CSEDU, Day 1, Keynote 2, “Mathematics Teaching: is the future syncretic?” (#csedu14 #csedu #AdelEd)

This is an extension of the position paper that was presented this morning. I must be honest and say that I have a knee-jerk reaction when I run across titles like this. There’s always the spectre of Rand or Gene Ray in compact phrases of slightly obscure terminology. (You should probably ignore me, I also twitch every time I run across digital hermeneutics and that’s perfectly legitimate.) The speaker is Larissa Fradkin who is trying to improve the quality of mathematics teaching and overall interest in mathematics – which is a good thing and so I should probably be far more generous about “syncretic”. Let’s review the definition of syncretic:

Again, from Wikipedia, Syncretism /ˈsɪŋkrətɪzəm/ is the combining of different, often seemingly contradictory beliefs, while melding practices of various schools of thought. (The speaker specified this to religious and philosophical schools of thought.)

There’s a reference in the talk to gnosticism, which combined oriental mysticism, Judaism and Christianity. Apparently, in this talk we are going to have myths debunked regarding the Maths Wars of Myths, including traditionalist myths and constructivist myths. Then discuss the realities in the classroom.

Two fundamental theories of learning were introduced: traditionalist and constructivist. Apparently, these are drummed into poor schoolteachers and yet we academics are sadly ignorant of these. Urm. You have to be pretty confident to have a go at Piaget: “Piaget studied urchins and then tried to apply it to kids.” I’m really not sure what is being said here but the speaker has tried to tell two jokes which have fallen very flat and, regrettably, is making me think that she doesn’t quite grasp what discovery learning is. Now we are into Guided Teaching and scaffolding with Vygotsky, who apparently, as a language teacher, was slightly better than a teacher of urchins.

The first traditionalist myth is that intelligence = implicit memory (no conscious awareness) + basic pattern recognition. Oh, how nice, the speaker did a lot of IQ tests and went from 70 to 150 in 5 tests. I don’t think many people in the serious educational community places much weight  on the assessment of intelligence through these sorts of test – and the objection to standardised testing is coming from the edu research community of exactly those reasons. I commented on this speaker earlier and noted that I felt that she was having an argument that was no longer contemporary. Sadly, my opinion is being reinforced. The next traditionalist myth is that mathematics should be taught using poetry, other mnemonics and coercion.

What? If the speaker is referring to the memorisation of the multiplication tables, we are taking about a definitional basis for further development that occupies a very short time in the learning phase. We are discussing a type of education that is already identified as negative as if the realisation that mindless repetition and extrinsic motivational factors are counter-productive. Yes, coercion is an old method but let’s get to what you’re proposing as an alternative.

Now we move on to the constructivist myths. I’m on the edge of my seat. We have a couple of cartoons which don’t do anything except recycle some old stereotypes. So, the first myth is “Only what students discover for themselves is truly learned.” So the problem here is based on Rebar, 2007, met study. Revelation: Child-centred, cognitively focused and open classroom approaches tend to perform poorly.

Hmm, not our experience.

The second myth is both advanced and debunked by a single paper, that there are only two separate and distinct ways to teach mathematics: conceptual understanding and drills. Revelation: Conceptual advanced are invariably built on the bedrock of technique.

Myth 3: Math concepts are best understood and mastered when presented in context, in that way the underlying math concept will follow automatically. The speaker used to teach with engineering examples but abandoned them because of the problem of having to explain engineering problems, engineering language and then the problem. Ah, another paper from Hung-Hsi Wu, UCB, “The Mathematician and Mathematics Education Reform.” No, I really can’t agree with this as a myth. Situated learning is valid and it works, providing that the context used is authentic and selected carefully.

Ok, I must confess that I have some red flags going up now – while I don’t know the work of Hung-Hsi Wu, depending on a single author, especially one whose revelatory heresy is close to 20 years old, is not the best basis for a complicated argument such as this. Any readers with knowledge in this should jump on to the comments and get us informed!

Looking at all of these myths, I don’t see myths, I see straw men. (A straw man is a deliberately weak argument chosen because it is easy to attack and based on a simplified or weaker version of the problem.)

I’m in agreement with many of the outcomes that Professor Fradkin is advocating. I want teachers to guide but believe that they can do it in the constriction of learning environments that support constructivist approaches. Yes, we should limit jargon. Yes, we should move away from death-by-test. Yes, Socratic dialogue is a great way to go.

However, as always, if someone says “Socratic dialogue is the way to go but I am not doing it now” then I have to ask “Why not?” Anyone who has been to one of my sessions knows that when I talk about collaboration methods and student value generation, you will be collaborating before your seat has had a chance to warm up. It’s the cornerstone of authentic teaching that we use the methods that we advocate or explain why they are not suitable – cognitive apprenticeship requires us to expose our selves as we got through the process we’re trying to teach!

Regrettably, I think my initial reaction of cautious mistrust of the title may have been accurate. (Or I am just hopelessly biassed by an initial reaction although I have been trying to be positive.) I am trying very hard to reinterpret what has been said. But there is a lot of anecdote and dependency upon one or two “visionary debunkers” to support a series of strawmen presented as giant barriers to sensible teaching.

Yes, listening to students and adapting is essential but this does not actually require one to abandon constructivist or traditionalist approaches because we are not talking about the pedagogy here, we’re talking about support systems. (Your take on that may be different.)

There is some evidence presented at the end which is, I’m sorry to say, a little confusing although there has obviously been a great deal of success for an unlisted, uncounted number and unknown level of course – success rates improved from 30 passing to 70% passing and no-one had to be trained for the exam. I would very much like to get some more detail on this as claiming that the syncretic approach is the only way to reach 70% is essential is a big claim. Also, a 70% pass rate is not all that good – I would get called on to the carpet if I did that for a couple of offerings. (And, no, we don’t dumb down the course to improve pass rate – we try to teach better.)

Now we move into on-line techniques. Is the flipped classroom a viable approach? Can technology “humanise” the classroom? (These two statements are not connected, for me, so I’m hoping that this is not an attempt to entail one by the other.) We then moved on to a discussion of Khan, who Professor Fradkin is not a fan of, and while her criticisms of Khan are semi-valid (he’s not a teacher and it shows), her final statement and dismissal of Khan as a cram-preparer is more than a little unfair and very much in keeping with the sweeping statements that we have been assailed by for the past 45 minutes.

I really feel that Professor Fradkin is conflating other mechanisms with blended and flipped learning – flipped learning is all about “me time” to allow students to learn at their own pace (as she notes) but then she notes a “Con” of the Khan method of an absence of “me time”. What if students don’t understand the recorded lectures at all? Well… how about we improve the material? The in-class activities will immediately expose faulty concept delivery and we adapt and try again (as the speaker has already noted). We most certainly don’t need IT for flipped learning (although it’s both “Con” point 3 AND 4 as to why Khan doesn’t work), we just need to have learning occur before we have the face-to-face sessions where we work through the concepts in a more applied manner.

Now we move onto MOOCs. Yes, we’re all cautious about MOOCs. Yes, there are a lot of issues. MOOCs will get rid of teachers? That particular strawman has been set on fire, pushed out to sea, brought back, set on fire again and then shot into orbit. Where they set it on fire again. Next point? Ok, Sebastian Thrun made an overclaim that the future will have only 10 higher ed institutions in 50 years. Yup. Fire that second strawman into orbit. We’ve addressed Professor Thrun before and, after all, he was trying to excite and engage a community over something new and, to his credit, he’s been stepping back from that ever since.

Ah, a Coursera course that came from a “high-quality” US University. It is full of imprecise language, saying How and not Why, with a Monster generator approach. A quick ad hominen attack on the lecturer in the video (He looked like he had been on drugs for 10 years). Apparently, and with no evidence, Professor Fradkin can guarantee that no student picked up any idea of what a function was from this course.

Apparently some Universities are becoming more cautious about MOOCs. Really.

I’m sorry to have editorialised so badly during this session but this has been a very challenging talk to listen to as so much of the underlying material has been, to my understanding, misrepresented at least. A very disappointing talk over all and one that could have been so much better – I agree with a lot of the outcomes but I don’t really think that this is not the way to lead towards it.

Sadly, already someone has asked to translate the speaker’s slides into German so that they can send it to the government! Yes, text books are often bad and a lack of sequencing is a serious problem. Once again I agree with the conclusion but not the argument… Heresy is an important part of our development of thought, and stagnation is death, but I think that we always need to be cautious that we don’t sensationalise and seek strawmen in our desire to find new truths that we have to reach through heresy.


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