Efforts to improve algebra instruction, as well as to evaluate the effectiveness of alternative approaches to the teaching of algebra, will depend on the development of new assessments of students’ and teachers’ learning.
The development of formative assessments for instructional purposes will need to test hypotheses about what is difficult for students to learn, as well as hypotheses about the kinds of scaffolds that provide support for learning when students are struggling. For classroom effectiveness, these assessments must be closely tied to instructional materials. An investment in the development of algebra assessments that capture all aspects of algebra proficiency, including the robustness and flexibility of conceptual and procedural knowledge and the ability to transfer learning to novel problems, will need to be developed if outcomes of alternative approaches to instruction are to be meaningfully compared.
Assessments will also be needed that can discriminate different kinds and levels of knowledge for the teaching of algebra. These should include both the knowledge of subject matter and pedagogical content knowledge.
Moreover, in order to compare differences in students’ opportunities to learn in circumstances in which the teacher or the curriculum changes, instruments to gather information about instruction itself will be important. For example, the representations and tools that are used and the type, frequency, and duration of their use needs to be captured. Measures of fidelity of implementation and of teacher support will be required as well. These investments in instrumentation and assessment tools at the start will allow for subsequent work to be far more powerful for guiding instructional practice.
Because algebra is increasingly seen as a K-12 strand of a mathematics curriculum, not merely as a high school course or pair of courses, the timing is right to design studies that track students across their school careers, investigating the develop-