A few weeks ago, I mentioned that I thought project 2061 had done a good job on evaluating textbooks recently. (Of course, that evaluation was panned in a typical knee-jerk manner by a certain self-styled educational expert.) In any case, I thought it might be of use to see what Project 2016/AAAS has to say about the categories, so here I have retyped the major headings and ideas of their evaluation process. Any typos are my own.
To repeat, I think they did a good job, and I think these ideas that can be shared and used by all math teachers and teacher-educators.
Guy Brandenburg ------------------------
Category I: Identifying a sense of purpose
I.1 Conveying Unit purpose: Does the material convey an overall sense of purpose and direction that is understandable and motivating to students? I.2 Conveying lesson purpose: does the material convey the purpose of each lesson or activity and its relationship to others? I.3 Justifying sequence of activities: does the material involve students in a logical or strategic sequence of activites (versus a collection of activities) that build toward understanding of the ideas in the unit or chapter purpose?
Category II: Building on student ideas about mathematics.
II.1 Specifying prerequisite knowledge. Does the material specify prerequisite knowledge/skills that are necessary to the learning of the benchmarks? II.2 Alerting teacher to student ideas. Does the material alert teachers to commonly-held student ideas (both troublesome and helpful) such as those described in "Benchmarks for Science Literacy", chapter 15 -- "The research base"? II.3 Assisting teacher in identifying ideas. Does the material include suggestions to teachers to find out what their students think about familiar situations related to a benchmark before the mathematical ideas are introduced? II.4 Addressing misconceptions. Does the material explicitly address commonly held student ideas?
Category III: Engaging students in mathematics.
III.1 Providing variety of contexts. Does the material provide experiences with mathematics in multiple, different contexts? III.2 Providing firsthand experiences. Does the material include activities that promote firsthand experiences with the benchmark ideas, when practical?
Category IV: Developing mathematical ideas.
IV.1 Justifying importance of benchmark ideas. Does the material suggest ways to help students develop a sense of the importance and validity of mathematical concepts or procedures? IV.2 Introducing terms and procedures. Does the material introduce terms and procedures only in conjunction with experience with them and only as needed to facilitate thinking and propote effective communication? IV.3 Representing ideas accurately. Does the material include accurate and comprehensible representations of mathematical concepts, procedures, and relationships? IV.4. Connecting benchmark ideas. Does the material explicitly draw attention to appropriate connections among benchmark ideas? IV.5 Demonstrating/Modeling procedures. Does the material demonstrate/model (or include suggestions for teachers on how to demonstrate/model) skills or the use of knowledge? IV.6 Providing practice. Does the material provide tasks or questions for students to practice skills or use knowledge in a variety of situations?
Category V: Promoting student thinking about mathematics.
V.1 Encouraging students to explain their reasoning. Does the material routinely include suggestions for having each student express, clarify, justify, and represent his/her ideas and how to get feedback from peers and the teacher? V.2 Guiding interpretation and reasoning. Does the material include tasks and/or question sequences that guide student interpretation and reasoning about benchmark concepts, skills, and relationships? V.3 Encouraging students to think about what they've learned. Does the material suggest ways to have students check their own progress?
Category VI: Assessing student progress in mathematics.
VI.1 Aligning Assessment. Are assessment items or tasks included that match the ideas, concepts, or skills of the benchmark? VI.2 Assessing through applications. Does the material include assessment tasks that require application of benchmark ideas, concepts, or skills and avoid allowing students a trivial way out, like using a formula or repeating a memorized term or rule without understanding? VI.3 Using embedded assessment. Are some assessments embedded in the curriculum along the way, with advice to teachers as to how they might use the results to choose to modify activities?
Category VII: Enhancing the mathematics learning environment.
VII.1 Providing teacher content support. Does the material help teachers improve their understanding of mathematics and its applications? VII.2 Establishing a challenging classroom. Does the material help teachers to create a classroom environment that welcomes student curiosity, rewards creativity, encourages a spirit of healthy questioning, and avoids rigidity? VII.3 Supporting all students. Does the material help teachers to create a classroom that encourages high expectations for all students, enables all students to experience success, and provides all students a feeling of belonging in the mathematics classroom?