It’s been a month since I posted something new in this blog. I have had enough time (I think) to be able to reflect on the use of SBG grading in Algebra 2 and AP Stats. First, I would like to address the use of SBG in Algebra 2 (mostly freshmen).

I have divided the course in units, approximately one chapter in length. For each unit I have put together 5 to 6 Learning Objectives (LOs). Every week, I give my Algebra 2 classes a quiz that covers 3 to 4 LOs. The quizzes are cumulative, and they consist of simple problems for each LO covered. The grading is 0 to 5 for each problem – sometimes with partial credit – and the grades are entered into a spreadsheet. The grades are automatically color coded in the spreadsheet – red for 0 to 3, yellow for 3 to 4 and blue for 4 to 5. Turnaround is usually 48 hours or less. Once a week, I eliminate the names from the spreadsheet, sort it by ID numbers and send this “public” spreadsheet to students and parents.

In general I am not overly enthused about what SBG accomplishes. First, the grading of the weekly quizzes and the entering of the data is very time consuming despite the help of two TAs.

More importantly, I have found that for my students, SBG does not seem to lead to improved learning. The big advantage of SBG for me is that by looking at a spreadsheet, I can see right away (color helps a lot here) which LOs the kids have bombed and which they have done decent or better.

While this helps me as a teacher, it doesn’t seem to help the kids. Even after reteaching and retesting, many kids still don’t get the concept and indeed repeat the same mistakes. If I reteach again, I still may get poor performance in some of the LOs. What I find most distressing is that we end doing the same kinds of problems so that an increase in performance is to the detriment of higher order thinking.

Here’s an example. I wanted to get across the idea that linear equations (can) arise from patterns where there are equal changes in two variables. I started with problems such as this:

Pattern # 20 21 22

The idea was to find a relationship between the number of triangles (y) and the pattern number (x). It took a few weeks of giving this type of pattern problems on quizzes, homework, in class work, before most kids were able to get the correct equation. Even then, asking a follow up question, such as how many tiles were in Pattern #5, gives rise to nonsensical answers or just plain wrong ones (sometimes due to simply faulty arithmetic).

Then, if I switch the question to one like: “Given the table below

x |
–2 |
–1 |
0 |
1 |
5 |

y |
13 |
11 |
9 |
7 |
? |

find the value denoted by the question mark”, it seems like a brand new problem, with no connection whatsoever to the pattern problems. We end up doing now table problems, until a majority of the kids get it – but it still looks to them as a separate type of problem. There is no synthesis, despite my calling attention to the similarities of the two types of problems.

To conclude, while SBG is helpful in alerting *ME* to weaknesses, it does not seem to be able to move the kids to higher order thinking. I am beginning to think that I could do just as well with summative tests and then reteach those areas that most kids get wrong in the summative tests.

There are a number of SBG-related issues that still are unclear to me. First, how much do SBG results depend on the population of students one deals with? My students – generally – are very poorly prepared for being in Algebra 2. True, most of them are freshmen with all the developmental issues this implies, but above and beyond the question of maturity (what do you mean you haven’t reviewed the results of the previous quizzes?) there is a stark issue of math preparation – or lack of it. For example, my students can not do fractions. Two problems in a recent quiz had to do with solving a system of two linear equations – standard fare for Algebra 2. One problem had the usual type of equations, in the other one the equations appeared as fractions. Result? 75% correct answers in the first problem and 5% in the second one. Would a population of better prepared students benefit more from SBG?

Second, how much of a “burden” should one put on SBG? Is it fair for me to expect that SBG will lead/help in getting higher order thinking from the kids? Perhaps SBG delivered all that it was meant to deliver – alert me to my students weaknesses. I ask this question, because in AP Statistics I am happy with detecting the weaknesses and reteaching – but then again, that is different level of course with a different population of students.

To be continued….