MATHEMATICS
Back to Table of Contents for the On Course I Workshop
1. Strategy: The Jigsaw
Application: Algebra
Educator: Deb Poese, Faculty, Mathematics & Director, Education, Montgomery College, MD
Implementation: In home groups of three, have students choose to become the group’s expert in one of three methods for solving quadratic equations:
- Factoring
- Completing the square, or
- Using the quadratic formula
To complete Step A, tell students about their resources (e.g., course text and practice problems in math lab) and time they have available to become their group’s expert (e.g., until the next class meeting). In Step B of the Jigsaw, have the three expert groups meet to plan how to teach their method to their home group members. Additionally, each expert group creates a practice test to evaluate the effectiveness of their teaching. Preview these practice tests, revising where necessary. In Step C, experts return to their home groups, teach their method, then administer and review the practice tests. The instructor answers questions about the three practice tests and later gives an instructor-created test that counts toward the students’ grades.
2. Strategy: Silent Socratic Dialogue (variation)
Application: Any math class
Educator: Beau Nunnally, Faculty, Mathematics, USAFA Prep School, CO
Implementation: Place students in groups of 2, 3, or 4. Put a set of problems on the board, one for each person in the group. Each student chooses a different problem to solve and they begin silently working on their problem. After a predetermined time (say, 5 minutes), give a signal and have students pass their problem to another student in the group. Upon receiving the new problem, students pick up where the other student left off and, without talking, continue solving the problem. If necessary, students can correct previous work. Keep giving the signal for students to pass their present problem to the next student and receive another problem. Students keep working on the problems in silence until all of the problems in their group have been solved or until time is up. At that point, answer questions that students have about the problems and discuss what they learned from the activity. Optional: Create a competition in which prizes are offered for the first team to complete all of its problems correctly. Afterwards, discuss whether or not this competition increased their anxiety; then segue into a discussion of how to manage test/math anxiety.
3. Strategy: Desired Outcomes, DAPPS & Language of Responsibility
Application: Introduction to College Math
Educator: Sue Sharkey, Faculty, Mathematics, Waukesha County Technical College, WI
Implementation: On the first day of class, have students identify their Desired Outcomes for the course using the DAPPS Rule (Dated, Achievable, Personal, Positive, Specific). Next lead a whole-class brainstorm of all the excuses they can think of for not achieving their desired outcomes in the class. (Encourage them to be creative in their invention of possible excuses.) Record the excuses. Now introduce students to the Language of Responsibility and ask them to translate each excuse into Creator language. Make a copy of the students’ desired outcomes, their excuses, and their translations, and distribute at the next class. Ask students to remain vigilant throughout the semester to identify self-sabotaging excuses, their own, their classmates’ or even the instructor’s. Encourage students to hold up two fingers in the “V” sign whenever they hear someone give an excuse.
4. Strategy: Language of Responsibility & Developing Interdependence
Application: Pre-Semester Workshop for Repeating Developmental Math Students
Educator: Linda Refsland, Associate Director, Basic Skills, William Paterson University, NJ
Implementation: Invite students who are repeating a math course to attend a small group workshop before classes begin. Where possible, organize workshops by section so students will meet and get to know other students who will be in their upcoming math class. Ask students to consider the questions “What happened that led you to be unsuccessful in your past math classes?” Have each student write a list of his/her “reasons”; then invite volunteers to share with the group. Next discuss Victim vs. Creator thinking and ask them to look over their list of “reasons” asking for each one, “Who was in control there?” Use that question to help students group their list into Victim and Creator statements. Guide the group though some examples of the two components of Creator language: 1) accepting responsibility and 2) creating a plan of action. Leverage this process with the statement, “These experiences and ways of thinking about them are likely to happen again, so we need an effective plan.” As a “Plan,” offer students alternatives to Victim choices that stress using available resources (counselor, peers, tutors, resource center, etc.). Encourage them to support one another throughout the upcoming semester to respond to their math course as Creators and not Victims.
5. Strategy: Inner Conversations
Application: Any mathematics class before handing back scores on first test or Tutoring Math
Educator: Nancy Fees, Faculty, Mathematics, Northwest College, WY
Implementation: Do this activity before handing back the results on the first math test of the semester. On slips of paper, write test scores – 60’s, 80’s and 100’s and put them in a bowl on folded-up pieces of paper. Ask each student to choose one piece of paper with a score on it and then to keep that score hidden. Each student in turn verbalizes an inner dialogue with him/herself about the test score they received without revealing the actual number. Other students guess the (imaginary) score that the student got on the test. Afterwards, students talk about what they could do, as Creators, to score well on the next test. When I introduced the strategy, it played so well! Abigail got a slip with a 60, and she started raging, “I should have studied harder! I’m going for a retake! I’ll make flash cards next time. I won’t watch any TV the night before. This is an unacceptable grade for me. I have to get through this school with straight A’s so I can go on with my next plans!” And poor old Mikey was immediately guessed for getting a slip with a score of 100 when he wistfully said, “I’ve never gotten a grade like this in math in my entire life!” Sad, but poignant. It was such a great exercise. It didn’t even take very long. While the best students shared their strategies for improving grades, the worst students for once got to rave on about a good or great grade. With a large enough class, it seems to me that chance should guarantee that at least one good student will choose a lousy grade, while one really poor student might get a great grade just once. When I then handed out their actual first test scores, everyone had some strategies for improvement that had just been verbalized by the best students in the class
6. Strategy: Group Quiz
Application: Mathematics & Study Skills/Life Skills
Educator: Alice Franey, Faculty, Mathematics, United States Air Force Academy Prep School, CO
Implementation: I handed out a quiz with 20 questions to my class. The students began the quiz thinking they had to do it all by themselves. After 7 minutes, I interrupted them and told them they could work together. They ended up working on it as a class, asking if anyone in the class knew the answer to each question. It was amazing that they seemed to find someone in the class who knew each answer. I ended up counting the quiz for extra credit. This led to a discussion about how each person has something to bring to the group and how much they are missing out on if they don’t take advantage of each person’s knowledge and talent.
7. Strategy: Graduation Game (Ring Toss)
Application: Adult Education, Math
Educator: Dennis Radice, Faculty, Adult Ed/Prep. Math, Central Florida Community College, FL
Implementation: Play the Graduation Game, and, afterwards, discuss results and insights. Next, present students with a contract that promises a passing grade to every student who earns 30 points in the course. Explain that to earn points, students must choose a performance level and successfully complete all of the actions in that level. The performance levels are as follows:
3-Foot Level: Successfully complete all class assignments (7.5 points), successfully complete all homework assignments (7.5 points), pass all quizzes (7.5 points) and pass the final exam (7.5 points). Second chances allowed for class assignments, homework assignments and quizzes.
10-Foot Level: Successfully complete all homework assignments (10 points), pass all quizzes (10 points) and pass the final exam (10 points). Second chances allowed for homework assignments and quizzes.
15-Foot Level: Pass all quizzes (15 points) and pass the final exam (15 points). Second chances allowed for quizzes.
30-Foot Level: Pass the final exam (30 points).
Finally, discuss the pros and cons of each performance level, relating it to the experience of playing the graduation game; have students complete and sign contracts individually. [Editor’s note: The choice offered to students in this activity appeals to students who are motivated by autonomy.]
8. Strategy: 32-Day Commitment
Application: Mathematics
Educator: Allison Rector, Faculty, Mathematics, Jackson Community College, MI
Implementation: Ask student to make a 32-Day Commitment to work 5 or more homework problems every day outside of class. Do not grade these homework problems; rather give a daily quiz that pulls problems directly from the homework. Periodically, ask students (no pressure) to report whether or not they are maintaining their commitment. Show graphs of quiz grade showing a comparison of students who are keeping their commitment and those who are not (all anonymously, of course).
9. Strategy: Letter to Myself
Application: Developmental Mathematics
Educator: Jody Rooney, Faculty, Mathematics, Jackson Community College, MI
Implementation: On the first day of the class, have students write a letter to themselves in which they set a goal for the course and list the actions they will take to achieve that goal. Also have them say why achieving their goal is important to them. Mail the letter to students at mid-term (or mail individual letters earlier if a particular student is struggling).
10. Strategy: Behaviors of Successful Math Students & Think/Pair/Square/Share
Application: Developmental Mathematics
Educator: Michael Lanstrum, Faculty, Mathematics, Cuyahoga Community College, OH
Implementation: After covering the syllabus in the first class, have students create a list of the Behaviors of Successful Math Students. Begin by having students brainstorm by themselves. Then have them work in pairs. Then in fours. And finally have the whole class contribute to a list. Refer to this list in class throughout the semester. Also, use the list to help struggling students decide on what they can do to improve their results in the course.
11. Strategy:
Application: Mathematics
Educator: Kristin LaGuardia, Faculty, Mathematics, Cuyahoga Community College, OH
Implementation: Use the Tracking Form to illustrate to students the relationship between consistent effort and success in a math course, as well as to encourage them to keep track of their own academic progress. To do so, modify the Tracking Form so there is a place for students to record their test and quiz scores along side of their academic efforts such as doing homework, studying in peer groups, attending math lab, and seeking assistance from the instructor. Recording the test scores and academic efforts together helps students to observe the effect that their efforts have on improving their comprehension of math and their grade in the course. In short, the more they do, the better their academic outcomes.
12. Strategy: The Jigsaw and Inner Conversations
Application: Developmental Mathematics
Educator: Curtis Kaschube, Faculty, Mathematics, Cuyahoga Community College, OH
Implementation: In Step A, form home groups of four and have students choose to become the group’s expert on one of the following math biases:
- Math is boring
- Popular people don’t like math
- People who like math are nerds, and
- Math can only be mastered by geniuses
In Step B, have expert groups watch a film clip appropriate to their chosen cultural bias against math. Choose from the following: Mean Girls (2004) in which Lindsey Lohan’s character is told, “You can’t join the math team…that’s social suicide.” Hook (1999) in which Peter Pan and the leader of the Lost Boys trade insults, with Pan, among many degusting names, being called a “math tutor.” October Sky (1999) in which the math guy is depicted as a total geek. It’s My Turn (1980) and 21 (2008) in which high level math discussions are depicted that sail way over most people’s heads dramatizing that that math is only for the gifted. Good Will Hunting (1997) depicts many negative stereotypes of mathematicians, and A Beautiful Mind (2001) shows a mathematician who struggles with mental illness. Lastly, no discussion of math biases is complete without playing the Jimmy Buffet classic “Math Sucks.” Perhaps play this song before the clips are viewed. After the groups view their film clip, have them discuss how their clip depicts a math bias and how that depiction relates to their own inner conversations about math. In Step C, experts return to their Home Groups and share what they have learned about math biases and themselves from the movie clips. Afterwards, in a whole class discussion, ask students to brainstorm how these cultural biases, having become part of their inner conversation, influence their attitudes and behaviors related to math. Finally, brainstorm how such cultural biases can be overcome.
13. Strategy: Intrinsic Motivation–Competence
Application: Mathematics
Educator: Mike Adams, Faculty, Mathematics, Modesto Junior College, CA
Implementation: Distribute a handout with problems already worked out. Tell students that almost every problem on the sheet has at least one mistake. The students’ goal is to act as the instructor and mark each mistake. The students have safety in this activity because the mistakes have already been made by someone else! By taking on the role of the instructor, students get to identify and learn how to avoid mistakes in solving problems, thus develop a feeling of competence in their math skills.
14. Strategy: After Math (Case Study)
Application: Mathematics
Educator: Steven Kuehl, Faculty, Mathematics, Bay College, MI
Implementation: After the first exam but before returning it to students, present the “After Math” case study. Split the class into groups that are picked randomly to get a wide range of students in each group. Have each group concentrate on one character from the case study and rate that character on each of the four emotional intelligence components from 1-10, finally getting an average for their character. Then, as a class, order the characters from 1-5 (least to most emotionally intelligent) and discuss why. In particular, have students identify wiser choices the characters in the case study could have made. The goal of the ratings and discussion is to have student understand better how to effectively handle the experience of studying for and getting back their first exam, helping them better approach future exams in your course, as well as future courses.
15. Strategy: Silent Socratic Dialogue (variation)
Application: College Algebra
Educator: Donato Fortin, Faculty, Mathematics, Johnson and Wales University, NC
Implementation: The goal here is to help students understand the different steps that can be taken to solve a (basic linear) algebraic equation. Pair students (A & B) and provide each pair with two sheets of paper, each containing a different equation that can be solved with a variety of steps. Each student writes the first step for solving the equation and then they exchange papers. As they read their partner’s work, students either accept or correct. Rules: 1) If the step is correct, it must be accepted, even if the “evaluator” student would have done it differently. 2) Accepting or correcting must be accompanied with a comment affirming the method employed (e.g., It’s good that you added 4 to both sides) or correcting the step (e.g., You needed to add 4 to both sides. The correct result is….) When they have accepted/corrected their partner’s work, they go on to take the next step for solving the problem and then exchange papers. The process of exchanging problems continues until both problems are solved. When students are first learning to solve equations, you may want to offer them the opportunity to refer to their text or notes for help.
16. Strategy: Eagles and Hawks
Application: Any Math Course
Educator: Wyatt Christian-Carpenter, Faculty Mathematics, National Park Community College, AR
Implementation: Pair students as Eagles/Hawks. Give a worksheet with five problems to the Eagles. Have each pair work on solving the first of the five problems, giving them enough time to complete the problem before ringing the chime. When the chime rings, partners switch with the Eagles holding on to the worksheet. With the new pairing, Eagles and Hawks complete the second problem. Eagles and Hawks change partners five times, giving each person five different people to work with, each time with a new problem to solve. Afterwards, go over the correct answers and discuss what the students learned from working with others about how to solve the kind of problems given. This activity could be set up so that Eagles get bonus points for each problem solved correctly and, in the next class, do an activity in which the Hawks can earn bonus points.
17. Strategy: Disputing Your Inner Critic
Application: Developmental Math
Educator: Jeff Shea, Faculty, Mathematics, Cayuga Community College, NY
Implementation: To address math anxiety and the negative self-talk students often have about math, do the following activity the first week of class. It also serves to help create a sense of community and support in the class.
- Divide class into an even number of groups, with no more than five people in a group.
- Each group lists 5 Inner Critic statements about their math ability.
- Groups trade their papers with another group.
- Groups write disputations of each the Inner Critic statements.
- Lists are returned to the original group for discussion.
- Hold a class discussion on best strategies for disputing one’s inner math critic.
18. Strategy: Silent Socratic Dialogue (adaptation)
Application: Mathematics
Educator: Jennifer Seaman, Mathematics Faculty, Housatonic Community College, CT
Implementation: Early in the semester, have students write a paragraph in response to the prompt: “What is your math story?” Direct them to describe positive/negative feelings about math and/or former math teachers/professors. Have students submit their writing to the instructor; the instructor writes a question in response to the essay and returns it to the student. This dialogue continues throughout the semester and is included in the student’s math portfolio at the end of the semester.
19. Strategy: Eagles and Hawks
Application: Any Math Course
Educator: Maritza Jimenez-Zeljak, Faculty Mathematics, Los Angeles Harbor College, CA
Implementation: Assign Eagles a math problem and Hawks a different but similar problem. Have students work individually to solve their assigned problem. Next pair Eagles with other Eagles and Hawks with other Hawks to go over their problem (which is the same): technique used, steps used, reasons for steps and common answers. Help out where needed. The goal is that Eagles become experts on their problem and Hawks become experts on their problem. Now pair Eagles with Hawks to compare the two problems. They each write the similarities and differences on a piece of paper with a final conclusion about the techniques that can be used on their type of problem. Do the pairing a few more times, encouraging students to add to their conclusions about the techniques that can be used on their type of problem. Wrap up with a large group discussion about the conclusions they drew.
20. Strategy: Next Actions List
Application: Any Math Course or Any Course
Educator: David Hyatt, Faculty, Mathematics, Washtenaw Community College, WI
Implementation: Use the Next Actions List to alleviate the concern students have at the beginning of the semester about the amount of work they need to do for the entire class. Instead of giving them a schedule at the beginning of the semester that shows all of the material that will be covered for the entire course, give them a Next Actions List that contains only the material to be covered in the first month. Repeat this for each month. This way the students know what to expect for each month of class but will not be overwhelmed with the full content of the course.
21. Strategy: Eagles and Hawks
Application: Mathematics
Educator: Nichole Klemmer, Faculty, Mathematics, Washtenaw CC, MI
Implementation: The goal is to help students use their peers to get their homework questions answered. Students come to class having completed homework assignments from the previous class. Students sit in pairs facing each other, and identify as either an eagle or hawk. For three minutes, they discuss one homework question on which they need help. The teacher announces “Eagles Fly” or “Hawks Fly” and students move to a new partner. They repeat the process either with a new problem or the same problem as needed.
22. Strategy: Thirty-two Day Commitment
Application: Any Math Course or Any Course
Educator: Jason Davis, Faculty, Mathematics, Washtenaw CC, MI
Implementation: I often have students come to me several weeks in to the semester who are failing the course due to unwise choices such as poor attendance, not completing homework regularly, or poor preparation for tests. When this happens, I create a 32-Day Commitment contract identifying the desired behaviors as well as the possible accommodations, such as forgiving some absences, allowing extra time to complete missed assignments, do test corrections, etc. We both sign the contract to complete the 32-Day Commitment. If at the end of the contract time the student has met the requirements, I provide the accommodations agreed upon in the contract.
23. Strategy: Jigsaw
Application: Mathematics
Educator: Bruce David, Adj. Faculty, Mathematics, Folsom Lake College, CA
Implementation: There are three forms of linear equation – the slope-intercept, point-slope, and standard forms. Each has a different technique to graph. In a Jigsaw setting, have the home groups consist of three members each. Each member becomes an expert on graphing one of the three forms. After meeting with expert groups, each expert teaches his/her home group the mastered technique.
24. Strategy: Jigsaw
Application: Freshman, College Algebra, First Class Day
Educator: Michelle Askew, Instructor III Mathematics, Lamar State College Port Arthur
Implementation: Learning Objective – to enable students to read and understand the course syllabus. After distributing the syllabus, divide students into four groups. Group One will explore the important dates of events identified. Group Two will explore the attendance policy. Group Three will explore the numeric values of homework, quizzes and tests. Group Four will explore the policy on My Lab Requirements. Finally, one person from each group will report to the class the findings of their group with an opportunity for questions.
