Students’ progress in their cognitive development varies widely. Students may appear cognitively sophisticated in one area but naive in another. New and difficult concepts should be taught by beginning at a concrete level and proceeding to the more abstract and quantitative. However, whatever the reasoning level of a student, improvement should be expected.

Research has clearly shown that students can use sophisticated reasoning with new and difficult concepts if the learning context is familiar to them. Therefore, whenever possible, such concepts should be presented in “real world” contexts. Where actual applications are not possible, analogies may be used. However, teachers need to take care to avoid generating confusion when using analogies. Attention should be drawn to similarities and differences between the two contexts being compared.

Students entering high school vary in their reasoning abilities and readiness to learn how two quantities might be related. Some students will struggle with understanding the implications of a relationship in which variables are directly proportional, whereas other students will be ready for inverse and other, more complex relationships.

The ability to generate a hypothesis is crucial to scientific literacy. This ability has been developed to some degree in prior years, but high school students should be able to go beyond earlier efforts by generating testable and alternative hypotheses. However, in testing these hypotheses, students often have difficulty differentiating among controlled, independent, and dependent variables. Similarly, many students and adults have difficulty interpreting claims about correlations among variables, and tend to assume a cause and effect relationship which may not be warranted. Furthermore, students often have difficulty understanding the uses of models in science. Teachers should provide students with opportunities to practice such challenging concepts and ideas in multiple contexts.