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...

Weighting grades

The following is a true story.

I am an advisor at my school. There are five students who make up my advisee group. One of my primary functions as Advisor is to monitor their academic progress (aka grades) and communicate to their parents how the advisees are doing. This means I send emails every two weeks to my advisee parents in which I write their current grades and my spin on those grades. You know, progress reports. Mostly, the parents care about the grades.

One of my advisees, let's call her Chris, is in AP Chemistry. Her parents have emailed me all of two times in the year and a half that I have been her advisor. So, you can see they are not the most hands-on parents. Thus, when Chris came to me with a question about her AP Chem grade, I figured it was from her, and not from her parents. Before Christmas break, Chris had a B+ in AP Chem. Since that report, Chris had earned an A for Participation and an A on the alternative assessment (a substitute for a final exams which were cancelled due to school being closed early... but that's a different story). So, essentially, she had a B+ in the class, and then two more grades were added to her AP Chem gradebook that were both higher. Her final grade for the semester? B.

So, Chris emailed me and asked me about this. I had not yet had a chance to notice the change in grades. I was happy she brought it to my attention. I looked into it and discovered that her grade had gone down despite her last grades being better. The reason? When the teacher had initially set up his computer gradebook, she had not set it up properly, or it had been changed on her, and the weighting was off. So, she had readjusted her weighting and that had changed grades a lot and resulted in Chris's grade dropping.

Do you know what a weighted average is? Google it. Teachers use it all the time. A grade may be on a 100-point scale, but those points are not distributed equally among the different kinds of assessments. Teachers usually calculate averages for each category, and then weight them according to their significance. For example, tests could be worth 60%, quizzes worth 25%, and homework worth 15%.

Anyway, the AP Chem teacher, let's call her Amy, weighted her assignments this way: tests 25%, quizzes 25%, labs 25%, homework 20%, and participation 5%. On the surface, there is nothing terrible with this distribution of weights. It is perhaps odd that tests and quizzes have the same weight, but I can imagine how this might be appropriate. Dig a little deeper, and an interesting fact emerges: there were only two quizzes while there were four tests. This means that each quiz was worth 12.5% (25% divided among two quizzes) of the course grade while each test was worth 6.25% (25% divided among four tests). Or, to put it another way, the teacher's weighting meant that a quiz was worth twice as much as a test in the course grade.

Now, I did not know how Amy viewed tests and quizzes for her AP Chem class, so I asked Chris about what her AP Chem teacher had said regarding the importance of quizzes. Chris remembered that her teacher had said quizzes were worth less than tests. Unfortunately, Amy's weighting did not make that a reality in the calculation of the course average.

I sat down with Chris and we looked at her averages and calculated her course average using a variety of weight distributions. In the end, it did not change Chris's letter grade. It certainly changed her numeric average, but it did not take her from a B to a B+.

However, it would be very possible that a change in the weighting could change the letter grade of a student whose numeric course average was on the cusp of the next letter grade.

For example, suppose Cory had a 92 test average, an 84 quiz average, a 90 lab average, a 90 homework average, and a 93 for participation. Using Amy's weights, Cory's numeric course average would be 89.2, which would be a B+. If the weighting were changed so that tests were 40% and quizzes were 10%, then Cory's average rises more than a full point to 90.4, an A-.

For those of you who know, the difference between a B+ and an A- to the University of California is huge. A B+ gets a score of three while an A- gets a score of four in Grade Point Average (GPA) calculations. Thus, this teacher's seemingly arbitrary designation of grade weights could have a very real consequence to a student in the college admissions process.

Do you still believe in grades?

Striving for the "acceptable" grade (Part 2)

When I last left you, Jolene had been wanting to switch math courses because she wanted to be able to get an A in math and spend less time achieving that grade. Our plan was for Jolene to take the next test and see how it went and she would decide based on that result.

Jolene earned an A- on the Unit 2 Test. She decided to stay in the honors course.

I know, this is kind of a quick ending to a long story, but it was really as easy as that. Why? Because there was only one important thing - her grade. There was no discussion as to how long she spent preparing for the test.

A few weeks later, she remains in the class and her grade is at an A-. But there's been no discussion involving me about whether her other classes are suffering or if she has, in fact, reduced the amount of time she devotes to her math homework.

Today, we had our Unit 3 Test. I have no idea how Jolene did and I probably won't look at the tests until Thanksgiving break. (Yes, I do school work during my "break". In fact, most teachers I know use their breaks to do work. Often a significant amount of work.) At the end of today's test, Jolene commented that the test was difficult. But, she didn't leave my room crying.

No, today it was Brenda who left crying. Brenda, my superstar. Brenda, like Jolene, is a new student at my school. She considered trying to move on to the third-year honors course. In the end, she opted to stay in my second-year honors course, and this has proven to be a pretty good fit for her. Her grades have often been near or at the very top of my class.  But, she has been learning a lot and the class has not been as simple as she had thought it might.

Today, Brenda melted down at the end of the test. Time was up and just as Brenda was about to hand her test to me, she noticed that there was a page 6. She looked at me and asked for time to complete page 6. I told her no, that I had not been able to give students in the other period extra time, so it would not be fair to give her additional time. Moreover, the last page had one problem that was worth 2 of a possible 34 marks. There is absolutely no way that 2 marks will have any impact on her semester grade. Brenda has already demonstrated to me remarkable mathematical skills. She readily recognizes pattern and is proficient at explaining how the ideas connect.  Despite all of this, Brenda broke down crying over not having gotten to do anything on page 6.

I'm not sure about this, but I'm guessing Brenda's breakdown has many more reasons behind it other than the math test she just took. Regardless, not finishing the test ignited her feelings and brought them to the surface. Since I don't know what's going on with her beyond my math class, it's not fair to say that the almighty letter grade is the main culprit here. But, the letter grade certainly has played a major role. It's as simple as this. If the test had no grade associated with it, would Brenda have left my class sobbing today?

Striving for the "acceptable" grade (Part 1)

I had an experience recently in my honors math class that reminded me of this blog. So here I am again. But only for 15 minutes. Go.

I got an email a few weeks ago from our registrar saying that Jolene (not her real name, of course) was dropping the honors course and changing to the Algebra 2 course. "Wow," I thought. What was this all about? My gut feeling was that Jolene was doing just fine. Maybe not at the very top of the class, but certainly in the top half. (And I suppose it's contradictory of me to have used my grades as a way to think this through. Do I contradict myself? Okay, then I contradict myself.) From my observations of Jolene in class, I certainly did not notice her struggling to the point of giving up. So, to check on my gut feeling, I checked my online grading program (my school requires me to use one to my revulsion) and discovered that her grade at the time was an A-.

I immediately emailed Jolene's advisor writing that this was not a good idea, that Jolene was doing very well from a grade standpoint and according to my observations and impression of her in class. (As I only had 12 students in that particular section at the time, I very much trust my classroom impression.) Jolene's advisor, Liz (not her real name), wrote back saying that Jolene was spending so much time on her math homework that she wanted to drop the honors course so she could devote more time to her other classes. Jolene had been relying on other students, it turns out, for a lot of help, and always worked to get a perfect homework assignment.

This, on the surface, sounded like a very good reason to change courses, but, I replied back and suggested that she could likely spend less time and still earn a B. Furthermore, homework assignments in my class are not graded and I have no expectation that a student get every question correct by the day it is due. Rather, my expectation is that the student do as much as they can on each problem and get help as needed. (I had other discussions with honors students around the same time that made me realize I had not adequately communicated these expectations to my student.)

Of course, the main sticking point was the grade. I found out that Jolene's preference was to switch courses so that they could get an A in math and have more time to spend on other subjects. She mainly wanted to switch because she was concerned she might not be able to get an A in the honors course.

Jolene, Liz, and I met to talk this over. I emphasized to her that she seemed to have a very good grasp of the ideas, that her results were indicative of this, but that it was certainly possible her grade could be a B. I did my best to emphasize that I did not think her getting an A was paramount. My opinion was that the Algebra 2 course would be too easy and she would be bored and that, in the end, this would lead her to a less rich education. Liz, her advisor, supported me on all of this, and we devised a plan: she would take the next test before switching and use that to make her ultimate decision. (Again, something that was grade-dependent, but at least something the student would identify as tangible.)

What happened? You'll have to wait for my next post as my 15 minutes are up.

This is a test. This is only a test.

Grades. Yuck. I don't like them. My students don't like them. Alfie Kohn doesn't like them.

Here I am sitting in my classroom while my Algebra 2 students are taking a "unit test". Why? Because I am supposed to assign each student a letter grade that is meant to represent their... what? Math ability? Feats of memorization? The ability to regurgitate what I told them? Their understanding of certain math problems on this particular day?

A test is a pretty easy way for a teacher to defend a letter grade. Compared to other forms of assessment, they do not take too long to create, correct, and grade. Math tests in particular tend to be easier since there is (normally) one correct answer and only a few different ways to arrive at that answer. It will probably take me two hours of work to correct and grade the test my students are taking right now.

But how valuable is it really? And I am in fact harming the love of learning that I want to instill in my students by giving this test? And if I think that I am, why on earth don't I stand up and say, "Stop! Put your pencils down and let's get something meaningful done."?

One, because I'm tired. Last night, when I sat down to write the test, I had a pretty good idea how long it would take me and by what time I would be able to let my head hit the pillow. As I said before, tests are easy. I want to spend time with my two-year-old and with my wife and I know how to write a test and how evaluate a test. It's a known quantity and is not scary for me. I feel pretty certain that after I finish this test, it will be a decent tool to help me assign semester grades to my students.

Two, I prefer to follow the paths of those who have gone before me. And all of my colleagues from all of my schools, as far as I know, depend on tests to determine grades as much, if not more, than I do. Frankly, it's a bit daunting to jump off the diving board if I've never seen someone else do it before me. If I try something totally new, something that no one I know has tried, then I run a greater risk of the experience not being meaningful or effective. I only have so many teaching days and if I lose a week, I don't get it back. If I know someone has tried a particular project, then I feel more confident. I have been searching for alternatives to tests, but so far, I lack the necessary gurus. And don't send me a web link. A web link is not going to help. I need someone to sit down with me, and explain what they did and how it worked and why they liked it.

Three, I don't know that my school would look very favorably on me not giving tests. I do that with my Advanced Mathematics class, but that is not a pre-AP class. In fact, the typical student in there is likely never taking a math class again. So nobody can tell me that tests are necessary to get them ready for some big standardized test to come. I believe, but am not sure, that if I did not give tests in my Algebra 2 class, that I would get a "talking to" by some one. I know for certain that I must give a final exam (which I was planning to write during this period, but, hey, this blog is better for my soul, right?). It may be that I have sufficient flexibility in the format of that exam that I could design something that is not so test-like. But, I have a fear that would not go over so well. Hopefully, my fears are irrational.

I am sure there are other reasons I continue to give tests. But, I don't want my posts to be too long. So, now I shall stop. The testing, however, will continue...