Lesson Study:
Preparing for Evidenceof Learning
Colleen M. Eddy from the University of North Texas
APEC – Tsukuba International Conference X
Innovation of Mathematics Education through Lesson Study:
Challenges to Energy Efficiency on STEM and Cross-border Education

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Defining Formative Assessment• Using evidence about student understanding• By teachers, learners, and peers• Make decisions on next step based on the evidence
rather than just following a prescribed plan

(Black & Wiliam, 2009)

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Focus:Short-cycle Formative Assessment
TypeFocus

Time Frame

Short Cycle
Minute by minute

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During instruction

A few seconds to a few
minutes

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Development of an Observation Protocol
for Short-cycle Formative Assessment
AssessToday (Eddy & Harrell 2013)

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Purpose:
Close achievement gap
LearningTarget

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Close the Gap

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Outcomes• Improve student self-regulation• Increase student success• Support teachers developing sustaining
formative assessment practices
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AssessToday Observation Instrument(Eddy & Harrell 2013)

Seven Components

Stages of Teacher Growth• Learning Target• Question Quality• Nature of Questioning• Self-evaluation• Observation of Student Affect• Instructional Adjustment• Evidence of Learning
APEC 2016• Novice• Apprentice• Practitioner• Master02/12/2016

What does it mean to prepare forEvidence of Learning?
Planning that includes


Research theme

 Objective(s) aligned with the standards
 Selecting a high cognitive task (activity/problem) Anticipating how students will respond Determining what and how student responses will facilitate understandingby all students

 Preparing questions to facilitate student learning and guide them tomastery of the objective

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Selecting(Smith & Stein 2011)
Research theme: for students todevelop critical thinking skills
relating to their mathematicalknowledge and potential to allow
them to communicate and engage
in their future endeavors withconfidenceObjective: Students will be able towork and characterize with infinite
sets of numbers.

The activity/problem: Which
numbers can be expressed as thedifference of two perfect squares?
(from Driscoll 1999)

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Texas Essential Knowledge andSkills (2012)

Algebra 12.D – Number and algebraic
methods.
The student applies the mathematicalprocess standards and algebraic
methods to write, solve, analyze, andevaluate equations, relations, andfunctions.
The student is expected to write aformula for the nth term of arithmetic
and geometric sequences, given thevalue of several of their terms…
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Anticipating

Which numbers can be expressed as the difference of two perfectsquares? (from Driscoll 1999)
ANTICIPATING:
StrategyCreate a table
Of consecutive perfect squares
Of any two perfect squares
Write an expressiona2 - b2


Writing a Solution
all odd numbers
2n + 1(n + 1)2 – n2 (this results in a positive integer)n2 - (n + 1)2 (this results in a negative integer)
all even numbers multiples of 44n (This does include 0 as a solution)n2 - (n + 2)2 (This does not include 0 as a solution)

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SELECTING & SEQUENCING:
Order12302/12/2016

Anticipating(con’t)

Which numbers can be expressed as the difference of two perfectsquares? (from Driscoll 1999)
ANTICIPATING:
StrategyNumbers not included
all even numbers not multiples of 4
all odd numbers multiplied by 2
up to 20 includes 2, 6, 10, 14, 18
4n – 2

SELECTING & SEQUENCING:
Orderinclude when parallel to thenumbers included for thefollowing strategies: create atable, write an expression andwriting a solution

Other Strategies
 not including zero as a perfect square 4n + 4 (This does not include 0 as asolution)
 2n+ 2 when n > 4 and even
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QuestioningWhat is a perfect square?

Work on writing an expression to represent the question.

How do you know the expression represents all the numbers included?

What do those numbers mean? (set of even differences)See if you can write a solution that includes all of the numbers.

How do you represent all the numbers that fit the problem?

What patterns are you noticing?

How do you represent the numbers that don’t fit the problem?

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Create a Table

For consecutive squares
For any two squares

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Write an Expression

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Included Numbers
Written Solution
Verbal Solution

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Further refining thesolution

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AssessToday Observation Instrument(Eddy & Harrell 2013)

Seven Components

Stages of Teacher Growth• Learning Target• Question Quality• Nature of Questioning• Self-evaluation• Observation of Student Affect• Instructional Adjustment• Evidence of Learning
APEC 2016• Novice• Apprentice• Practitioner• Master

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Questioning Quality(Eddy & Harrell 2013)

Indicators
Open ended questions



Mix of Bloom’s high and lowquestions



Master – Teacher consistently andappropriately uses multiple, varied,and differentiated questions toscaffold instruction.
Open ended questioning – Teacher consistently
and appropriately uses open-ended questions
that challenge students to think critically duringinstruction.

Bloom’s high and low order questions – Teacher
uses appropriate high-level and low-level
questioning throughout the entire lesson cycle.
The combination of the questions is aligned withthe learning target(s). Evidence of planningessential questions related to instructional
learning target is present. Teacher consistently
and appropriately matches Bloom’s levels to thelearning target(s) and/or standards.

Prior knowledge – Teacher’s expectation of priorknowledge and student ability to scaffold
learning from prior knowledge are appropriatelyaligned. Learning grain size is appropriate andeffective for learning.

Connect to students’ priorknowledge

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Questioning Quality
Indicators
Open ended questions



Mix of Bloom’s high and lowquestions

Connect to students’ priorknowledge

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Examples

How do you know the expression
represents all the numbers included?

What do those numbers mean? (set ofeven differences)See if you can write a solution thatincludes all of the numbers.

How could you represent all the numbersthat fit the problem?

How could you represent the numbersthat don’t fit the problem?

What patterns are you noticing?

What is a perfect square?
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Evidence of Learning Indicators(Eddy & Harrell 2013)

Indicators
 All student responses
 Individual responses
 Artifacts

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Master – There is evidence oflearning for almost all of thestudents according to suggestedindicators.
Individual responses – Teacher collects
and uses information from almost all thestudents through verbal responses relatedto the lesson.

Artifacts of learning – Almost all of thestudents complete an authentic
assessment to demonstrateunderstanding. Traditional assessments
are never used as the sole assessment for
demonstrating understanding. When used,
traditional assessments should always bepaired with authentic assessments.

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Evidence of Learning
example of consecutive perfect squares• What patterns are you noticing?
• Does this represent all thenumbers for the difference oftwo perfect squares?

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Evidence of Learning
See if you can write a solution that
includes all of the numbers.

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Evidence of Learning
Con’t

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Revisiting the Purpose
The activity/problem: Which numbers can be expressed as thedifference of two perfect squares? (from Driscoll 1999)

Research theme: for students to develop critical thinking skills
relating to their mathematical knowledge and potential to allow
them to communicate and engage in their future endeavors withconfidenceObjective: Students will be able to work and characterize with
infinite sets of numbers.

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Questions & Discussion
Colleen.Eddy@unt.edu
Thank you!
This material is based upon work supported by the Teacher Quality Grants under theNCLB of 2002: Public Law 107-110 . Any opinions, findings, interpretations,conclusions or recommendations expressed in this material are those of its authorsand do not necessarily represent the views of the Teacher Quality Grants.
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References
Black, P. & Wiliam, D. (2009). Developing the theory of formative assessment. EducationalAssessment, Evaluation & Accountability, 21(1), 5-31.
Bloom, B. (1984). The 2 sigma problem: The search for methods of group instruction as effective as
one-to-one tutoring, Educational Researcher, 13(6), 4-16.
Eddy, C.M. & Harrell, P.E. (2013). AssessToday: A short-cycle formative assessment observation
protocol.
Heritage, M. (2010). Formative Assessment: Making it Happen in the Classroom. Thousands Oaks,
CA: Corwin
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. InstructionalScience, 18(2), 119-144.
Scriven, M. (1967). The methodology of evaluation. (Vol. 110). Boulder, CO: Social Science
Education Consortium.
Wiliam, D., & Thompson, M. (2007). Integrating assessment with learning: What will make it work?

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