Schools of Thought

In an additional effort to clarify why I believe that Authentic Education is the course that will ultimately lead to all children gaining the skills to achieve their highest potential, let's look at a research study. I've provided statements of ideology and evidence supporting its genesis, and I've demonstrated some concrete examples, so this "objective" level seems the natural next step. Sadly, there are so very few schools that actually embody what I consider Authentic Education that it's difficult to point to a bevy of scientific studies.

Moreover, schools aren't laboratories, and while controlled, carefully designed scientific experimentation is of course crucial and should always be the goal (and science should always be the basis for policy), the fact that one class of students can be markedly different from another class in the same school in the same grade leaves things thornier than in most any other field. Thus, this research approaches Authentic Education somewhat indirectly, but is still extremely edifying. I don't pretend to say that it proves my case conclusively nor that the methodology is perfect; I simply offer it as another piece of evidence. Keep in mind while you're reading that Authentic Education is not synonymous with constructivism and does not demand a one-size-fits-all style of teaching.

As an aside, after this post I'm going to try to move on in terms of post topics. Authentic Education will be a heavily recurring theme on the blog, but there are plenty of other things going on right now in the world of education policy that are worth talking about. So, without further ado, the study I'm going to quote at length was explained by its author in EdWeek back in 1999:

Two schools in England were the focus for this research. In one, the teachers taught mathematics using whole-class teaching and textbooks, and the students were tested frequently. The students were taught in tracked groups, standards of discipline were high, and the students worked hard. The second school was chosen because its approach to mathematics teaching was completely different. Students there worked on open-ended projects in heterogeneous groups, teachers used a variety of methods, and discipline was extremely relaxed. Over a three-year period, I monitored groups of students at both schools, from the age of 13 to age 16. I watched more than 100 lessons at each school, interviewed the students, gave out questionnaires, conducted various assessments of the students' mathematical knowledge, and analyzed their responses to Britain's national school-leaving examination in mathematics.

At the beginning of the research period, the students at the two schools had experienced the same mathematical approaches and, at that time, they demonstrated the same levels of mathematical attainment on a range of tests. There also were no differences in sex, ethnicity, or social class between the two groups. At the end of the three-year period, the students had developed in very different ways. One of the results of these differences was that students at the second school--what I will call the project school, as opposed to the textbook school--attained significantly higher grades on the national exam. This was not because these students knew more mathematics, but because they had developed a different form of knowledge.

At the textbook school, the students were motivated and worked hard, they learned all the mathematical procedures and rules they were given, and they performed well on short, closed tests. But various forms of evidence showed that these students had developed an inert, procedural knowledge that they were rarely able to use in anything other than textbook and test situations. In applied assessments, many were unable to perceive the relevance of the mathematics they had learned and so could not make use of it. Even when they could see the links between their textbook work and more-applied tasks, they were unable to adapt the procedures they had learned to fit the situations in which they were working.

The students themselves were aware of this problem, as the following description by one student of her experience of the national exam shows: "Some bits I did recognize, but I didn't understand how to do them, I didn't know how to apply the methods properly."

In real-world situations, these students were disabled in two ways. Not only were they unable to use the math they had learned because they could not adapt it to fit unfamiliar situations, but they also could not see the relevance of this acquired math knowledge from school for situations outside the classroom. "When I'm out of here," said another student, "the math from school is nothing to do with it, to tell you the truth. Most of the things we've learned in school we would never use anywhere."

Students from this school reported that they could see mathematics all around them, in the workplace and in everyday life, but they could not see any connection between their school math and the math they encountered in real situations. Their traditional, class-taught mathematics instruction had focused on formalized rules and procedures, and this approach had not given them access to depth of mathematical understanding. As a result, they believed that school mathematical procedures were a specialized type of school code--useful only in classrooms. The students thought that success in math involved learning, rehearsing, and memorizing standard rules and procedures. They did not regard mathematics to be a thinking subject. As one girl put it, "In math you have to remember; in other subjects you can think about it."

The math teaching at this textbook school was not unusual. Teachers there were committed and hard-working, and they taught the students different mathematical procedures in a clear and straightforward way. Their students were relatively capable on narrow mathematical tests, but this capability did not transfer to open, applied, or real-world situations. The form of knowledge they had developed was remarkably ineffective. At the project school, the situation was very different. And the students' significantly higher grades on the national exit exam were only a small indication of their mathematical competence and confidence.

The project school's students and teachers were relaxed about work. Students were not introduced to any standard rules or procedures (until a few weeks before the examinations), and they did not work through textbooks of any kind. Despite the fact that these students were not particularly work-oriented, however, they attained higher grades than the hard-working students at the textbook school on a range of different problems and applied assessments. At both schools, students had similar grades on short written tests taken immediately after finishing work. But students at the textbook school soon forgot what they had learned. The project students did not. The important difference between the environments of the two schools that caused this difference in retention was not related to standards of teaching but to different approaches, in particular the requirement that the students at the project-based school work on a variety of mathematical tasks and think for themselves.

When I asked students at the two schools whether mathematics was more about thinking or memorizing, 64 percent of the textbook students chose memorizing, compared with only 35 percent of the project-based students. The students at the project school were less concerned about memorizing rules and procedures, because they knew they could think about different situations and adapt what they had learned to fit new and demanding problems. On the national examination, three times as many students from the heterogeneous groups in the project school as those in the tracked groups in the textbook school attained the highest possible grade. The project approach was also more equitable, with girls and boys attaining the different grades in equal proportions.

It would be easy to dismiss the results of this study because it was focused on only two schools, but the textbook school was not unusual in the way its teachers taught mathematics. And the in-depth nature of the study meant that it was possible to consider and isolate the reasons why students responded to this approach in the way that they did. The differences in the performance of the students at the two schools did not spring from "bad'' teaching at the textbook school, but from the limitations of drawing upon only one teaching method. To me, it does not make any sense to set any one particular teaching method against another and argue about which one is best. Different teaching methods do different things. We may as well argue that a hammer is better than a drill. Part of the success of the project school came from the range of different methods its teachers employed and the different activities students worked on.

So, there's another block on the tower.

This entry was posted on Sunday, September 11, 2005 at 1:59 PM. |