Download A Problem Solving Approach to Mathematics

What We’ve Learned About Assessment,
Part 3:
Descriptive Feedback: Moving to the Next
Level
New Wisconsin Promise
January 2009
Cynthia Cuellar
Milwaukee Public Schools
Math Teaching Specialist
[email protected]
Bernard Rahming
Milwaukee Public Schools
Math Teaching Specialist
[email protected]
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy
(MPA), is supported with funding from the National Science Foundation under Grant No. EHR-0314898.
Participants will . . .
•Examine what research says about the effects
of feedback.
•Deepen their understanding of different types
of feedback.
•Analyze student work in mathematics to
practice identifying types of feedback.
•Discuss ways to use feedback in the classroom
to guide student learning of mathematics.
Research by: Richard Stiggins
“Achievement
gains are maximized in context
where educators increase the accuracy of
classroom assessments, provide students with
frequent informative feedback (versus
infrequent judgmental feedback), and involve
students deeply in the classroom assessment,
record keeping, and communication process. In
short, these gains are maximized where
teachers apply the principles of assessment for
learning.”
Research by: John Hattie 1992
“The most powerful single
modification that enhances
achievement is feedback. The
simplest prescription for improving
education must be ‘dollops of
feedback’.”
Type of Feedback:
Motivational




Goal is to make the learner feel good.
Feedback that is intended to encourage and support
the learner.
It does not give guidance on how to improve the
learner’s reasoning.
Since it is not intended to move students forward
in the learning process, it can be given on
summative assessments.
Type of Feedback:
Evaluative




Goal is to measure student achievement with a
score or a grade.
Feedback that is intended to summarize
student achievement.
It does not give guidance on how to improve
the learner’s reasoning.
Since it is not intended to move students
forward in the learning process, it can be given
on summative assessments.
Type of Feedback:
Descriptive



Goal is to improve student achievement by
telling the learner how to move forward in the
learning process.
Feedback that is intended to tell the learner
what needs to be improved.
Feedback isn’t as effective in getting students
to move forward in the learning process.
Type of Feedback:
Effective





Goal is to get student to internalize the effective
feedback to use the suggested strategies independently on
future work.
Feedback that is intended to be used by the learner to
independently move their reasoning to the next level.
Criteria-based phrases are used to describe the strengths
and weaknesses of the learner’s work.
Limits feedback to one or two traits/aspect of quality at a
time.
Students should have an opportunity to “redo” their work
based on the effective feedback.
Examples of Feedback
1. I agree with the pattern that you have
identified in the table. I am not
convinced that the rule you wrote works
for all the values in the table. How could
you prove this?
Descriptive
& Effective
2. I like how you completed the assignment.
Motivational
Examples of Feedback
3. Your explanation of your work is the
best that you have done. Nice use of
sequence words in your explanation.
4. You accurately found the number of
students in 4th grade who said chocolate
ice-cream was their favorite. You now
need to divide this number by the total
number of students to get the percent
who said chocolate ice-cream was their
favorite.”
Evaluative
Descriptive
What Does Effective
Feedback Look Like?
Effective Feedback Should:
 Describe and inform, not judge
 Be specific, not general
 Be clear to students
 Suggest what students should do to
improve
Adapted from Formative Assessment Strategies for Every Classroom,
Susan M. Brookhart, ASCD
Think-Pair-Share
Instructional Strategy
Think
On your own, think about what type of feedback is
represented by each statement.
Pair
Turn to a partner and share your thoughts. Come to
agreement on the type of feedback represented.
Share
Share with the whole group some of your thoughts
and discussions.
Type of Feedback Activity
Motivational
Evaluative
Descriptive
Effective
Feedback is
primarily
motivational
Feedback is
primarily
evaluative
Descriptive
feedback primarily
tells the student
how to correct their
reasoning.
Descriptive
feedback asks the
student what to do
to move their
reasoning to the
next level.
Purpose: to
encourage and
support the learner
Purpose: to
measure student
achievement with a
score or a grade
Purpose: to
improve learning
by indicating to the
student what needs
to be improved
Purpose: to
improve learning,
by moving student
reasoning to the
next level
More Summative
More Formative
Classroom Assessment Based on Standards
Ted’s Café
A lunch combo at Ted’s café consists of one sandwich, one vegetable and one cookie.
Sandwiches
Grilled Cheese
Hamburger
Turkey
Ted’s Café
Lunch Menu
Vegetables
Carrots
Corn
Cookies
Chocolate Chip
Oatmeal
What is the probability that a customer will order a combo that includes a
chocolate chip cookie?
Answer: ___________________________
Use what you know about probability to justify your answer.
Mathematics Grade 6
Classroom Assessment Based on Standards
“Ted’s Café”
MPS Learning Target: Statistics and Probability
MPS Learning Target #8: Gather and display data from
experiments and analyze outcomes based on theoretical and
experimental probabilities to determine likelihood and fairness of
events and to solve problems.
Mathematics Grade 6
Classroom Assessment Based on Standards
“Ted’s Café”
Wisconsin Assessment Framework for Mathematics
Objective: E. Statistics and Probability
Subskill: Probability:
Descriptor: Describe and determine the number of combinations of selecting 3 items from
4 or more items.
Objective: A. Mathematical Processes
Descriptors:
• Use reasoning and logic to perceive patterns, identify relationships, formulate questions,
pose problems, make conjectures, justify strategies, and test reasonableness of results
• Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a
variety of ways (e.g. using words, numbers, symbols, pictures, charts, tables, diagrams,
graphs, and models).
• Solve and analyze routine and non-routine problems.
What Mathematics Am I Assessing?
Description of Assessment:
School:
Grade Level:
CABS Assessment Overview
After working through the assessment, reflect on what you expect students to do. Complete the following table
before developing your descriptive feedback.
Identify appropriate Key Mathematics Features
students may develop as a response to this
assessment:
Connections to the
Comprehensive
Mathematics
Framework
o
o
o
o
o
Understanding
Reasoning
Computing
Engagement
Problem-solving
o
o
o
o
o
Understanding
Reasoning
Computing
Engagement
Problem-solving
o
o
o
o
o
Understanding
Reasoning
Computing
Engagement
Problem-solving
Identify misconceptions you anticipate students will
demonstrate:
Identify misconceptions identified after analyzing student
work:
Analyzing Student Work Samples


Analyze student work samples.
Identify the type of feedback
represented on each work sample.
Assessment Identification: Ted’s Cafe
Description of Assessment: Find the probability of
picking a combo with a chocolate chip cookie.
Effective Feedback Summary
Match the descriptive feedback to the student work.
Teacher:
C. Cuellar
Date: 12/20/07
Indicate to the student, “The anticipated answer is 6/12, 6 out of 12, 6:12, ½, 1 out of 2, 1:2 or 50%”
Student
Names:
Effective Feedback to Student(s)
(Frame the effective feedback in a way that challenges students to revise, redo, relearn, or
expand.)
I see a nicely organized list of all possible combos. What are some ways we practiced
providing a written explanation in class that you might use here?
You accurately identified 7 menu choices. How does the number of menu choices affect the
number of possible combos?
You accurately identified there is 1 cookie choice that is chocolate chip. I am unclear how you
determined there were only 3 combos. How might you use a strategy we practiced in class to
support the number of combos?
You clearly explained your reason for determining a probability of ½. How might you
determine the probability of picking a combo with grilled cheese and chocolate chip cookie?
I see all the combos that have a chocolate chip cookie nicely organized to support the 6 in your
fraction. How can you use one of the strategies we discussed to further support the 12 in your
fraction?
You accurately identified there are 6 combos with chocolate chip cookies. That was the hard
part. Now, could you use the same reasoning, to correctly determine the denominator in your
probability?
Let’s talk during small group time.
How to Manage the Use of
Feedback in the Classroom
When should I use feedback?
 A success story
 The Gail Burrill Strategy

Research by: Richard Stiggins
“Achievement
gains are maximized in context
where educators increase the accuracy of
classroom assessments, provide students with
frequent informative feedback (versus
infrequent judgmental feedback), and involve
students deeply in the classroom assessment,
record keeping, and communication process. In
short, these gains are maximized where
teachers apply the principles of assessment for
learning.”
Reflections
An idea that squares with my beliefs. . .
A point I would like to make. . .
A question or concern going around my
head. . .
Forecast
What We’ve Learned About Assessment,
Part 4:
A Guide to Formative Assessment
www.mmp.uwm.edu
This material was developed by the Milwaukee Mathematics Partnership (MMP) with
support by the National Science Foundation under Grant No. 0314898. Any opinions,
findings and conclusions or recommendations expressed in this material are those of the
authors and do not necessarily reflect the views of the Foundation.
Additional Documents to Correspond with this Presentation can be found at the MMP Website
• 6th Grade Statistics & Probability CABS (www4.uwm.edu/Org/mmp/_resources/cabs.htm)
•