Florida’s K – 3 Mathematics
Formative Assessment System
Introduction to Formative Assessment and Research
Findings
Laura Lang, Principal Investigator
Mark LaVenia, Methodologist
2012 FCR-STEM Conference
St. Petersberg, FL
Overview of presentation
Introduction
Definition and process
Research Overview
Results of MFAS studies
Effect on the gender gap in 3rd
grade FCAT mathematics
scores
Discussion
The importance of K-3 math
• Researchers have documented
that student knowledge and
achievement in mathematics in
preschool and the earliest grades
predicts later school success in
elementary years and even
through high school.
• Scientists typically score at the
90th percentile or above in
mathematics in high school.
The importance of K-3 math
• Based on an analysis using the Early
Childhood Longitudinal Study of the
Kindergarten Class of 1998-99 through
5th grade, boys in kindergarten do
better at the top of the distribution
and worse at the bottom.
• By third grade, boys do better than
girls across the distribution.
Gender Achievement Gap in Grade 3 Mathematics
Reflection and Discussion
1. What are the biggest challenges facing your
teachers in elementary mathematics
teaching and learning?
2. What tools do you foresee as essential to
remove roadblocks for students?
Florida’s definition of formative
assessment
Formative assessment is a
process used by teachers and
students during instruction that
provides feedback to adjust
ongoing teaching and learning to
improve students’ achievement
of intended instructional
outcomes.
(McManus, 2008, p. 3)
Summative assessment
vs. formative assessment
• Summative is an assessment
OF learning.
• Formative is an assessment
FOR learning.
(Black, Harrison, Lee, Marshall, & Wiliam, 2004)
What is formative assessment?
• A process, not a test
• Reveals student thinking in addition to
whether or not the answer is correct
• Embedded within a learning activity
• Reveals gaps in knowledge and understanding
that derail student progress
• Targets instruction to strengthen the core
concepts and processes essential for
mathematics learning
• Used not only to “inform” instruction, but
more importantly to “form” instruction.
How does formative assessment work?
Formative assessment elicits students’ thinking,
helping teachers to:
• Diagnose critical misconceptions and errors.
• Identify students’ progress toward standard
mastery.
• Differentiate instruction based on students’
understanding (i.e. individualize interventional
strategies and regroup students for optimal
learning opportunities).
• Provide students the deep understanding needed
for future mathematics learning.
K-3 MFAS - CCSS tasks and rubrics
For each K-3 Mathematics Common Core
State Standard, there will be a minimum of
four formative assessment tasks and
rubrics.
Sample MFAS task
Materials
Instructions
Background on Task
Sample MFAS rubric
Misconception Student
or
Work Questions
Error
Examples
Eliciting
Thinking
Instructional
Implications
Engage Students
• Provide pencil, paper, base ten blocks, and number
line.
• Ask each student to solve the following problem:
38 + 13
Eliciting evidence of student understanding
Student solution: 38 + 13 = 51
• T: How did you get that solution?
S: I added 3 and 1 to get 40. Then, I added 8
and 3 to get 11. With 40 and 11, I have 51.
• T: Is there any other way that you could have
solved the problem?
S: I don’t know, maybe.
T: Will you show me what you are thinking?
S: [explains another possible route]
When to implement formative assessment?
•Before introducing a topic, essentially
identifying students’ prior knowledge
•After introducing a topic, with additional
instructional time on the horizon
Basic formative assessment process
Select
benchmark
to teach
DECISION
Select a new benchmark to teach
Or
Implement another MFAS task
related to the benchmark
Or
Continue instruction for student(s)
who has not demonstrated
mastery.
Implement instructional plan targeted
to the needs of individual students.
Discuss results with your team and
develop a plan to differentiate
instruction, targeting gaps in the
student’s knowledge of the
benchmark.
Develop a
thorough
understanding of
the benchmark
and related MFAS
task(s).
Draft a sequence of
tasks related to the
benchmark.
Become familiar with selected
MFAS task and associated rubric.
Implement MFAS task with
student.
Take notes describing each
student’s response(s)—
identifying gaps in knowledge.
Provide descriptive feedback to
students; encourage self- and
peer- assessment.
Research: Self-Assessment
Research shows that when students take an
active role in “monitoring and regulating their
learning, then the rate of their learning is
dramatically increased,” in fact in some
instances doubled.
(NCTM, 2007, p. 3)
Research: Collaboration
In non-threatening, collaborative classroom
environments:
• Students trust their teacher as well as their
peers.
• Differences in ideas and opinions are respected
and appreciated.
• Teachers exhibit model behaviors and
demonstrate how to provide appropriate
feedback.
(Wiliam & Thompson, 2007; CCSSO, 2008)
Research: Peer Assessment
• Evaluating peer work and providing productive
feedback allows students to practice and build
skill in improving their own work.
• Effective peer assessment requires two critical
elements:
– Students must work as a group not just in a group.
– Each student must be held accountable for his or her
contribution to the group.
(Slavin, Hurley, & Chamberlain, 2003)
Research: Descriptive Feedback
Helps the student answer three basic questions:
1. Where am I going?
2. Where am I now?
3. How can I close the gap?
Feedback should also force students to engage cognitively:
1. Find errors themselves
2. Reflect on teacher and peer feedback
3. Act on that feedback
(CCSSO, 2008)
Research: Quality Feedback
 Provide students evidence-based feedback that is directly linked to
the learning outcome and criteria for success.
 Effective feedback needs to focus on the quality of student learning
rather than on the student or the accuracy of the student’s
response.
• Verification tells students whether or not their answers
are correct.
• Elaboration provides information to guide students
towards the correct answer.
Research indicates that quality feedback should include
elements of both types of feedback.
(Shute, 2008)
Research: Comparative Effects
Research indicates that well-designed and
implemented formative assessment is an
effective strategy for enhancing student
learning.
Intervention
Extra Months of
Learning Gained per
Year
Class-size reduction by 30% (for example, from 30
to 20 students)
3
Increase teacher content knowledge from weak to
strong (2 standard deviations)
1.5
Formative assessment
6 to 9
(Wiliam, 2007)
Relation between Classroom Practice and Grade 2 Student Achievement
Classroom observation
protocol subscale
Clarifying and sharing
learning intentions
Estimate
(SE)
0.48
(0.11)
p-value Effect Size
< .001
0.61
Eliciting evidence of learning
and providing feedback
0.36
(0.13)
.006
0.45
Student self- and peerassessment
0.25
(0.15)
.089
0.29
MFAS Efficacy Trials
Three randomized controlled trials have been
conducted on MFAS:
1. a nine-week pilot study in 2010 with K-3 teacher
teams using tasks aligned with Florida’s NGSSS;
2. a semester-long pilot study in 2012 with grade
2-3 teacher teams using tasks aligned with
Florida’s NGSSS; and
3. a year-long study currently underway in 2012-13
with K-1 teacher teams using tasks aligned with
the CCSS.
Study Samples
• 2010 nine-week pilot study
– 14 schools from one district
– 169 K-3 teachers
– 1939 students
• 2012 semester-long pilot study
– 21 schools across three districts
– 160 grade 2-3 teachers
– 2756 students
2010 MFAS - NGSS Pilot Study
2010 MFAS - NGSSS Pilot Study: Implementation Data
Other Findings from the 2010 MFAS – NGSSS Pilot Study
• Teachers’ knowledge of mathematics moderated the
student mathematics outcomes
• Principal support is critical in the implementation of
formative assessment.
• Many of the treatment group teachers initially rejected
the tasks because they believed the tasks to be too
difficult for students.
– After implementing the tasks and seeing that their
students learned to successfully solve the problems when
instruction targeted the gaps in their knowledge, these
teachers reported major changes in beliefs and increased
expectations for students in mathematics (Lang, Schoen,
Howell, & Davis, 2010).
2012 MFAS - NGSSS Pilot Study: Effect of MFAS Task Usage on Grade 2 and
Grade 3 Math Performance
2012 MFAS – NGSSS Pilot Study: Effect of MFAS on Grade 3 Mathematics
Achievement by Gender
MFAS-CCSS Project
2011 - 2013
• Development of at least 376 formative
assessment tasks aligned to the CCSS for K-3
Math.
• Produce four introductory modules in CPALMS,
three for teachers and one for school leaders.
• Create 18 lesson study toolkits aligned to the
domains of the CCSS for K-3 Math.
• Test the effect of the use of MFAS on K-3 student
achievement and teacher knowledge of content
and pedagogy.
• Updates to CPALMS.
• All components will be available June 30, 2013.
Closing
• MFAS leaves teachers to decide whether tasks
are implemented in one-on-one interviews,
small groups, or whole class.
• MFAS is focused on formative assessment
occurring day-to-day and minute-to-minute.
• MFAS is focused on teacher collaboration
around student thinking and instruction.
• MFAS is designed to support differentiated
instruction.
The 2011 – 2013 MFAS-CCSS Team
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Laura Lang, Principal Investigator
Robert Schoen, Co-Principal Investigator
Maureen Oberlin, Project Manager
Michael Anderson (Pinellas)
Charity Bauduin (Okaloosa)
Zachary Champagne (Duval)
Michelle Robinson (Seminole)
Linda Walker (Walton)
Andy Reeves (Pinellas)
Mark LaVenia, Methodologist
Anabelle Andon, ELL Support
Questions and Contact information
Laura Lang, Principal Investigator
llang@lsi.fsu.edu