Download Elem MS 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
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•
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•
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Curricular Content
Learning Processes
Teachers and Teacher Education
Instructional Practices
Instructional Materials
Assessment
Research Policies and Mechanisms
INSTRUCTIONAL DESIGN:
SO WHAT?
Instructional
Design
Curriculum
Evaluation
Curriculum
Selection
Curriculum
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
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 lowachieving 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?
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.”
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?
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?
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?
Example Selection
Number of examples
Introductory and discrimination examples
Sequence of examples
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
16
52
38
85
47
•Prompt each problem
•Work each problem
•Check each problem
•Work Each Problem
•Check Each Problem
Teacher assistance gradually fades
•Work a block of problems
•Delayed check
Characteristics of Scaffolding
-highly structured
-less structured
-guided practice
-independent
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
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
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
t
• SBAC 4-step formative assessment process:
•
•
•
•
Clarify intended learning
Elicit evidence
Interpret evidence
Act on evidence
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
4 2 6
+ =
5 3 8
10
5´ 4
+
=
æ
6
4
6 ç ´4
ç 12
12
12
è
5
2
5
2´3
+
ö
æ ´3
÷ 4 ç
÷
ç 12
ø
è
15
ö 12
÷
÷
ø
=
Remediation
DIAGNOSIS
10
5
2
5´ 4
+
=
æ ´4
6
4
6 ç
ç 12
12
12
è
5
2´3
+
ö
æ ´3
÷ 4 ç
÷
ç 12
ø
è
15
=
ö 12
÷
÷
ø
DIAGNOSIS AND REMEDIATION
Analyze Error Patterns
Diagnosis
4 2 6
+ =
5 3 8
10
5
2
5´ 4
+
=
æ
6
4
6 ç ´4
ç 12
12
12
è
5
2´3
+
ö
æ ´3
÷ 4 ç
÷
ç 12
ø
è
15
ö 12
÷
÷
ø
=
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
16
16
4 2 4 æ ´ 4 ö 2 æ ´ 8 ö 32
+ = ç ÷+ ç ÷=
8 4 8 è ´ 4 ø 4 è ´ 8 ø 32
32
32
4 2 4æ ö 2æ ö 6
+ = ç ÷+ ç ÷=
5 3 5 è ´ 3 ø 3 è ´ 5 ø 15
15
15
Diagnosis
Remediation
DIAGNOSIS
16
16
4 2 4 æ ´ 4 ö 2 æ ´ 8 ö 32
+ = ç
÷+ ç
÷=
8 4 8 è ´ 4 ø 4 è ´ 8 ø 32
32
32
DIAGNOSIS AND REMEDIATION
Analyze Error Patterns
16
16
æ
ö
æ
4 2 4 ´ 4 2 ´ 8 ö 32
+ = ç ÷+ ç ÷=
8 4 8 è ´ 4 ø 4 è ´ 8 ø 32
32
32
Diagnosis
Component skill error:
student did not find least
common multiple. Note
that answer is correct.
Component skill error:
4 2 4æ ö 2æ ö 6
+ = ç ÷+ ç ÷=
student failed to multiply
5 3 5 è ´ 3 ø 3 è ´ 5 ø 15
numerator
15
15
Remediation
Teacher points this out
but emphasizes it’s
important to find the least
common multiple. Extra
practice on finding LCM.
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
1. Using the available commercial programs –
locate and analyze instruction on
measurement conversion.
2. Design differentiated instruction.
3. 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