A Mathematical Message for Parents

Michael Round

August 11, 2009

A Follow-Up

I've posted part of a previous column below this conversation taking place yesterday.  I was asked about things I've been doing with math education.  Here is how the dialogue went:

Answer:  "Many things, many programs, lots of stuff."

Question:  "Who's it for?"

Answer:  "Kids at home - on their own and at their leisure."

Question:  "Why not in the classroom?"

Answer:  "I've given up on math-reform in the classroom.  It will never happen".

Question:  "Why do you say that?"

Answer:  "Look at how math has been for the past 1/2 century.  It's been horrible.  And people are still complaining about it.  You try to do something new and it has to conform to the standards set by a group of people responsible for creating the results we see right now."

Question:  "So what would you do to change it?"

Here I stopped.  What if I answered the question?  I've given his question years of thought.  I've developed a number of programs.  I've written a number of books.

What has he done?  How much thought has he given to the problem?  What's the use of even answering the question?  His failure to understand the system, the problems, etc., would only make me mad if I explained it and immediately saw the fact he didn't get it! 

He has no idea - absolutely none - of the magnitude of the problem I just described.  He has no idea No Child Left Behind only makes me less optimistic of the future of math education in this country.

Moreover, the average parent has heard the talk for decades about math reform and promises the failures of the "New Math" were corrected by "new math programs", etc.  More likely, my credibility would be questioned:  why should someone believe Mike when there are teams of professionals working on this?

But what about talking about this to the people who do have an idea - the math professionals?  Hopeless.  They're caught in the system that says, "First arithmetic - then algebra - the geometry - mix in some statistics - blah blah blah."  Tell them something new you're working on and you may get a "neat" response.  It will immediately be followed with a "But how does it fit in with Standard X.1.4.a and Y.4.2.b, blah blah.

I can't blame them.  This is what they know.  It's what they've been taught.  But I also do not have time for it any more.

And things seem hopeless.

But I don't think they are!

But if the math professional is not the target, and the average parent doesn't understand the nature of the problem, what's to do?

The average parent may not understand the nature of the problem, but they could!  To understand the logic of why the system is what it is, why reforms have not helped, and why there is little hope for the future - given the way things are the way they are.

And to see there IS a way out - if we ourselves take back math education!

My next math book is geared towards parents.  Parents of kids.  Parents who are sick and tired of hearing of "math reform", "new math", etc., decade after decade, and seeing the same results, the same nonsense, etc.

And while most books like this are hundreds of pages long - and unreadable - this one will be 40 pages long (maximum) and readable by everyone!

Stay tuned ...

The 21^st Century and Math

in the United States

 The May 19, 2009 Boston Globe reported the following:

"Nearly three-quarters of the aspiring elementary school teachers who took the state's licensing exam this year failed the new math section, according to results being released today that focus on the subject for the first time."

What are your first thoughts regarding this story?  Anger?  Puzzlement?  The former, perhaps, in response to the sentiment, "How can so many adults not pass a math licensing exam for elementary schools?", the latter, maybe surprisingly, with the same question!

What is going on here?

Before we rush to judgment, ridiculing the many aspiring teachers failing the exam, let's take a look at what the state licensing exam consisted of. As this was an exam certifying teachers to teach elementary school, my thought is the test would consist of elementary-level math.  Let's see.

Here are a couple problems from that exam:

Sample Question #3

The measurements in this diagram are shown rounded to the nearest whole number.  Which of the following is a possible value of A, the area of the rectangle?

My initial answer to the area is 8.  Obviously, it's not right.  There is no '8' to choose from.  Oh, that's right.  There can be rounding, so the "real width" can be as low as 1.51, and as high as 2.49.  Similarly, for the length, the minimum width is 3.51, the maximum 4.49.  Using these, I can calculate the minimum and maximum areas of the rectangle:

Once again, I know the right answer is 5.5 square inches - only because the other three choices (5.0, 11.5, 12.0) are outside my range.

Problem after problem is like this.  I'm not sure of the answer.  The only way to get an answer is to look at the given answers.  It's awful.

Let's try a couple more, quickly.

Sample Question #4

A book distributor is trying to divide an order of textbooks into equally sized groups for shipping in cartons.  The textbooks can be divided into groups of 12, groups of 15, or groups of 18, with no books left over.  Which of the following inequalities is satisfied if N is the smallest possible total number of textbooks?

I'm honestly still trying to figure out what this question means.  Even the four answers provide me little clue:

A.  100 <= N < 150

B.  150 <= N < 200

C.  200 <= N < 250

D.  250 <= N < 300

Sample Question #5

The prime factorization of a natural number n can be written as n = pr² where p and r are distinct prime numbers.  How many factors does n have, including 1 and itself?

I get the right answer - eventually - by doing a few examples, but hardly anything approaching an answer I'm entirely comfortable with.  I hope I get the answer right - 4.

Then, I come upon a gimme - the type of problem I'm great at:

Sample Question #6

Given that 100 milliliters is equal to approximately 0.4 cup, 205 milliliters is equal to approximately how many cups? 

I love this type of problem, because I can structure it so I'm certain things work out right - because I'm always canceling units.  The answer is easy:  0.82 cups.

This is but one of several methods ... there's also one of proportions, where I could do the following and solve for x, which, of course, gets me the same result:

However, when I go to find the right answer, I see the problem was not even asking for an answer!  It was asking "which expression models the solution to the problem?"  The possible answers are:

A.     (100 - 0.4)(205)

B.     105% of 0.4

C.     (205 - 100)(0.4)

D.     205% of 0.4

What is this?  Where's (205)(0.4)/100?  It's not there!  I've got the answer plus two beautiful methods, and none of this appears anywhere!

A Little Bit of Empathy

My initial reaction regarding the headline, one of incredulity about the ignorance of adults not being able to do elementary math, has been replaced with the emotion of anger at what the test actually was.  What was it testing? 

Certainly not much related to what the average adult would be considered important regarding math and elementary-aged students!

Instead of anger, I feel empathy - perhaps even shedding a mathematical tear - towards the real victims in this case:  the teachers - and yes, the eventual students.

We see too, with this small review, better teachers and more money would solve nothing.  Like the miller's daughter in Rumplestiltskin, if this tested material at all mimics the actual elementary curriculum, teachers are being asked to spin straw into gold.

But the test was intentional.  Someone wrote the questions.  Who?  Why? To what end?  So too is the underlying curriculum.  Where does this come from?  

And what has this to do with the problems we've seen in math over the past 1/2 century, continue to see today, and likely will see into the future?

Unless something can be done.