growth-based grading in mathematics

Growth-Based Grading in Mathematics

Ava SpindtEarly College Alliance (ECA)Mathematics Instructor

Caitlin DonnellyWashtenaw International High School (WIHI)Mathematics Instructor

Initial Observations: Student behavior in math courses is predictable:

1. Student positively responds to feedback and increases mastery2. Student negatively responds to feedback and decreases mastery

Student progress 2016-2017

Change in Mastery Over Course of One Semester *Bars represent Slope X 1000

Decrease IncreaseMidterm Final Exam1st Assessment

Quiz #

The Problem:Students that earn multiple below-average test scores are less likely to recognize the importance of continued effort and perseverance in their math courses. This consequently propagates the “fixed mindset” that diminishes comprehension of material throughout the course and sets students up for failure on future assessments and in future math courses.

Midterm Final Exam1st Assessment

The “Fixed Mindset” Group

Quiz #

Research Questions:1. How can educators minimize or

reverse the downward progression of mastery and consequently maximize long-term mathematical comprehension?

2. How can students overcome the negative thoughts common after consistent poor performance and consequently build mathematical confidence?

Quiz #

Quiz #

GBG at the ECA

Research Methods: Growth-Based Grading (GBG)1. Students with below a 75% course grade after midterm are invited to participate in the

growth-based grading system; participation in grading system is completely voluntary

2. Students receive a weekly “growth goal” from instructor via email; student track goal and develop a study plan for how to reach goal.

3. If student meets/surpasses weekly goal for entire semester, student is guaranteed at least a 75% in the course*

*Final exam can replace entire grade if the score is higher than the course average

Sample Initial Email Sample Final Email

Research Methods: Tracking Growth

1. Students complete a comprehensive initial diagnostic

2. Students complete post-assessment after each unit that reassesses mastery of standards from diagnostic

3. Growth from diagnostic to post-assessment calculated and tracked; data used for setting goals

Examples of mastery tracker

Research Methods: Tracking Perception of Growth

1. All students are given a mindset survey twice during the semester: a. 1st Survey: Prior to Initiation

of Growth-Based Gradingb. 2nd Survey: Prior to Final

Exam 2. Responses are recorded and

changes between 1st survey and 2nd survey are measured

Example of mindset tracker

Examples of mindset survey questions

Initial Results: Mastery (Fall 2017)(Algebra II; 48 students)

Non-GBG Students● Initial Average Mastery:

84% ● Final Average Mastery:

82%● Gains:-2%

GBG Students● Initial Average Mastery:


72% ● Gains: 13%

GBG Implemented

Non-GBG GBG

2% Decrease

13% Increase

Initial Mastery vs. Final Mastery

Time (weeks)

Initial Results: Mastery (Winter 2018)(Pre-Algebra/Geometry/Algebra II; 108 Students)

Non-GBG Students● Initial Average Mastery: 79%

● Final Average Mastery: 84%

● Gains: 5%

GBG Students● Initial Average Mastery: 58%

● Final Average Mastery: 72%

● Gains: 14%


14% Increase

5% Increase

GBG Implemented

Non-GBGGBG

Time (weeks)

Initial Results: Mastery (Spring 2018)(Statistics; RANDOMIZED TRIAL; 52 students)

Control● Initial Average Mastery:


51% ● Gains: -2%

Treatment● Initial Average Mastery:


65% ● Gains: 14%

GBG Implemented

14% Increase 2%

Decrease

ControlTreatment


Time (weeks)

Initial Results: Mastery (Fall 2018)(Full Department; RANDOMIZED TRIAL+OTHER TEACHERS; 120 students)

Control● Initial Average Mastery: 62% ● Final Average Mastery: 58% ● Gains: -4%

Treatment● Initial Average Mastery: 61% ● Final Average Mastery: 67% ● Gains: 6%

GBG Implemented

4% Decrease


6% Increase

GBG Students (Department)● Initial Average Mastery:58% ● Final Average Mastery: 64% ● Gains: 6%

Control Treatment

6% Increase


Time (weeks)

Initial Results: Mastery (Winter 2019-Fall 2019)(Full Department; OTHER TEACHERS+ROLLING ADMISSIONS;

Control● Initial Average Mastery: 79% ● Final Average Mastery: 82% ● Gains: 3%

Treatment 1 (Implemented after 2nd Quiz)● Initial Average Mastery: 50% ● Final Average Mastery: 67% ● Gains: 17%

Treatment 2 (Implemented after 3rd Quiz)● Initial Average Mastery: 40% ● Final Average Mastery: 48% ● Gains: 8%

Treatment 4 (Implemented after Midterm)● Initial Average Mastery: 69% ● Final Average Mastery: 83% ● Gains: 14%

Treatment 3 (Implemented after 4th Quiz)● Initial Average Mastery: 57% ● Final Average Mastery: 73% ● Gains: 16%

Initial Results: Mindset

Fall 2017:(Algebra II; 48 Students)

Winter 2018: (Pre-Algebra/Algebra II/Geometry; 108 Students)

● Non-GBG Group: No Change

● GBG Group: 6% Increase

● Non-GBG Group: 0.8% Increase

● GBG Group: 15% Increase

GBG GBGNon-GBG Non-GBG

Initial Results: Mindset

Fall 2018: RANDOMIZED TRIAL(Pre-Algebra/Algebra II; 73 students)

Spring 2018: RANDOMIZED TRIAL(Statistics; 52 students)

● Control: 7% Increase

● Treatment: 3% Increase

GBGTreatment Non-GBGControl

Fall 2018: OTHER TEACHERS(Pre-Algebra; 47 students)

● Control: -2.04% Decrease

● Treatment: 2.45% Increase

● Non-GBG Group: 4.1% Increase

● GBG Group: 3.89% Increase

Treatment Control

Example Student Written Response

GBG AT WIHI

Standards Based Grading vs. GBG

Students graded on individual ObjectivesThis semester had 14 different topic grades such as Exponential Growth and Calculating 3D Surface Area

We have an 8 point IB scale: 8= 100%

4= 75%

All Scores here for the topics are averaged for overall grade

Screenshot of a Objective Grade in PowerSchool

Students graded on individual ObjectivesWithin each topic a student’s grade is decided based upon pattern and growth

We aim to give at least 2 or 3 in class attempts at the objectives which are tests, quizzes, or retakes


A student’s overall score (which is what we saw on the PowerSchool screenshot) is determined by patterns of growth and consistency

What score do we think this student would get OVERALL ?


If all assessments are equal levels of difficulty- the student would get An 8 AKA 100% as that is where there grew to and are at currently!

However, even this growth minded SBG practice does not always mean students do grow...as it does not explicitly help them to learn the approaches to learning to help them grow

How will my grading look with SBG and GRG

Traditional Grading: Keeps track of all the times someone falls off their bike when learning to ride it. Uses all those

failed attempts as a consequence to calculate final score,

even though they eventually learned from the falls!

Standards Based Grading: Does not punish based on

number of attempts or falls. Instead, person receives scores

from when they have training wheels to when they can pop

wheelies. Once they can ride the bike, their score reflects that they obtained the standard.

Growth Based Grading: Does all the above, but teaches students concrete ways to get back on the bike

Where I am at in this process right now...

Just invited students

I am already seeing more students engage in class even though that is not

one of their growth goals

Current Extensions

Current Extensions: Growth-Based Grading Gradebook

Online Gradebook :

● Gradebook will generate goals

● Gradebook will communicate

goals and progress to students

regularly

● Gradebook will track student

performance on standards

throughout course

Future Research:

1. What are the impacts on student success in other teachers’ classrooms?

2. What are the impacts on student success in future mathematics

courses? 3. What are the impacts on student mastery if growth-based grading is

implemented prior to midterm assessments?4. What are the impacts on student mastery if growth-based grading is

implemented for every student?

5. Can alternative grading system be implemented in non-mathematics courses? If so, how?

Growth-Based Gradebook Pilot Program Sign-Up

Need Help Implementing GBG?

Caitlin [email protected]

Ava [email protected]

growth-based grading in mathematics

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