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Mathematics Instructional Materials Analysisand Selection
Supporting TEKS Implementation
Laurie Mathis, Ph.D., Program Director
Patti Bridwell, Senior Program Coordinator
Fall 2007
Goals
What are your goals for the day?
Copyright 2007, Charles A. Dana Center at the University of Texas at Austin Mathematics Instructional Materials Analysis and Selection 1
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Learning Expectations
• Develop an understanding of—and practice usinga set of tools designed to help analyze andselect— high-quality TEKS-based instructionalmaterials
• Generate a set of next steps
Mathematics Instructional Materials Analysisand Selection
IS . . .• Practicing a process• Generating next steps• Building capacity for TEKS
implementation
IS NOT . . .• Endorsing a particular
resource or pedagogy• Criticizing resources or
publishers• Providing the ‘inside scoop’
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Instructional Materials
What are some of the underlying assumptions we haveabout instructional materials?
Instructional Materials
Instructional materials are a critical part of theinstructional process. They often serve as the…
• Primary resource influencing classroom curriculum,instruction, and assessment;
• Central core of a school’s mathematics program, and
• Primary influence on a student’s day-to-day experiencein class.
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Instructional Materials
What are some of the underlying assumptions aboutthis instructional materials selection process?
Instructional Materials
As educators study and better understand the TEKS,they discover that their instructional materials often
• contain content not in the TEKS for their grade level;
• have errors in their correlations to the TEKS;
• do not promote the level of rigor required in the TEKS;
• repeat content across grade levels instead ofdifferentiating content among grade levels, and
• are inconsistent in their connections and transitionsacross grades.
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Effective SchoolsThe effect of schools and teachers
Students entering at 50th percentile, leave…
96EffectiveEffective78EffectiveAverage37EffectiveIneffective3IneffectiveIneffective63IneffectiveEffective50AverageAverage
Student PerformanceSchoolTeacher
* After two years. Measured inpercentile.
Robert J. Marzano. (2003). What Works in Schools: Translating Research IntoAction. Alexandria, VA: Association for Supervision and Curriculum Development.
What the Research Says
• Home atmosphere• Learned
intelligence andbackground
• Motivation
• Instructionalstrategies
• Classroommanagement
• Classroomcurriculum andlesson design
• Guaranteed andviable curriculum
• Challenging goalsand effectivefeedback
• Parent andcommunityinvolvement
• Safe and orderlyenvironment
• Staff collegiality andprofessionalism
StudentTeacherSchool
Robert J. Marzano. (2003). What Works in Schools: Translating Research IntoAction. Alexandria, VA: Association for Supervision and Curriculum Development.
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Instructional Materials
The
TEKSare
non-negotiable
Mathematics Instructional Materials Analysis
Phase 1: Studying the TEKS
Phase 2: Narrowing the field of instructional materials
Phase 3: Assessing mathematical content alignment
Phase 4: Assessing vertical alignment of instructional materials
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Phase 1: Studying the TEKS
Before analyzing instructional materials, thoseinvolved should have a current and functionalworking knowledge of the TEKS.
In this phase, participants collaborate anddevelop a common understanding of the TEKS.
Texas Essential Knowledge and Skills
Introduction / Basic Understandings• Describes the primary focal points for a grade or course,
the general work in the grade level band, and thegeneral context for all mathematics
Strands• Organize the knowledge and skills around broad areas of
mathematics
Knowledge and Skills statements• Delineate what students need to know and be able to do
Student Expectations• Describe what knowledge and skills students must be
able to demonstrate
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Format Packet
At this point, participants use the format packetprovided.
Texas Essential Knowledge and Skills
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Texas Essential Knowledge and Skills
Note: The number of strands varies by content and grade.
Texas Essential Knowledge and Skills
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Bloom’s Taxonomy
Probe, Identify, Compare, Examine, Contrast,Organize, Illustrate, Differentiate, Distinguish,Categorize…
Judge, Rate, Justify, Compare, Contrast, Validate,Determine, Interpret, Assess, Critique…
Make, Plan, Create, Develop, Generate,Compose, Predict, Rearrange, Categorize,Hypothesize…
Breaking down into parts, identifying motivesor causes, making inferences, and findingevidence to support generalizationsAnalysis
Combining elements into a pattern not clearlyestablished before
Synthesis
Judging the value of something according tocriteria and stating why
Evaluation
Benjamin S. Bloom (ed.). (1956). Taxonomy of Educational Objectives: The Classification of Educational Goals, vol. 1, Cognitive Domain. White Plains, New York: Longman. Reissued by Pearson Education, 1984.
Bloom’s Taxonomy
Who, How, What, Tell, Where, Name, List, Define,Select, Identify, Match, Memorize, Describe…
Use, Solve, Explain, Select, Predict, Collect,Classify, Determine, Show, Establish, Develop…
Tell, Infer, Report, Show, Explain, Classify,Discuss, Translate, Summarize, Identify,Describe…
Knowing factual answers, recognizing, testingrecallingKnowledge
Translating, interpreting, extrapolatingComprehension
Applying situations that are new, unfamiliar, orhave a new slant
Application
Benjamin S. Bloom (ed.). (1956). Taxonomy of Educational Objectives: The Classification of Educational Goals, vol. 1, Cognitive Domain. White Plains, New York: Longman. Reissued by Pearson Education, 1984.
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Vertical Articulation
Big Idea: ________________
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Bar-type and Bar Graphs
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Picture Graphs and Pictographs
Vertical Articulation
Using Patterns to Understand RelationshipsK.5, K.6A1.42.6B, 2.6C3.6A, 3.6B, 3.7B4.75.5A, 5.66.3A, 6.3B, 6.3C7.3A, 7.3B, 7.5A, 7.5B8.3B, 8.5A, 8.5BAlg I A.1(B), A.1(c), A.1(E)Alg II 2A.1(A), 2A.1(B)Geometry G.5(A), G.5(B), G.11(C)Pre-Calculus P.3(A-E), P.4(A), P.4(B), P.4(D)MMA M.2(A), M.5(A), M.6(B)
Linear Measurement (K-8)K.10A1.7A, 1.7B, 1.7C2.9A3.11A, 3.11B4.11A, 4.11B5.10A, 5.10B, 5.10C6.8A, 6.8B, 6.8D7.9A8.9B, 8.10A
AdditionK.41.3A, 1.3B, 1.5D, 1.5E2.3A, 2.3B, 2.3C, 2.3D, 2.5C3.1C, 3.3A, 3.3B, 3.5B4.3A, 4.3B5.3A, 5.3E, 5.46.2A, 6.2B7.2B, 7.2C, 7.2F8.2A, 8.2BAlg I A.4(A), A.4(B)
Equivalent Fractions (K-8)K.3A, K.3B1.2A2.2A, 2.2B3.2A, 3.2B, 3.2C, 3.2D4.2A, 4.2C5.2A, 5.2B, 5.2C6.1A, 6.1B, 6.2A, 6.2B7.1A, 7.1B, 7.2A, 7.2B8.1A, 8.1B, 8.2B
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Instructional Alignment Chart
Strand(s): _______ Big Idea: ____________ Grade / Course: ______
Instructional Alignment Chart
Strand(s): _______ Big Idea: ____________ Grade / Course: ______
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Guidelines for Sequencing Mathematics Activities
Step 1: Provide Developmental Activities
• Emphasize problem solving.
• Use interesting problems to frame and motivate exploration.
• Use problem situations that relate to the lives of your students.
• Guide student thinking using questions.
• Do not answer your own questions. Give students time to answer.
• Use models that can be manipulated and studied.
• Emphasize concrete objects and pictures before introducing symbols.
• Work along with students, observing their progress carefully.
• Concentrate on preventing misconceptions instead of correcting them.
• Give corrective feedback as quickly as possible.
• Use observation and oral questions to evaluate, rather than just pencil andpaper tasks.
Guidelines for Sequencing Mathematics Activities
Step 2: Provide Reinforcement Activities
• Create stimulating explorations that build upon previous developmentallessons where students worked together.
• Expand upon the activities that you started in the developmental lessons.
• Use materials in a variety of ways to connect concrete models, pictures,arithmetic processes, and number sentences.
• Emphasize problem solving.
• Organize small cooperative groups where students can share ideas andhelp each other.
• Let students in small groups take responsibility for making presentations,explaining processes, and creating problems.
• Prepare problem solving bulletin boards and learning centers.
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Guidelines for Sequencing Mathematics Activities
Step 3: Provide Drill and Practice Activities
• Create stimulating games where students work together.
• Change the directions for worksheets to create interesting puzzles andexplorations.
• Emphasize problem solving.
• Use problem situations to motivate practice.
• Give short sets of exercises, and evaluate student progress.
• Do not give long and tedious assignments in which students might practicetheir own misconceptions.
• Never introduce drill before proper concept development and reinforcementhave taken place.
Phase 1: Studying the TEKS — Reflection
Now What?
So What?
What?
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Instructional Materials
Educators trust instructional materials will
• Meet all the TEKS;
• Develop the intended levels of rigor;
• Develop mathematics appropriately across grade levels,and
• Use appropriate instructional strategies.
Mathematics Instructional Materials Analysis
Phase 1: Studying the TEKS
Phase 2: Narrowing the field of instructional materials
Phase 3: Assessing mathematical content alignment
Phase 4: Assessing vertical alignment of instructional materials
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Phase 2: Narrowing the field of instructional materials
In this phase, participants take a holistic andbroad survey of the many instructionalmaterials under review to reduce the number ofmaterials down to a manageable size. Thereduced number of materials will be reviewed ingreater depth in the following phases.
Phase 3: Assessing mathematical content alignment
Participants conduct in-depth examinations ofthe 2-3 materials selected in Phase 2. Thisdeeper analysis will examine the degree towhich the materials are aligned to the TEKS.
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Phase 4: Assessing vertical alignment of instructional materials
Participants consider the vertical nature of theTEKS to determine how well the materialspresent concepts and develop ideas across gradelevels.
W-Hair Are We?
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Learning Expectations
• Develop an understanding of—and practice usinga set of tools designed to help analyze andselect—high-quality TEKS-based instructionalmaterials
• Generate a set of next steps
Generate Next Steps
Using the descriptions in the Overview packetand your knowledge gained today, consult withyour colleagues and generate your next steps.
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End-of-Day Reflection
1. What was most useful?2. What was least useful?3. What is your comfort level implementing this process? Very easy Very difficult
4. I plan to use this process. Not at all Very much
Additional Comments:
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