My own research

November 5^th, 2008

Well, after discovering that students did not perform as well on the procedural question as they did on the conceptual question, I really began thinking. I really started to wonder where these kids were with regard to their performance in math compared to where the class I had last year been at this time. This led me to decide I was to give a test. Yes, a test. At this point, we had covered outcomes from the first two units. I decided to take the two unit tests I gave last year and mesh them together to create one. I looked at the final product and was not happy with what I saw. The two tests that I gave last year were about 85% procedural with 25 questions that were closed, (multiple choice, fill-ins, and short answer questions) with only two conceptual questions. Oh my gosh! What was I thinking? Those poor kids. How was I really able to assess their UNDERSTANDING? So, I took some of the more procedural questions and made them more open, using the different strategies as identified previously. I did this to ensure I had an even number of procedural and conceptual, as I wanted to see how they performed on the procedural compared to conceptual as well as how they compared to last year’s class. (I know this is not a real valid test, but I think the results say something.) I gave the test without students knowing about it before hand, and ironically, and honest to God, the class average of this year’s grade 6’s was the exact same as last year’s class.

Let’s take a closer look into this. Last year, students completed many questions that were very similar to the test questions; they were given an assignment, a study guide and two hours for review. This year’s class was not given any of this and they were still able to perform as well, percentage wise as last year’s group. Actually, I would argue that this years class knew more of the concepts than last year, given they had no review or notice of the test.

Given this information, I then studied the test more closely. I wanted to see how students did procedurally versus conceptually. I looked at the assessment and calculated the percentage correct on procedural tasks and then calculated the percentage correct on conceptual questions. I then broke it down further into boys and girls. Here are the results:

	Boy	Girl
Procedural Correct	69%	79%
Conceptual Correct	67%	80%

From this table you can see that girls are outperforming the boys both procedurally and conceptually. This coincides with Boaler (2002) in her study as she suggests that a problem based approach to teaching math may in fact favor girls’ disposition and quest for understanding math, and not just playing the ‘math game’, as boys sometimes are seen to do. Boaler (2002) discusses the dissatisfaction of girls at Amber Hill School, where math is taught in a more traditional approach. Boaler (2002) state that “women tend to value connected knowing, characterized by intuition, creativity, and experience, whereas men tend to value separate knowing, characterized by logic, rigor and rationality” (p.138). Boaler (2002) then goes on to note that as a result of doing many studies and other data sources she is convinced that “it was this desire to understand, rather than any difference in understanding, that differentiated some of the girls from the boys” (p. 140). I see this in my classroom as the girls are always engaged in their tasks and always trying to understand why this is or that. One girl in particular has said to me on numerous occasions that she likes math a lot better this year because she finally understands what is going on. The boys, on the other had, also resemble what Boaler is talking about. I see them wanting to just finish their work and to them, it seems that it doesn’t matter if they understand or not. I asked a student (male) one day if he understood why the pattern worked in the particular way it did, and he replied “Not really miss, but I have it done, and now I don’t have to do it for homework.”

Am I concerned that the boys are not performing as well as the girls? Am I worried that using this approach is favoring one gender over the other? Yes I am, but according to Boaler (2002), she insists that although the boys in her study stated that they did not enjoy the open approach, “there were no significant differences in the achievements of girls and boys” (p.150). I have to keep believing this approach will work for both boys and girls.