Compare explanations of key concepts. Explanations should use clear language, unfold in a logical pattern, and integrate both procedural understanding (the "how") and conceptual principles (the "why"). For example, an explanation of multiplication might include both empirical evidence of how the concept is derived (with pictures of groups of objects representing numbers in a simple equation) along with step-by-step demonstrations of the algorithm.
Compare the exercises. Useful exercises provide opportunities to practice and build skills for an overall problem-solving approach. This includes giving the student opportunities to gather data and to form and test hypotheses. Word problems, for example, are valuable because they require students to apply mathematical logic to real situations. Problems that encourage students to interact with their environment are also helpful.
Evaluate skill-progression strategies. Research in curriculum design emphasizes the value of a "spiral" approach, which leads students through a process of skill mastery that returns to the beginning to reinforce key concepts. This approach helps students measure their progress and better understand how the parts of the process fit together.