Attitude

On the first observation day of my B.Ed. program at MUN, I observed a French immersion class that was the picture of a perfect classroom. Students were engaged, behavior was a non-issue, the atmosphere was comfortable and relaxed, and the teacher seemed to be enjoying himself. When I spoke to the teacher afterward, I made a comment about how it must be nice to teach French immersion because the students in your class are the “cream of the crop” I believe were my exact words. The teacher pointed out that the students were not in French immersion because they were highly capable, but because their parents valued education. He believed that if parents valued education, the students in turn valued education, which was what made for the idyllic state of his classroom. This short conversation has stuck with me over the years and has been validated time and again in my own teaching experience.

I’m sure this teacher was not trying to say that parents who did not put their children in French immersion did not value education. Rather, he was simply pointing out that in order for a student to end up in French immersion, the parents must believe in the importance of education. While there is much research showing a positive correlation between achievement and socio-economic status, there are surely parents and students from all walks of life that view education as valuable. The point of the story is not to highlight these particular trends in research, but rather to illustrate how a positive attitude towards learning can heavily impact the value of that learning.

A study by Mura (1995) showed that university professors viewed mathematics as “either a formal abstract system ruled by logic, or a model of the real world.” This dichotomy also seems evident in Boaler’s (2002) study of Phoenix Park and Amber Hill. While Amber Hill delivered their curriculum in a more abstract, traditional behaviorist manner, Phoenix Park chose a constructivist project-based approach. These two approaches had significant implications for the attitudes students developed towards mathematics. Phoenix Park students saw no difference between their school-learned mathematics and the mathematics they encountered outside of the classroom, whereas Amber Hill students struggled to connect the two. At Phoenix Park it was their attitude towards mathematics that allowed them to perform comparably to Amber Hill students on standardized assessments, as well as be able to adapt their knowledge to a variety of other practical situations.   

Last week’s blog focused on the idea that a mix of both traditional and reform methods would be the most effective approach in mathematics. After some more thought and trying to imagine what a Phoenix Park math class would actually look like, I wonder if the open-ended, project-based approach carried out in this school is not already a hybrid of sorts, containing snippets of traditional instruction, as students require them. Even without considering the three months spent at the end of their final year, the Phoenix Park students would have at some point been directly instructed in some form of traditional manner throughout their educational careers. It would not make sense to lean so far in the other direction that students were left without some reasonable level of guidance. Then I consider perhaps it is not so much the mode of instruction but rather the practice time that is holding us back from becoming fully and completely constructivist. While the social context of their learning allowed Phoenix Park students to easily adapt their knowledge to a variety of situations, these students will still require the basic procedural skills necessary to manifest conceptual knowledge into the solution to a problem. Project-based learning helps students in planning towards a solution, but procedural knowledge is a requirement for carrying out that plan. As I said last week, our scales currently feel unevenly tipped in favor of traditional approaches necessitated by a mainly procedural curriculum. Again the discussion leads back to the issue of standardized testing, and its omnipresent erasing of teacher and student creativity. To echo the concerns of one of my fellow classmates Margaret Senior, we have to look at whether these standardized assessments are actually testing what they should be testing. On the GCSE taken by the students at Amber Hill and Phoenix Park, only 30% of the questions were deemed to be conceptual by Boaler. What does this say about the type of knowledge that is valued by the education system?

In terms of the best approach, it comes down to knowing each student individually and constantly transforming the balance of the approach to best fit their needs. Focusing on student engagement and developing positive attitudes towards mathematics should be our primary focus. The challenge is doing so within the confines of time, money and curriculum.

Mura, R. (1995). Images of mathematics held by university teachers of mathematics education. Educational Studies in Mathematics, 28, 385-399.

Boaler, J. (2002). Experiencing school mathematics: traditional and reform approaches to teaching and their impact on student learning. Malwah (NJ): L. Erlbaum.