When Good Teaching Leads To Bad Results....

As educators and parents we all want our students and children to be part of a classroom that is successful - that is, well managed and well taught, with impressive performance measures and results. Yet, how many of those same classrooms are probably, mind you unintendedly, "an important and illustraive failure?" We have been cultured and have accepted and truly believe that an A in math surely equates proficiency int he subject area. However what is behind that grade, what was required to attain such a desired status? In Schoenfeld's article the alarm is sounded that many perhaps many of us are victims of learning and possessing a fragmented understanding of many math topics with frail backgorund to make connections between different subject matter streams. Have we been learning inacurately? We are teaching inacurately? Is this accepted and justified system impeding, as Shoenfeld says, the acquisition and use of other mathematical knowledge.

Shoenfeld talks brings to leight several empirical standards that he discovered during his research. While reading about his findings I realzied many similarities here in our own provincial system comapred to his studies in America. As a teacher of CRT and public exam courses there is a high degree of pressure put on the teacher from government and school districts to get the marks up in provincial assessments. The primary focus on many professional development days included how to move our district from the bottom in pronvical testing results. Are governments suggesting to test design boards to lower the degree of difficulty in public exams so that the pressure will be lessened from parents? In our B.Ed. programs we always joked about what the right answers were to the questions posed when interview time came around. "Oh, I'll teach my math course according to the outcomes, follwoing the suggested guidelines as prescribed in the provincial curriculum." We gave the textbook answers, the ones they wanted to hear. In actual fact we all knew we'd have to follow the system and teach to the public exam. Here we were fresh, new, innovative teachers and already at Day 1 we felt the pressure to cover off ourselves and our students by teaching according to how the public exams were developed. Schoenfeld hits home when he says that the amount of time given to teacher and the way to teach it for "mastery" of the topic is the centerpiece of many assessment outlines today. Accuracy and speed has without a doubt compromised the ability of many student's to understand math. Look through many CRT and public exams- the amount of credit given to explaining and answeris minimal. Really, it's pathetic!

I agree with his findings that students have this notion that any math problem should be solvable in a few minutes. Many will give up or not even attempt problems that they'r enot compeltely sure of. Yes, there needs to a place for drill exercises and exploratory problems. However, as Shoenfeld points out our system needs to allow to students to become engaged in real mathematical thinking, where concrete and abstract thinking can occur, where relationships are made with real-life phenomeon. Non-routine problem solving seems to be disappearing from our curriculum entirely. I remember back in the ninth grade we would have three non-routnine word problems to solve each week ongoing throughout the entire year. Just last week a teacher commented to me how great the new math program is in grade eight because the worksheets developed for the course gives an examples of every type of problem the student would ever be expected to know. I immediately thought, is that really what we want?

While reading about Shoenfeld's findings on the "form of mathematical answer is what counts" I recall seeing as a student myself and as a teacher copy of tests in which very little credit was given for the workings wrote down in response to the question on a test. Granted the answer was not correct, but if time was given to really look through the workings you would very often find many correct ideas being used in the problem. But because it was not written in the way taught in class students very often do find themselve sbeing punished for venturing outside the narrow guidelines from class. Much improvement has been made in provincial assessments but really how much of it goes uncontrolled in the typical classroom? Again, relating back to Sir Robinson's idea, how often is the creativity of the students (in this case solving, or attempting to solve, the problem in an alternate form) rejected? How can we move students beyond the point where they simply view themselves as "passive consumers of others mathematics"? How do we allow them to see that through their own mathematical modelling and experimentation and study they can make new discoveries for themselves and deduce meaning for why and how things happen in their own lives through the use of math.

Schoenfeld leaves us with many wonderful ideas to ponder and reflect on. One that struck out to me was that "if we intend to affect practice, we will need to become deeply involved in the development and testing of instructional material." We need to examine our practices as educators in how we test and evaluate our students. To do that the curriculum we're given to teach does need revising, do need to include more real mathematical thinking opportunites, does need to provide us with irection for how we can improve our evaluation and assessment strategies. We just need the round table to not just be heard, but to also feel heard.

SAW