WHAT FORMATIVE ASSESSMENT PR ACTICES LOOK LIKE:
RESULTS FROM A CASE STUDY IN SOUTHERN CALIFORNIA
CHRISTINE ONG, KEVIN SCHAAF, JOAN L. HERMAN,
AND DEBORAH LA TORRE MATRUNDOLA
CRESST/UCLA
FINDINGS
PROJECT OVERVIEW
This poster explores case study findings from a larger National Science Foundation study
examining formative assessment in mathematics (FAM). The case study (Phase III of FAM)
examines how teachers currently incorporate formative assessment (FA) in their daily math
activities in a small number of schools in Southern California. We examine key research
questions from the study in this poster, specifically:
• What does FA look like across case study classrooms?
• What strengths and areas for improvement were observed in how teachers conduct FA?
• What supports and resources do teachers need in order to practice FA effectively?
We view formative assessment as a series of dynamic processes and interactions between a
teacher, and students and/or peers. High quality tools are also an essential component of FA
activities (Benett, 2011). Together, these components provide useful feedback or answers to the
questions: Where am I going? How am I going? Where to next? (Hattie &Timperley, 2007).
1
SUMMARY
2
WHAT WERE SOME STRENGTHS OBSERVED?
Teachers were frequently observed using systematic strategies to get all students involved.
There were also relatively high collaborative climate ratings given for most classrooms. In
addition, teachers frequently engaged in questioning students, although their questions
tended to focus on procedures.
We observed some examples of high level questioning to elicit reasoning and instances of
teachers adjusting instruction based on student responses. For example, one teacher asked
students a series of questions within a lesson to get at higher-level thinking/reasoning:
• “Discuss why…make sure you talk about
why one number is greater than another.”
• “What happens if I add one more million
to 999,000,000?”
• “How do you know?”
• “What does that mean?”
• “How do you know your answer
is correct?”
• “Explain that.”
WHAT WERE SOME AREAS FOR GROWTH?
Feedback was rated relatively low in comparison to other dimensions as teachers rarely built
upon student responses in feedback loops. Feedback provided tended to focus on correct
responses vs. process or conceptual understanding (e.g., “What comes next? Look at the
Procedure Poster and follow the steps.” ). While peer groupings were a common activity, the
structure/quality of peer feedback activities appeared to vary across classrooms.
The criteria for success were typically left implicit rather than being clearly communicated.
We noted no instances of teachers involving their students in ensuring deep understanding
of the criteria (for example, by co-developing a rubric).
Teachers receiving higher ratings in Criteria for Success across observations were systematic
in their approach and also had higher ratings in Learning Goals. In these classrooms,
students read and repeated goals and criteria from posters before each lesson, midway
and/or end to reiterate which goals had been met and which were still to come.
METHODS
FEEDBACK QUALITY AND DISTRIBUTION
CRESST team is currently developing a toolkit of activities to assist teachers in
SAMPLE
Four schools (two elementary, two middle) selected based on evidence of “promising” FA
practice and key characteristics. Criteria included:
• Achievement scores (i.e., API state rankings > 4, similar school ratings of 7-10)
• Ratings of assessment artifacts & survey responses (Phase II)
4
3.75
3.50
• providing them with feedback in relation to criteria for success.
3.38
3
3
2.88
2.63
2.50
2.25
2.36
1
GRADE 2
(ES02.T01)
GRADE 4
(ES02.T02)
GRADE 5
(ES01.T01)
GRADE 5
(ES01.T02)
GRADE 6
(MS01.T02)
GRADE 8
(MS01.T01)
GRADE 8
(MS02.T01)
GRADE 8
Feedback
Involvement
of Students
Complexity
of Math
Teacher Support
for Meaning-Making
BRIEF DESCRIPTION
Clearly communicating learning goals; connecting current
lesson to broader themes, prior and future learning
COLLABORATIVE CLIMATE
• Teacher supports, resources
Articulating what success looks like including explicit examples of
what is needed to meet learning goal (rubric, checklist, exemplar
work)
Consistently assessing progress; providing wait time and
scaffolding to students; making appropriate inferences based
on responses
Seeking multiple viewpoints; seeking to deepen learning;
including student-student and teacher-student collaboration
1.00
GRADE 2
(ES02.T01)
GRADE 4
(ES02.T02)
GRADE 5
(ES01.T01)
GRADE 5
(ES01.T02)
(MS01.T01)
GRADE 8
(MS02.T01)
GRADE 8
(MS02.T02)
GIVE US FEEDBACK
• Is the structure feasible?
4
Sample Prompt: Munching at McDonalds
Student Workout
3.38
2.50
2
Minute Mind Stretch: Let’s start with an easy problem: If McDonalds
sold 5 milkshakes every second, how many milkshakes would it sell in 2
seconds? In 3 seconds? What math are you doing to get these answers?
How many milkshakes in x seconds?
3.38
3
1.69 (0.67)
3
2.75
2.57
2.50
2.13
2.13
Alexa read online that McDonalds serves 150 hamburgers every 2
seconds.
2
1.67
• How can this prompt be improved?
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• Are there better ways to get at
student reasoning?
Work-out problems: Try your best to figure out the following problems.
Please show your work.
2.25
2.54 (0.66)
1.70
1.63
1. How many hamburgers would McDonalds sell in 30 seconds?
2. Graph the number of hamburgers sold by time.
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$("%$3,%#(&6.4%(5.77(,%7+(
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3. Describe the relationship between hamburgers and seconds.
2.57 (0.71)
1
GRADE 2
(ES02.T01)
Including all students in math lesson.
2.63 (0.86)
GRADE 4
(ES02.T02)
GRADE 5
(ES01.T01)
GRADE 5
(ES01.T02)
GRADE 6
(MS01.T02)
GRADE 8
(MS01.T01)
GRADE 8
(MS02.T01)
GRADE 8
(MS02.T02)
1
2.60 (0.60)
choices you made to figure out the answers to numbers 3 and 4.
1.00
GRADE 2
(ES02.T01)
GRADE 4
(ES02.T02)
GRADE 5
(ES01.T01)
GRADE 5
(ES01.T02)
FORMATIVE ASSESSMENT
2.24 (0.63)
4. How many hamburgers are sold in 1 minute? Explain the
1.38
1.25
1.99 (0.62)
Mathematical errors; math language; probing for accuracy and
explanations; scaffolding; tapping prior knowledge
(MS01.T02)
GRADE 8
CRITERIA FOR SUCCESS
2.88
Building on and clarifying students’ responses; pushing for
elaboration; engaging more students in thinking
Multiple representations; complex numbers; non-algorithmic
thinking; requiring decision-making, reasoning, and multiple steps
GRADE 6
Toolkit activities will focus on 8th grade math, specifically connections between proportional
relationships, lines, and linear equations (8EE 5-6) and constructing viable arguments/critique
the reasoning of others (MP#3).
Below is an intro. activity supporting standards 8EE5-6.
MEAN (SD)
2.00 (0.90)
1
(MS02.T02)
4
Collaborative
Climate
• Rubrics & examples;
1.50
Two researchers were present for approximately half the observations. Reliability across
raters was above .80 for teacher overall ratings. Teachers and principals were also
interviewed about FA views and practices.
Questioning
Strategies
2.00
1.88
1.75
Observation protocols were created after reviewing several sources, most notably FAST
SCASS (2012). Two teachers from each school were observed over four days of math
instruction in Winter-Spring 2013 (41 class periods observed total). Observers took
fieldnotes, completed short checklist & four-point rubrics on eight FA dimensions.
Criteria for Success
2.25
2.00
2
PROCEDURES
Learning Goals
This toolkit is part of a larger FAM intervention study and includes:
• Prompts & probes (i.e., short warm-up activities);
2.75
2
DIMENSION
• gathering & analyzing student work that captures students’ understanding of content and
reasoning;
4
• School demographics (i.e., serve disadvantaged students)
2
The dimensions of criteria for success and feedback are linked with one another because the
judgments teachers make, and the feedback they give students, are inherently based on the
criteria held by the teacher (Tunstall & Gipps, 1996). In addition, these two dimensions are
critical in developing self-directed student learners (Nicol and Macfarlane-Dick, 2006) and are
linked to common Core Math Practice Standards that expect students to reason, persevere, and
critique the reasoning of others.
NEXT STEPS
TEACHER’S INVOLVEMENT OF STUDENTS
1
Two dimensions in which teachers appeared to need additional support were articulating
criteria for success and providing formative feedback. In addition, there were relatively few
instances of students engaged in mathematical reasoning tasks/discussions. What we saw in our
observations seem to mirror the literature. Teachers frequently do not make clear the criteria for
success (Moss, Brookhart, and Long, 2013) and often have difficulty generating feedback that
provides students with next steps for learning (Heritage, Kim, Vendlinski, and Herman, 2009).
Finally, Hiebert and Grouws (2006), among others, have noted the persistent lack of attention to
deep conceptual development and reasoning in U.S. math classrooms.
GRADE 6
(MS01.T02)
GRADE 8
(MS01.T01)
GRADE 8
(MS02.T01)
IF A TEST LEFT WESTWOOD TRAVELING AT 600 MPH, WOULD IT HELP IMPROVE
STUDENTS’ REASONING BY THE TIME IT RETURNED FROM REDONDO BEACH?
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305C080015 to the National Center for Research on Evaluation, Standards, and Student Testing (CRESST). The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.
The
work reported
reported
This
is supported
by awas
grant
from the National
Science
Foundation
(#1020393).
would like toCenters
acknowledge
the support
from NSF,
in particular
guidance
and support from
Julio Lopez-Ferrao.
The research
work
herein
supported
under the
Educational
Research
and We
Development
Program,
PR/Award
Number
Award the
Number
R305A050004.
TheDr.
findings
and opinions expressed in this poster do not reflect the positions or policies of the National Center for Education Research, the Institute of Education Sciences, or the U.S. Department of Education.
GRADE 8
(MS02.T02)
Class Reflection
Partner Stretch: With your partner discuss….
•
What steps did you take to answer the questions?
•
Do you know if your answers are correct?
•
Does the information in your graph match your table or t-chart?
•
Can you represent this information in an equation? How many
hamburgers in x seconds? In x minutes?
Check Your Pulse: Compare your work to our criteria and rate your
understanding so far.
YES
NO
Have lots of questions,
but need help.
Almost got it,
but need practice.
Got it.
Ready to move on.
Final stretch: Burger King serves 2000 hamburgers every 30 minutes.
Compare the Burger King rate to the McDonalds rate. Explain your
thinking using as many different representations as possible such as
words, numbers, equations, charts, graphs, and pictures.
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*Adapted from an introduction to 8 EE5 - Ready for Proportional
Relationships (p. 72) found in California Go Math! Middle School
Grade 8 (Houghton Mifflin/Harcourt text). Also considered
example tasks, structures, and advice from MARS, Noyce
Foundation Problem of the Month, Engage NY, and El Paso
Collaborative for Academic Excellence.