Mastery-Based Testing

A Gateway to Alternative Grading

Erica Oldaker�Assistant Professor of Mathematics

Outline

• What is “Alternative Grading”?
• Who would subject themselves to this? (Me)
• How does Mastery-Based Testing (MBT) work?
• Why would I want to do this (or not)?
• How might I do this myself?

Alternative Grading

What is it and why should I care?

Are These Students Really the Same?

Clark, David. Traditional grades are not objective, Grading for Growth, 21 Nov. 2022, https://gradingforgrowth.com/p/traditional-grades-are-not-objective.

Does This Seem Fair?

Clark, David. Traditional grades are not objective, Grading for Growth, 21 Nov. 2022, https://gradingforgrowth.com/p/traditional-grades-are-not-objective.

Four Pillars of Alternative Grading¹

• Clearly defined standards
• Helpful, actionable feedback
• Marks as progress indicators (not arbitrary numbers)
• Reassessments without penalty
• “Feedback loops”

1. Talbert, Robert. Finding Common Ground with Grading Systems, Grading for Growth, 30 Aug. 2021, https://gradingforgrowth.com/p/finding-common-ground-with-grading.

My Journey with Grading

A tale of what NOT to do…

Excited First Year Grad Student!

Round One!

Round Two!

Listener, it was…

• Confusing!
• Time-consuming!
• Impractical for full-time faculty

?

Ready for full-time teaching

Some faculty development talk at W&L

Mastery-Based Testing

How does it work?

The Basics

• Course is broken down into content objectives, or “topics”
• Students only receive credit for mastery of topics
• There is no penalty for reattempts
• Overall exam grade is calculated using number of topics mastered

More Details

Calculus 2 (MAT 122)

• 15 Topics (broken down by quad and type)
• Quad 1 (7) vs. Quad 2 (8)
• CORE (6) vs. Non-Core (9)
• Linear scale by type
• CORE is 9% and Non-Core is 5%
• Three levels of grading
• Mastered (M), Progressing (P), Needs Work (N)
• 4 full Mastery Days, 2 half Mastery Days, and Final Exam

Concepts of Math (MAT 205)

• 17 Topics
• Equally weighted(-ish)
• Piecewise-linear scale
• First topics mastered worth more
• Three levels of grading
• Mastered (M), Progressing (P), Needs Work (N)
• 4 full Mastery Days, 1 half Mastery Day, Mastery Week, and Final Exam

MAT 122 Topics

1. The Definite Integral and Area
2. Numerical Integration
3. Volumes of Revolution
4. Slicing and Work
5. Advanced Integration Techniques I
6. Advanced Integration Techniques II
7. Identifying Integration Techniques

8. Vectors and Vector Products
9. Lines, Planes, and Surfaces
10. Graphical and Conceptual Interpretation of Partial Derivatives
11. Computing Partial Derivatives
12. Tangent Planes and Linear Approximation
13. Extrema of Functions of Several Variables
14. Double Integrals
15. Triple Integrals

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MAT 205 Topics

1. Sets
2. Logic
3. Numbers and Place Value
4. Models of Addition and Subtraction
5. Algorithms and Properties of Addition and Subtraction
6. Models of Multiplication and Division
7. Algorithms and Properties of Multiplication and Division
8. Identifying and Comparing Fractions

• Addition and Subtraction with Fractions
• Multiplication and Division with Fractions
• Decimals
• Signed Numbers
• Number Classification
• Angles
• Polygons and Their Properties
• Perimeter and Area
• Ratio, Proportion, and Percent

Sample Mastery Questions

The Pros of MBT

And a few Cons as well

Points vs. Mastery²

Points

• Understand bits of everything, but not entirely
• “How can I get more points here?”
• Give it your best shot and move on
• Review key concepts for the final (maybe)
• Failure is to be avoided
• One bad test could “ruin” GPA
• Time wasted scrutinizing solutions
• “How many points should I take off?”

Mastery

• Understand some concepts fully
• “What do I need to study to gain mastery here?”
• Keep trying until you get it
• Review key concepts now
• Failure is a chance to grow
• No one test can harm grade
• Mastery is spotted quickly
• “Will the student benefit from studying this concept again?”

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2. Mohr, Austin. “Mastery-Based Exams Are Self-Evidently Better than Traditional Exams.” Mastery-Based Testing in Undergraduate Mathematics, 14 Feb. 2017, https://mbtmath.wordpress.com/2016/04/25/mastery-based-testing-is-self-evidently-better-than-traditional-testing/.

Why I Love Mastery-Based Testing

• Content objectives are clear
• Flexibility for life circumstances
• Takes into account different speeds of learning
• Better overall for both strong and weak students
• Written feedback matters
• Grading is faster
• Relatively easy to adopt in a course without a total overhaul
• NO POINTS

Some Challenges I’ve Encountered

• Students falling behind (and feeling behind)
• Midterm grades require guesswork
• Before the final, almost everyone looks like they will fail …
• …then after the final almost no one does
• Writing multiple versions of a question takes time
• Canvas doesn’t always play nice
• Perfectionists beware!

What Do Students Think?

• “I personally loved the mastery idea because it was extremely helpful for me”
• “The mastery tests has been helpful for me because I just have to grasp the concept of math, instead of getting 100% on exams.”
• “At first, I was really suspicious of the whole "Mastery Based Testing" system … but I actually REALLY enjoyed this testing system… I totally prefer the mastery system over "normal" tests and exams. It was very effective in helping me get an overview on the material we learned in class.”
• “Dr. Oldaker's mastery system is the best---everyone should implement her grading system”

• “I had trouble…with the mastery exams. I couldn't seem to master anything until the second to last exam which was very stressful… Some people like the structure of the mastery exams, but I think I would prefer a number grade on each test.”
• “I…felt that the mastery testing was extremely difficult to actually grasp the content. By not being able to move on from things and constantly having prior material looming, it was hard to focus on learning new things without having to think about so many old things… I enjoy that with regular tests you prepare for what you just learned and if it doesn't go well you can move on and learn the new stuff with a fresh slate.”

Adopting For Your Courses

A How To Guide

Is MBT Right for Me?

• Is my course based around regular examinations?
• Can I envision how I might split content into topic areas?
• Is my class size too big to make this practical?
• Do I have enough space for sufficient mastery opportunities?
• Probably 3 in-class + a final at minimum
• Consider Mastery Weeks, quizzes, or take-home exams

If not, there are other forms of Alternative Grading that may be a better fit.

How to Get Started

• Topic List
• Best advice: start with a previous (cumulative) final exam
• Rough draft of topics list (one question from final = one topic)
• Revise as needed (split up/combine)
• Topic Weighting
• Easiest: Mastery grade = (# Topics Mastered)/(Total # Topics)
• Pass/fail divide: How many topics = passing grade?
• Core Topics: Yes or no?

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How to Get Started

• Grading Rubric
• Two-Level: Mastered/Not-Mastered
• Three-Level: Mastered/Progressing/Needs Work
• Four-Level: Exceeds/Meets/Almost Meets/Does Not Meet
• Repeated or single mastery
• Exam Timing
• Traditional or MBT final exam
• Retesting only on exams vs. intermediate quizzes

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Resources�(a small selection)

• “Mastery-Based Testing in Undergraduate Mathematics” Blog
• mbtmath.wordpress.com
• “Grading for Growth” Blog
• gradingforgrowth.com
• The Grading Conference
• thegradingconference.com
• Specifications Grading by Linda B. Nilson
• Slack Community and Google Drive Shared Folder

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Thank you!

Any questions?