This is amazing. This guy has done incredible things with Wolfram Alpha and now shares his ideas on maths teaching and in particular the place of computers in teaching.
Reading Dan Meyer’s blog today I came across a discussion on ‘pseudocontext’. Those pointless, make believe, so called contextual maths questions that I have railed against for years. They are neither useful nor inteteresting and go a long way to removing both the beauty and utility of mathematics.
Very glad to read:
“The real test of whether a math problem is “relevant” is not “do you use this in ‘real life’,” whatever that means, but “do you want to solve it?” It’s not that you want to solve it because it’s relevant; wanting to solve it is what it means to be relevant.”
“Something I’m realizing in all of this is that it doesn’t matter how I reply when a student asks “when will I ever use this in real life?” I’ve already lost. Because that student isn’t asking a question about an uncertain future; she’s lodging a complaint about a frustrating present.”
Now go read the rest….
“A mathematician who is not also a poet will never be a complete mathematician.”
—Karl Theodor Wilhelm Weierstrass
I’ve been discussing this with a number of staff recently. I wish I could remember where I first read this so I could link to what I remember as a very interesting piece. The more I discuss this the more it seems to be both obvious and necessary. However, I am still struggling to come up with any ideas on the ‘how to’ front.
I have noticed that I usually have to explain this idea two or three times before the real meaning is understood. The first response seems to be that this is all very nice and a good way to be kind to the less able kids. This is definitely not the idea (although it is a fortunate side effect.)
So, to the reasoning.
Students, almost without exception, seem to have lost any sense of a causal link between effort and reward. For many, “I’m going to fail anyway,” and so make no effort. For others, “I’m going to do fine,” and so make no effort. Whilst we continue to value and reward achievement levels more than anything else students will continue to be unmotivated and demoralized.
By making ‘effort’ what we value and reward, we start to empower students. To some extent achievement is independent of the student whereas effort certainly isn’t. Intelligence will be something that the students have inherited and in the short term can’t do much about. It is what they have brought with them. It has already happened and so can’t be changed. How much effort they make is very much in their control and can be changed for the future.
Re-establishing this link between effort and reward will train good long term habits. A belief in “I can improve if I make some effort.”
Self esteem is improved by being in control of your own destiny. Being able to control what is valuable and not be so susceptible to external factors goes a long way to improve your self esteem.
Dan very succinctly and clearly lays out the case for what I call ‘removing the scaffolding’.
‘Problem Solving’ has been a phrase I have heard lauded ever since I began teaching (not so short and not so long ago.) And yet the methods proposed and the rationale presented have never seemed quite complete.
Far too often maths curricula have interpreted this to mean inserting some, all too often, spurious context or introducing more puzzles and games into each or some lessons. At best there seems to be a very prescriptive approach to how you solve a problem and questions designed to lead to a very clear and algebraically perfect answer. Collect the data – put it in a table – find the pattern….
So, we just had a very constructive year 10 “Growing Mathematicians’ meeting. Actually, I’ve just invented that title but a title always makes you feel part of something and not just like going to another meeting so maybe it will stick.
Craig presented one lesson idea which was the very simple “Reflective Flags” exercise. And yet from a very clean and simple (and strangely addictive) activity a whole range of quality maths ensued.
Some important ideas that stood out for me were:
- There are skills that we as teachers/mathematicians have but which very few of our students do. These are not the skills of being able to rotate a quadrilateral or find the area of a triangle but a range of skills which enable us to have a pretty good crack at any problem that might arise.
- These skills are often hidden and require significant higher order thinking and in particular meta cognition.
- It is important for these skills/approaches to be made explicit, both from ourselves as teachers but even more importantly from the students.
- Our job as teachers is to tease out these skills and empower students to feel able to attack any problem. This role of teaching seems meaningful to me. A truly honourable endeavour.
- This approach does not mean finding the right answer quickly or easily but having the confidence that we will be able to figure something out.
- This feeling is deeply empowering.
- Giving students the problems and letting them go is not enough, however excited and motivated they may be. Busy is not good enough. The true skill in teaching is how to take these learning exercises and to facilitate a growth in the students’ confidence and ability.
- Monitoring/evaluation is important in this. What do we want to achieve?How are we going to check to see if that has been developed?
- Many skills may be being developed but it may only be possible to fully evaluate and report on a couple of these per task.
- Some (in fact in my experience, many) students find this approach deeply unnerving. I think this is due to the fact that they feel lost and don’t believe they will be able to find their way out. We need to be able to develop mathematical thinking in students, allowing them to feel they have a range of approaches at their disposal and a toolkit of ideas which should work. Notice, this is confidence in a process not in ‘finding the right answer’.
- A sign of success for me is when students accept challenges willingly and don’t run and hide at the onset of confusion.
I think we do need to talk more about how we go about this process of growing these skills in our students and I think how to monitor and evaluate will be an important aspect in this.
Today’s meeting had a lot of great discussion and feedback as well as ‘doing maths’, which I think is something we should do more of and apologize less for. I hope future meetings continue to discuss and hone these ideas.
I am also keen to keep these valuable resources and ideas properly documented. It is all too easy (for me at least) for these things to be forgotten with no real change taking place. Not sure how I’m going to do that yet, though.
This man ‘walked the earth’ for three decades and for seventeen of those years did not speak. This is one of those videos that I am always so grateful for stumbling upon and which seem to come along every once in a while. It is of course inspiring but raises many questions for me. Not least, ‘What have I done?’
So, only a few days until I present prezi at the i-connect mini conference. The more I prepare the more I wish I had 3 hours rather than just 45 minutes. Quite what I can achieve in such a short time I’m not too sure. And, as always, once I start looking around at all the web 2.0 offerings the more really cool stuff I find.
I need to be a bit more ruthless in considering what is just really cool and what might actually be practical. However, some stuff is just too awesome to leave out.
Possible web 2.0 offerings
- diigo – great research, online storage and collaboration tool. Annotate websites, share within a group and conduct discussions.
- wiffitti – display screen for received messages texted from mobiles or entered from computer (reminds me of those big screens in the Concorde in Brighton!) Very cool and lots of potential once we allow students to start using their mobile phonesl.
- aviary – looks like it might be an amazing music and image editing tool.
- newsdots – social media linking of current news. Nice idea but doesn’t seem to have been updated for a while.
- xtranormal – create animated dialogue. Kids will love it.
- 360cities – great way to visually explore the world. Cool geography tool.
- don’t forget google docs
- wordle create word clouds in seconds
- issuu – create magazines from a pdf. Looks amazing but I’ve not used it yet.
Some of this I have gleaned from an awesome site: Web Tools for Teachers
Well worth further investigation.
This could encapsulate a whole presentation in itself (or indeed conference) but it would surely be remiss not to mention it.
The way I see it this it falls into two categories. Students blogging as part of their studies, and teachers reading and writing blogs as part of their professional development. How much time is there to discuss professional leasrning communities?
- Tumblr – social network blogging but also a very easy way to blog (big buttons!)
- WordPress – the king of all blogs
- Blogger – if you are addicted to google
What it is, what it can do and a brief, hands on how to use it.
- 3 min intro video
- Engaging Web 2.0 Tools
- Acadamy: inserting animations
- Create a prezi – prezi and other 2.0
Maybe some mention of the danger of bullets.
Again the power of prezi is twofold:
- interesting presentations
- a more dynamic and interlinked way of thinking – think mind mapping etc
…or more to the point, “What am I teaching my students?”
It seems the only honest answer to this is “exactly the same as has been taught for the last 200 years.” Of course, there is the human factor. The day to day interactions. The ‘just by being who you are’ kind of random effect. But what actually is it that is intentionally being ‘taught’? What is it I plan to deliver and how am I planning to deliver it?
My natural instinct is to believe that being stuck (already a judgement laden word) with an ancient methodology and an antiquated curriculum cannot be a good thing. But this may not, of course, be true. Just because it is old does not make it broken. Indeed its longevity may indeed be proof of its efficacy and maybe it has become refined and perfected over so many years of experience. But somehow that doesn’t seem to be true. It is not what I instinctively believe. Indeed I am hearing many voices which argue, with good evidence, the contrary. There again, just because there is noise, does not guarantee correctness.
So, as a starting point I need to know if there is a need for something different. In fact, I want to start from scratch (not an unusual position for me.) What and how would I teach now if no pre-existing system were there? What works? What is needed? Only then will I feel comfortable to ask how I might do it.