Math Placement and Diagnostic
Feedback Together!
Bruce Arnold
CMC-South Annual Conference
November 6, 2015
Abstract
Diagnostic assessments about student
preparedness for specific courses can help place
students appropriately and simultaneously
provide teachers and students meaningful
feedback.
Math Placement & CCSSM
“During these transitional years in which the
CCSS-M are being implemented across the state
with updated instructional approaches, new
math sequences, and new pacing of content, it
is a critical time to carefully examine students’
course trajectories.”
- Finkelstein & Fong (2014)
Math Placement & CCSSM (cont.)
“As school districts across the country move toward
full implementation of the (CCSSM), districts will be
examining course sequencing and the placement of
students in existing and new courses. … If the
Common Core unfolds as envisioned, the result
could be more students developing strong
foundations in math concepts in the middle school
years, leading to greater success in high school and
beyond.”
-Finkelstein, Huang, & Snipes (2014)
Impact of Incorrect Placements
“Math placement decisions for middle school
students can have profound effects on their
math course trajectories in high school.”
-Finkelstein & Fong (2014)
Math Trajectories & Placement
• Accelerated Placement
– MS acceleration can allow students to take AP
Calculus in senior year of HS
• On-Track Placement
– Without MS or HS acceleration, students can take
Precalculus in senior year of HS
• Below Track Placement
– Without any acceleration, students can only take
Geometry/Math II in Grade 11 and Algebra II/Math III
in Grade 12
Differences In Placement Among
Minority and Non-Minority Students
1. High-achieving minority grade 7 students were
less likely (21%) to take calculus by grade 12
than their non-minority peers (36%)
2. Academically similar minority and non-minority
students were equally likely to repeat Algebra I
in grade 9
3. Using multiple academic measures is a way to
make more accurate decisions for both minority
and non-minority students
-Finkelstein & Fong (2014)
High-Achieving Minority Students Less
Likely to Reach Calculus by Grade 12
“Among the high-achieving grade 7 students,
students who took Algebra I in grade 8 had a
much higher chance of taking calculus by grade
12.” (34% vs 7%)
-Finkelstein & Fong (2014)
Academically Similar Minority and Non-Minority Students
Equally Likely to Repeat Algebra I in Grade 9
Among students who took Algebra I in grade 8
and scored between 350-370 on grade 8 CST:
1. And had average grade 8 Algebra I GPAs
between 3.0-3.25, 18.5% and 11.1% repeated
Algebra I in grade 9
2. And had average grade 8 Algebra I GPAs
between 2.5-3.0, 17.5% and 12.2% repeated
Algebra I in grade 9
-Finkelstein & Fong (2014)
Multiple Measures May Improve
Placements for All Students
• As indicated in the last slide, there may be a
lack of alignment between math GPAs and
math CST scores for certain students.
• Among students with grade 7 math GPAs
between 1.5-2.0, on the grade 7 CST 10%
scored FBB, 33% BB, 35% Basic, 19%
Proficient, and 3% Advanced.
-Finkelstein & Fong (2014)
Multiple Measures
•
•
•
•
•
•
Course grades
Teacher recommendations
Math CST scores (usually a year old)
Student/parent preferences
Counselor recommendations
Non-cognitive factors: behavior, motivation
-Finkelstein, Huang, & Snipes (2014)
Reliability Issues in Placement
• Reliability refers to the consistency of students’
test scores over repeated administrations of the
same test
• Think of a student’s test score as a random
sample of one many possible test scores
• Observed score = true score + standard error of
measurement
• Scores more/less than 2 SEM from the placement
test’s cut score are more valid than scores near
the cut score
False Positives & False Negatives
• False negative: incorrect placement when true score
> cut score but observed score < cut score
• False positive: incorrect placement when true score <
cut score but observed score > cut score
• False positives and false negatives may account for
7-10% of all placements
Reducing False Positives/Negatives
• Include other measures in determining
placement
• Allow retakes of placement test
• If supports are available and required, can
reduce cut scores to allow more students to
promote
• If supports aren’t available or required,
recommend lower placement
Recommendations for Accurate and
Equitable Math Placement
1. Use multiple measures (combine or use independently)
2. Use multiple placement recommendations to place
students and provide diagnostic feedback to students
about their course preparation
3. Consider allowing placement exam retakes
4. Use ETS A Primer on Setting Cut Scores on Tests of
Education Achievement to set initial cut scores
5. Evaluate placement criteria annually for effectiveness
MDTP Test Results Aid in Placement
and Support
“The MDTP (Algebra Readiness) test identifies a
set of measurable skills that predict Algebra I
proficiency. Practitioners may want to consider
using MDTP results to aid in Algebra I placement
decisions … ”
-Finkelstein, Huang, & Snipes (2014)
Role of Math Placement
• Identify students who aren’t ready
• Identify students who are ready without
support
• Identify students who are ready with support
• Help students achieve success in their math
courses
UCSD Math Placement Exam
Placement recommendations for Math 3C
(Precalculus) and 10A (Calculus):
• Math 10A ok
• Math 10A ok, review
• Rec Math 3C, 10A ok
• Math 3C
MDTP Test Results Aid in Support
“Practitioners may want to consider using MDTP
results … to identify areas for focused support
aimed at helping students succeed in Algebra I.”
-Finkelstein, Huang, & Snipes (2014)
Identification of Specific Areas
MDTP readiness tests identify:
• Weak topics
• Specific misconceptions/errors
Weak Topics at Class Level
Fractions (FRAC) Topic
Topic Scores by Student
Student Report of Topic Scores
MSP July 2015 Focus Group
November 02, 2015
To: Lisa Claes
Here are the results of the diagnostic test, Algebr a Readiness (AR45A10), that you have recently
taken. Your Score, the Critical Level, and the Total Possible score for each topic are reported below.
The Critical Level for each topic is the minimum number of correct responses for you to show
adequate preparation in that topic.
Your
Score
Critical
Level
Total
Possible
Congratulations! Your results indicate that you have done well in
each of the following topics:
- Data Analysis, Probability, & Statistics
- Integers
- Literals & Equations
4
4
6
4
4
5
6
6
7
However, your results indicate you need review in the following
topics:
- Exponents and Square Roots; Scientific Notation
2
3
4
Your results indicate you need substantial review in the following
topics:
- Decimals, their Operations & Applications; Percent
- Fractions and their Applications
- Geometric Measurement & Coordinate Geometr y
1
2
2
6
6
4
8
8
6
Your total score is 21 out of 45, which is 47%. We hope you find this information helpful. Please
contact your teacher for specific activities and assignments that will aid in an y necessary review.
Identifying Common Errors
Example of Common Error
Using Placement Test Data Formatively
• Teachers determine supports to target weak
areas
• Teachers adapt instruction to address
common errors
• Provide feedback to students regarding weak
areas vis-à-vis placements
Target Weak Areas
• Tailor instruction to specific MDTP topics
• Use mastery of five MDTP topics as an
instructional target
• Conduct a content analysis of grades 5-7 math
courses to determine how closely the content
taught aligns with the MDTP topics that
predict Algebra I proficiency
-Finkelstein, Huang, & Snipes (2014)
Adapt Instruction to Target Common Errors
• Analyze error or misconception
• Consider alternative ways of teaching concept
or skill to help students unlearn error or
misconception
• Provide students multiple opportunities to
demonstrate learning
• Assess for desired learning and reteach, if
necessary
Provide Feedback to Students
• Specific, constructive feedback
• Minimally address weak topics
• If possible, identify specific errors and
misconceptions
Why Feedback Is Important
Feedback to students can help them:
• take ownership of their learning
• unlearn errors/misconceptions and learn
correct concepts and processes
• assist in learning current course content
• leads to greater success in math courses
MDTP’s New CCSSM Tests
MDTP released three new tests in August 2015
aligned to the CCSSM:
– Grade 7 Math Readiness
– Grade 8 Math Readiness
– High School Math Readiness
References
Finkelstein, N. & Fong, A. (2014). Math
Placement: The Importance of Getting It Right
for All Students. WestEd
Finkelstein, N., Huang, C., & Snipes, N. (2014).
Using assessment data to guide math course
placement of California middle school students.
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