Category Archives: cooperative learning

Final Exam Weekend Cram Session

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I offer a lot of math assistance for my students. I
basically make myself available before school, during lunch, during 7th
period and after school and many of my students benefit from this support. Even
with all this, as first semester finals approached, I felt the need for more. In
addition to the students who were desperately trying to improve their
performance in order to get a passing grade (C- or higher) for the semester, I
also had students who really wanted to perform well on their final exam. In the
spring, I had offered two AP Calculus “Boot Camp” sessions for my students on the
weekend before their AP exam. Because this had been successful, I decided to
offer some weekend study sessions for all of my math students on the weekend
before Final Exams. Just like last year I started out with a survey to gauge
interest and to determine what times would meet the needs of the most students.
The response was very positive and I decided to offer one 2-hour session on
Saturday and one 3-hour session on Sunday. Because there would be students attending from all 3 of the different courses that I teach, I could do no formal instruction. Instead, what came to pass was a giant study session where students were working collaboratively using the variety of resources that I had provided for them to prepare for their final exams. There was much use of the white boards and a lot of small group
discussion. While I periodically had to reteach concepts to some of the
students, I actually spent more time
Saturday end-of-day group selfie

serving as a sounding board for their
ideas and asking leading questions so they could make their own conclusions. Eleven
girls signed in on Saturday and fifteen on Sunday although more students were
actually there each day. There was really good energy in the room and the girls
seemed relaxed and productive. Many, many students thanked me before leaving
for Christmas break for giving them this extra support. I am glad that they
felt it was time well spent.

Sunday end-of-day group selfie

Inverse Trigonometric Functions War

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The ability to evaluate inverse trigonometric functions correctly is a fundamental and critical skill that a student needs for Calculus. For whatever reason, many Precalculus students struggle to master this skill and many who do master it do not retain it by the time they take Calculus. I decided to step outside the box and have my students play a game that would force them to make more sense of the range of answers that can be found when evaluating inverse trig functions.
I had read on some math blogs about teachers using the card game War to help students evaluate logarithmic functions and so I thought I could make this work for my situation. War is a card game in which each player gets half of the deck of cards. For each turn, the players each flip a card. The player with the higher valued card wins both cards. The player with the most cards at the end wins the game. I adapted the game with homemade cards that had all the inverse trigonometric functions that use angles found on the unit circle. I prepared a visual aid that diagramed the allowed range of answers for the six functions. I divided the students into groups of three: two players and a referee. I explained the rules and then let them play.

It was slow at first while they got used to the rules and got comfortable with evaluating the functions. I circulated the room, checking in with students and responding to questions. It was very apparent to me just how many students really didn’t understand what they were doing. Group by group, I responded to their questions. As soon as one in the group understood, I would leave that person to explain to the others. Slowly but surely, they started to “get” it.

While I doubt that anyone would claim that this was a particularly fun game, I had many students tell me on their way out how much this helped them gain confidence with these functions. While I was circulating around the room I also witnessed many “aha” moments where students for the first time seemed to grasp the purpose of evaluating these functions. I’m not sure how I will be able to assess how well this extra day and extra activity really served to improve their understanding and retention of the subject, but subjectively I conclude that this was definitely time well spent.