Monday, January 27, 2014

When final exams should trump “formative” assessments

One current trend in K12 is a growing aversion to summative assessments like final exams. At the very least, many US educators feel, summative assessments shouldn’t be, as they are in many other countries, the major determiners of course grades. Here in America, of course, essays, lab reports, and other homework assignments have long figured significantly in course grades—and reasonably so—for most subjects. But what about a highly cumulative subject that doesn’t (or shouldn’t) involve essays, research projects, and lab reports? I’m thinking, of course, of math.

Here, arguably, stellar performance on the final should override everything else. For imagine a student who hasn’t turned in a single homework assignment and/or has performed poorly on earlier tests and quizzes. Now suppose that student gets almost everything right on a well-constructed, comprehensive, cumulative final. Then shouldn’t s/he should get an A in the course rather than the B, C, or D to which those earlier “formative” assessments drag him down?

This idea, naturally, won’t resonate with many of today’s educators—trained as they are to favor process and portfolios and other, supposedly more authentic, “formative” assessments, and to lavish students with partial credit and “points for trying.” Along with those multiple “entry points” that are supposed to welcome multiple “learning styles,” surely there should be multiple ways to demonstrate mastery?

But mastery is an end result; not a process. And, in a subject like math, a comprehensive, cumulative final exam is the ultimate measure of that mastery at that crucial end point, i.e., the course’s conclusion. In the spirit of multiple learning styles (or multiple learning strategies), therefore, shouldn’t we allow multiple pathways, not all of which involve turning in assignments and studying for quizzes, to attaining mastery by the end of the course?


Lsquared said...

I'm a big believer in summative assessments (aka tests), but I'd be uncomfortable with giving a grade based only on the final exam. If a student does fabulously well on a final exam, when failing the previous exams and assignments, I'd be likely to suspect cheating rather than studying. I'd like to think that a student could go from not understanding during the bulk of the course to really understanding for the final, but I've never seen it happen. The theory that it's possible to learn all of first semester calculus in the last two weeks (after trying and failing in the previous 10 weeks) seems to be disproven by the evidence of all of the students I've ever taught.

On the other hand, there are a few students who will ace all of the tests while not doing any of the assignments. Those students I'm quite happy to give B's to (B not A because the longest trickiest problems appear only on homework assignments, and not on exams, and I want to encourage distributed practice).

Anonymous said...

I think my take depends on how comprehensive the cumulative exam is. In my higher level math classes, at a tech university, the math exam would not have been cumulative of all the homework, which was more extensive (covered more problems and longer problems and deeper problems) than could be covered in even a long exam. I also believe that this is the case in my child's 7th grade math class -- that *some* of the homework (and by this I mean work done at home) is deeper, more creative, more integrative than the work covered in an exam.

But, I do agree that the practice work (some of the homework, in which the kids are practicing the same skills that are tested in the exam) could reasonably be superseded by the exam. For some students, that would be a bad incentive -- because they might make the assumption that they don't need the practice when they do. But, for others, it would save them from useless tedium.


Anonymous said...

yes, I always ignore the issue of cheating, which is not a reality that arises in my own life or with my children, but it is one that teachers have to consider (for both homework and test work). I do worry about homework being overly loaded in the grade when there is a very realistic fear that it has not been done independently.

Kids can be tricky about getting others to solve problems that they find difficult. Sometimes neither the helper nor the student even knows that's happened, until they try to do the problem alone.


gasstationwithoutpumps said...

As with the others here, putting too much weight on a single exam means having the grade depend on only a fraction of the material—and that the easiest stuff, since there isn't time for the hard stuff.

In my (college senior and grad student) courses, I generally don't use exams, but use multiple week-long assignments that measure what I really want students to be able to do. Anything that can be answered in an hour is too trivial for me to be interested in whether students can do it.

Auntie Ann said...

One of the smartest things a teacher of mine did was to say that every Thursday is quiz day. He said that there might not be a quiz, but that you should always be prepared for one. (Obviously, the students who had him later in the day were at an advantage, because they would know from their peers who had an earlier class whether there would be a quiz or not.) This was a physics class, so systematically climbing to the summit was important. The possibility of a quiz each week meant you had to make some effort to keep on top of the material. I think he understood what a recent study showed, which was that practice tests are an excellent way to learn material. (I think they were, cumulatively, worth about 10% of our grade.)

As for homework grading, I think it's more important for a student to receive feedback and make corrections than to get graded on the first submission. Homework should be where you learn what it is you are doing wrong, so you can make an effort to do it correctly. An iterative system of submission and corrections, where a student might be graded on the last version seems smart to me.

This is perhaps even more important in writing classes, where grammar, spelling, depth of argument, use of phrasing, etc. can all be subject to the red pen and iterative corrections. In writing-oriented classes, there is a big difference between getting an assignment done and doing it well; between going through the motions and writing a concise, cohesive, well-written essay. It is also much easier, when there is often no correct answer, to b.s. your way through and never really learn to write well and come up with a persuasive argument. Every student needs at least one teacher who will stop a student in their tracks, rip their work to shreds, and teach them how it really is done. That take an iterative process of at least a first draft and then a final one.


The biggest problem I've seen with grading in our kids classes is the dreaded rubric, with their cookbook-style assignments. They rely more on following the step-by-step instructions than actually attempting to get kids to understand the material. The ones our kids have gotten also put a maximum limit on effort. If a student reads: paragraph 2 should have 5-6 sentences, you can bet they won't dare do 7 or--heaven forbid--8! even if the material and their observations of it indicate a more in-depth response.

Anonymous said...

I used to tell my students that there were two ways to pass my class and only one to fail it.

A: If they learned all the material, they would pass the class.
B: If they came to class every day, participated, and did all the work, they would pass the class.

If they did neither, they would fail the class.
If they did both, they would get an A.

Depressing how many students still did neither, year in and year out. Remarkable how students who chose Path B never failed the final.

lgm said...

One of the nice thing about the "A on the final = A in the course" is that it allows students who have poor teachers time to get a tutor and make up for the bad teaching. This is valuable in today's middle and high schools that don't bother issuing math texts - which is what the students assigned to dud teachers in the past used to learn the material.

Anonymous said...

Teaching at a community college, I have a lot of students who just aren't good test takers. So, as a result, I keep my exams pretty straightforward and they only count for 40% of the final grade.

I've been giving project work for 10 years now and it has worked pretty well. The projects count for 40% of the final grade and daily quizzes (about 25 quizzes in a ten week quarter) are the other 20%.

My first year, I realized that the math lab tutors were undermining my projects by simply giving out the answers, so I began to ask that students justify and explain each step in their solutions. Then, of course, I had the issue of students copying from each other. I gave them zero on the project, but it didn't make any difference, they kept doing it.

Then I realized - if they don't turn it in, they get a zero, and if they get caught cheating, they get a zero - there was no difference to them. So, I began to give students who cheated on the projects failing grades for the course. My VP fought me hard on this one, but I kept doing it and it worked.

After having one case of plagiarism every term during my first 2 years, I went to having one per year, and then none at all for the last five years.

I gave a presentation last spring on some of these projects that dealt with complex numbers - the presentation is at:

Anyone who's interested can see some of the other projects at:

Many of my students have said that they really learned a lot from doing the projects, which is about the best complement I could hope for. Of course, a small number of students simply don't even try and complain that they shouldn't be expected to write at all in math class, but this is such a small number of students and the benefit I see to the students who do follow through is so great, I've stuck with it.

My inspiration for doing this was the experience I had while working on my master's at UMaine. I saw a few of the projects that were given in their College Algebra course and built on that to make my own projects.

I think that's why graduate education can make people better teachers. It's not so much about the content or curriculum, but the experience and mathematical/educational community that you're a part of, that helps to inform your own understanding of math and math education.

Rich Beveridge