A (brief) farewell to the Memory Enhnacer

RIP Memory Enhancer - February 14, 2015

I laid to rest recently an assessment I have been using in some form or another throughout my teaching career. Memory Enhancers I called them because a desired outcome was that students enhanced their memory of mathematical ideas of days past. They were known as Review Sheets once upon a time and were derivations of the Friday Sheets that were used by all teachers at my first school. The department chair at that school developed Friday Sheets as part of his masters degree and decreed that all teachers under his purview would use them.

I liked the Friday Sheets primarily as an alternative to tests. Some teachers base grades solely on tests and quizzes. But what are quizzes other than mini-tests? Friday Sheets were take-home assignments that reviewed previously learned material and students could work on them over a week. Handed out on Friday and due the following Friday. My department chair had designed them to be sequential in his courses, so they built off one another and were another way for students to improve their understanding.

I did not like having one every week. It was a lot of grading and it was on top of the work the students were already doing. Students usually waited until Thursday nights to do them and cheating happened. When I changed schools, I renamed them Review Sheets and made them less frequent. I started using Review Sheets also as a place to ask longer problems, problems that were not really fair in a timed test setting. They were also a place for me to experiment with different types of problems and ones where students could work on graphing skills.

When I changed schools next, Review Sheets were reborn as Memory Enhancers. I started to use them as another way to present new ideas. Students were asked to deal with ideas that had not been discussed in class. I wrote open-ended problems where answers would not all be the same.

I carried the Memory Enhancer with me to my current school and started focusing anew on them. I tried to make them sequential so that students would learn one idea in Memory Enhancer #1 and that idea would be further developed in subsequent Enhancers. I even started having students do them in pairs. I was able to write some problems I really liked and students had usually 10 days or so to complete them. They were encouraged to see me for help and I highlighted time when I was available.

Some students have loved these assignments. Some have recognized that here were assessments where test anxiety need not be a factor. They could work on them over multiple nights. They could spend 20 minutes on a problem, figure out that they had traveled down the wrong path and then go back and start over and not worry about running out of time. They could use their books, their notes, and old homework.

But, here and there, students would succumb to temptation and cheat. The inevitable awkward and uncomfortable confrontation between teacher and student would ensue and often lying was used a means to cover up plagiarism. Due to the nature of the assignment, administrators were unwilling to respond too severely; they believed we could not prove the cheating if students did not admit to it. Me? We are not a court of law. We are a school. We are here to educate. Part of that education in my mind is teaching a student to be honorable. I tried different tactics, including having them write an honor pledge (based on the Davidson College Honor Code).

This year was rough. With each Memory Enhancer, I found myself doubting the originality of the work of multiple students. By the time I got to #5, I was questioning more than 10% of the papers turned in. This is after having confronted multiple students. Some of the questioned papers were repeat offenders.

The frustration this was causing me was too much. Enough, I said, and I made the decision to not assign them again this semester. I was sad over this decision because I knew there were students who saw them as a saving grace in contrast to the big bad tests. I do think my students are missing out on their education by not having these to do. Most students probably don't appreciate this. Most are probably happy about this decision.

I am planning on re-introducing them in the fall. This was by far the worst of the copying I have encountered, so I am expecting it is an extreme example and not a sign of things to come. I will do things somewhat differently and maybe that will help. I want to help students learn about honor and trust and ethics and I think these assignments can be a means of doing that. But I won't wait until February next time if they start frustrating me. It's just not worth my health.

To grade or not to grade

Is it fair to not tell students they are being graded?

Today, my students worked on an in-class group activity. It was an ungraded activity. They were shown a video of a water tank draining out of a spout and asked to figure out how long it would take the tank to empty. I withheld nearly all of the necessary facts, figures, and formulas. They were required to ask me questions. If I knew the answer to their question, I would answer it. For some of the answers, I gave them cards I printed ahead of time with information like the height of the tank or the formula for volume. Some of the information was in the form of a video of the spout filling a 2-cup measure. Ultimately, the calculations involved were rather ordinary and simple: multiplication and division. The activity was designed to help them develop their problem solving strategies and have them consider what information is important and necessary to solve the problem.

Some groups predictably got straight to work and proceeded quickly through the problem and found an answer in relatively short order. Other groups, just as predictably, took their sweet time and spent many a minute idly chatting and not worrying much about solving the problem. Experience told me that some groups just need a bit longer to warm up and realize that, in fact, I am not going to give them the information they need unless they actually do something. Others lack confidence so they need a bit more prodding. But while some students sit inert because they lack confidence or are unsure what to do, other students do nothing because they are seemingly apathetic.

It got me thinking that this experience is one that really ought to be formally evaluated. This was real math. A timed individual test is not a place typically for creative thought and does not allow enough time usually for one to start down a path, come to a dead end, and go back and start anew. But, the students today had ample time to play with the numbers, reflect on answers, think about what information they needed and the questions they would have to ask to get that information. Groups that were most effective had the best communication and students asked each other for help. The most dysfunctional groups sat back and hoped that one member would just do all the work for them.

Perhaps, I thought, I should make this a graded exercise after all. Would that be so unfair? Why not create learning opportunities without deciding ahead of time whether or not to make it a graded exercise? Why not wait and see if the exercise is a good evaluation tool before committing to making it graded? Sort of like a reverse pop-quiz. Surprise! I am going to grade what you just did.

In my eyes, today's activity would have provided a very authentic evaluation of a student's commitment to learning and of their problem-solving skills. But, I did not feel it fair to do this as I had never told the students ahead of time that this might happen. I think I could have justified it, but I did not want to deal with the predictable complaints from the students.

But, as I write, this sounds like something I may try going forward.

Would students feel that they were constantly being judged? Would that be a bad thing?

The Portfolio - Incarnation 2014

In art courses, students often develop a portfolio over the course of a semester. Students place all of their work in the portfolio, or maybe just the best of their work. The idea is to have a collection of art that, when considered together, is meant to represent a student's output for the semester.

I really like this idea as another means of evaluating a student. I like that the students choose what work goes into the portfolio and that they can make decisions such as layout and formatting and the like. I think it might encourage students to be proud of their accomplishments. Also, by it being a collection of work throughout a term, students get a chance to show off their development.

In my vision of the typical American high school math class, students don't get to choose what gets evaluated by their teacher, nor do they have the opportunity to design their own assessments. Rather, all students take the same assessments (tests and quizzes largely) that were created by their teacher (or by some publishing company) and a student is judged by their work on these. A student's semester grade is often determined based on how she or he does on these assessments.

I am establishing a new course this year at my school: Math 2 Standard. This is an integrated course that is much more similar to our honors math courses. I believe the integrated aspect alone is reason enough for the change as I believe (and I think research supports this notion) that an integrated math course produces better learning outcomes than the traditional American math progression of Pre-Algebra, Algebra 1, Geometry, Algebra 2, Trigonometry, Pre-Calculus.

But, by having a new course to design, I made the decisions to do some experimentation, so I dug up the Portfolio. I had attempted to have my math students create a portfolio in years past, most recently at my last school. But, that was just them collecting all of their work and storing it in a three-ring binder that was kept in my classroom. I never ended up assigning a grade to that portfolio, nor did I really have the students do anything with it.

In the fall semester of this year, however, I gave much more detailed directions. Students were to find a certain number of problems (not entire assignments) that they had already submitted for evaluation, and were to revise their solutions in an attempt to improve. I have long championed mistakes as being useful, that mistakes are necessary in the learning process. I suggested that by reflecting on mistakes, students can improve their understanding and thus establish true learning. So, the Portfolio was an attempt for me to put my money where my mouth had long been. I would evaluated a collection of work, work chosen by the students, that they offered to me as evidence of their improvement. As a part of the Portfolio, students were to write a page or so about their process: how did they improve on their work?

For the most part, I feel this project was very useful and productive. Looking over some Portfolios, it looked like some students truly improved a lot, that they took the project seriously. Some students, however, appeared to have just copied the work of others and taken the path of least effort. But, all in all, I was glad I did it and I do think it was a valuable learning experience. It was definitely better than a final exam.

Unfortunately, it produced an immense amount of work for me to grade. It was as if 58 students took 58 different final exams and wrote 58 reflection essays, all of which I evaluated during my holiday, ahem, break. By far, this assignment took me longer than any other to correct. So, I won't be doing it again in exactly the same format. Instead, I will evolve it to make it more practical for me.

This semester, there will again be a Portfolio. This time, I will limit it to 2 or 3 large-ish problems and students will write a reflection on each problem and how they went about revising it and how they improved their learning from it. I really like the idea of students choosing for themselves work that they want me to evaluate. I really like the idea of them going back and re-doing problems, trying to better understand the ideas and the processes and what it all means. So, if I can keep up with my blog, I will write again about the Portfolio in 5 months' time. I wonder if I will do it again next school year...