Modules 18/22: Designing and Differentiating instruction WASHINGTON STATE 21st Century Grant Project Core/Time/Digital January 2017 Modules 18/22: Designing and Differentiating instruction Marcy Stein, PhD University of Washington Tacoma

Learning Targets Participants will: Strengthen CCSS math content knowledge in evaluating and modifying instruction as a means of differentiating instruction. Discuss strategies for integrating the 4-step formative assessment process into instruction: (1) Clarify intended learning; (2) Elicit evidence; (3) Interpret evidence; and (4) Act on evidence.

National Center for Intensive Intervention (NCII) Differentiated instruction refers to an educator’s strategies for purposely adjusting curriculum, teaching environments, and instructional practices to align instruction with the goal of meeting the needs of individual students. Four elements of the curriculum may be differentiated: content, process, products, and learning environment.

National Math Panel (NMP) Executive Summary Main Findings and Recommendations Curricular Content Learning Processes Teachers and Teacher Education Instructional Practices Instructional Materials Assessment Research Policies and Mechanisms

Instructional Design: So What? Curriculum Evaluation Selection Modification/ Differentiation

Goals of Curriculum Evaluation The goals of curriculum evaluation are to: determine the extent to which instructional programs are grounded in research; reliably determine substantive differences among programs; and provide a framework for differentiating instruction to meet the needs of all students: prevention and intervention

Major Topics in Curriculum Evaluation General Program Design Instructional Strategy Design Teaching Procedures Formative Assessment

General Program Design Evidence of Effectiveness   1.   Is there published evidence of the effectiveness of the program? 2.  Is there evidence that the program has been field tested with large groups of students?  

Scientifically Evaluated Math Programs Scientifically based reading (math) programs have been evaluated in valid scientific experiments. These experiments must include: meaningful measures of achievement and compare several schools using a given program with several carefully matched schools that did not. Slavin, 2003

Scientifically Based Math Programs Reading (math) programs based on scientifically based research: incorporate the findings of rigorous experimental research. Slavin, 2003

General Program Design Is there a strong level of coordination among the program components? Strand vs. Spiral Relationship between computation and problem solving Relationship between instruction and assessment

Spiral Curriculum

Strand Curriculum

Intervention Research Lessons Learned from Intervention Research Based on current knowledge base, effective mathematics instruction would include: a. initial explicit strategy instruction, b. high levels of interaction between teacher and students and students and students, c. an extensive period of supported instruction where students gradually transition to independence, and d. a final phase of individual accountability. Baker, S. Gersten, R. & Lee, D.S. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-92

Instructional Strategy Design 1. Are the steps in the strategy explicitly identified in the program? 2. Component skills taught or reviewed? 3. Math vocabulary taught? 4. Adequate practice and review provided? 13

05/17/100 NMP Recommendation “Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computation. Results are consistent for students with learning disabilities, as well as other students who perform in the lowest third of a typical class.” 10

Explicit Strategy Instruction: Volume

Explicit Strategy Instruction: Volume

Explicit Strategy Instruction: Volume

Explicit Strategy Instruction

Comments Rote Instruction vs. Strategy Instruction Strategy Design vs. Task Analysis Tests of Good Problem Solving Strategies

Instructional Strategy Design 1. Are the steps in the strategy explicitly identified in the program? 2. Component skills taught or reviewed? 3. Math vocabulary taught? 4. Adequate practice and review provided? 13

Subtraction with Regrouping Component Skills: Subtraction with Regrouping Is the student proficient with subtraction facts? Does the student understand the right to left sequencing? (Is the subtraction being carried out in the proper direction?) Does the student know when to borrow? Does the student know from where to borrow? Conversion: Does the student make the appropriate conversions in the adjacent columns?

Instructional Strategy Design 1. Are the steps in the strategy explicitly identified in the program? 2. Component skills taught or reviewed? 3. Math vocabulary taught? 4. Adequate practice and review provided? 13

Math Vocabulary (Explicit Instruction)

Instructional Strategy Design 1. Are the steps in the strategy explicitly identified in the program? 2. Component skills taught or reviewed? 3. Math vocabulary taught? 4. Adequate practice and review provided? 13

Example Selection Number of examples Introductory and discrimination examples Sequence of examples 14

Math Vocabulary (Explicit Instruction)

Teaching Procedures Scaffolded Instruction 1.  Is teacher modeling specified? 2. Is there a model in text? 3.  Is teacher assistance gradually faded?

Scaffold Instruction: Progressing from Easy to More Difficult Contexts 34 52 85 16 38 47 Prompt each problem Work each problem Check each problem Work Each Problem Check Each Problem Work a block of problems Delayed check Teacher assistance gradually fades

Characteristics of Scaffolding -highly structured -less structured -guided practice -independent 16

Formative Assessment Does the program contain placement tests? Multiple entry points? Other Assessment Options?

Learning Targets* Participants will: Strengthen CCSS math content knowledge in teaching equivalent fractions/adding and subtracting fractions with unlike denominators. Discuss strategies for integrating the 4-step formative assessment process into instruction: (1) Clarify intended learning; (2) Elicit evidence; (3) Interpret evidence; and (4) Act on evidence.

Lesson Planning CCSS Standard used: Lesson Objectives:

Lesson Planning: Lesson Content Introduction Declarative Knowledge (Component Skills) Conditional Knowledge (Example Selection) Development Procedural Knowledge (Explicit Strategy)

Lesson Planning: Lesson content Development (cont.) Differentiated Instruction (prevention) Formative Assessment (diagnosis and remediation) Closure

Lesson Plan CCSS.Math.Content.5.NF.A.1 Objective Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Objective Use equivalent fractions as a strategy to add and subtract fractions with unlike denominators.

INTRODUCTION: Declarative Knowledge Component Skills (integration of skills) Finding least common multiple (LCM) Rewriting fraction as equivalent fraction

INTRODUCTION: Declarative Knowledge Component Skills *Equivalent Fractions “When you multiply a fraction that equals 1, the answer equals the number you start with.” Conceptual Understanding Dynamic or Concrete Presentations, Pictorial Representations

INTRODUCTION: Declarative Knowledge *Equivalent Fractions “When you multiply a fraction that equals 1, the answer equals the number you start with Applicable to: Adding/subtracting fractions with unlike denominators Ratios Solving Algebraic Equations

INTRODUCTION: Conditional Knowledge Example Selection Considerations Sufficient number of examples Sequence of examples – easy before more difficult Introductory and discrimination examples addition and subtraction some problems that don’t require rewriting 14

Development: Procedural knowledge Explicit Strategy (Prevention) Determine problem can’t be worked as is Determine least common multiple (denominator) Determine fraction equal to one Rewrite fractions with appropriate denominator Solve problem

DEVELOPMENT: Formative Assessment SBAC 4-step formative assessment process: Clarify intended learning Elicit evidence Interpret evidence Act on evidence Modeling Problems -> Ratio -> patterns developed (equivalent ratios, fraction expressions, etc) -> Solve problems (unit price, rate) -> more problems such as proportional relationships ->

Fractions with UNLIKE DENOMINATORS Four Steps of Formative Assessment Formative assessment process involves any teaching or learning strategy that effectively completes one or more of the formative assessment attributes.  1. Clarify intended learning. The teacher identifies the instructional goal, communicates the goal to students, and provides the criteria by which learning will be assessed so each student and the teacher knows whether the student is successfully progressing toward the goal. 2. Elicit evidence. After a period of instruction, the teacher checks for students’ understanding. This could be the first draft of an essay, a ticket out the door, an answer to a question on a white board, pair-and-share observations, or a paragraph on how to solve a mathematics problem. 3. Interpret evidence. The teacher and each student interpret the evidence and reflect on the student’s progress toward the learning goal. 4. Act on evidence. The teacher makes adjustments to the ongoing instructional activities, while students also adjust their procedures for learning. The teacher and students continue to use strategies that work and eliminate strategies that are not effective

Diagnosis and Remediation/Differentiation Diagnosis - Informal means of assessment: Individual responses during instruction Independent work Mastery Tests End-of-unit tests Interviews with students Remediation Strategy Errors Component Skill Errors Fact/Calculation Errors

Diagnosis and Remediation Analyze Error Patterns Diagnosis Remediation

Diagnosis

Diagnosis and Remediation Analyze Error Patterns Diagnosis Remediation Strategy error: student adds denominators Present entire format for fractions with unlike denominators Fact error: student multiplied 2  3 incorrectly Teacher works on 2  3 fact. No reteaching of fraction format necessary.

Diagnosis and Remediation Analyze Error Patterns Diagnosis Remediation

Diagnosis

Diagnosis and Remediation Analyze Error Patterns Diagnosis Remediation Component skill error: student did not find least common multiple. Note that answer is correct. Teacher points this out but emphasizes it’s important to find the least common multiple. Extra practice on finding LCM. Component skill error: student failed to multiply numerator Reteach strategy for adding fractions with unlike denominators.

CLOSURE: Summative Assessment Did students learn what you intended to teach?

Curriculum Evaluation and modification CCSS.Math.Content.5.MD.A.1 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Analyze Measurement Instruction Using the available commercial programs – locate and analyze instruction on measurement conversion. Design differentiated instruction. Design related formative assessments.

Measurement: Conversions 1. Determine whether new quantity is a bigger or smaller unit. 2. Multiply if changing to a smaller unit; Divide if changing to a larger unit. 3. Determine the equivalence fact.

Measurement: Conversions Three types Converting to next smaller/larger Converting to mixed number Converting to a unit twice removed

Measurement: Conversions Component Skills Equivalencies Example selection guidelines One unit should be base unit Half convert one direction etc. Half whole numbers Amount multiplied/divided change

Operations Difficulties? Renaming Preskill: Conversion skills When to rename; what numbers to use