Math Homework: Grading for Completion versus Accuracy

Project Rationale

There has been a long-heated debate on grading math homework on completion versus accuracy.  Proponents of completion state that homework mistakes should be encouraged.  In addition, it puts less pressure on students to perform knowing that homework is intended as a learning opportunity.  People who feel that accuracy has more value believe that accuracy encourages students to put effort in to deliver correct answers.  They state that students who are required to complete their homework accurately, and thus make fewer mistakes, perform better on testing.

This research is designed to compare both methods both in terms of testing scores as well as student's apprehension and emotional well-being.

Project Context

The research was conducted at AD Henderson University School with a specific focus on students in Algebra I and Geometry.  AD Henderson is a research focused elementary and middle school in Boca Raton, FL.

The initial survey was conducted with forty-five students who had experienced one year with math grading based on completion as well as currently experience homework grading on accuracy.  Diagnostic scores are compared among all students in Algebra and Geometry, comparing last year versus this year.

Supportive Literature

A recent study conducted by McJames et al. (2024) has illuminated the significant advantages of assigning daily homework in mathematics, particularly for middle school students. The research indicates that engaging in homework for a duration of 15 to 60 minutes each day correlates with improved test scores, suggesting that consistent practice is vital for academic success in this subject area. However, a critical debate arises regarding the methodology of grading this homework: should educators prioritize accuracy or completion in their assessments (Zielinski, 2016)?

Proponents of grading homework based on accuracy argue that this approach encourages students to invest more time and effort into solving mathematical problems. According to Hoff (2023), students who are assessed on their accuracy are more likely to engage deeply with the material, leading to a better understanding of mathematical concepts. This grading method not only provides valuable feedback to students and their parents but also fosters a sense of accountability in the learning process (McCormick Teaching Excellence Institute, 2024). However, there are notable drawbacks to this approach. The expectation for students to consistently solve problems correctly can create a high-pressure environment, leaving little room for error. This pressure may contribute to heightened anxiety levels among students, particularly in contexts where academic performance is closely tied to future opportunities, such as scholarships and college admissions (Hough, 2023). The pursuit of perfection can overshadow the learning process, making students fearful of making mistakes, which are essential for growth and understanding.

On the other hand, grading homework for completion offers a different set of advantages. This method encourages students to engage with the material without the fear of failure, allowing them to make mistakes and learn from them (Zielinski, 2016). By focusing on completion, educators can create a more supportive environment where students feel safe to explore and experiment with their understanding of mathematical concepts. However, this approach is not without its pitfalls. One significant concern is that completion grading may lead to an inaccurate representation of a student's true comprehension of the subject matter. As noted by Hoff (2023), a student could easily fill a page with illegible scribbles and still receive full credit, leading parents to mistakenly believe that their child has mastered the content. This disconnect can become particularly problematic when subsequent formative assessments reveal gaps in understanding that were not apparent through the completion grading system. In conclusion, the debate between grading for accuracy versus completion in math homework raises important questions about educational practices and student well-being. While grading for accuracy can enhance accountability and understanding, it may also contribute to anxiety and a fear of failure. Conversely, grading for completion fosters a more forgiving learning environment but risks misrepresenting student mastery. Educators must carefully consider these factors to strike a balance that promotes both learning and mental health in their students. Ultimately, finding an effective grading approach requires ongoing dialogue among educators, students, and parents to ensure that assessment methods align with the diverse needs of learners while supporting their overall development.

Research Methods

The participants for this research consist of 85 middle school students: 40 in Algebra 1, 30 in Geometry, and 15 in Algebra 2. Thirty-seven of the students in the latter two classes had me as their teacher in the previous year with the rest being new or coming from a dual enrollment class taught by another instructor. The breakdown among all the students is 30 male and 55 female. The students also consist of 62 eighth-graders, 20 seventh graders, and three in sixth grade.

A pre-survey was given for all students who were in the Geometry and Algebra 2 classes to gauge their opinion on homework being graded on completion versus accuracy. Last year, and the first quarter of this year, homework was graded solely on completion. At the start of the second quarter and going forward, homework is graded on accuracy. A similar post-survey was given at the start of the fourth quarter.

The first seven questions had five answers generally ranging from very effective to very ineffective.

1. How do you feel about the effectiveness of grading homework based on completion in improving your understanding of math concepts?
2. How do you feel about the effectiveness of grading homework based on accuracy in improving your understanding of math concepts?
3. How does grading by accuracy (versus completion) affect your motivation to complete math homework?
4. How confident are you in your math skills when your homework is graded based on completion?
5. How confident are you in your math skills when your homework is graded based on accuracy?
6. How do you perceive the impact of homework grading on your test performance?
7. How do you feel about the effectiveness of grading homework based on accuracy in improving your understanding of math concepts?
8. In your opinion, which grading method better prepares you for tests? (completion, accuracy, both equally, neither)

Lastly, an open ended question is given for students to share their feedback on both methods and any impact not considered in the survey.

The exit questionnaire, submitted at the end of the third quarter, where students had a semester of grading by accuracy, consisted of the following questions:

1. How do you feel about the effectiveness of grading homework based on accuracy in improving your understanding of math concepts?
2. How confident are you in your math skills when your homework is graded based on accuracy?
3. How has grading based on accuracy affected your confidence when taking tests compared to taking tests based on completion?
4. The current method for grading homework is to take your graded score and round UP to the next 5%. What is your opinion on this?
5. In your opinion, which grading method (completion or accuracy) better prepares you for tests?

Again, an open-ended question is provided for general feedback.

At the start of the third and fourth quarters, students among all three classes are given comprehensive diagnostics in ALEKS, an online teaching resource. Their diagnostic scores will be compared to the scores from last year to look for growth and mastery to compare grading methodologies. Although the EOCs will be conducted after the deadline of this research project, it will also be compared to look for differences in growth.

Results

The question that was asked of this research project was ‘does grading math homework for accuracy, rather than completion’ result in higher standardized testing scores.  Before addressing the results, briefly recapping the manner in which homework was graded last year versus this year.  Last year, 2023-2024, homework was generally graded on completion.  Students would show me their homework, and I would spot check it to ensure a modicum of effort in attempting all of the problems, regardless of the results.  This year, for 2024-2025, after a few changes in the grading process, grades were in the end assigned by looking at the homework score earned for their correct answers and rounded up to the next 5%.

To get an idea of the effectiveness, I will compare the students’ initial diagnostic scores for their respective class, taken during the first week of school, to their spring diagnostic scores, taken the first day after spring break, looking at overall growth over the course of the year.  Although it is outside of the scope of this paper in light of time frames, EOC scores will also be compared.

Looking at figure 1 above, the differences in algebra growth were negligible.  Students in this year’s class started the year off higher at 44% mastery of all topics and grew on average 21 points, ending at 65%.  Last year’s class started at 39% and ended at 63%.                                      

Comparing Geometry scores between the years, the results are similarly negligible.  The students started this year off stronger, at 53% mastery versus last year’s 43% mastery.  By the spring diagnostic, this year’s students ended with 81% mastery compared to 76% from last year.  Figures 1 and 2 demonstrate that growth in 2023-2024 with completion grading varied little from 2024-2025 where grading was based on accuracy.

Next, I considered the thoughts of the students who have had math homework graded on accuracy as well as completion over the past two years to get their thoughts.  A final survey was given at the same time as the spring diagnostic. 

Based on figure 3 above, as a whole, students felt grading based on accuracy helped them to better understand the material when compared to grading based on completion.  Despite that, they also stated that they feel less confident when graded on accuracy as seen in the question in figure 4.

Lastly, when asked which method makes them feel better prepared for tests, while there was a slight lean towards completion, the majority did not show a preference one way or another as seen in figure 5 below.

In conclusion, the overall opinion of the students polled, the preference leads to grading by completion.  A common response is that while accuracy overall leads to more confidence for assessments, it also adds a level of stress in students wanting to achieve high grades and the fear of making mistakes during what they see as practice.  Statistically, the results in either case are similar regardless of the method of grading. 

Implications

At the outset of this project, there was no clear consensus regarding whether mathematics homework should be graded based on accuracy or completion. Both approaches offer distinct advantages, and each warrants careful consideration. My initial hypothesis posited that grading based on accuracy would foster greater student accountability and promote independent mastery of mathematical concepts outside the classroom. However, the findings suggest that this assumption may not hold true, as both grading methods appeared to yield comparable outcomes.

Looking at the results, it seems plausible that the level of student engagement and intrinsic motivation plays a more significant role than the grading method itself. Students who are committed to academic excellence are likely to exert the necessary effort on homework assignments regardless of how they are graded, focusing instead on long-term achievement and preparation for assessments. Conversely, students who lack interest or motivation are likely to circumvent the system—through copying, seeking excessive assistance, or other means—regardless of whether accuracy or completion is prioritized in grading. Such behavior has been a persistent challenge throughout the history of education and is unlikely to be mitigated by grading adjustments alone.

Looking ahead, it would be valuable to explore more robust strategies for assessing student understanding while minimizing opportunities for academic dishonesty. One possible approach could involve the implementation of individualized homework assignments, tailored to each student's current proficiency level and generated dynamically to reduce the likelihood of answer sharing. This method may offer a more effective balance between promoting accuracy and maintaining academic integrity.

References