## Trying to find math inside everything else

### My Final Exam

My second post was about the game Facts in Five and how I thought the scoring system would be helpful for my assessments. I had also been having thoughts about the way to measure synthesis while using SBG. So I thought having a final exam specifically designed to measure synthesis would be the best way to go about it. Here’s how I went about it. (This was the final for the Fall semester, since for the Spring they have the Regents.)

In each bin, I put a slip of paper containing a question. Students will go to the bins and choose which questions they would like to answer, and compile them into a coherent exam.

Those aren’t fractions on each bin label, though. They denote which Learning Goal each question consists of. Instead of having each Learning Goal have its own questions, they mix. But each goal still has 4 questions that apply to it, like so:

Not every topic can be combined with others, but now the student can choose which goals to work on: either they can try to improve a Learning Goal that they got a lower grade on, or pick ones they did well on and show they can perform Synthesis, which is above mastery. But, of course, all of these questions are harder than what they’ve done before.

To score the exams, I use the same scoring system as in Facts of Five, with students squaring what they get right in each Learning Goal. So they will get more points by focusing on completing a goal, instead of jumping around. An example:

Here this student got a decent score by focusing on completing four of the learning goals (9, 11, 16, and 18), and receiving assorted other points.

I definitely like the idea here, but I do need to refine the delivery. It was hectic. But I did not want to print out all 44 questions for everyone, when not everyone will do all of them. That would be a lot of paper. Suggestions are welcome.

#### Comments on: "My Final Exam" (6)

1. Interesting stuff here. I suppose I’m wondering how you’re defining synthesis. Implicitly, I’m reading your definition as “different concepts in random order on the same exam,” in which case your approach works. Synthesis, as I have understood it, is “different concepts in the same questions,” in which case we still don’t have a solution.

• I think you misunderstood, or perhaps I just wasn’t clear. Each question does have different concepts in it. So while ey might have one learning goal, LG7 – Exponent Rules, and another, LG8 – Scientific Notation, on this exam there might be a question, LG7&8, where they have to multiply two numbers that are in scientific notation and write the answer in scientific notation, thus combining the two concepts. Another example from the exam was determining if a survey was biased by looking at the histogram of the results, combining LG9 – Bias, and LG12 – Histograms.

• If you look at the picture of the student’s score sheet, you see each question is at the junction of two learning goals. So that student got the box for LG1 & LG4, and gets credit for both. And thus is she can fill out column (and thus combining LG1 with LG2, LG4, LG10, and LG15) she proves that she can synthesize LG1. (And has gotten some credit towards the others in the meantime.)

2. Mary Watson said:

Wouldn’t you need to print out all questions for all students regardless of whether they are all on one page or cut out individually? Wouldn’t there be a possibility that all students chose the same question, thereby, you would need an entire classroom set for each question? Or did you have some way of determining which questions students were more/less likely to choose and, therefore, only printed a few of some questions and more of others?

• Well, I made sure to have at least a class set for my first section, but after I could check the bins and see which ones were low, or even check the exams and see which ones were taken, and then refill as needed.

Also, I could fit more on a page with cutting because I didn’t need to leave space for student work. Since they pasted the questions on their own paper, they could have as much space as they need, no more or less.

3. Jennifer Neuse said:

Try quiz star http://quizstar.4teachers.org/. You may be able to group questions into learning goals