Too Many Kids Hate Maths
Richard Andrew
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Paul Swan from Edith Cowan University, in his article I Hate Maths, cites the work of Wain, who paints a very dark picture of the image of mathematics:
… many intelligent people after an average of 1500 hours of instruction over eleven years of schooling, still regard mathematics as a meaningless activity for which they have no aptitude...it is difficult to imagine how a subject could have achieved for itself such an appalling image as it now has in the popular mind ... to think that all our effort has led to a situation of fear and loathing is depressing. (Wain 1994 as cited by Westwood, 2000, p. 31)
Think about that for a moment! 1500 hours of maths instruction leading many intelligent people to a poor attitude towards mathematics.
What other industry would tolerate such a poor return for effort? Imagine Nike undertaking 1500 hours of advertising, and all the while, the ads are turning most people off Nike!
Now, I’m not suggesting that maths teaching is akin to marketing. However, there are parallels. As maths teachers, most of us - surely - have as a major aim to turn kids onto maths - to have them enjoy the experience of exploring mathematical systems, pondering problems and collaborating with their peers?
We could argue that turning kids onto maths should be our #1 aim. We could do this by providing activities that have students thinking through for themselves, being less reliant on replicating the teacher's instructions from the board, more reliant on being autonomous? We could aim to have most students feeling “I might not be brilliant, but I enjoy learning maths”?
The Wain quote above references ‘many people’ (regard maths as meaningless). What portion of people do we suspect the ‘many’ to be? Twenty per cent?
A twenty per cent failure rate would be way too high for a Nike marketing campaign (they might tolerate a few per cent failure rate). If we were turning off twenty per cent of our maths students, that would be a bad outcome. But what do you suspect the actual number might be?
I have a number for you …
... seventy-ish per cent!
Now, before you spill that coffee down your front, allow me to explain how I derive this seventy per cent number.
I’ve been running The Unintentional Mathematics Attitude Survey for over forty years. In fact, every maths teacher, like it or not, runs The Unintentional Mathematics Attitude Survey. The Unintentional Mathematics Attitude Survey operates in any social situation, somewhat like this:
Richard: Hi, I’m Richard. Nice to meet you.
New Person: Oh hi. I’m Jo.
After some chit-chat …
Jo: So Richard, what do you do for a crust?
Richard: I’m a maths teacher (or anything maths-related)
Jo: Oh, I hated maths at school …
Now, not everyone says they hated maths, were hopeless at maths, or sucked at maths. However, about seventy per cent do. And the other thirty per cent are just as enthusiastic about telling you they loved maths at school. Nevertheless, those seventy per cent who suffered at school don’t hold back their displeasure of school maths.
And despite being a bit of a bow to draw, I have every reason to believe the Seventy Percent number also applies to current maths students. I say this because I'm convinced that in 20 years' time if we were to randomly interview 1000 adults between the ages of 25 and 47 (the cohort of students at school now) we will find 70% of them claim they never got maths at school. (Anyone prepared to disagree?)
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Not blaming mathematics teachers
But here’s the thing. It’s not the fault of maths teachers. Maths teachers are, in my experience, some of the hardest working people on the planet. (Want to know the definition of ‘a tough gig’? Try teaching mathematics to a classroom of disengaged students who hate maths. It ain’t easy!)
Swan closes the I Hate Maths article by citing the Australian Education Council who recognised - over a decade ago - the link between students’ engagement with maths and those who pursue maths in the long term. The Australian Education Council recommends that mathematics curricula explicitly address students' development?of positive attitudes towards mathematics.
Why this hasn’t been obvious for the last hundred years is, I find, incredulous. And why?authentic engagement?in today’s maths education is awarded mere ‘lip service’ rather than being a major thrust is also, in my view, a tragedy.
The Way Mathematics is Taught
Swan cites Skemp (1986) (who suggested that)?the way in which mathematics is taught contributed to the development of anxiety toward mathematics. He suggested that rote learning of mathematics caused children to develop anxiety toward mathematics. Children are often successful in learning simple mathematics based on rote learning, but as mathematics becomes more complex, they can no longer just learn rules to cover all situations. As they become exposed to problem-solving situations, children can no longer apply rote-learnt methods. This helps to explain why many children start off enjoying mathematics but as they get older turn off mathematics.?
That rote-learning is an ineffective way of teaching mathematics is, in my experience, obviously true. Yet I have reason to suspect that most maths teaching today has a foundation of rote learning, albeit with an attempt to explain conceptually what's happening.
One of the issues is that when we teach students a new procedure, we often do so without providing students with an understanding of the concepts upon which the procedure is based. In other words, we are trying to get students to learn something in the absence of conceptual understanding. And when was the last time you tried to learn something you couldn't make sense of? It's an almost impossible task!
Arguably, rote learning is at play anytime we ask students to learn a routine or procedures in the absence of conceptual understanding. After all, the natural way learning works is to learn through understanding, through connecting the dots. If we don't understand - if we can't connect the dots - then our only option is to learn by rote.
It, therefore, makes sense to have students?explore concepts first up before they experience the related procedure.
Why haven’t we changed?
I suspect every maths teacher has tried approaches alternative to that of procedurally-focused rote-learning, approaches that are more conceptual, strategies that are more student-centred, activities that make more sense to students. However, the pedagogy required to make such strategies work differs from the pedagogies needed for a traditional, procedural approach. When a teacher tries an alternative task, they may be inspired to use such a task on, for example, a monthly basis. But rarely do teachers' experiences of these alternative approaches give them the confidence to adopt them as a default. They appear too messy and time-consuming. So nearly always, the procedural status quo remains.
Give me a road map!
In my experience, teachers need to see the need for change to change. But then they need a roadmap! There are ways to present mathematics with students engaging in explorations, understanding the concepts, and taking ownership of their learning. However, teachers first need to understand WHY these strategies are an effective way forward. Then they need to see the HOW ... they need a roadmap.
In my work with teachers, I encourage using strategies that have students using their own thinking as they explore concepts before presenting them with the related procedures. I refer to this as an Understanding-first, Procedures-second approach. The transition required to adopt this approach is laid out for them.
I recently wrote an article series on this idea. The?first article is here.
Paul Swan’s ‘I Hate Mathematics’ article also suggests some engaging ideas for the maths classroom.
Someone famously suggested changing what you are doing if you want different results.
Maybe we should start employing - as the default - efficient strategies that require students to ‘do maths’ - to explore, to investigate, to collaborate, to tackle problems through using their own thinking, so that - first up - students get to understand the concepts.
Maybe.
Maths Educator at Marianapolis, Bien Hoa, VN
3 年Indeed, a nice article! In addition to rote and disengaged learning and what Mr. Staples has included, I'd add two additional elements that I can see as not being good for students' understanding: 1) timed mathematics and 2) contrived problems. With timed mathematics (especially in the younger grades) students are rewarded for finishing quickly which drives the expectation that math needs to be done or can be done quickly...(I'm not referring to math fact fluency here), but instead the process at arriving at a solution. Some students do finish quickly through experience or insight, but what about the other students who don't finish quickly? Are they provided enough time to connect those dots? Next, students spend those 1500 hours of instruction often solving contrived problems that can be completed in just a few steps at best which again drives an unrealistic expectation that math problems can be solved with just the right insight with few steps. Again, I'm not referring to those difficult problems with elegant 1-2 line proofs, but rather a typical textbook problem from any high school math subject. I get that students must gain procedural fluency first, but then what are they offered after that, I'd question?
Founder | CEO | Teacher | EdTech Specialist | Learner | Lover of Mathematics
3 年"teachers often conclude that the alternatives are too messy and too time-consuming. So nearly always, the status quo remains - ‘teach the procedures’ remains the default approach." A lack of confidence, maths anxiety of their own, pressure to 'be in control', failure in the classroom being seen as incompetence, and a crowded curriculum, all hinder teachers willingness to teach for understanding, explore maths through number sense, more inquiry/play based learning. The type of learning that makes sense of maths, builds deep understanding, enjoyment and retention. Instead, we teach abstract procedures, rote learned algorithms (that seduce children), and a binary approach to answers. So kids (who turn into adults) learn to see maths as irrelevant, based on rules, binary and boring. An attitude that is very difficult to break. Took me until university!
Computational Thinker, Mathematician, Physicist, Educator
3 年Keith Devlin’s column on “A Mathematician's Lament” by Paul Lockhart clearly expresses the same sentiment. Quoting Lockhart: "I want them to understand that there is a playground in their minds and that that is where mathematics happens.”
Co-Author of Mathematical Whetstones a resource for teachers, students and mathematics enthusiasts.
3 年An excellent article, but, gee, what a challenging problem to solve. What I could show you however is a senior school calculus text book written in 1931 that has substantially the same headings as that shown in any modern text. The book, Elementary Calculus by F Bowman, is well written for its time but the chapter exercises look very very familiar (I taught senior maths for 30 years). It seems what we teach and the way we assess it has remained unchanged for almost a century. Some students can’t get enough of this stuff, but many others become anxious and uncertain about it all, and eventually fall away. The subject becomes polarising. My strong feeling is that, in general, teachers are railroaded by what they teach and how they teach it because of the expectations placed on them by their state assessment regimes. And because the curriculum is crowded with age old algorithms, then that becomes the ultimate focus. Yes, they try to push on the boundaries with interesting project work and assignments and alike, but in the end they have no choice but to fall in line. Until that changes I don’t think there is much hope. Yet, there is so much scope for change if we could only risk it. The contemporary maths world is so exciting.