Scaffolding Maths is numbing our students minds

Today I saw the video below for the first time “Math class needs a makeover” by Dan Meyer from his TED talk back in 2010. Dan describes how today’s math curriculum is teaching students to expect – and excel at – paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. In his talk, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

As a former Maths teacher his message really resonated with me. Last year  I had been encouraging some of my teaching peers to introduce more open inquiry SOLO Taxonomy task based questions into Mathematics. This has been brought about by my own experience of the benefits of this model of learning in the Social Sciences supported by digital technologies, an area where I have a particular passion for and which I had been teaching over the last few years. What I have found particularly troubling, but understandable up to now, is that many Mathematics Teachers  argue that their subject is different and must be treated as such: “Students need ongoing repetition of skills practice in maths to enable them to learn properly” and there is the often argued point in New Zealand, and likely in other countries “we don’t have the luxury of time to do investigate stuff, we have so much content to get through and so little time”. But, the counter to that I would argue, and that Dan alludes to is: that we constantly have to review content that the students forget anyway.

Why not do it differently and turn it on its head. Let us throw away those hapless mind-numbing textbooks, the ones that scaffold the questions down and make the maths so mind-numbing as so simply demonstrated by Dan. Why not ask simple interesting questions and get the students to unpack the problem and develop the solution in their own ways. We can be there to assist when they need it. This has been my model of student inquiry in the Social Sciences and the students really do switch on – why not in Maths? A number of Maths teachers will no doubt roll their eyes and say “we need to get real, we have assessments to worry about”. However, the failure rate and disinterest in Maths as a subject is too large to ignore, along with the ongoing demand for extra Maths tuition which has become a burgeoning industry.

Taking it Further with Inquiry & Investigation

Removing the scaffolding as described by Dan is a great step to allowing students to think. I suggest going further and and bringing more open-ended research and inquiry into Mathematics. Motivated and engaged students seeking answers to real questions, who will go online and investigate, and will come up with all sorts of amazing alternative answers and theories. Students who will operate in collaborative groups to tackle problems and identify for themselves what parts of a particular problem are the most significant. Where learners are given multiple opportunities to operate at the SOLO Taxonomy Extended Abstract Level: Planning and Prioritising, Arguing, Predicting and Reflecting – then Evaluating and Justifying their results and the approach they took. Let us turn our schools into centres of rich authentic learning, inquiry and research. Let the Mathematics have real meaning and application where the student seek out, identify and learn the skills, with the support of their teacher, when they are needed. Don’t let our schools be places that kill the creative and inquiring mind.

Here are just a few investigate Mathematics Questions for Secondary School that I came up with after watching the video:

  1. “What is New Zealand’s most successful Sports Team?” – topical as New Zealand are about to play in the World Cup Cricket Final, and play in the World Cup Rugby Final Tournament later this year – this question opens up interpretations of “success”, measurements of wins, losses, percentages. Nr of teams performing. Good debate. Research. Statistics. Class project. Historical Research
  2. “Are there enough fresh water resources to provide for the needs of the world population?” – this problem would allow for debate as New Zealand faces a polluted rivers crisis. How much fresh water is needed for the current world population? What is population growth rate? What is the water pollution rate? Where are fresh water sources? This could be broken down to research local (New Zealand), to global
  3. “Is it really worth buying a house in Auckland?” – Currently New Zealand’s largest city has a housing crisis with prices rising fast, along with the population, but houses in short supply. These factors would be good to look at along with investment returns on houses. There are a range of good maths issues here. Also opportunity to include spreadsheets, graphing.
  4. “Minimum wage or living way? Which is fairest?” – Political arguments in New Zealand could be used to introduced this one as some have put forward the idea of a “living minimum wage”. Students could explore the background and then determine what it is, what is the cost of living, and what is inflation.
  5. “What is Uber and why are taxi drivers complaining?” – Uber is threatening the taxi industry and police have recently cracked down on Uber causing possible law changes. Students could explore what Uber is. What do Taxis charge and what does it cost to run a Taxi/Car (very relevant). How does Uber work and how do they charge. Will it put Taxis out of business?
  6. “Where is the best position on a rugby field to take a conversion after a Try is scored on the 5 metre line?” – Kickers often take a kick back a certain distance to take a conversion (try to place kick between the posts) after scoring a Try in Rugby (the equivalent of a Touchdown in American Football). Is there an optimum distance back for the kicker. This introduces the idea of angles. One could walk out to a rugby field or similar and take a look.
  7. “What is the quickest that a large jumbo passenger aircraft can get to its optimum cruising altitude?” – I have seen some of those Aircrash movies about planes not being able to ascend too steeply, otherwise they will fall out of the sky. I am sure students will be able to gather enough information to find out about cruising altitudes, maximum angle of ascent and takeoff speeds and speed, distance and time. This question gives them plenty to work with. You could then go beyond this question to ask: How far does the plane get? At what altitude can get get to before it can start turning? (I am sure these answers are available online).
  8. “What is the maximum number of people that can be packed into a rock concert?” – I have used this myself after telling a story. The students were fully engaged and we could fit the whole population of the world in a small geographical area of New Zealand. Great memories of some of my Year 10 classes.

There are a multitude of rich questions I am sure that other current Mathematics Teachers will have thought of. Again, fantastic video I wish I had seen earlier.

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