Tiered Assessment for Geometry

A wonderful colleague Ms. C. (now at a different school, alas) and I were inspired four years ago by a guest speaker at our school (I believe his name was David Holden) to create an assessment system for our Geometry classes based on a 4-point scale. I believe this would fall under the umbrella of SBG but it’s a bit different from what I see most folks talking about on their blogs. For one thing, we don’t use a rubric. It reminds me of a workshop I attended long ago on the topic of tiered instruction so I refer to it as tiered assessment, to differentiate it from rubric-based SBG. I don’t claim that it’s better, just different.

We decided to make each page of a test deal with just one objective, listed at the top of the page. We created four questions, one at what we felt was a D level (student was awake at some point during class), one C (if student leaves my class only knowing this much, I won’t be a complete failure), one B (student knows how to put some pieces together), and one A level question (student has this objective down cold). We tried to keep Bloom’s Taxonomy in mind when writing the questions, though Bloom could have been more accommodating by only having four levels for us to work from.

Here is one version (we always made two) of one of our assessments, which roughly corresponds to the first four sections of chapter 6 in our old (Glencoe) textbook.

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We decided not to have each question worth individual points. Instead we marked each question with a +, √, or -, which roughly correspond to full credit, half credit, and no credit. Then we created a decidedly complex grading system whereby each page (i.e., each objective) received a single score from 0 to 4, based on the combination of marks on the page.  The simple examples are these: If a student only got the D question right they earned a 1. If they got the D and the C question correct they received a 2. D, C, and B correct yielded a 3, while a perfect page earned a perfect score of 4. Other combinations were given intermediate scores, and half-credit on a question dropped the overall score a certain amount based on which level of question had the half-credit. You can see, I’m sure, how the entire grading scale turned out to be rather byzantine. I should also mention that we made it very clear to our students that a B or A question would never receive even partial credit if there was no work shown. (There were probably a few exceptions, but none come to mind presently.)

These took forever to grade at first, but I noticed one day that Ms. C. had memorized the grading scale and I was inspired by her example to do so myself. This sped things up considerably, though in truth grading these assessments never got to be a brief task for either of us. Nonetheless we liked the results we were getting. A student taking one of our quizzes always knew what we thought was deserving of an A or any other grade, and the grades they received lined up nicely with how well they appeared to know the material in our formative assessments. You couldn’t get an A by answering 90% of a bunch of B and C (and D) level questions, which is what the tests that came with the book were like. After implementing this system I had less A’s in my class, but also less grades below C level. (That’s a pun–ha ha!) The students who only wanted a C–just to pass the class–knew exactly what they had to do to get there. And the B questions were always right there in front of them, hopefully to entice them to try and reach a little higher. And again, you couldn’t get an A just by working hard; you had to really learn the concepts deeply. (I don’t claim that every assessment we wrote meets this standard, but it was always our target.)

One other thing we did was to not give an overall quiz score. Instead the students received all of their scores filed under specific objectives. There was a 0 to 4 score in our grade book for all 70+ objectives we had for the year. We also allowed students to retake any page (one objective, all four questions, in a different version from the one they had taken before) one time and didn’t penalize them if their score went down. Score reductions didn’t happen very often though, as most students who bothered to re-test made a point to try and understand the material better beforehand. There was very little chance that they could improve their grade significantly otherwise.

Ms. C and I decided to start making our homework look much like the assessments, so that the students would have a better sense of what we thought “A” work looked like before they were tested on it. (We did try to avoid having the homework questions look just like the test questions but with different numbers, especially the B and A questions.) Two and a half years later, we finally had tests and homework for every objective. And for what it’s worth, I wrote my own class notes and posted them online (in particular for students who missed class), so my students and I ended up hardly ever using the textbook at all.

As you might expect, parents were often confused about how our grading system worked, since we weren’t working by percentage but the grade-reporting program the whole staff was required to use would still show a percentage no matter how hard we tried to avoid it. We had to adopt a grading scale that looked bizarre by normal standards, with 25% being the lowest D, 45% for a C, 65% for a B, and 85% for an A. These percentages were a never-ending source of wonder (to put it nicely) that we got to explain to parents ad nauseam, but when the end of the semester came and you paired up the grades with the names, our students all seemed to get what they deserved. It felt like we had done something right.

Why is all of this written in the past tense? Because, as I mentioned in an earlier post, we have new books this year and they are very different from our old ones. I haven’t made a final decision yet on how I want to formally assess my Geometry students this year, but I don’t think I’ll be able to just re-tool all that Ms. C. and I have created. I have high hopes for our new curriculum (CPM) but it’s a shame that so much previous work will probably just end up in the academic museum. So it goes.