Wednesday, February 11, 2015

Lucia Traditional vs Reform Mathematics in NZ and the US

The Promised Part II on the Failure of Mathematics Teaching in New Zealand...



I really, really like mathematics. I understood it easily at school, came first in my entire 6th form year in Maths, Physics and Chemistry in the mid-80's, and enjoyed teaching it to my boys when we were homeschooling. I grew up to be a computer programmer (and software developer and more). In other words, I moved into a STEM field with ease.

Strangely enough, I have discovered that people's eyes glaze over when you talk too much maths. Even just a little bit can be too much. For instance, no one has commented on my previous post: Mathematics in NZ at NCEA Level in a dismal state.  Ok, there were a couple of comments on Facebook, but one of those comments was about the picture I accidentally chose for the post.  Also, I've gone and on about these same issues and more to my husband, and after listening politely, he is unable to comment much and changes the subject.

Hopefully this will be an easier post to read and understand now that I've got the previous one out of my system, so to anyone whose eyes haven't glazed over, I'll just remind you that of the philosophical way that mathematics is supposedly taught in New Zealand before I launch into my comparisons of the two styles. Here is a quote by  Derek Holton, from the Forward of the 2009 Findings of the NZ Numeracy Projects:

An emphasis on letting students explore and absorb number sense, rather than teaching them learned algorithms without any understanding, seems to be the right way ahead for students to gain an understanding of number and, possibly more importantly, of liking and feeling comfortable with mathematics itself.  At all costs, we should ensure that we never return to the hundreds of algorithms that have made mathematics a wasteland full of rote learning of incomprehensible rules.
This style of mathematics is called "Reform Math" or "New Math".  It has some laudable aims, as can be inferred from the quote I've given above.  In the post from the other day where I linked to Nigel Latta's television programme on education of school children in New Zealand, you get the idea that because it's not like it was when most of us were at school, very few of us understand it, and have trouble knowing whether or not it's better or worse.

I think it's worse, much worse than what was being taught back in my day (I did 6th form maths in the mid-80's), but unfortunately I have very little memory of exactly what I was taught.  I haven't been able to find any maths text books from that era, so if anyone can help me with that, I would be very appreciative.

However, I have found a very interesting report (Mathematics Educators: Shaping the Curriculum?, that goes into a bit of the change that occurred in NZ maths, first in the 1960's, lead by university mathematicians, and then in the 1990's lead by maths educators*.  It's the result of what occurred in the 90's that I'm taking serious issue with. Thankfully I was taught in the 1960's style:

It is useful in a comparison of influences in the two periods to have some understanding of the nature of the curricula and how they are different. The 'New Maths' of the 1960s had its origins in the structure of mathematics itself and was concerned with children learning the laws of mathematics from its axiomatic base. Content was organised around algebraic structure and there was little concern for pedagogical matters (Neyland, 1991). Emphasis was placed on rules and the one way of solving a mathematical problem.
The curricula which came out of this were 'teacher proof and textbook driven (Apple, 1992a).

In contrast to this, changes in mathematics curricula in the 1990s focus on the teaching and learning of mathematics with an emphasis on problem solving and multiple ways of 'doing mathematics'. The curriculum aims to "help students to develop a variety of approaches to solving problems involving mathematics, and to develop the ability to think and reason logically" (Ministry of Education, 1992, p8). It is stated that
"mathematics is best taught by helping students to solve problems drawn from their own experience ... real-life problems are not always closed, nor do they necessarily have only one solution" (Ministry of Education, 1992, pl1). Students construct new knowledge and refine their existing knowledge and ideas (Ministry of Education, 1992). The use of technology is encouraged as a tool for learning. Mathematics is perceived as a human activity, culturally produced and socially constructed (Walshaw, 1994).

In the United States, most probably because of their much larger population which doesn't let the government get it's own way, there have been and continue to be major math battles over the curriculum.  Many parents and maths teachers don't like the new or reformed math, and will go to war with the teaching authorities to get the Reform Math turfed out.

From the New York Times : The Faulty Logic of the ‘Math Wars’

At stake in the math wars is the value of a “reform” strategy for teaching math that, over the past 25 years, has taken American schools by storm. Today the emphasis of most math instruction is on — to use the new lingo — numerical reasoning. This is in contrast with a more traditional focus on understanding and mastery of the most efficient mathematical algorithms.

A mathematical algorithm is a procedure for performing a computation. At the heart of the discipline of mathematics is a set of the most efficient — and most elegant and powerful — algorithms for specific operations. The most efficient algorithm for addition, for instance, involves stacking numbers to be added with their place values aligned, successively adding single digits beginning with the ones place column, and “carrying” any extra place values leftward.

What is striking about reform math is that the standard algorithms are either de-emphasized to students or withheld from them entirely. In one widely used and very representative math program — TERC Investigations — second grade students are repeatedly given specific addition problems and asked to explore a variety of procedures for arriving at a solution. The standard algorithm is absent from the procedures they are offered. Students in this program don’t encounter the standard algorithm until fourth grade, and even then they are not asked to regard it as a privileged method.
[...]
Reform math has some serious detractors. It comes under fierce attack from college teachers of mathematics, for instance, who argue that it fails to prepare students for studies in STEM (science, technology, engineering and math) fields. These professors maintain that college-level work requires ready and effortless competence with the standard algorithms and that the student who needs to ponder fractions — or is dependent on a calculator — is simply not prepared for college math. They express outrage and bafflement that so much American math education policy is set by people with no special knowledge of the discipline.
From the American Thinker: Reform Math Must Be Destroyed Root and Branch:
The common denominator of all these inferior programs is an artificial complexity, and an emphasis on learning concepts and “meaning” without actually being able to do problems.  These programs teach algorithms that parents don't know.  A tremendous separation is created between the generations.  Parents are rendered irrelevant.  The children are frustrated to tears.  In a few years, in all of these Reform curricula, the kids end up dependent on calculators.

I think a little of these maths wars must have erupted in NZ to a certain extent, otherwise why would there be so much support for the NZ Government implementing National Standards for primary and intermediate school children?  Unfortunately the Standards are themselves contaminated by Reform Mathematics, as well, as I noticed when I first looked into them, so National Standards can do very little to raise maths standards.

To be continued ...

* Updated 5:16pm - had the two groups mixed up.

3 comment(s):

excuse me said...

Well said, Lucia. Whatever else a student learns, familiarity with the traditional 'basic' algorithms is fundamental to feeling comfortable with numbers in everyday situations - without the eyes glazing over whenever numbers, fractions or percentages appear. I look forward to your next instalment.

johnwhytenz said...

Hi Lucia,

As a son of two teachers (one maths one physics) and now with a young family I am reading your comments with interest. I remember my early maths (up to form 5) being very much focused on 'real life examples'. I remember quite a lot from that period.

7th form calculus was a lot more rote. I actually re-learnt last year that integration was the area under the curve. I also didn't know until last week 'e' was actually a number, I thought it was a magic formulae. This is not to say I was bad at calculus, I did very well at it, but I certainly didn't retain the real work applications of it.

Kevin O'Brien said...

Maths teaching is appailing. One of my sons 5 years ago was still being taught how to calculate GST% in year 11!
Some years ago I think it got sidetracked when the program expected all kids to have "maths brains" and naturally derive algorithims from indirect encounters with number and set theory. Wrong! Most people don't think like mathematicians and many young women in particular have an aversion to anything not verbal. We waste pupils tolerance and state resources by not teaching to personal types and abilities. But do we have the teachers capable of doing that?


Children's ability has not diminished but course expectations have. Once children in NZ at year 8 were expected to be competent in arithmetic. For many that was the end of their schooling and that was sufficient.

When I started high school in Wellington in 1953 we were into algebra in the first week. We were not bored silly.There is good reason for streaming and differential teaching but with no one being to be seen to be allowed not to pass why bother with excellence?

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