Semester Exams

Finished my semester exams today, all on moodle, which means my grading is done.

I have been a moodle user for the past couple of years, and have used moodle to incorporate a weekly spiral review of algebra and geometry topics (among other things I use moodle for). This year, I decided to use it for my semester exams.

Here's how it worked, along with some background.

These weekly moodle assignments are my student's only homework for me...twenty questions a week. I use the calculated question feature to create a hundred versions of the same problem, so different students will have the same questions, but in a different order, and with different numbers. My hope is that my students will talk about the problems (and they do), and not just copy answers (which they can't).

When they submit an answer, they know immediately if their answer is correct. If it is correct, they receive full credit for the problem. If it is incorrect, they receive a 20% penalty. They can attempt the assignment as many times as they want with the understanding that each attempt will mean a new version of the assignment with the same questions but with different numbers. I simply record their best score for the week.

Grading this way, I would hope that every student gets a perfect score. Even with an unlimited number of attempts each week and regular moodle moots I hold for students to stop in and ask questions, this does not happen. Nevertheless, I feel this is an effective way to get the kids to stay sharp on old content.

Over the course of the semester, I have created almost 200 questions like this, categorized by content (Triangles, Circular Areas, Trigonometry, etc). Many of these questions assume the use of GeoGebra or NspireCAS. Other questions require kids to make a choice: Should I complete this by hand or use GeoGebra?

Their exams were constructed the same way, from the same questions, with just a couple of exceptions.

(1) Every student had a different exam. I finally figured out how to randomly include any number of questions from a question category. For example, every student had three right triangle questions selected from 20 possible right triangle questions.

(2) The students could attempt the exam as many times as they wanted in the 2-hour time period. Just as on the weekly assignments, students knew immediately if their answer was correct or incorrect. However, when they attempted the exam again, their correctly answered questions were on the new attempt, along with their answers.

(3) Students could know their grade at any time. Because they could make repeated attempts on the exam, when they finished one attempt, they knew what their grade was on that attempt. This, of course, meant that no one needed to get a perfect score on the exam, because they only needed to get 90% of the questions correct.


Of course, this is not perfect. To use the calculated questions feature in moodle means I am asking a question that can be solved by applying an algebraic algorithm. I guess this could be good or bad. If I ask a question like

Quadrilateral ABCD is a square. Point A has coordinates (8,19). The diagonals intersect at point M, which has coordinates (1,-3). The vertices are labeled in a counter-clockwise direction. What is the x-coordinate of point B?

students need to know something about a square, how to construct it, that the diagonals are congruent and perpendicular, that is possesses 90 degree rotational symmetry.


I am not concerned that my students had seen the exam questions before on their weekly assignments. I am concerned more about the two hour exam period (we do this, the argument goes, to get our kids ready for college. Why, then, don't we have class just three days a week?) than if the kids have seen the questions. Besides, I'm not sure the kids even realized this until they took the exam, even though I had told them this numerous times before.

Anyway, this will work for now. My grading is done.

The Social Construction of Learning Disabilites

I was reminded of the article The Social Construction of Learning Disabilites by Curt Dudley-Marling after sitting through an IEP re-evaluation meeting the other day. After all, if you have attended an IEP meeting, that is all the regular education teachers do is sit through them.

This student's recognized disability is in the area of mathematics. I call it "recognized" because I am not sure I believe there is a disability. The results of the test administered by the special educators to support this claim looked to me like the results for any one of my students. The test ranked her below average, average, or above average on a dozen or so different content strands.

Let's see...on the handful of strands that concerned mathematical operations, this student was ranked as "below average," estimated to be performing somewhere in the 7th to 9th grade level (this student is an 11th grader). Nothing out of the ordinary there. I would reckon that the majority of my students would fall in this range on these strands. Somewhere earlier in their schooling, someone decided that an appropriate modification for this student would be to allow them to use a calculator. These sections of this test were completed without a calculator. No wonder.

Let's see...on the handful of strands that involved operations with fractions and real numbers, this student scored below average, again estimated performing in the 7th to 9th grade range. Again, par for the course when it come to the majority of my students. For some of these sections, the student was permitted to use a calculator. I guess who ever decided on the calculator modification forgot to teach how to use a calculator. I wonder what calculator they used? Did they use their TI-84? Did they use one of my NspireCAS handhelds? Was it one of the Ohio Graduation Test calculators?

Let's see...on the handful of strands that are actually addressed in my classes - Algebra, Measurement, Geometry, Probability, Shapes - this student was ranked in the average to above average range on all, performing in the 10th grade to 11th grade range. I would imagine and expect that the majority of my students would be here.

I guess I do not understand how this disability works, or how it is constructed.