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.