• PART I

PLACE VALUE, ARITHMETIC MODELS & ARITHMETIC ALGORITHMS

MENTAL MATH

• PART III

PRIMES & DIVISIBILITY

• PART IV

FRACTION ARITHMETIC

• PART V

WORD PROBLEMS & MODEL DRAWING

Part 5vi: Model Drawing

A Brief Word on ‘8 Step Model Drawing’

During the previous clip one of the teachers asked if I would be teaching them the ‘8 step’ method of model drawing. I responded that I would not, and I would like to elaborate on my reasoning.

In the clip I mentioned that during a previous professional development course I taught, teachers that used the 8 step process for a particular problem were ‘wrong’. That was a slight misrepresentation; the teacher in question (who, incidentally, was exceptionally strong mathematically) made a mistake on a particular problem when using the 8 step process. That alone is not the reason that I do not endorse the 8 step process, after all, there could have been any number of reasons for her mistake. At the time I didn’t know much about the 8 step process, so when I tried to diagnose her mistake by asking her how she tried to solve the problem, I was surprised when she responded by first saying “I started by drawing bars of equal length.” This is one of the 8 steps listed in the 8 step process, and the major reason that I warn people of all ages against this procedure.

One of the guiding principles of this website is that everything in mathematics makes sense, and teachers should strive to make sense out of everything they teach their students. As such, no procedure should ever be taught without a mathematical understanding of why it is valid; of all of the procedures we have seen so far (arithmetic algorithms, mental math techniques, techniques for computing GCF and LCM, etc.), we have explained why the procedures are valid in every case. This, in my opinion, is the main problem with the 8 step process; it is just a step-by-step procedure that has very little mathematical reasoning to back it up. The step that bothers me the most is the one I mentioned in the previous paragraph that tells students to start by ‘drawing unit bars of equal length’. This makes absolutely no sense mathematically; it is simply a procedure to be memorized.

To illustrate this further, consider the following problem (taken from clip 5iv):

Mike is two times as tall as James. If their combined height is 105 inches, how tall is Mike?

The 8 step process tells us to start by drawing bars of even length.  How does this make any sense mathematically? If a student were to ask a teacher, “Why do we do this?” what possible response could a teacher give other than “It is one of the 8 steps.” That is not an explanation; it has as much mathematics behind it as “Because I said so.”

To summarize, my main problem with the 8 step process boils down to the following test: If after explaining a topic to your students, you can’t give them a mathematical reason for why it is valid, you need a new explanation.