I have been teaching senior high mathematics for a number of years. As one of our divisional AAC assessment specialists since 2002, attending the seminars and AAC conferences has encouraged me to try different assessment strategies in my classroom. For instance, in the first semester of 2004, I implemented a couple of the strategies in my Pure Mathematics 30 class… and I didn't see too much difference. In fact, I wasn't too happy with what I did see. When I look back now, I wasn't making a commitment to really try anything. It was Pure Mathematics 30 after all, and what if the results were bad? What if the school mark I submitted was totally out of range from what the students achieved on the diploma exam?

In September 2005, I decided that either I was going to make a commitment to all of these strategies I was hearing about, or I was going to stop pretending. I decided to make a commitment.

I had a class of 23 students, 4 coming to me with performance levels of 80%+ from Pure Mathematics 20, 3-4 between 70-76%, and the rest between 50 - 67%, with about 9 or 10 in the low to mid 50's. I did not teach them in Pure Mathematics 10 or 20, but I did have them in other classes and had a good relationship with the students before Pure Mathematics 30.

So here's what I did…

I created brand new hand-in assignments, quizzes, unit tests and school final exam, administered about 10 days prior to the provincial diploma exam. I did not want any contamination with previously used assessments in case students had copies, and I knew some did.

I have always presented learner outcomes to my students from the Program of Studies at the beginning of the semester. I usually would quickly review them, believing that at this point in their learning it didn't really mean much to them. What was different this time is that I referred to the outcomes on a regular basis, every time we took up a new concept, and especially when we talked about the diploma examination. I had the students go through the list of outcomes at the end of a unit when they were reviewing, checking off what they knew and highlighting what they still needed to learn. Did all of them do it? No. But some did and others started.

One of the big changes in my classroom had to do with major assignments. Students had daily assignments that we took up the following class. There was, however, a major assignment due just before the unit exam that they received at the beginning of the unit and had the length of the unit to work on it. Normally I would collect the assignments on the due date, mark them that evening, and return them the next day before they wrote the exam. We would go over the main difficulties. However those students who did not complete the assignment or didn't get it in (and those weren't many) just watched me do the questions. Here's what I did this time… When students handed in the assignment, I would record the ones I had, call up the ones who didn't hand one in, and make arrangements for the assignment to be handed in the next class. Usually it was because there were major problems in doing the assignment, so extra help- after school or at noon- was arranged. With the rest, I would mark the work that evening and record the marks. The class immediately prior to the unit exam is always scheduled as a review to prep for the exam.

They had review questions to work on. At the start of the next class I would call up the students who did poorly on the assignment, and ask "What was the problem with question …?" The usual response was, "I didn't know how to do it." So I had them pull up a seat and we would go over the question. I would do the work on scrap paper and talk the student through the work. Then I would hand the assignment back to the student and tell them to re-do the questions on their own and hand it in next class. They would look at me in a strange way and ask if I was going to re-mark it. When I answered "Yes", someone said, "But you just showed me how to do the questions." My response was "No, I did the questions, now you need to show me that you know how to do them on your own". Once the students realized I wasn't going to allow them to not do assignments, they came to me before they were due to get extra help.

Other strategies I used, not new to my classes, were returning quizzes or assignments and putting students in groups to work through the corrections. Having students make corrections on quizzes in written form, and showing me their work really works to improve student learning.

The biggest change in my classroom was offering my students the opportunity to rewrite unit exams. The first time this came up was on the Exponents, Logarithms, and the Geometric Series unit. Several students did very well, the top mark was 95%, but there was a large group of students in the 35 - 55% range with one getting 11%. So this is what I offered them... They could rewrite the exam (a new exam with the same number and style of questions), but had to meet the following requirements- the rewrite had to be on their own time, noon hour, spares or after school and they had to come in for extra instruction to 'fix' the problems. Arrangements were made for extra help at noon hour or after school and we set a reasonable deadline for when the exam had to be written. I recorded who planned to rewrite, set tentative dates, and when they came in.

The rewrites raised marks from 2% to over 40%. Personally, I think the rewrite was a little tougher. Not everyone chose to rewrite the first time. I offered rewrites on 4 units and each time they came in and they learned and the marks went up. As time went on they were specific in what they needed to learn, and we began setting up times to review a specific concept rather that 'everything'. Through all of this, I still wasn't confident in what I was doing and many times I had my 'letter of resignation' written in my head as I worried about a huge spread in my marks and the marks they were going to get on the diploma exam.

Not everyone was happy either. My top student came to me after that first rewrite and said it wasn't fair that he got 95% on the exam and I was giving everyone else a chance to catch him or beat him. We talked about whether or not he really believed that was going to happen, and that I wasn't doing this so the other students could compete against him, but so that they could learn and do better for themselves. I also told him that there may be a unit that he was not satisfied with and would choose to rewrite. I also offered him a challenge. I told him that I had never had a student achieve 100% on a Mathematics 30 diploma exam and that was what I would like him to work towards. He was pacified, but not totally convinced. The time did come when he only got 82% on an exam (Permutations and Combinations) and rewrote. He got 97% on the rewrite. Now he was happy.

The first time I realized it was working was about the end of November. At that time we were talking about a concept on the board when a student said, "Oh, I see how they are going to ask that question on the diploma exam, they are going to do this… and use this… as the distracters." Other, students (normally the weaker students) got into the discussion about how the errors were going to occur and what they had to watch for.

I just stood back and thought, "They know; they are learning!"

In the month of January, I have always offered evening review sessions to go over the units and work on old diploma exam questions. It is set up in consultation with the students in early December so those with part time jobs and other commitments can plan around it. We work from 3:30 to 6:00 on specific units on specific evenings. I would usually get as much as half the class showing up, not necessarily consistently and not usually the higher achievers. Well, they all came almost every time. And if they couldn't come because of prior commitments, they let me know and asked if they could come in at noon or some other time.

The day of the diploma exam, I was nervous still thinking about writing that 'letter'. I had a pretty good feeling about it though because as students were walking out of the exam (particularly the 2nd part), they were coming to me all excited and asking about question #32 or #34 because they did such and such and were they right. One of my 50% students said that he felt he was almost cheating because the exam was so familiar to him; there was nothing he didn't recognize. It turned out he got 58%. I was ecstatic!

The average of the marks I submitted for my students and the average of their marks on the diploma exam varied by 0.3%. I had my first student achieve 100% on the exam and more importantly almost all of my 50%'ers raised their marks. My student who got 11% on her first unit managed a 50% from me and got 45% on her diploma exam, which averaged to 47.5% which rounds to 50%. You would swear she got $100 000.00! Only two students had significantly different marks, one went in with a low 60% and got 46% on the exam, and I don't believe he bought into the process of doing his own learning throughout the semester. Another one went in with 65% and got an 85% on the exam. She said she was just lazy for the first part of the semester and decided to get serious at the end.

Does assessment for learning work? You bet it does!
Was it a lot of work? You bet it was!
But was it worth it? Absolutely!
I am a true believer in the strategies of assessment for learning. It is my single most powerful tool in promoting student learning.

Carol Fedoruk, Assessment Specialist
Peace River School Division

For all we hear about standards stifling "creativity", the very opposite is true. Where teachers deviate from common, essential standards, we see deadening, irrelevant activities proliferating. Mike Schmoker (Results NOW, ASCD, 2006, 17)

AAC Blog
The AAC Blog is a new interactive feature of the web site (www.aac.ab.ca). Blog is short for 'weblog'. A weblog is an online journal (or newsletter) that is frequently updated and intended for general public consumption.

Here are the first two comments in response to the AAC Blog questions:

• What issues do you face as assessment for learning finds its place in the classroom?
• What solutions have you discovered along the way?

seeker said...

The biggest issue I face is knowledge. I now know more accurately than ever where each of my students is in understanding the concepts. Now I have to act on this knowledge. It's not okay to teach one thing to all of my students, because I know that it meets only the needs of one group. The main thing I am working on now is differentiated instruction.

One solution that I have discovered is a choice board. I make up a selection of activities based on Howard Gardner's Multiple Intelligences to go with a unit of study. I introduce them to my students and then let them choose the activities they would like to do either independently, with a partner or in a small group. All of the students are eager to choose an activity. As students complete the activities they share them with the class. This inspires other students to try the activity as well.

January 7, 2007 8:23 PM

searcher said...

Hello Seeker:

Thank you for sharing your activity strategies; your willingness to tap into your students skills/talents/interests and in so doing, engage their learning is impressive. Having students share their work/learning certainly "ups the ante" so to speak. Over my many years of teaching, I've discovered that having students present to various audiences (other than me!) raises the bar of their performances; they seem to "own" or "invest" more deeply into what they are doing when they are given the opportunity to share with others. Often, I included a component of the presentation to include a discussion of what they found challenging/easy, or what they would do "differently" next time (as a "heads up" guide for other students who may tackle a similar activity at some point) or what aspects they were most proud of, or warranted special highlighting - the "metacognitive" journey serves immense value on many levels.

Your strategy has piqued my curiosity and given rise to a whole raft of questions. Would you be willing to share some examples of the activities you have created? How do you assess these activities: at stages along the way, or at the conclusion? What kinds of criteria do you use in your assessments, given the vast array of activities/assignments being created? Do students have opportunities to revise their activities, given what they might receive in terms of feedback/response from their peers and/or you? Do you encourage students to "try" activities that ask them to challenge the "intelligence" that is not necessarily their strength to see what they might be able to accomplish with guidance/encouragement drawn from others' experience? Will you (or do you) allow students to 'design' their own activities?

I know - lots of questions, but I think you're on to something exciting that has real potential in addressing the potential gains that can be made when differentiated instruction is coupled with assessment for learning. Looking forward to hearing from you!

January 8, 2007 10:56 AM

When teachers recognize that knowledge for improvement is something they can generate, rather than something that must be handed to them by so-called experts, they are on a new professional trajectory. Hiebert, J. & Stigler, J.W., Journal of Staff Development, 25(4), 2004, 15

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