Supporting TEKS Implementation - Charles A. Dana Center · develop a common understanding of the...

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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 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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What are some of the underlying assumptions aboutthis instructional materials selection process?


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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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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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.



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Note: The number of strands varies by content and grade.



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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.


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.


• 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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Step 3: Provide Drill and Practice Activities

• Create stimulating games where students work together.

• Change the directions for worksheets to create interesting puzzles andexplorations.


• 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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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






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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.


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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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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