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Incorporating Student Contracts to Improve

Success in a Developmental Math Class

This article is based on a talk I have given at several conferences (AMATYC 2008 - Washington DC, ICTCM 2009 – New Orleans, Cherry Blossom Congress 2009 – Alexandria, VA) on incorporating student contracts to improve student success in a developmental mathematics class.

Background

I am a community college math instructor at College of the Sequoias in Visalia, CA. In our department meetings we never focus on mathematical questions such as “What is the best way to teach the section on the quadratic formula?” or “How do we teach students to find the LCM of two numbers quickly?” At this point in our careers we are all very comfortable with regards to the mathematics. We very rarely disagree on which topics should be emphasized or left out of our courses. What we spend a lot of time discussing are different ways to motivate our students.

It can be very frustrating when you feel you are doing an excellent job lecturing on mathematics but the students are not giving the necessary amount of effort. I believe that students, with the proper effort, can learn the material we teach in our developmental mathematics courses. Proper effort, to me, includes a consistent effort on homework for the entire semester. Unfortunately, many students do not see any immediate reward from doing their homework. It’s funny because when I ask students on day 1 if they plan to pass the course, they always reply that they do plan on passing. If your plan doesn’t involve doing the homework, then I say you are actually planning on failing.

One colleague and I used to discuss the lack of motivation our students have and we were equally frustrated. He used to weight his homework as 10% of the overall grade, and students wouldn’t do it. He raised the weight to 15% with no significant improvement. The same thing happened when he went to 20% as well. So, I asked him, how high do you have to raise it in order to get the students to do their homework? He told me he thought about making it 50% of the grade, adding the condition that students must pass the final exam in order to pass the class. The 50% seemed a little extreme to me, but I knew that if he tried this policy and students still wouldn’t work then we might as well give up.

About the same time our college president, Bill Scroggins, shared an instructional strategy he used as a community college chemistry instructor. His idea was: Take the student behaviors that you think are most important to student success and incorporate rewards into your syllabus for students who demonstrate these behaviors. He valued attendance, taking quality notes, and getting help outside of class at the tutorial center or his office. Any student who met his conditions could upgrade their score on one exam.

So I thought about this approach for a while, and decided that the student behaviors that I valued were attendance, effort, and performance. What follows is the first version of the contract I used in my Intermediate Algebra course in Fall 2007.

Contract Requirement #1

I wanted my students to be in class, so the first requirement of my contract was that a student could be absent for no more than 2 days. I felt that this gave some wiggle room to the student with the flu or a sick child, but still showed that I felt their attendance was crucial to their success.

Contract Requirement #2

I wanted my students to display a consistent and thorough effort throughout the semester, so the second requirement of my contract was that a student had to earn 100% on each homework assignment.

I use MyMathLab to assign and collect homework. Students are allowed 3 attempts at each problem that I assign. If a student gets a problem incorrect they can request a similar problem and they can do this until they eventually get it right or the deadline passes. There are built-in features to assist students with the homework – they can see a similar example, they can be walked through that problem, or they can view a video segment involving a similar problem. Students have all of the tools they need to work through the problems, provided that they make the effort. The bottom line is that any score below 100% is an indication of a lack of effort and persistence.

Contract Requirement #3

I want my students to be able to synthesize material from different sections. I give two quizzes per chapter - one for the first half of the chapter and a second for the whole chapter. The third requirement of the contract is that students must average 80% on these quizzes.

I use MyMathLab for these quizzes. One difference from the homework assignments is that the built-in help features found in the homework section are unavailable to students while they are taking a quiz. I do allow students to take the quiz as many times as they’d like before the deadline. MyMathLab randomly generates the problems, so students see a different quiz each time. The idea is that a student completes a test, looks at the problems they missed, and tries to figure out why. MyMathLab helps students to self remediate. If a student can determine there areas of weakness, then those areas can be addressed and fixed prior to the exam.

Contract Requirement #4

Everything I do as an instructor focuses on preparing my students for their pencil & paper exams. (OK, I know that’s not completely true. My main goal is to help my students learn and understand mathematics, but in my students’ eyes it’s all about the exams.) The fourth requirement of the contract is that students must average at least 70% on their in class exams.

The purpose of this requirement is to push each of my students to be a passing student in terms of the exams. If they have met this requirement, then they have demonstrated a passing knowledge of the material.

Contract Payoff

If any student meets all four of my requirements, they are allowed to complete a final cumulative assignment on MyMathLab instead of taking the cumulative in-class final exam. Many developmental mathematics students lack confidence, especially concerning “that one big exam at the end”. My contract used this lack of confidence to inspire and motivate my students to give their fullest effort for the entire semester, and it was successful beyond my wildest dreams.

Regarding the final assignment, this was a cumulative assignment of over 150 problems. The assignment also served as a final review for students who still had to take the final. A student had to complete the assignment prior to the last day of class in order to complete their contract and opt out of the final exam. By completing this assignment with a score of 100%, students are demonstrating that they can do any problem covered during the course of the semester and that they are prepared for the next class.


Results

Here’s the data from the first semester I used student contracts.

Retention

I began with 54 students enrolled, and 49 of them were still enrolled on the last day of class. The retention rate was 90.7%. For all other sections of Intermediate Algebra offered that semester on campus, the retention rate was 82.1%, so my retention rate was 8.6% above the campus wide rate that semester. (As another reference point, my retention rate for the same course during the previous semester was 85.9%.)

Success

30 students of the original 54 students, or 55.6% of the class, satisfied the contract and passed the class. Think about that! More than half of the students scored 100% on every homework assignment that semester, averaged at least 80% on all of their quizzes, averaged at least 70% on all of their exams, and missed no more than 2 days of class. If someone told me on day 1 that I would have results like those, then I would consider that semester a success.

Another 7 students passed the class without meeting the contract’s requirements, bringing the total number of successful students to 37 out of 54 or 68.5%. This was roughly 20% higher than the campus wide success rate for this course that semester. There were 12 students (22.2%) that failed the class, and another 5 (9.3%) that dropped the course. The following table compares these results to my intermediate algebra classes taught the previous semester as well as the campus wide results for intermediate algebra that semester.

 

My Class
With Contract

My Classes
No Contract

Campus
Wide

Pass

68.5%

49.4%

48.3%

Fail

22.2%

36.5%

33.8%

Drop

9.3%

14.1%

17.9%

Retention

90.7%

85.9%

82.1%

Test Grades

The test scores seem to have been positively affected by the use of a student contract. 35% of the students had an A test average, 74% had a test average that was a B or higher, and 86% had a test average that was a C or higher. (The cut off for an A is 90%, 80% for a B, and 70% for a C.) The following table compares these results to my intermediate algebra courses that were taught the previous semester.

Average

With Contract

No Contract

A

35%

12%

B

39%

21%

C

12%

36%

D

8%

9%

F

6%

22%

I also noticed that a greater percentage of the students were passing each exam. The following table lists the success rate (C or higher) for each exam, and compares it to the results of my Intermediate Algebra classes from the previous semester.


Success Rate On Each Exam

 

With Contract

No Contract

Test 1 – Transition

83%

74%

Test 2 – Radicals

79%

55%

Test 3 – Quadratic

80%

62%

Test 4 – Functions

76%

61%

Test 5 – Exp./Logs

71%

36%

Test 6 – Conics

94%

92%

Finally, here are the mean scores for each exam. Again, notice the amount of increase. The increase was highest on test 2 (Radicals) and test 5 (Exponential & Logarithmic Functions). Students traditionally struggle with these topics, but my students did very well.

Mean Score On Each Exam

 

With Contract

No Contract

Test 1 – Transition

83.0

77.6

Test 2 – Radicals

79.6

67.6

Test 3 – Quadratic

79.7

73.8

Test 4 – Functions

81.0

71.8

Test 5 – Exp./Logs

75.0

58.3

Test 6 – Conics

93.1

88.5


Benefits

Here are some benefits of this approach.

Students remediate themselves.

One of the reasons for assigning homework is that we want students to work on material they haven’t mastered yet. When they struggle with a particular topic, we want them to seek out help. MML gives students the immediate feedback that will help students identify their problem areas, and also gives numerous support options to help them to self-remediate.

Students learn proper notation.

Because students have to type their answers using correct notation, their pencil and paper work is stronger in general.

Students form bonds with classmates.

I had students visiting the MathTutorialCenter and Computer Labs in small groups to help each other out with their homework.

Students work ahead.

I often post assignments the day before they are covered in class, and several of my students work on the assignments before I even discuss them in class.

Students put in an enormous amount of time and effort.

We know that effective time on task is a key indicator of success in a math class. Here’s a breakdown of the average amount of time spent working on homework and quizzes for the entire class over the first 4 exam periods.

Test 1: 6 hours, 46 minutes
Test 2: 8 hours, 20 minutes
Test
3: 10 hours, 40 minutes
Test
4: 12 hours, 37 minutes

Students learn where their “issues” are and ask for help.

Students find out where their trouble spots are in a timely fashion. They email questions to the instructor, ask for help from tutors and instructors in the MathTutorialCenter and Computer Labs, bring questions to class and my office, and help each other.

Students do their homework the way we want them to – they want to make sure they understand before it’s time for the quiz.

When my students have trouble with a particular problem, they take notes on that problem in case they face it on a later quiz or test.


Student Satisfaction

They like it – they really like it! I gave an anonymous survey to 50 students who were in attendance one month before the end of the semester.

Question 1: How much time and effort have you devoted to this course, compared to your previous math courses?

Much Less 1

Slightly Less

2

Same

9

Slightly More

15

Much More

23

38 of the 50 students (76%) reported that they had devoted more time and effort that they had in their previous math courses.

Question 2: How much has the grading policy affected the time and effort you have devoted to this course?

Not At All 2

 

0

Somewhat

6

 

8

A Lot

34

48 of the 50 students (96%) reported that the grading policy had at least somewhat affected the time and effort the devoted to the course. 34 students (68%) replied the grading policy affected their effort “A Lot”.

Question 3: How much has MyMathLab increases your understanding of the material in this course?

Not At All
0

 

1

Somewhat

16

 

8

A Lot

25

49 of the 50 students (98%) reported that the use of MyMathLab had at least somewhat increased their understanding of the material in the course. 25 students (50%) replied “A Lot”.

Question 4: How has your performance on exams been compared to your expectations prior to the beginning of the semester?

Much Worse
4

Slightly Lower

6

Same

13

Slightly Higher

15

Much Higher

12

27 of the 50 students (54%) reported that their performance on the exams was higher than they expected. Only 10 students (20%) reported that they were doing worse on the exams than they had expected.

Question 5: If you had to take the final exam in this course, what grade would you expect to earn on that exam?

A
6

B

22

C

19

D

2

F

1

47 of the 50 students (94%) felt that they would pass the final exam if they were to take it, which shows a dramatic increase in their own confidence.

Question 6: If given a choice, would you take your next math course using MyMathLab?

Yes
45

No

5

90% of the students indicated that they would use MyMathLab in their next math course if they were given a choice.


I still use student contracts in my classes. I have made some changes, and will discuss some of those changes in another paper.

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