Predicting Exam Questions

This is the first of a 5-part series on activities that could be used for review before an exam.




Review Activities To Make Real Students


As a high school student I worked through problems in the textbook to study for my math exams. As a teacher, however, I'm finding that my students don't seem to realize what the test problems will look like even though I tell them exactly what topics will be covered. Here is my solution.

• I put my students in groups of 4 and gave them the task of creating 3 problems that could be on our first exam. Each problem had to have 2 parts and each had to match one of the 3 concepts that were being tested.

• I only allowed the students to use their notes and their homework assignments in order to give them a feel for how notes, homework, and exams were all related. They couldn't use the actual problems from the assignments and examples, but they could emulate them.

• The groups used poster paper to put their problems up around the classroom.

• After we assessed that everything looked okay, I told the students that they now had a good selection of practice questions and instructed them to write them down. We did this in sort of a walk about fashion with each group starting at a different poster and working its way around the room.

• We ran out of time, but my next step was to have each group post the answers to their problems so their classmates would be able to check their work.

This little activity worked out a little better than I expected. Many of my students wanted to just start making up problems that were like those on the homework without regard to whether or not they covered the topics that would be on the test. I discovered that many of my students didn't relate inductive reasoning to the first lesson that we did. My goal was to help my students take the mystery out of what they'd see on the test. I believe that students who learn this test taking skill will have less anxiety and perform better. I guess I'll get to check this little conjecture when I grade their exams later today.

Review Activities to Make Real Students

Every teacher has her favorite review game. I like Jeopardy even though it's a lot of work to put together. My pal Mike W loves Trash Can Basketball. As a matter of fact, the Algebra teachers in our department recently decided to pool their resources and each create review games for a couple of chapters. Games are fun. However, if the students aren't solid with the material then the game goes stale.

This is what compelled me to think about what I could do to help my students get the most out of review. As I did, I realized something. I've been doing this teaching thing a little backwards. Instead of trying to put geometry into the student I need to put the student into geometry. That is, I need to create activities that will teach my young men and women to be better students as they review for exams.

Thus, a series is born. Beginning Monday I will write a series of posts describing the ideas that I came up with. The post titles are listed below. In the meantime, I would love to hear about any ideas that you may have (so I can steal them, of course). Enjoy!

• Monday - Problem Predictions
• Tuesday - Expert Study Teams
• Wednesday - Problem Trees: A Graphic Organizer
• Thursday - Round Tables
• Friday - Ideas From Other Really Cool Professionals

Are You Smarter Than Your SmartBoard?

Last spring I felt a little like Tom Cruise in Minority Report. After 3 years of hearing about them the SmartBoards had finally arrived. This technology, though not new to our students, was novel to our staff. After two short, one-hour training sessions we were ready to go.

Then summer happened and with it, summer school. What was once a useful tool is now a kind of burden. My computer monitor doesn't work correctly and the SmartBoard is constantly wiggling itself out of alignment. I've spent hours these past few weeks creating slides for my lectures. Lectures ... hmmm.

The beginning of the school year is always non-traditional for me. I need to buy some time as our counseling staff switches students from this class to that and I don't like to do a lot of lecturing. As I await the start of Survivor Geometry, I'm getting a chance to play around with the cool interactive ruler and protractor. My initial attempt at using the compass was comical. However, after a short (very short) tutorial, I think I've got it down. I could use some lifts, however, to help me reach the toolbar at the top of the board. You see, I keep forgetting that I can move it to the bottom.

I feel like the ... uh ... SmartBoard is making me, well, less smart. As I talk over my shoulder, I imagine that my students hear only what sounds like Charlie Brown's teacher. I wish the big board came with a clipboard that transmitted images to it. That way I could look into all those bright cheery faces as I bore them to death. I'm not worried though. With a little research and creativity this could turn into quite an adventure. For now, I'll just keep playing around with my new teacher-toy.

Survivor Geometry

Zzzz ... Zzzz ... What's going on? The nerve of some people. I can't believe that any student would dare to fall asleep during such an exhilerating lecture!

Zzzz ... Zzzz ... Hold on! It's me that's asleep!

Last spring I grew tired of the mundane day to day business of trying to teach Geometry to a bunch of rowdy teenagers who were more interested in discussing pop culture than in getting an education. I decided that the problem wasn't their boredom, but mine. I went home, laid on my bed and stared at the ceiling. Then it hit me. Survivor Geometry!

I got the idea from Karen Lyn Davis, the creator of CoolMath.com. I'd used her Survivor Algebra with my Algebra 1 students once before, but it didn't work as well as I thought it would so I tweeked some things to get the results that I wanted.

The students were put into tribes and could earn extra credit by getting the highest tribe average on an exam (called a challenge instead). Since my Algebra students didn't work together to help each other learn the material, I added a daily competitive element. At the beginning of the lesson I asked one member of each tribe a question from the reading assignment. The tribe earned 2 points if the student answered the question correctly and 1 point if the answer was incorrect, but the student gave an honest answer. The latter was to help eliminate the fear of giving a wrong answer.

After what I called the 8 question challenge, the students took the 2 problem challenge. I gave points to the first 3 tribes to get the correct answer to both problems. The 1st winner received 4 points, the 2nd winner received 2 points and the 3rd winner received 1 point. All of this occurred before the lecture in order to stick to the concept of having the students struggle a little with the material first.

I also rewarded each tribe that turned in 100% of the week's homework assignments with 5 points. The tribe with the most points at the end of the week earned extra credit.

This year, however, I will give the 2 problem challenge after the lecture and group work (called tribe time) in order to motivate the students to work even harder to learn the material. I will also have the tribes research a math concept at the beginning of the year and use the concept to choose their own tribe names. I really like Karen's tribe names, but last year my student's couldn't remember what their names were.

Last year's version of Survivor Geometry surpassed my expectations by far. My worst class was suddenly filled with engaged students. The competitions made learning the math more meaningful because there was immediate feedback and a little reward. In addition, the 2 problem challenge gave me an opportunity to quickly assess understanding. I will need to mix things up from time to time though. I don't want anymore snoring events to occur in my classroom.

Lessons from CPM (and other thoughts on promoting deeper understanding)

Just in case you're thinking that I'm stuck in the middle of a text message, let me tell you that CPM stands for College Prep Math. OK, stop laughing. You may think I made that up, but CPM is a math program developed through UC Davis in which a bunch of math teachers and 2 UCD professors got together and wrote several courses that require students do problems and participate in activities in order to develop their knowledge of mathematics.

I've taught Algebra, Geometry, and Algebra 2 using these materials. In fact, I'm one of the original authors of Course 3. I am a fan. However, years ago I had to concede to the fact that only one other member of my department would use the text. This created a problem for any student that the counselors moved into or out of our classes so we both agreed to teach the mundane textbook version of our courses. I have since tried to integrate the CPM problems into my curriculum, but that proved too daunting a task. This year I decided to take advantage of some of the CPM strategies instead. Here are some of my ideas for the upcoming year.

Algebra Review Lessons That Students Can Do On Their Own
The CPM text has Algebra review problems scattered throughout the course. There are also focused lessons on some of the more important concepts that usually appear at the end of traditional Algebra books. I thought I might give my students a quick assessment at the start of each chapter so they would know what they needed to work on. Then I could either put problem sets up on our school website or refer them to another site. (Suggestions anyone?)

Spiral Homework Problems
CPM homework assignments contain a fair range of problem types. New ideas are covered as well as concepts studied from previous chapters. I will have to create all of my homework assignments for each chapter in advance so that I can be sure to include problems that vary in both topic and level of difficulty.

Use Big Problems to Focus Each Chapter
Each CPM chapter begins with the introduction of a problem. The students solve this "big problem" at the end of the chapter. I would like to do the same, but I would use more open-ended problems.

Concept Exams Revisited
I used to give my students this long list of concepts at the beginning of each semester. Each concept was tested on 3 exams in a row. Students had a chance to improve their scores by doing better each time. I went away from this because it was so time consuming. After reading dy/dan and f(t), I decided to return to this strategy with the following changes.

1. I'll use a much shorter list of concepts.
2. Each concept will appear only twice. This should make the exams much shorter and easier to grade.
3. Students will have opportunities outside of class to remediate.
4. I will give a midterm exam to reinforce the idea of true test taking. This should balance my inner conflict between do-overs and getting the students ready for college.

Here are some other ideas that are not generated from the CPM materials.

Pre-reading Activities at the End of Class
I'm currently attending the Reading Institute for Academic Preparation through Sacramento State University. As a result, I've come to realize the importance of emphasizing reading strategies as they apply to math textbooks. Since I will require my students to prepare for each class session by reading their textbook, I want to end each class with a short activity designed to build each student's prior knowledge.

Teach Students to Annotate Text
My students are not allowed to write in their textbooks so I will teach them to annotate their texts using sticky notes. I'm contemplating letting them use these notes on their exams. They would then be required to turn the notes in with their exam so I can hold them accountable for the process. (Let me know what you think about this one.)

In Conclusion
I want two things to occur. I want to see greater student success in terms of exam scores (That's admin for mastery). I also want my students to have a deeper understanding of Geometric concepts as a result of my training them to self-assess, self-remediate, and utilize college level study techniques. The next few weeks may be long and exhausting, but the end results should be well worth it.