Math Placement and Diagnostic Feedback Together!

Bruce ArnoldCMC-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 retakes4. Use ETS A Primer on Setting Cut Scores on Tests of

Education Achievement to set initial cut scores5. 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

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. WestEdFinkelstein, N., Huang, C., & Snipes, N. (2014). Using assessment data to guide math course placement of California middle school students. REL West

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