-Whole, Comparison, Before-After Concepts) ...................................... 14 
                                     4.  Modifying the Question in the Problem ....................................................................................... 15 
                                          i.    Restating the Problem ............................................................................................................. 16 
                                          j.    Simplifying the Problem ........................................................................................................... 16 
                                          k.  Solving Parts of the Problem .................................................................................................... 17 
                               E.  Problem-Based Learning for Joyful Learning in Primary Mathematics Instruction ...................... 18 
                                     1.  The Nature and Characteristics of Problem-based Learning ........................................................ 18 
                                     2.  Version of PBL ............................................................................................................................... 22 
                                     3.  PB Template .................................................................................................................................. 23 
                               F.  Some Ideas of Problem-Based Learning .................................................................................... 27 
                               G.  Closing Remarks ...................................................................................................................... 28 
                                                                                                                                                                                                                  
                               H.  References .............................................................................................................................. 29
                               I.    Appendices.............................................................................................................................. 31 
                                     1.  A Guide to Problem-Solving Techniques (Schoenfeld, 1985: 24) ................................................. 31 
                                     2.  Problem-solving Process Flowchart (Foong, in Lee, 2007: 80) ..................................................... 32 
                                     3.  A Format of a Problem-solving Lesson Plan (Foong, in Lee, 2007: 81) ......................................... 33 
                             
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