Test 2 Results (Elem. Algebra)

Is it possible to be happy and disappointed with the results of an exam? Absolutely. First the good news – the overall success rate for the exam was 75%. Thirteen students leveled up, and they all passed the exam. So that means no retests for this exam. There were 19 students who did not level up, and 11 of those 19 passed (58%).

So, why disappointed? I suppose I should be happy that 13 of my students scores 90% or better on each homework assignment and 70% or above on both quizzes, but I’m not. I’m more focused on the 19 that did not level up. I wonder how many of the 8 students who did not pass the exam would have passed if they had done all of the homework.

I took the time to talk to the class about missed opportunities. The 11 students who passed were reminded that they would have earned more points on the exam if they had leveled up. The 8 students who failed were reminded that they need to be more responsible for their learning. The entire class was reminded that the purpose of homework is to help them to understand the material.

I have found that students need to hear “the speech” from time to time. Here’s hoping that this one was effective.

Retest 2 (Int. Algebra)

Just got finished with the retests for the second exam, and the results were strong. Although not all of the students who qualified for the retest took it, the students who did come in to take the retest all passed. Their average score was 87%, which showed that their remediation efforts did work.

Test 2 Results (Int. Algebra)

Sorry for the break – was speaking out of town and am just catching up.

For Test 2 (radical expressions and equations), there were 36 students who leveled up and 34 who did not. (There are a few students who did not take the exam, so I have left them out of the tallies.) This is a slight decrease in terms of the percentage of students who leveled up.

32 of the 36 students who leveled up passed the exam, while 20 of the other 34 students passed the exam. (89% passed versus 59%)

The median score for the group that leveled up was 11 points higher than the group that did not level up, and the mean was 16.7 points higher. The first quartile for the group who leveled up was 74.5, meaning that 3/4 of the students scored 74.5 or higher. This compares favorably to the median from the other group, which was 73.

summary stats

I presented these facts to the class, and hopefully it will convince more students to give a full effort on the online homework. I suppose I could be happy that half of my students are doing so well when it comes to effort, but I really want more.

I will give an update on the retest in a future post.

Test 1 Retest Results

Between the 3 classes, I had 8 students who qualified for the retest. (That means that they leveled up by scoring 90% on every homework assignment and 70% on both online quizzes, but scored below 70% on the exam.) That’s not unexpected as students are getting used to a new instructor and how my exams are structured. I encouraged each student to spend the week going over their errors on the exam, spend some time in our tutoring lab or my office, and work on review problems to prepare.

I had two students who asked questions before and after class nearly every day. Not surprisingly, these students really improved on the retest. I could tell that each student has gained a great deal of confidence and I expect big things from them on the next exam.

There were other students who improved by enough to pass the exam, as well as some who fell short. Students who are beginning their college math careers are often lacking self remediation skills. For the second exam I will incorporate retention techniques that students must participate in before they are allowed to retake the exam, including taking a personalized review quiz/homework assignment.

Students know how to learn in the organic environment of a video game, mostly through trial and error. But learning mathematics takes a more structured approach. As teachers we need to help our students learn how to self remediate and eventually take complete responsibility for their education.

Retests & Mastery Learning

My son always talks about video games and learning. He points out that when we play video games we often learn through failure, through trial and error. We try going down that hallway, and when it doesn’t lead us to where we want to be we open another door and try something else. When one weapon does not work on a foe, we look for another weapon that may be more successful. I remember playing Mike Tyson’s Punchout on my old NES, trying to find just the right trick that would allow me to be successful versus a certain boxer and I was happy that I could hit the reset button after losing so I could try again.

Mastery learning is built upon this same foundation. Students take a test to see what they do know and what they don’t know, then after some time and remediation they come back to try again.

My students experience mastery learning while attempting their homework and online quizzes. They can repeat randomly generated homework questions until they get them correct.

Try. Fail. Try something else. Repeat until successful.

My students can take the online quizzes as many times as they would like, with only the highest score counting. Hopefully they remediate themselves before a second attempt – tutorial center, classmate, office hours. The quiz diagnoses where my students are having trouble, and retaking the quiz allows them to measure their progress.

Try. Which problems did I miss? Why did I get them wrong? Remediate myself. Try again. Repeat until successful.

If students have already put in the time and effort to level up, I figure that they have earned the right to take a second swing at the exam. The bonus points are not available – they simply earn 1 point for passing and 0 points for failing. I’m afraid that if students could still earn 2 or 3 points on the retest they would not give their fullest effort on the first attempt.

I have had a handful of students who level up while not trying to learn and understand the material, and their exam scores reflect this. When they arrive for the retest not much changes. The exam is different, shorter than the original exam and more difficult. Without the self-remediation that goes along with mastery learning, we cannot expect understanding (and scores) to improve.

Tomorrow I will summarize the results from the first round of retests. I had 8 students qualify from my three classes.

Do the Coins Make a Difference?

For all 5 semesters, I have been giving an unexpected reward to students who have earned a perfect score of 3 on an exam. (To earn a perfect score on an exam, a student needs to level up and score 80% or above on the exam.) The reward is the ability to reopen 1 homework assignment or 1 quiz. It’s a nice reward that allows students extra time for a particularly hard section, or even the ability to choose to take a night off if they choose.

You would think that this would be a big deal to students. The first semester I just told students that they had the ability to open an assignment, but very few used this benefit even though they missed an assignment. When you play a video game there is a status screen that constantly reminds you of exactly what you have. Without a reminder that they have this benefit, students forget to use it.

I was walking through a party supply store when I saw a bag of plastic gold coins and it struck me – I needed a physical reminder of their award. From the instant I started using the gold coins, students took advantage of their benefit at a much higher rate. I think they see the coin as a benefit that was paid to them, and even when they turn it in to reopen an assignment they are reminded of the honor they received.

I must admit that it is a lot of fun handing out the coins after the first exam, when students have no idea what is happening.

I have a friend who has tried a similar approach, but uses poker chips instead. There’s probably no limit (pun intended) to what you could use.

Leveling Up, But Not Passing?

Now that the dust has settled from the first exam …

Between my 3 courses I had 63 students level up, and 55 of them (87%) passed the exam. But what about the 8 students who leveled up but did not pass? Obviously I understand that this can happen, but the goal is that if students are doing their homework with the goal of learning and understanding the material they should pass the exams. Of the 8 students, most were in the upper 50’s or 60’s. To me, that is close enough that they may have understood the material and had a bad day. It was their first test with me, and that can be an adjustment period.

In the past I have had a handful students who leveled up (90% or higher on all online homework, 70% or higher on all online quizzes), but score really low on the exam. In fact, the scores are so low that it’s hard to believe that the homework scores are true reflections of what the student knows. One problem is that many students have trained themselves to do the homework to accumulate points rather than knowledge. Using MyMathLab, students can over rely on learning aids such as “Help Me Solve This” or “Show An Example” and be tricked into thinking they are learning when they are not. They can have their resources available while working on their homework or quizzes, and may not realize that they can only solve the problems while using reference materials. Unfortunately these materials and the MyMathLab learning aids are not available during the in class exams.

Another problem could be the overuse/reliance on a personal tutor. I had a student who did the homework with a tutor, and I am fairly confident that the tutor was doing a lion’s share of the work. This will always show up on exam day.

At the beginning of the semester I make a big deal about the purpose of the homework. I use homework to allow my students to practice, to learn, to explore, to understand. Their goal should be to use the homework to gain a thorough understanding of the material, NOT to accumulate points. Since my students can only earn points by passing exams, they (for the most part) gain the correct perspective. I’m afraid that many students in our classes do homework because it’s something they are supposed to do, and have no idea about the goal of the homework.

In the past I have noticed that two things occur on the second exam. First, more people will level up because they understand how important that is. Second, the proportion of leveled up students who pass the exam increases, because they get the message that “understanding the math” is the goal and they make the necessary adjustments. Time will tell …