In Appendix 1, we give further tables from TIMSS 2003 showing that pupils in R.Macedonia spend over 38% of their instructional time working on topics from Geometry. This is the highest percentage of any of the participating countries. The international average is 26%. [Table A.1.1] In addition, 99% of the material in TIMSS is covered by the R.Macedonia curriculum. The international average is 69%. [Table A.1.2] Each and every subtopic in geometry in TIMSS is covered 99-100% by the R.Macedonia curriculum. [Table A.1.3] And yet, our pupils only got 39% of the question correct in 2003, down from 42% correct in 1999. [Table A.1.4] In 1999 pupils from R.Macedonia were within international averages in geometry; in 2003 R.Macedonia had dropped to significantly below international averages. [Table A.1.5].
In Figure 3 below, we give an actual question from TIMSS 2003. A list of all the released questions in mathematics can be found in [TQ03].
Figure 3: Actual question from TIMSS 2003
On this question,
Recall that Geometry is an area in which all of the material was covered 99-100% by the curriculum of R.Macedonia. The fundamental formula that the three angles of a triangle sum to 180º is covered in Grade 5. Congruent and similar triangles and their properties are covered in detail in Grade 6. Transversals and their properties are covered in detail in Grade 7.
Notice that this problem can be solved with careful inspection of the picture and application of the fundamental formula.
Why can’t they solve this problem? Do they know the facts, but lack problem solving strategies? Do they know the fundamental formula, but lack reasoning skills?
What is clear is that something vital is certainly missing from their math education.