This project collects evidence supporting the validity of test instruments and initial characterization of high school teachers' background and use of materials and pedagogies. The project is constructing and validating multiple forms of test instruments that can be used for the evaluation of interventions (e.g. professional development, implementation of new curricula) and the measurement of aspects of teacher knowledge (e.g. subject matter, knowledge of student misconceptions).
- Represent central ideas in the subject matter;
- Focus on the meaning of facts and procedures; and
- Require more complex responses than traditional multiple-choice problems.
Several small-scale experimental classroom studies Star and Rittle-Johnson demonstrate the value of comparison in mathematics learning: Students who learned by comparing and contrasting alternative solution methods made greater gains in conceptual knowledge, procedural knowledge, and flexibility than those who studied the same solution methods one at a time. This study will extend that prior work by developing, piloting, and then evaluating the impact of comparison on students' learning of mathematics in a full-year algebra course.