Mathematics and mathematics pedagogy content knowledge

• Teaching mathematics knowledge that future primary and secondary teachers acquired by the end of their teacher education varied considerably among individuals within every country and across countries.
• The difference in mean mathematics content knowledge (MCK) scores between the highest- and lowest-achieving country in each primary and secondary program group was between 100 and 200 score points, or 1 and 2 standard deviations.
• Differences in mean achievement across countries in the same program group on mathematics pedagogical content knowledge (MPCK) were somewhat smaller, ranging from about 100 to 150 score points.
• On average, future primary teachers being prepared as mathematics specialists had higher MCK and MPCK scores than those being prepared to teach as lower primary generalists.
• On average, future teachers being prepared to teach lower and upper secondary grades had higher MCK and MPCK scores than those prepared to teach lower secondary grades only.

Beliefs

• Future teachers in several countries (Chile, Chinese Taipei, Poland, the Russian Federation, Singapore, and Spain) endorsed the belief that mathematics learning consists of memorizing a set of rules and procedures.
• In general, educators and future teachers in all countries were more inclined to endorse the pattern of beliefs described as conceptual or cognitive-constructionist in orientation.
  • Georgia’s endorsement of this pattern was relatively weak, however.
  • Educators and future teachers in Botswana, Georgia, Malaysia, Oman, the Philippines, and Thailand endorsed the pattern of beliefs described as computational or direct transmission; educators and future teachers in Germany, Norway, and Switzerland for the most part did not.
• In some high-scoring countries on the MCK and MPCK tests, future teachers endorsed both beliefs—that mathematics is a set of rules and procedures, and that it is a process of enquiry. The TEDS-M findings thus showed endorsement for both of these conceptions within mathematics teacher education.

Opportunities to learn

• Teachers who are expected to teach in primary—and especially the lower-primary—grades had few opportunities to learn (OTL) mathematics content beyond that included in the school curriculum.
  • The pattern among future secondary teachers was generally characterized by greater and deeper coverage of mathematics content.
  • However, there was more variability in OTL among those future teachers being prepared for lower secondary school (known in some countries as “middle school”) than among those being prepared to teach Grade 11 and above.
• The countries with programs providing the most comprehensive opportunities to learn challenging mathematics had higher scores on the TEDS-M tests of knowledge.
  • In TEDS-M, primary-level and secondary-level teachers in high-achieving countries such as Chinese Taipei, Singapore, and the Russian Federation had significantly more opportunities than their primary and secondary counterparts in the other participating countries to learn university- and school-level mathematics.

Context and policy

• TEDS-M showed that teachers’ careers and working conditions ranged
  • from those where teachers are carefully selected, well compensated, and highly regarded
  • to those where there is less selectivity, low salaries, and low status.
• These careers and conditions were shaped in part by
  • the differences between the two major systems of teacher employment (career-based and position-based) found in the world’s public schools,
  • as well as by the various mixed or hybrid models.
• The TEDS-M data indicated a positive relationship between the strength of quality assurance arrangements and country mean scores in the TEDS-M tests of mathematics content knowledge and mathematics pedagogy knowledge.
  • Countries with strong quality assurance arrangements, such as Chinese Taipei and Singapore, scored highest on these measures.
  • Countries with weaker arrangements, such as Georgia and Chile, tended to score lower on the two measures of future teacher knowledge.