The problem with videos for teaching maths and stats

The message of many popular mathematics and statistics videos is harming people’s perceptions of the nature of these disciplines.

I acknowledge the potential for conflict of interest in this post –  critically examining the role of video in learning and teaching mathematics and statistics – when StatsLC has a YouTube channel, and also provides videos through teaching and learning systems.

But I do wonder what message it sends when people like Sal Khan of Khan Academy and Mister Woo are applauded for their well-intentioned, and successful attempts to take a procedural view of mathematics to the masses. Video by its very nature tends towards procedures, and encourages the philosophy that there is one way to do something. Both Khan and Woo, and my personal favourite, Rob Tarrou, all show enthusiasm, inclusion and compassion. And I am sure that many people have been helped by these teachers. In New Zealand various classroom teachers ‘flip” their classrooms, and allow others to benefit from their videos on YouTube. One of the strengths, according to Khan, is that individual students can proceed at their own pace. However Jo Boaler states in her book, Mathematical Mindsets, that “Sadly I have yet to encounter a product that gives individualised opportunities and also teaches mathematics well.”

So what is the problem then? Millions of students love Khan, Woo, ProfRobBob and even Dr Nic. Millions of people also love fast food, and that isn’t good as a total diet.

In my work exploring people’s attitudes to mathematics, I find that many, including maths educators, have a procedural view of mathematics, which fails to unlock the amazing potential of our disciplines.

Procedural maths

Many people have the conception that to do mathematics is to work out the correct procedure to use in a specific instance and use it correctly in order to get the correct answer. This leads to a nice red tick. (Check mark) That was my view of maths for a very long time. I remember being most upset in my first year of university when the calculus exam was in a different format from the ones I had practised on. I was indignant and feared a C at best, and possibly even a failing grade. I liked the procedural approach. I felt secure using a procedural approach, and when I became a maths teacher, I was pretty much wedded to it. And the thing is, the procedural approach has worked very well for most of the people who are currently high school maths teachers.

Computation was an important part of mathematics

I recently read the inspiring “Hidden Figures”, about African American women who had pivotal roles in the development of space travel. For many of them, their introduction into life as a mathematician was as a computer. They did mathematical computations, and speed and accuracy were essential. I wonder how much of today’s curriculum is still aiming to produce computers, when we have electronic devices that can do all of that faster and more accurately.

Open-ended, lively maths

In parallel to the mass-maths-educators, we have the likes of Jo Boaler and Youcubed, Dan Meyer and Desmos, Bobbie Hunter and Mathematics Inquiry Communities, Marian Small, Tracy Zager, Fawn Nguyen and pretty much the entire Math-Twitter-Blogosphere spreading the message that mathematics is open-ended, exciting and far from procedural. Students work in groups to construct and communicate their ideas. Wrong answers are valued as evidence of thinking and the willingness to take risks. Productive struggle is valued and lessons are designed to get students outside of their comfort zones, but still within their zone of proximal development. Work is collective, rather than individualised, and ability grouping is strongly discouraged.

I find this approach enormously exciting, and believe that it could change the perception of the world towards mathematics.

The problem of the social contract

Thus I and many teachers are keen to develop a more social constructivist approach to learning mathematics at all levels. However, teachers – especially at high school – run into the problem of the implicit social contract that places the teacher as the owner of the knowledge, who is then required to distribute said knowledge to the students in the class. Students want to get the knowledge, to master the procedure and to find the right answers with as little effort or pain as possible. They are not used to working in groups, and find it threatening to their comfortably boring, procedural vision of maths class.

Some years ago I filled in for a maths teacher for a week at a school for girls from privileged backgrounds. I upset one class of Year 12 students by refusing to use up class time getting them to copy notes from the whiteboard. I figured they had perfectly good textbooks, and were better to spend their time working on examples when I was there to help them learn. Silly me! But I was breaking with what they felt was the correct way for them (and me) to behave in maths class. In fact their indignation at my failure to behave in the way they felt I should, actually did get in the way of their learning.

So who is right?

I guess my working theory is that there is a place for many types of learning and teaching in mathematics. Videos can be helpful to introduce ideas, or to provide another way of explaining things. They can help teachers to expand their own understanding, and develop confidence. Videos can provide well-thought-out images and animations to help students understand and remember concepts. They can do something the teacher cannot.  I like to think that our StatsLC videos fit in this category. Talking head or blackboard videos can act as “the kid next door” tutor, who helps a student piece something together.

Just as candy cereal can be only “part of a healthy breakfast”, videos should never be anything more than part of a learning experience.

We also want to think about what kinds of learning we want students to experience. We need our students to be able to communicate, to be creative, to think critically and problem solve and to work collaboratively. These are known as the 4 Cs of 21st Century learning. We don’t actually need people to be able to follow procedures any more. What we need is for people to be able to ask good questions, build models and answer them. I don’t think a procedural approach is going to do that.

The following table summarises some ideas I have about ways of teaching mathematics and statistics.

Procedural approach Social constructivist approach
Main ideas Maths is about choosing and using procedures correctly Maths is about exploring ideas and finding patterns
Strengths Orderly, structured, safe, cover the material, calm Exciting, fun, annoying
Skills valued Computation, memorisation, speed, accuracy Creativity, collaboration, communication, critical thinking
Teaching methods Demonstration, notes, practice Open-ended tasks, discussion, exploration
Grouping Students work alone or in ability grouping Students discuss as a whole class or in mixed-ability groups
Role of teacher Fount of wisdom, guide, enthusiast, coach. Another learner, source of help, sometimes annoyingly oblique
Attitude to mistakes Mistakes are a sign of failure Mistakes happen when we learn.
Challenges Boredom, regimentation, may not develop resilience. Can be difficult to tell if learning is taking place, difficult if the teacher is not confident.
Who succeeds? People like our current maths teachers Not sure – hopefully everyone!
Use of worksheets and textbooks Important – guide the learning Occasional use to supplement activities
Role of videos Can be central Support materials

If we are to have a world of mathematicians, as is our goal as a social enterprise, then we need to move away from a narrow procedural view of mathematics.

I would love to hear your thoughts on this as mathematicians, statisticians, teachers and learners. Do we need to be more careful about the messages our resources such as textbooks and videos give about mathematics and statistics?

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Dr Nic, Suzy and Gina talk about feelings about Maths

This hour long conversation gives insights into how three high achieving women feel about mathematics. Nicola, the host, is the author of this blog, and has always had strong affection for mathematics, though this has changed in nature lately. Gina and Suzy are both strongly negative in their feelings about maths. As the discussion progresses, listen for the shift in attitude.

Listen here to the podcast.

And here is a picture of the three of us.

Dr Nic, Gina and Suzy

Dr Nic, Gina and Suzy.

Here are some of the questions we discuss over the hour:

  1. Tell me about your relationship with maths.
  2. How do you think your feelings about maths have affected your life?
  3. If you saw this as an opportunity to talk to people who teach mathematics, what message would you like to give them?
  4. How do you feel about the idea that you could change how you feel about maths?

Lessons for a budding Social Enterprise from Elevate

Statistics Learning Centre is a social enterprise set up by Dr Nic Petty and Dr Shane Dye after leaving the University of Canterbury. Our aim is to help the world to feel better about mathematics and statistics, by inventing, creating and disseminating resources and ideas to learners and teachers. We believe that facility and confidence with mathematics and statistics is as important as literacy in enabling individuals to participate fully in their world.

We didn’t always have our mission or aim or vision as well articulated, and if asked we tended to give some vague description like – “we make stuff to help people learn maths and statistics.”

StatsLC identifies as a social enterprise because we are driven by a purpose beyond making profit for shareholders, and our purpose is a social good – in this case education. A social enterprise exists in the continuum between a business which operates for profit, and a charity, which is strictly not-for-profit, but measures its effectiveness in different ways. We wish ultimately to be self-sustaining so that we are not at the mercy of grants or contracts with outside providers.

Ākina Elevate

We, the directors, have spent the last eight months, on and off, working on our purpose, customer focus, financials and operations as part of an Elevate course with Ākina. The course is aimed at social enterprises, and we have been participating with between five and eight other social enterprises based in Christchurch, New Zealand.

At our last session Ākina wanted to know what value we have gained from the course, what it does well and what can be improved. Ākina itself is a social enterprise that helps other social enterprises. Social Enterprise is a popular phenomenon, particularly in our area, where recently Ākina hosted the World Forum.

Impact

The first unit of four sessions, one morning per week, addressed our impact. We needed to identify what we are trying to achieve, why and how. We talked about vision, mission and purpose. This would help us later to think about who are our customers and who are our beneficiaries.  I still find the delineation between vision, mission and purpose a bit confusing. Our vision has expanded during the course. This is where we are up to now, though it is still a work in progress.

Vision – a world of mathematicians

Purpose: We invent, create and disseminate resources and ideas to enable people to learn and teach mathematics and statistics enjoyably and effectively.

We invent resources to enable people to learn mathematics enjoyably
create and and and and
disseminate ideas teach statistics effectively

As we considered our impact we realised that we are making an impact. We have over 1000 views of this blog daily. There are over 35,000 subscribers on our Youtube channel. Hundreds of children and teachers have been inspired and enthused by our “Rich Maths” events. You can see more about our impact here: Statistics Learning Centre Impact.

We have not been doing well at specifying exactly what impact we aim to have, and measuring it. Originally our impact was with teachers and learners of secondary and university level statistics. However we are now thinking bigger, and wish to create a world of mathematicians.  We truly believe that education is a political act, and knowledge of maths and statistics empowers people, allows greater career choice and enables informed citizenship.

Customer

The “customer” or marketing section of the course was the one we felt most in need of, and probably are still most in need of. We learned that we need to ask what problem we are solving and for whom. This has led to serious thought and discussion on our part as we have so many ideas about how we can do good, and for whom. However, the point of social enterprise is that you are not a charity, so need to trade or provide services for money in order to be sustainable. So we need to identify our customers – the people and organisations that will pay money for what we do – either for them or for others.

At the time we were gearing up for a holiday programme, and we used some of the ideas to advertise on Facebook. One outcome of the course is that we have decided we need to employ someone to help with the marketing.

Financial

As we already have an accounting package, Xero, and work with an accountant, the need for help here felt less imperative. We have developed different systems in using Xero that will help us analyse our progress. One idea that was valuable was to do with the value of our time. Time and money emphasis did not have to be commensurate in all circumstances. Two sessions on budgets were helpful when thinking about grant applications. We have thought more about cashflow, though a crisis at the end of 2016 had already made us aware of potential problems. We started paying ourselves.

What has become clear throughout the course is that we do not have enough time between the two of us to do all the things we need, as well as maintaining cashflow through contracts. This has helped us to recognise the need to employ someone to cover our areas of weakness, in particular marketing. We also need to develop more passive income streams.

Operations

What was extremely valuable in this section was learning about employment contracts and health and safety. We are now formalising our contracts with staff. Being a responsible employer, even for family members, takes a bit of work.

Another useful session concerned governance, management and operations. As a small enterprise, both of us tend to fill all three roles. At this point we need to get some advice at the governance level – even just having someone to ask us questions and to report to periodically. It can be easy to spend too much time chipping away at the coalface, and losing direction. It can also be seductive to spend all our time discussing visionary ideas for future development, rather than getting on and producing. Like most of life, the answer lies in a balance.

Other thoughts

A common expression in social enterprise is Mission Drift meaning letting the commercial aspects over-ride the social impact focus or mission.

We tend to suffer from something similar, that I call mission lurch. I’m not sure it is the right term, as it is more that we are adapting our mission in order to align it better with activities that will lead to sustainability. Our problem is that we need to be doing some more activities that bring in revenue to sustain our mission.

One big benefit from participating in the programme has been making contact and building relationships with others in similar circumstances. This builds confidence.

Big lessons

For me the big lessons from this course are

  • Articulating our mission
  • Confidence to do something big

A year ago I was quite happy to dabble around in the edges of business/social enterprise. We were not really making enough to keep us going, but had hope that something might change. Over the course of 2017 we have had contracts with Unlocking Curious Minds, to take exciting maths events to primary schools. We have also gained contracts writing materials for other organisations. Our success in these endeavours, along with the help from the Elevate course has helped us to think bigger.

Watch this space!