Two-Tiered Approach to Analyzing Mathematics

Instructional Resource Materials

  • Use the first tier to narrow the larger field of resources to a short list of potential resources for your school.
  • Use the second tier to examine potential resources in more explicit detail.

Tier 1 – Analyze(using the tool below) based on some key instructional characteristics

Tier 2 – Examine using an in-depth tool created by a reputable institution

  1. Mathematics Instruction Materials and Selection tool
  2. Achieve Open Education Resource Alignment with CCSS

Tier 1 Analysis Tool[1]

These resource documents will be needed to interpret the language of the analysis tool.

  1. PARCC Model Content Frameworks
  1. Common Core State Standards for Mathematics
  1. Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students – Heather C. Hill (Harvard Graduate School of Education), and Deborah L. Ball and Stephen G. Schilling (University of Michigan), Journal for Research in Mathematics Education, 2008, Vol. 39, No. 4, 372–400
  2. Learning Progressions: SupportingInstruction and Formative Assessment – Margaret Heritage, National Center for Research on Evaluation, Standards, and Student Testing (CRESST)

Analysis Rating Scale

0 = this element is not evident in the instructional material being evaluated

1 = some evidence of this element is in the instructional material being evaluated

2 = this element is a component of the instructional material being evaluated

3 = this element is very evident in the instructional material being evaluated

ENGAGES AND SUPPORTS AN ONGOING FOCUS ON THE STANDARDS FOR MATHEMATICAL PRACTICE AS “HABITS OF MIND”

_____ engages and supports students in making sense of problems and persevering in solving them

_____ engages and supports students in reasoning abstractly and quantitatively

_____ engages and supports students in constructing viable arguments and critiquing the reasoning of others

_____ engages and supports students in modeling with mathematics (makes meaningful connections within mathematics, to other content areas, and to situations in everyday life, society, and the workplace)

_____ engages and supports students in using appropriate tools strategically (use technological and other tools to explore and deepen conceptual understanding)

_____ engages and supports students in attending to precision (use appropriate mathematical language, vocabulary, and notation to represent ideas, describe relationships, and model situations)

_____ engages and supports students in looking for and making use of structure

_____ engages and supports students in looking for and expressing regularity in repeated reasoning

CREATES A DEEPER UNDERSTANDING OF CONTENT

_____ is mathematically accurate

_____ builds conceptual understanding through a logical sequence of related mathematical ideas reflecting key advances from the previous grade and within-grade dependencies

_____ develops concepts using multiple representations (concrete/geometrical, numerical, graphical, verbal, and symbolic)

_____ provides opportunities for in-depth student investigation of grade level appropriate focus areas

_____ provides students with opportunities to explore worthwhile mathematical tasks that have multiple solution paths and/or solutions

_____ reflects the content focus and emphases of the grade/course (as identified in the PARCC Model Content Frameworks Content Emphases by Cluster)

_____ builds toward fluency expectations and culminating standards of the grade/course

SUPPORTS EQUITY THROUGH A STUDENT-CENTERED APPROACH TO LEARNING

_____ provides worthwhile mathematical tasks with multiple entry points that allow a range of learners to engage in mathematics with appropriate rigor

_____ promotes critical thinking, problem-solving, and reasoning

_____ facilitates inquiry-based explorations through a variety of approaches

_____ encourages students to conjecture, observe, experiment, explain, predict, refine, validate, and defend their ideas in a variety of ways

_____ supports varied methods of instruction, learning styles, and cultures

_____ includes materials and resources that accommodate English Language Learners

_____ allows for whole group instruction, small group collaboration, and individualized instruction

_____ respects a balance between ethnic background, gender, age, handicaps, and careers

UTILIZES COMPREHENSIVE ASSESSMENT

_____ incorporates strategies for gathering diagnostic information about students’ prior knowledge, background, and misconceptions

_____ incorporates strategies for gathering continuous on-going formative assessment information for students and teachers

_____ incorporates strategies for gathering appropriate summative assessment data at a variety of levels (e.g., memorization, understanding, reasoning, and problem solving)

PROVIDES SUFFICIENT SUPPORT FOR TEACHERS

_____ provides information on the specialized content knowledge (the mathematics beneath the mathematics as defined by Deborah Ball)

_____ provides information on knowledge of content and students (as defined by Deborah Ball) and/or learning progression (construct maps)

_____ includes suggestions for effective instructional planning

_____ provides both intervention and enrichment activities

_____ integrates ways to communicate/correspond with parents regarding the goals and objectives of the resource

_____ organizes units in an easy-to-follow format that is appealing and functional

_____ suggests additional resources to extend student learning

SUMMARY RECOMMENDATIONS:

(include strengths and weaknesses of this resource)

[1]Portions of the analysis tool are adapted from the New Mexico State University MathStar textbook evaluation form.