Two-Tiered Approach to Analyzing Mathematics
Instructional Resource Materials
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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
a. Mathematics Instruction Materials and Selection tool
http://www.utdanacenter.org/indiana/
b. Achieve Open Education Resource Alignment with CCSS
http://www.achieve.org/oer-rubrics
Tier 1 Analysis Tool1
These resource documents will be needed to interpret the language of the analysis tool.
A. PARCC Model Content Frameworks
http://parcconline.org/parcc-content-frameworks
B. Common Core State Standards for Mathematics
http://corestandards.org/the-standards
C. 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
D. Learning Progressions: Supporting Instruction and Formative Assessment – Margaret
Heritage, National Center for Research on Evaluation, Standards, and Student Testing
(CRESST) http://www.cse.ucla.edu/products/misc/cse_heritage_learning.pdf
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
1
Portions of the analysis tool are adapted from the New Mexico State University MathStar textbook evaluation form.
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)