Classroom practice - Making sure maths solves real problems
This should be the golden age of maths in schools. After generations of benign neglect, the subject has been thrust into the media spotlight. Politicians, educators and private companies maintain that effective maths learning is the key to everything from smarter workers and savvier consumers to improved national competitiveness.
And in truth, research does suggest that maths is key. It provides the underpinnings for a problem-solving mindset that is applicable in every sector of society. From research to manufacturing and the service economy, modern enterprises run on computers, whose coding principles are rooted in the rigorous logic of mathematical thinking. Studies presented by children's charity Unicef show that maths achievers excel - and earn higher salaries globally - in any profession they enter.
Yet many students still flee from maths in the classroom. Engagement is plummeting. Even those who recognise the compelling arguments for advancing their careers regard maths classes as an ordeal.
So what's the problem? Many educational research organisations believe that traditional maths instruction is out of date and that new approaches are necessary. Among the solutions offered is one adopted by a growing number of teachers where apps and web-based videos enable students to rehearse maths skills online.
Cornerstone Maths lies at the more ambitious end of this spectrum in the UK and US. It is still in the early stages of development, but the idea is that it uses software programs to teach essential but hard-to-grasp mathematical concepts to 11- to 14-year-olds, including linear function, geometric similarity and algebraic expressions. Over the course of three weeks, students use the software to undertake guided explorations and real-world activities - designing a rally race mobile phone game, for example, to teach linear functions - that help them to visualise the maths topic being investigated. This approach aims to foster reasoning and collaboration.
In large-scale experiments in Texas and Florida in the US conducted by non-profit research company SRI International, students from a wide range of backgrounds made learning gains using the Cornerstone method. A similar study in the UK run in partnership with the London Knowledge Lab and funded by the philanthropic Li Ka Shing Foundation hopes to trial Cornerstone in about 100 schools this year.
Some, however, believe that the problem is more deeply rooted than simple pedagogy. It is not how maths is taught, they claim, but what is being taught. They maintain that the entire subject is bogged down in endless drills and hopeless irrelevancy. The argument, simply put, is that the focus on mastering calculating skills means that maths as a subject is no longer required by the real world.
"There is worldwide maths confusion," says British technologist Conrad Wolfram (pictured, inset). A passionate advocate for reform, Wolfram founded the educational project ComputerBasedMath.org (CBM) in 2010 to promote the use of computers in teaching the subject. His brother Stephen, meanwhile, created the popular Mathematica software. According to Conrad: "People know there is something called maths that is important. And yet we have this subject in schools that everybody thought was the subject but it isn't. It's disconnected."
Wolfram burst into the public eye more than three years ago with a TED talk that has since been viewed nearly 900,000 times. The essence of the talk is that although maths requires a combination of problem formulation, abstraction, calculating and communicating, schools remain steadfastly focused on calculating. The alternative is to teach mathematical thinking and hand the drudge work to computers.
"You've got to get rid of the crud that people don't need. Let's assume you have a computer, like you will in real life," Wolfram says. To demonstrate the ease with which computers calculate, Wolfram pulls out his iPhone and asks Siri - Apple's voice-activated digital assistant - to calculate an equation, which it happily does. "So why are we just teaching calculation?" he asks.
Fight for survival
Wolfram sees uncanny parallels between traditional approaches to teaching maths and subjects like Classics. When people stopped needing Greek and Latin in everyday life, schools continued to teach Classics, but as a proxy for learning English grammar. "With maths there is a real-world subject but what we are teaching is a proxy," Wolfram says. "The proxy isn't working that well. People hate calculating. They don't understand what they are doing.
"My argument to mathematicians who oppose this is: if you stick with your current subject it will turn into Classics. Because in the end you can't justify spending billions of dollars a year around the world teaching a subject that basically nobody is using. It will not survive as a general-purpose subject."
So what needs to be done? Wolfram believes there are two choices: "Essentially a new subject starts to replace maths, or we change maths into the subject it ought to be. In one way or another it's got to match the real world."
According to Wolfram, categories of algebra and geometry are not the "real subjects" any longer. "Today's maths is a proxy for real maths. We have real subjects. Why are we not teaching them? Why not start from a problem you want to solve or a kid wants to solve, and use maths as a tool to help?"
Wolfram is fond of quoting the late Apple co-founder Steve Jobs, who once praised Mathematica as something that would "revolutionise the teaching and learning of maths by focusing on the prose of mathematics without getting lost in the grammar".
What might a new maths curriculum include? CBM has a list that includes: "mathematical thinking; everyday maths; finding patterns in information; knowing where you are in space; mathematics in the natural world; mathematics in technology; winning; and money maths".
Wolfram's approach has attracted many supporters, notably the government of Estonia: TESS reported in March how officials had invited CBM to bring newly designed statistics courses to the nation's schools. Jaak Aaviksoo, Estonia's minister for education and research, says: "We believe in the enthusiasm and potential of the internet generation - they are ready for computer-based mathematics. It will also give them a competitive advantage in the labour market."
However, computer-based maths teaching has its share of critics. Traditionalists include parents, teachers and educators who staunchly support training students how to calculate because they believe it is the foundation of maths understanding. Another important issue is whether those with traditional training will be able to teach the new approach. Finally, and most seriously, the educational assessment community has not signed on yet. Assessment providers are organised to measure calculating skills and maths content as a body of knowledge, not the open-ended understanding Wolfram espouses.
The latter describes CBM as a multidimensional "helix" that includes abilities such as the confidence to tackle new problems, abstraction, and planning and managing computations - not to mention "an instinctive feel for maths". Mapping these goals to traditional assessment outcomes will not be simple, Wolfram admits. Moreover, school leaders believe that they have to teach to the standard tests.
Some assessing agencies are starting to recognise the issue. "The problem is that we assess facts and not procedures. If you want to assess critical thinking you have to teach critical thinking," says Helen Eccles, director of development at Cambridge International Examinations.
Yet change is always a challenge. Because of the multitude of obstacles, Wolfram has set a 25-year time frame to put maths on a new track for the real world. "I know this won't be easy, that's why I've dedicated my life to it," he says.
Stuart Gannes is a US-based education journalist and president of the Fab Foundation. www.fabfoundation.org
Although maths skills are seen as essential by everyone from politicians and business leaders to scientists and teachers, students are still not embracing the subject.
A growing number of people believe that this is the result of the wrong "type" of maths being taught in the wrong way.
An approach that embraces real-world maths, taught using a collaborative and software-based methodology, is growing in popularity.
However, this has opponents, and also presents practical challenges for examinations.
Let's get metaphysical, urges maths guru Conrad Wolfram.
Catch up on your listening with these TES Connect maths podcasts on everything from probability to flipped learning.