Good math students or happy math students?

This study has been making the rounds lately and it was in my mind while watching my Geometry and Algebra classes the last couple of days. Basically, researchers found a connection between how much a student enjoys math and how well he or she does. Surprisingly, however, the students with the lower confidence are those that are more successful. The author of the study, Tom Loveless (I do have it admit seeing a man named Loveless say "happiness is overrated" makes me think this came from The Onion), argues that these findings mean that math teachers spend too much time worrying about how students are enjoying the material and not enough time actually teaching the material. Of course, most of us work under the assumption that students will be willing to work harder and spend more time for a class that they enjoy.

In my classroom, I don't see the pattern the authors found. In my experience, the students that seem to show the least confidence are not the best students or the worst students, but more of the middle of the curve. In other words, the highest-scoring students seem confident in the abilities, as do the lowest-scoring students. My high-scoring students do well and know they do well. Although it does not match the pattern found by Loveless, I do not find it surprising or unusual. Likewise, am not surprised that my lower-scoring students show more confidence than other students.

I think this is really a question of cause and effect. Most teachers seem to work under the assumption (one that I found to be enforced though much of my educational coursework) that raising a student's confidence and enjoyment will lead to better performance. Loveless concludes that there is not a connection and the issue is a lack of clear expectations. I believe that both views are oversimplifications. The connection between performance and confidence is also tied to both natural ability and to general academic interests. To clarify, let me break down the three groups (and a couple subgroups) of students I deal with in my math classes:

1. Students who score well - two subgroups:
-- a. Students with strong natural abilities in math. They study little, but grasp concepts quickly and trust their abilities to succeed. Their confidence is a direct result of their natural abilities. Many of them don't claim to be very interested in math, but do well because it does not require much work on their part. For a large majority, they will eventually reach a level of math that does not come so easily and success will require more work than it ever has. I know some of the students will be willing to put in that effort and some will not.

-- b. Students with strong work ethics and spend a great deal of time on the class work. These students do not show the same strong natural abilities of the other successful students but put in the work overcome any deficiencies. These students are willing to work hard either because they enjoy the subject (a rare but not impossible quality to find in middle school math students) or they are simply driven to be successful in school regardless of the subject. They are confident, not as much in their natural skills as mathematicians, but as hard workers.

2. Middle of the curve students:
These students do not find that material comes easily, but they work hard to understand enough to get decent grades. I see a lot of frustration in these students due to both subgroups of the successful students. First, they see the first group of students and are upset by the fact that many of their peers do not work nearly as hard as they do and still do better. They often feel that they "deserve" a better grade because they work harder. Secondly, they see the group of students that do work as hard as they do but get better results. There is a strong desire to succeed with this group, but the lack of results leads to much lower confidence.

3. Students who score poorly:
These students rarely are interested in doing well and show much less effort than their peers. Although I often hear stories about students that try very hard but just cannot get a passing grade, I generally do not see that student in my classroom. In my experience, students that work hard get decent (though not always great) scores. Students who don't have the interest or desire to work for the class do poorly and are not bothered by their results. They often enjoy the time they spend in class, though not necessarily because they like the material or enjoy math. They aren't frustrated by their grades and therefore have fairly high levels of enjoyment and confidence.

Overall, there is a connection between my students' scores and confidence levels, but it is not a simple or obvious one. In order to get a full understanding of the issue, factors such as natural ability and general academic drive must be added to the picture. Students are complicated and understanding how they do or do not succeed is complicated.

That last sentence may be the most obvious result of this entire post.