Companion teacher materials for a curriculum should include a “metaguide” that explains its links to principles of learning, reflects pedagogical content knowledge concerning the curriculum, and promotes flexible use of the curriculum by teachers. The guide should include discussion of expected prior knowledge (including typical preconceptions), expected competencies required of students, and ways to carry out formative assessments as learning proceeds. Potentially excellent curricula can fail because teachers are not given adequate support to use them. Although instructional guides cannot replace teacher training efforts, the meta-guide should be both comprehensive and user-friendly to supplement those efforts. Finally, both formative and summative tests of learning and transfer should be proposed as well.

Once developed, field-testing of the curricula should be conducted to amass data on student learning and teacher satisfaction, identifying areas for improvement. Clearly, it is easier to field-test short units rather than longer ones. Ideally, different research groups that are focusing on similar topics across different age groups (e.g., algebra in elementary, middle, and high school) would work to explore the degree to which each of the parts seems to merge into a coherent whole.

Once again, careful attention should be paid to the criteria used to evaluate the learning that is supported by the materials and accompanying pedagogy. Achievement should measure understanding of concepts and ability to transfer learning to new, related areas.

3. Conduct research on formative assessment. A separate research effort on formative assessment is recommended. The importance of making students’ thinking visible by providing frequent opportunities for assessment, feedback, and revision, as well as teaching students to engage in self-assessment, is emphasized throughout this volume and in the proposals above. But the knowledge base on how to do this effectively is still weak. To bolster the understanding of formative assessment so that it can more effectively be built into curricula, this research effort should:

  • Formulate design principles for formative assessments that promote the development of coherent, well-organized knowledge. The goal of these assessments is to tap understanding rather than memory for procedures and facts.

  • Experiment with approaches to developing in students and teachers a view of formative assessment and self-assessment as an opportunity for providing useful information that allows for growth, rather than as an outcome measure of success or failure.



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