Thinking Strategies in Mathematics Instruction: How Is Testing Possible?
The query in the title suggests other questions. While testing refers to instruction, thinking strategies seem to be the learner's privilege. How are instruction, testing, and thinking interrelated? Our questions raise the problematic issue of evaluating instruction ( Mislevy, 1992) and, specifically, mathematics instruction. It is not enough to identify thinking strategies; if they are worth being taught, they have to be justified by general instructional goals, and tools must be developed to somehow diagnose and measure them. Which general goals and what thinking strategies? Globally formulated general goals may allow a bird's eye view of the intended mathematics instruction, but these are still unsatisfactory; more concreteness is needed. In this chapter, goals and thinking strategies will be discussed, while respecting the close connection between teaching and learning.
To give some idea of what we mean by thinking strategies, we first consider and analyze two examples. We then examine general goals suggested by developments in the Netherlands (Proeve van een National Programma) and compare them with those in the United States and the United Kingdom. In all three countries, one notices an unmistakable turn from reproductive to (re) constructive learning and an increased emphasis on such tools as thinking strategies. Thinking strategies are reconsidered, followed by a definition of heuristic mathematics education of the type