By Murray Bourne, 02 May 2005
In her book "Math Wars, A Guide for Parents and Teachers", Carmen Latterell desribes the 'math wars' as the struggle between an ever-swinging pendulum. On one hand, you have the "back to basics" crowd who want to drill mathematical facts and techniques into every student, and on the other you have the "new math" crowd who stress the understanding of mathematical concepts and can see the advantages in using technology for achieving this aim.
Story of US mathematics education
Latterell's brief history of mathematics education in the US is interesting - from almost none at all in the early colonial days to an approach which stressed basic arithmetic only. Of course, the biggest shock for the Americans was when the Soviets were the first to send a man into space. There was a lot of soul-searching about the dismal state of mathematics and science in the States and huge resources were poured into this area. This was also the end of the era for "new math" when everything boiled down to whether you could understand Venn diagrams and decide whether something belonged to some set of numbers or not.
The pendulum swung again in the 1980s to "problem solving" where drilling of basics was 'out' and constructivist, sociological approaches were 'in'. She describes the last 15 years as "The Time of NCTM" (National Council of Teachers of Mathematics). Latterell is trying to be objective in this book, but seems to be somewhat against the NCTM and its encouragement of technology-based mathematics teaching, because "basics take a back seat".
So to the present, where George Bush's acoountability drive is pushing everyone "back to the basics" and causing a lot of angst. (It's not the only angst that Dubya produces, but that's another story for other posts.) Interestingly, it is also pushing out the "Singapore Math" approach that the US was increasingly adopting. (They liked Singapore Math on the grounds that "it made Singapore win all those math competitions, so it must be good").
So what mathematics should we teach?
So what is important for the vast majority of students? Remember, most people never use the mathematics that they learn at school. They stress up and freeze when reminded of algebra, trigonometry and logarithms and would not even be able to read a mathematics exam paper any more, let alone attempt it (ask any parent of teenagers how they feel when their son or daughter ask for help with their homework...). Even many engineers admit that they almost never use most of the mathematics that they learned at university. So why are we treating everyone as though they are going to become pure mathematicians, when clearly they are not? Sure, we need to give enough grounding for them to go on in whatever career they choose, but when almost no career requires (for example) rationalising a denominator, why do we make them all do it? Because it is good for them? Bah, humbug.
So should they all learn heavy-duty algebra? Where do we draw the line? Where do we let the technology do the grunt work so humans can do what humans do best (solve problems)? Don't get me wrong here - I am all for students' learning "the basics" so that they have sufficient building blocks for solving real problems. It's just that we need to debate more on where to draw the line. Should we do less algebra and devote more time to problem solving and communication of mathematical concepts? After all, what will be remembered the following semester, the following year, one decade later?
Traditional vs NCTM
But I digress - back to the book. Most of the rest of the book compares 'traditional' and 'NCTM' curricula, giving examples of each approach to lessons. For example, in a traditional approach, students will learn to solve 'gems' like
x + √(x − 4) = 4,
while in a NCTM approach, they will learn how to interpret graphs drawn from real data measurements of an oil spill. Seems a no-brainer to me as to which is more useful down the track.
College level disconnect
Latterell goes on to describe the problems that students face when they have been brought up in a non-traditional, NCTM style and they hit the college level which is far more traditional - and they get lost. There is also a section on the reform calculus movement, which is an approach to differentiation and integration which emphasises meaning and understanding rather than algebraic processes. College teachers tend to teach in a traditional way ('it was good enough for me') and wonder why students have no idea what they are talking about. There are many such disconnects in education - mathematics is one of the more stark ones.
The section on international comparisons is particularly interesting (once again, the issues of poor TIMMS results for the US comes up). She describes the Japanese situation, where students get a NTCM approach during normal schooling and a traditional approach during juku (cram school) in the evenings. An important difference is that Japanese mathematics education is firmly based on the students' thinking processes. In comparisons with China, the statement is made that Chinese elementary teachers know mathematics more fundamentally and deeply than their US counterparts, hence Chinese students are more successful at TIMMS-type mathematics comparisons.
Interesting resources that are mentioned are: Mathematically Correct [no longer available], which is maintained by the traditionalist side and of course the NCTM argues the other side.
"Math Wars" is a recommended read for those that are involved in mathematics education (hey - isn't that every one of us?) - especially those that are struggling with 'traditional' (often boring) approaches and 'innovative' approaches (often bells and whistles but where are the goods?). Her style is somewhat jerky (it often feels like she has so much to say that she is actually puffed when she is writing it all down).
I will leave you to discover Latterell's ultimate solution to the Math Wars.
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