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

Math Autobiography

The year was 1988 and I began my first days of official math class as a mighty Kindergarden learner. I recall our classroom very well. The chairs had never been sat in, the crayons have never been used, the blocked brand new. We were the first cohort in a brand new school and little did I know we had manipulatives galore. Tackling our counting numbers came with many bright blocks, hand-size bumble bees with sticky backs we could use on our counting boards. I always remember working in primary and elemtary grades in groups for mathematics, sometimes in pairs, but usually groups of four. From what I can remember my teachers did use the textbooks extensively back then, often page by page progressing chapter by chapter through the book. For the frist three grades we used the MAth Quest 1 and 2 where we'd write in the actual books. I remember it being so cool but I also recall when we'd have to practice carrying the questions over from the books to our own exercises at the start of grade 3.

I remember math being very easy with much drill and practice. I never recall games or investigations that we did play, but my teachers were colorful so I'm sure some fun things were done as well. In elementary grades I do not recall the fraction strips we see in today's classrooms but rather a set of rules that we just had to know. All in all though I found the math easy, probably too easy, often bored at times. I just got it, immediately very often. I remember my teachers telling my parents at PT interviews that I was gifted in the subject area and should study it further probably as an account because get this (I could do better than a teacher - haven't we all heard that encouragement before!) There was no enrichment from what I can remember, no math competitions eithers. One thing I remember from my cousins who struggled a bit more with the maths back then was that their parents seemed to be able to help them (Is this still true today given how much the math has changed accoring to today's parents?).

So I guess my worst memory was that the math was never really challenging for me most of the time. Therefore, my greatest memories includes being able to help my friends in class, proud that I was able to be the teacher's helper when I got my work done. Now, more than 20 years later I look back on the way it was then and realize that there needs to be a greater spread in the curriculum, opening up room for more capable students to still keep their interests peaked, and also more investigative, hands on methods for young children to understand the math their expected to learn in a manner they are capable of applying. Sure, there needs to rules and reminders but they cannot be the essence of an introduction to a topic with students expected to micmic the laws of math with just pencil and paper work exclusively. I remember my teachers for the most part being the leader in the class. I don't recall much student-centered learning taking place during my elementary years. The chalk board was very often the centre of our classes. My teacher's seemed to enjoy teaching mathematics, and provided enthuasism especially for word problems in middle school years. We would practice four steps to solving a problem: 1) Re-write the question in our own words; 2) indicate which operations we'd have to use 3) Solve the problem 4) State the answer in a sentence. Ourside of formal tests I don't remember there ever being journal entries, portfolios, or other alternate assessments (besides assignments) at any point until grade 9. Most tests I recall were a combination of selected response items and constructed response items, however the lack of graphics still remians in my mind.

My high school days of mathematics were much different than the first 10 years of class. I was in one of three classes in the province that were part of the pilot program for the present stream of Math 1204, Math 2205, Math 3205, Math 3207 courses. There was no textbook but rather a series of booklets which contained very little direction, practice, or help. The courses were clearly way too loaded with material. I recall spending a lot of our classes going through very tedious investigations that needed much pruning and modifications. Math classes were very frustrating for both us and our teacher, a woman with more than 24 years of experience in the math classroom. Again, I found the "math" part easy, but it was frustrating working through all the cracks and gaps in the curriculum we were given to work with.

I went through my B.Sc. degree, completing 18 math courses in the Applied Mathematics program. Ranging from calculus to linear algebra to numerical analysis, including ODE's and mathematical modelling my program provided a wide range of mathematics to study. Do I engage in mathematics in major ways in my life? Well as a math teacher of course the answer should be yes, and it is, but to to the extent that I wish it would be. I really would like to be able to devote more time to researching mathematics, learning and exploring more issues and new theories in the area. In my three years in the profession thus far I've served in several school district committees in the areas of improving test design, adopting and faciliating technology into the classroom, and improving math interest through "math fun days" held at the school. At the college level I took part in curriculum modifications for entry-level math courses and developed a MPT for registered students at the CNA-Q campus.

All in all I'm very much enjoying the role that teaching and learning mathematics is serving in my life. I realize its importance, I see its potential, and I strive to engage and open up more young people's minds to the possibility that the maths have.

SAW

Creativity At Its Best Or Worst?

I must admit that my years of being educated and educating never once have I heard such a brillant point of view on schools usefulness in the creativity department! Sir Ken Robinson has spectacularly brought out for us the notion that the system we have been manipulating and pruning for more than two hundred years since the Industrial Revoultion, the same system we claim is the only true, guaranteed, systemic means out of poverty, is in fact the same one that is destorying and rejecting the creative capabilites of today's and tomorrow's children. Can it be true that the ingenuity of many children are being "squandered ruthlessly" by the creators, protectors, and servers of our education system?

After watching this video I gave some thought to the children I've had as part of my classes over the past three years, and even before then as a student myself, a peer. We've all had them in our class - the guy who never is willing to freely engage in class discussion, the girl who mkaes excuses for why her work is not compelte, the one you think is just too lazy to put forth the effort required to pass on the grading rubric. Am I a boring teacher? I hope not. Are they just not interested in learning and being successful? I think not, well most anyways. But in all honesty I think we've all had could-be's, should-have beens in our class. Granted our math classes weren't the nail in the coffin to elimiate and defer a child's true potential from their passions and goals, but we are part to blame - unconscious of it as we are.

Robinson's words must make us realize the power and ability we as teachers have to evoke change, instill dreams, and provide hope. We should tread lightly with our most vulnerable clients, not isolate them further from the norm, but rather integrate them and their potentials into something that become meaningful. Be realistic, too. Take the time to show the doors that open when education, integerated with determination are put into play. All too often we point to the university educated as our most successful, to those with more letters after their name than Kellogg's has Corn Flakes to provide exemplars for our young. Why is that? Because we've been taught this way and we're simply "paying it forward." We, as teachers, as graduate students are examples of a mind-set which pays homage to B.A.'s and M.Eng.'s , rightly by society, wrongly by the Sir.

So let's use our math classrooms and schools as more than just a place to turn algebra tiles over, more than just a place to cruch numbers through algorithms, and even more than just places to make spectacular discoveries through discovery and calculation. Let's reach into our student's and talk with them through formal and informal instruction about their goals, their expecations of us as their teachers, and themselves. Are we ready for that? How creative can we be?

On Board!

Hello everyone! My apologies for the very late delay in starting here. I'll be doing catchup now over the next few days to respond to Mary's blog entries. Enjoy the last few hours of summer!