Schoenfeld Article Good Teaching, Bad Results

The Schoenfeld article, “When Good Teaching Leads to Bad Results: The Disasters of “Well Taught” Mathematics Courses”, while written in 1988, certainly lends itself to discussion about what is happening in our provincial Math program today. The Newfoundland Labrador Curriculum Guide 2009, Interim Edition, for the Grade 5 Program states that “students need to explore problem-solving situations in order to develop personal strategies and become mathematically literate. They must realize that it is acceptable to solve problems in a variety of ways and that a variety of solutions may be acceptable” (p.2). Schoenfeld (1988) writes that the child should be an active interpreter of its experience.

The article also discusses that one of the most commonly used instructional procedures to help students solve problems was the “key word procedure”. I, too, have used this approach in my teaching, because for a number of years, it was an accepted teaching method used to develop problem solving.

The article also mentions that in New York, strict adherence to the curriculum was even more likely because of the state-wide Regents exam. While reading this section, I couldn’t help but think how we adhere to the CRTs while teaching our Math programs.

Many students in our school system did indeed struggle when faced with open-ended tasks because the strategies taught in schools simply required finding the correct formula. In this article, Schoenfeld explores the way students gained proficiency at doing the
procedures of Mathematics without understanding.

That was the way math was taught for many, many years. Focus was on performing a series of steps, without the understanding.

According to the Curriculum Guide (2009), Mathematical reasoning helps students think logically and make sense of mathematics. “Higher-order questions challenge students to think and develop a sense of wonder about Mathematics” (p.7).

Last week, in my own Grade 5 classroom, these two situations arose. In discussion on numeration, children were asked to make a six-digit number (up to one hundred thousand) on the Place Value Chart using only 8 counters. Once the number was modelled, the students had to write the Standard Form, Expanded Form and write the number in words. Out of 18 students, only two students put all of the 8 counters in the hundred thousands place to make their number 800 000. While they saved themselves a bit of work, I would venture to say this was mathematical reasoning and logical thinking on their part.

One other student placed the eight counters in the ones place and therefore made his number 8. He was showing reasoning also but was lacking number sense. However, when questioned about what he had done, he knew right away where his mistake was. Of course, he said, “I meant to put the 8 in the hundred thousands place.”

Most students modelled the number while placing the 8 counters in each value of the chart, thus showing their understanding of Place Value.

The Provincial Curriculum Guide (2009) states that when planning for instruction, teachers must decrease emphasis on rote calculation, drill and practice, the size of numbers used in pencil and paper calculations, and allow more time for concept development. “Problem solving, reasoning and connections are vital to increasing mathematical fluency, and must be integrated throughout the program (p.14).

As the Provincial Curriculum Guide (2009) writes – students learn by attaching meaning to what they do. Therefore, they need to construct their own meaning of Mathematics.

Rosemary' s Math Autobiography

Math Autobiography Education 6630

Wow!! I have to go back quite a few years as I think about my early Math Education. What I do remember is that Math class was being a very rigid and very structured experience. All students, regardless of ability were on the same page, at the same time (one size fits all approach). Concepts were taught in the abstract without the use of any manipulatives.

It was also a school system where one didn’t ask questions but just listened quietly and tried one’s best to be successful. I had older brothers and sisters who helped me with my homework. My parents also sat with us children to do homework. I was very lucky in that any concepts I didn’t understand in school were taught to me at home. In primary and elementary school the very basics were taught and drilled. For some reason, I remember Geometry as first studied in Grade 7.

I would think one of the worst memories was being afraid in school to ask for help.
One of my best memories was having the ability to grasp all math facts quite easily.

There was never any group work and very limited individual assistance. While I never really struggled with Math, Language Arts was my strongest point.

The role of the teacher was to instruct – which they did indeed. Math was an everyday subject and an every night homework assignment. There was a huge amount of drill and practice and I really believe it never hurt me. As I got older, the reasoning came. All homework completed the night before was corrected the next day in school. There was no such thing as a calculator so it was all brain power!

Assessment in Math was 100% testing. I don’t remember ever having marks based on projects and the work completed over the year. At the end of each term there were tests and then at the end of the year there was one test based on the whole year’s work. High school back then was Grade 9, 10 and 11. In high school, I did CHE exams (Government exams) based on the whole year and these also were worth 100%. Every High school student in the province was writing the same test per grade level, at the same time, for one week after school closed in June. You either passed or failed the year, based on that one exam.

What I remember about the Math in High school was much like elementary school. Geometry was the worst concept for me and I really can’t remember why. Today, I really enjoy teaching Geometry. I’m not crazy about Transformational Geometry but I do tolerate it!! I cannot remember anything about high school Algebra. I know I really disliked it and that is probably why I can’t remember!!!!

I took one education Math course years ago at MUN. I have never taken any Math electives. In my teaching career, I have had a number of PD Days based on the Math programs that I have taught. I have a ½ PD session on this new program coming up on September 30.

In my early teaching years, I taught math much the same way as it was taught to me, BUT I always made sure I helped my students individually and made sure that if they didn’t understand what I was doing, they had to ask for help (that memory of always being afraid to ask for help still haunts me).

Right now I feel that we try to teach too many concepts in the Math Program in a short period of time. With my small class size, I do have time to individualize instruction. I have resources and many manipulatives available to accommodate the different ability levels in my classroom. The new Program does challenge children to reason logically about concepts that they are being taught. 10 minutes of Mental Math activity is part of my daily routine in school. Assessment is continuous throughout the program.

One of the drawbacks that I see with the program is for those students who have problems with written output in Language Arts. While I have had students who were good at computational Math and could verbalize their reasoning and solutions, being able to express their thinking in writing poses a problem. For me, as the classroom teacher, I can accommodate my students but when it comes to CRTs, many times, these accommodations cannot be made.

I do think parents today are confused with the new Math. Many admit they cannot help their children with any Math homework. One of my homework projects for this week is for students to scan the newspaper for the largest numbers they can find. If only homework had been so creative when I was in school! It should be interesting to hear parental comments about this homework activity.

I enjoy the new program and am, many times amazed at the ways children can arrive at solutions to problems. As educators, enabling our students to become critical thinkers is a major part of all curriculum areas in child development. When I began teaching the new Math program a few years ago, I did much critical self-reflection as I tried to better understand the experiences that informed my practice as a math teacher. I enjoy teaching the new program better as children can verbalize and show their logical reasoning much more. With this program, children are not afraid to take chances.

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