NOTE: The article referred to in this entry was updated. In keeping with this “moving the goal-post” type of journalism, I too have updated this post.
Like most articles one sees in newspapers about math education, this one assumes that students are taught via rote memorization without any context of the conceptual underpinning. The article argues that the problem with math education is that it fails to teach students “complex problem solving” skills in high school. Actually the article fails to look at how students are being taught in the elementary grades (K-6). As a reaction against traditional math–mischaracterized as rote memorization without understanding–students are subjected to a push of conceptual understanding. Students are often not allowed to learn and/or use standard methods or algorithms until they have learned the conceptual understanding in the mistaken but widespread belief that standard algorithms eclipse the holy grail of “understanding”. Students who are ready to move on are held back until they can show what amounts to the “rote understanding” that teachers want to hear. Memorization, in fact, would actually be far more easy and benefit many more students.
But the reporter of this article like most journos who don’t know what they don’t know about math education, offers the standard narrative of how to fix the problems that traditional math teaching has supposedly caused:
There is a growing chorus of math experts who recommend ways to bring America’s math curriculum into the 21st century to make it more reflective of what children in higher-performing countries learn. Some schools experiment with ways to make math more exciting, practical and inclusive.
And there you have it: the standard troika of how to fix math education: 1) The magic bullet of how higher-performing countries do it: conceptual understanding. No mention of their reliance on the traditional techniques that are held to cause the low scores in math in the US, and that students there actually do rely on memorization.
2) Make math more exciting: The article fails to mention how, but the usual reasons are to give problems that are more than just computation (and therefore useful not only in daily life but as a means to move on to solving more complex problems). Give them more mathematically oriented problems, as well as open-ended, multiple answer problems. The belief is that there are core competencies (like problem solving) that can be learned independently of the type of problems one has to solve. This is referred to as “habits of mind”. The belief is that a steady diet of challenging one-off type problems will develop a problem-solving “schema” that will allow students to transfer these skills to any type of problem they come across. This belief is carried out with the help of making no distinction between how novices learn differently than experts.
3) Make math more practical and inclusive: This is the other side of their mouth speaking. Students should be given more of the everyday problems held to be un-exciting and which turn children off of math. As far as inclusivity, problems should embody aspects of different cultures rather than the white western culture which has prevailed and oppressed free thought for centuries.
So to get more perspective on the problem and how to fix it, the reporter turns to Jo Boaler, who is regarded by many journos as the be-all end-all of math education.
Most American high schools teach algebra I in ninth grade, geometry in 10th grade and algebra II in 11th grade – something Boaler calls “the geometry sandwich.” Other countries teach three straight years of integrated math – I, II and III — in which concepts of algebra, geometry, probability, statistics and data science are taught together, allowing students to take deep dives into complex problems.
Let me talk about that for just a bit. You don’t have to have the geometry sandwich as she calls it. You could have students take Algebra 1 and 2 in sequence. The reason for not doing this is supposedly that geometry prepares them for the trig aspect of Algebra 2. This is nonsense. I had some time at the end of an Algebra 1 course so I taught the basics of trig–which by the way was at the end of the book, and it wasn’t uncommon for algebra 1 textbooks to do so. The prior knowledge the students needed to grasp it was already there via their understanding of similar triangles and right triangles.
As far as math being taught differently in high schools overseas, it is true that they use an integrated approach: i.e., a mixture of algebra, geometry and trigonometry throughout the year, with each year getting more advanced. Greg Ashman, who teaches in Australia and who writes a blog about education
is embarking upon a PhD in education from John Sweller. Greg makes this comment about integrated math:
“In Australia, I teach integrated maths and I always have. However, I teach it directly and explicitly. Other schools may choose less effective approaches. It seems to me that the math reformers are trying to use integrated maths as a Trojan horse for discovery maths. That’s a hard tactic to counter because there is some logic to integrating maths – it should lead to more contact with the various concepts over time, more retrieval practice and better formed schemas.”
In the US, the integrated math programs are by and large discovery math programs as Greg alludes to in his note. IMP is one of them as is Core Plus. The newest is MVP Math, an integrated math program heavy on inquiry-based, student-centered learning, with teachers serving as handmaidens/facilitators of an ineffective program. Blain Dillard, a parent who lives in North Carolina where MVP is being foisted upon an unsuspecting population was sued by MVP for speaking out against its ineffectiveness. (The lawsuit was dropped when Blain countersued).
Boaler is quoted throughout the article. At one point, she says:
“There’s a lot of research that shows when you teach math in a different way, kids do better, including on test scores,” said Jo Boaler, a mathematics professor at Stanford University who is behind a major push to remake America’s math curriculum.”
What research? She doesn’t say, nor did the reporter ask, apparently. What different way of teaching math? She doesn’t say, and again it appears the reporter did not ask. Boaler provides a hint in this indirect quote in the article:
“In higher-performing countries, statistics or data science – the computer-based analysis of data, often coupled with coding – is a larger part of the math curriculum, Boaler said. Most American classes focus on teaching rote procedures, she said.”
Which then leads the reporter to discuss a podcast of Freakonomics author Steve Levitt on math eduation:
“Levitt is engaged in the movement to upend traditional math instruction. He said high schools could consider whittling down the most useful elements of geometry and the second year of algebra into a one-year course. Then students would have more room in their schedules for more applicable math classes.”
A friend of mine who teaches high school algebra and majored in physics at Harvard has this to say about Levitt:
“Someone needs to engage Steven Levitt in active debate on that topic. Learning data science will do nobody any good if they lack the basic skills to apply and comprehend the underlying math, and conceptual overviews just don’t cut it. I’ve noticed a trend in software that has been dumbing down the features available to power users, with the idea that few people know how to use them in the first place, and if that widespread adoption of brain-dead approaches starts happening more in the realm of big data, then we are in for all kinds of complexity-related problems down the road.”
This article, like most that appear in the press, takes the word of math reformers as gospel and rarely questions their assumptions. My friend characterizes the reform math stance as follows:
Well said. And in fact if you have anything to say about the tropes in the USA Today article, or about math reformers in general, I need your help: Please add your comments here.