When Good Teaching Leads to Bad Results: The Disasters of "Well Taught" Mathematics Courses

Schoenfeld (1988) makes some great points about one of the main problems with the learning of mathematics.  He makes the claim that if the lesson runs very smoothly (i.e. students are behaving, paying attention, doing their work and achieving the outcomes) there can still be major problems with their deep mathematical understandings.  As Boaler (2002) points out, the students of Amber Hill are well behaved and are working well but they are learning in a manner that allows them to understand only the surface of completing repetitive practices.  

As stated by Schoenfeld (1988, p.4) routine exercises do not lead to significant understanding of the subject matter and the students in his study showed to have attained the curriculum outcomes but not to have attained an overall connection of the subject to real life applications.  As Jeffery Wilhelm (1997, p. 16) emphasized in his book “You Gotta BE the Book”, in order for students to be successful, they need to have an interest in what they are learning and the subject must be relatable to their own experiences.  

Students are often led to believe that there is only one correct way of completing a mathematical problem and as Schoenfeld pointed out only the correct steps for constructions were correct and the method counted more than deriving the correct response.  We see this every day in our math classrooms.  Students are frequently taught “tricks” to solve problems without really understanding what they are doing.  For example, multiplying two binomials is often taught using the FOIL method.  Students just memorize the steps First Outside Inside Last without understanding that they are multiplying each term in the first bracket by each term in the second bracket.  This often results in many mistakes especially when integers are involved.  Additionally, students seem to find difficulty in completing word problems with fractions or decimals.  The questions may be written the exact same way as if there are whole numbers but once they see a fraction they don’t understand what operation to use or how to complete the question at all.  It shows that Schoenfeld is right, students memorize a method without a deep understanding of what is truly going on!

References:

Boaler, J.  (2002).  Experiencing School Mathematics.  New York: Routledge.

Schoenfeld, A. H. (1988).  When good teaching leads to bad results:  The disasters of "well taught" mathematics courses.  Educational Psychologist, 23(2).

Wilhelm, J. (1997). You Gotta BE the Book: Teaching Engaged and Reflective Reading with            Adolescents.  New York: Teachers College Press.