We need an inquiry about inquiry

The default position of many who are charged with reviewing curricula at all levels of Irish education seems to be to suggest more discovery or inquiry-based approaches to teaching and learning.  Personally, I find the whole thing bizarre because I would have thought that academics, of all people, would have a real, almost innate, thirst for knowledge as opposed to process. And I can’t understand why teacher-led approaches are perceived as being passive or boring because kids love facts and love asking questions.

Anyway, whether it’s the new Junior Cycle Science Curriculum or the recent STEM report, the solution to our perceived woes (and it is not clear at all what our woes are) seems to be that if we get students to act like mini-scientists, they will learn better. They won’t because of the novice-expert divide. But education, as a discipline, is highly ideological and I can’t imagine that I’m going to convince anyone here of the problems with inquiry-based learning; so I won’t try.

However, the figure below from PISA 2015 should be setting off alarm bells throughout the Irish education establishment because inquiry-based methods do not come out well. In fact they come out very badly. The OECD was “surprised” by this, suggesting, perhaps, an ideological bias on their part.

Indeed, is worth noting that a few weeks back, it became clear that the PISA 2012 results demonstrated (although this seems to have been buried by the good people of OECD Education) that inquiry-based methods were equally ‘problematic’ in mathematics teaching.  But again, no one in the world of Irish education seemed concerned.


Of course, we can choose to ignore the PISA findings (as we probably will) but we would want to have a damn good reason to do so. We can’t pat ourselves on the pack because our PISA reading scores have gone up and then choose to ignore findings about how best to teach maths and science.

There is a lot at stake here. The PISA results have shown that even the best educational systems can go into decline and, in Canada at least, there is prima facie evidence that the use of inquiry methods has contributed to the decline in their maths scores.

Wouldn’t it be more sensible to at least have a conversation as to how much time we intend to devote to inquiry-based methods and what exactly we mean by inquiry methods? Inquiry methods have a shape-shifting quality about them and when they go bad it’s often claimed it’s because they weren’t real inquiry methods at all.

The PISA results have shown that within the ‘space’ defined by the PISA tests, our education system is performing extremely well despite the lack of resources. The biggest problems we have relate to issues around equity rather than academic quality.

So those who advocate for significant change in how we teach, especially at first and second level, need to be sure that their proposals are backed up by solid evidence. Plausibility or anecdotes from third level lecturers is not enough. And, crucially, everyone has to recognise that student engagement is not the same as student learning.

PISA 2018 will be interesting.

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What PISA 2015 says about how to teach science

Given that Ireland has just gone through a review of STEM teaching, it is interesting to have a look at what PISA has to say. A very quick glance through Vol II of their report reveals the following. My comments are in bold;  text in italics represents quotes from the report.

My conclusion is this: if we want our students to learn science well, then we need to recruit good teachers and the teacher has to be a lot more than a ‘guide on the side’. They need to actually teach. However, adding in some ‘engaging’ activities, like a bit of enquiry-based learning, probably helps to generate some actual enthusiasm for science.


Who performs well in science?

Australia, Canada, Ireland, Slovenia, Portugal, Singapore and the UK are high performers in science. Their 15 year-olds hold strong beliefs about the value of science enquiry, and larger-than-average proportions of students in these countries expect to work in a science-related occupation later on.”

The value of extra-curricular activities

Schools that offer science competitions score 36% higher in science. Their students are 55% more likely to pursue science-related careers. For schools that have science clubs, the numbers are 21 and 30% respectively.

It’s really all about the teacher

PISA results show that when teachers frequently explain and demonstrate scientific ideas, and discuss students’ questions (known collectively as teacher-directed instruction), students score higher in science, they have stronger beliefs in the value of scientific enquiry (what are known as epistemic beliefs) and are more likely to expect to work in a science-related occupation later on. Adapting to students’ needs, such as by providing individual help to struggling students or changing the structure of a lesson on a topic that most students find difficult to understand is also related to higher scores in science and stronger epistemic beliefs.”

Students don’t learn so well when taught using enquiry-based methods but seem to develop some enthusiasm for science when enquiry methods are employed

Perhaps surprisingly, in almost no education system  do students who reported that they are frequently exposed to hands-on enquiry-based instruction  score higher in science. After accounting for students’ and schools’ socio-economic profiles, in 56 economies and countries, greater exposure to enquiry-based instruction  is associated with lower scores in science. However, across OECD countries, more frequent enquiry-based teaching is positively related to students holding stronger epistemic beliefs and being more likely to expect to work in a science related occupation when they are 30.

[My Note: it would appear that both teacher-led instruction and enquiry-based learning correlate with stronger epistemic beliefs. This is consistent with the next point about time, i.e. any exposure to science is good!]

Time is important

High performance in science is strongly related to the time students devote to learning science and how their teachers teach science.

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A very, very quick Look at PISA 2015


Ireland:  A lot to be proud of. Our science and maths scores are pretty static but there is significant improvement in reading. We’re ranked 19 in the world in Science. It looks to me like we’re 5 in Reading and 17 in Maths. Our average score over Maths, Science and Reading is better than the UK’s. (I know, I know, I’m falling into the habit of obsessing about the UK and whether we’re better than them!)

However, if I am interpreting the results right, we only have an average number of top performers in our classes, something that is broadly consistent with the recent TIMSS results. The worry might be that our best students are not being challenged enough.

Estonia’s results are fantastic – I predict hordes of delegations to that country to find their secret!

Finland is going backwards in everything (as many anticipated based on a perceived move towards more ‘progressive’ forms of teaching)

Canada is going backwards (but not hugely) in Maths (as many anticipated based on their emphasis on inquiry-driven approaches to maths teaching. Irish curriculum reformers take note.).

Denmark is boringly consistent, even more so than Belgium.

The Swedish decline continues.

New Zealand and Australia are going consistently backwards.

France, Spain and Italy really should be doing a lot better.

Albania, Georgia and Moldova are making very significant progress across all subjects. I wonder what’s going on in that part of the world?

CABA (which is Buenos Aires I believe) is making extraordinary strides forward.

Israel, the so –called ‘Start-Up Nation’, isn’t all that hot at science but is making some progress in maths.

Qatar is improving enormously. I wonder if the World Cup has anything to do with it.


Now, back to marking lab reports!

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Some quick thoughts on TIMSS

TIMSS (Trends in International Maths and Science Study) doesn’t roll off the tongue quite like PISA but it is important nonetheless. The results from the 2015 tests have just been released and the Irish Report is available here. For a small country on the periphery of Europe, we are doing quite well. The headline results are as follows:

Fourth Class Rankings (Primary)

We are ranked 9 in Mathematics and 19 in Science. In maths we are ahead of countries like the US, England, Australia, Canada and New Zealand but, interestingly, we are behind Northern Ireland who are ranked at 6. England, the US and Finland are ahead of us in Science.

Second Year Ranking (Secondary)

Again we are ranked 9 in Maths but we’re better at science, coming in at 10. In both maths and science we’re effectively indistinguishable from England and the US.

Distributions Effects

All that sounds good, and it is, but there are some things to think about. At Fourth Class, our average improvement since 1995 has largely occurred because our weakest students are performing better. Our best students are performing just about the same. This pattern is repeated in the Second Year Results. What precisely this means is debatable but  it may suggest that our best students are not being challenged sufficiently, perhaps as a result of our syllabi and our assessments becoming more ‘accessible’ (as they say!).

Relative Strengths and Weakness – Content

In comparison with international benchmarks, our Fourth Class Students were:

relatively weak in geometry and relatively strong in number; relatively weak in physical sciences and relatively strong in earth science.

Our Second Year Students were:

Relatively weak in algebra and geometry and relatively strong in number, data and probability; relatively weak in chemistry and physics and relatively strong in biology and earth sciences

Relative Strengths and Weakness – Cognitive

In comparison with international benchmarks, our Fourth Class Students were:

relatively weak in mathematical reasoning but relatively strong in mathematical knowledge; no obvious trends in the science

Our Second Year Students were:

Relatively weak at applying mathematics but relatively strong at knowing maths; in science they were relatively weak at knowing and no other obvious trends were observed.

So, all in all it makes interesting reading and for me four things stand out:

  • We need to get to grips with our weakness in physics and chemistry and to do so as early as possible
  • There is a sense that there might be a bit too much rote learning going on (no surprises there)
  • If our students have a weakness in algebra then that is something we need to fix because you can’t get through a third level course in maths, physics, chemistry or engineering if your algebra is sub-standard.
  • We need to ask if our best students are being sufficiently challenged
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The need for a bit of quiet in science

If you peruse the STEM hastag in Twitter, you’ll be struck by the extent to which those who buy in to the STEM concept seem put an almost obsessive emphasis on ‘active learning’, coding, hacking, ‘making’ and a general sense that every STEM thing is fun and generally awesome. The emphasis is overwhelmingly on the ‘T’ in STEM. To some extent this is understandable because Twitter users probably have an in-built bias towards all things ‘tech’.

The ‘active learning’ bias also tends to dominate in modern science museums like Belfast’s W5 which I visited recently. Here the emphasis is on encouraging youngsters to ‘engage’ with all sorts of ‘fun’ exhibits. Sure enough, the kids were having lots of fun (the noise was incredible!) but it looked to me like they were actually learning very little and it is hard to see how they might be inspired in any way. They all appeared to be suffering from a sort of sensory overload and they were jumping, rapidly, from one exhibit to another, playing around with random phenomena without pausing to think about the scientific concepts that the various displays were meant to demonstrate. In fact they couldn’t possibly do so because they didn’t have the necessary knowledge in their heads to make any sense of what they were observing or doing. Chaos theory or electromagnetism or the venturi effect doesn’t mean a whole lot to eight year-olds and because they lack basic knowledge, they are unaware of the deep connections that exist between seemingly unrelated phenomena. Although aimed at the under-twelves, W5 and similar museums would actually be far more beneficial to college students who have a bit of background knowledge.

Every now and then I bring my son to the Natural History Museum, known affectionately to Dubliners as the ‘Dead Zoo’. It’s quiet, free from gimmicks, and everyone moves through the exhibits at a much slower pace than they do in places like W5.  Kids and their parents stop to pull out drawers and peer closely at insects or sharks’ teeth or crabs or whatever. Of course, kids are naturally drawn towards animals so it’s not quite the same but you do get the sense that if we want to inspire kids with science, we really need to create spaces that encourage them to stop and think and wonder. Isn’t that how most of the great scientific discoveries have been made; by people stopping to think?

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Comments on the STEM report

As far as I can make out, the STEM report arose out of a belief that

  • Students entering college lack basic STEM skills, especially in mathematics. (True)
  • Even college students lack ‘higher order’ skills like problem solving, analytical thinking etc. (Only partly true)
  • As an economy we need more school-leavers to pursue STEM careers especially at the ‘hard’ science and technology end of the spectrum. (I’m not altogether convinced)

Given these assumptions, the report makes lots of sensible suggestions as to how we might ensure that our STEM teachers are as competent and inspiring as possible.

But when the report gets into teaching modalities, that’s where I get confused. To address both (i) and (ii), the suggestion is that teaching should shift in the direction of inquiry and problem-based methods. The idea is that by building the curriculum around students solving real world problems, picking up knowledge and skill as they go along (I think!), they will ultimately be better prepared for the rigours of third level  STEM education. I simply don’t buy that, as my last post suggested, and I don’t think there is any other area of life, whether it’s sport, the arts, or many forms of music, where an inquiry approach would be recommended. Excellence in all of these disciplines nearly always requires instruction combined with lots of practice and a gradual loosening of the reins as the student/performer acquires the skills, the knowledge and the self-awareness to forge their own path. Sure, we encounter self-taught prodigies every now and then but they are the exceptions. I honestly don’t follow the reasoning of those who advocate for IBL and PBL. How can devoting lots of time (and IBL and PBL are very time consuming) to real world problem-solving increase a student’s proficiency in algebra, for example? I just don’t get it.

As for (iii), I’m genuinely confused here. As I stated in a recent post, 42% of science/maths graduates go on to further education, 25% of engineering grads do so and 15% of ICT grads do. Those numbers are not consistent with an economy that is clamouring for more ‘STEM’ graduates. Or maybe it’s that our STEM graduates are not as good as we think and employers don’t fancy hiring them. That would seem to suggest that as a nation we need to conduct some sort of social engineering in which all of the many excellent students who are currently drawn to health-related (and female dominated) careers should be nudged towards STEM disciplines, especially ICT and engineering. As I’ve said before: good luck with that.

One final thing that bothers me about the whole maths education thing and it is this: do the educationalists ever stop to actually talk to practitioners? I’m talking about mathematicians, engineers, physicists, chemists, actuaries and anyone working in quantitative finance. Every time I talk to people like this, people who ‘engage with real world problem-solving’ every day,  they stress the importance of knowing the basic rules of mathematics off by heart. But nobody seems to be listening.


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How should we teach maths?

I’ll be upfront and say that this is how I think we should teach maths:

  1. The teacher should chart a course through the subject, explaining key and threshold concepts along the way. Students may not  ‘get’ everything at the first attempt but as Fields Medallist, Timothy Gowers says: “It is quite possible to use mathematical concepts correctly without being able to say exactly what they mean. This might sound like a bad idea, but the use is often easier to teach and a deeper understanding of the meaning often follows of its own accord”. So, once the student commits the basic language of mathematics to his or her long term memory (I admit that motivating students is a challenge here and that is where the skill of the teacher comes in), they will be able to progress on to the next level and become proficient at the doing of mathematics, building confidence and hopefully some enthusiasm along the way. In time, they might return to those rules that they didn’t quite understand and look at them in a new light and with new insight. (I’ve done this many times myself and had to think very hard recently about what raising a number to an irrational power actually means. And that’s 32 years after getting my engineering degree.)
  2. The students’ understanding (which is really only another form of memory – what else could it be?) of mathematics and their ability to think critically and even creatively is built up by challenging them with lots and lots of problems of ever increasing difficulty and ever increasing breadth, drawing on more and more of their prior learning. The better posed the problems are, the more the student will learn: too hard, or if students simply don’t have the tools to tackle the problem, and they will switch off; too easy and they will be unstimulated and get bored. And, the more interesting these problems, the better. Ideally, you don’t want the student to ask “so what?” after spending half an hour getting an answer. (People who really love maths never ask the “so what?” question.) If the student is fully committed and studies independently using scientifically sound study methods, they have every chance of becoming proficient at mathematics. But the key in all of this is that the teacher is knowledgeable, motivating, encouraging and supportive. Mathematics, after all, is fundamentally abstract. There is no getting away from that fact and most mathematics (as opposed to arithmetic, perhaps) can be classified as biologically secondary knowledge so learning it doesn’t come easily to the majority.
  3. Of course, you can’t talk about teaching without talking about assessment and if we want our students to become critical thinkers then we need to adopt methods of assessment that require them to think critically. In effect this means that when it comes to assessment, students should expect the unexpected. However, there is a belief abroad, at least in Ireland, that the unexpected is unfair so a change in mindset is needed; from students, teachers and parents.

In the last couple of decades there has been a steady shift away from this approach, which could be classified as ‘traditional’, towards more ‘progressive’ approaches of which inquiry/discovery-based methods are a significant part. Canada, especially the state of Ontario, has gone down the discovery route and there are those who would suggest that this has been a disaster.

By and large, discovery methods, which have an air of plausibility about them, are seen as inherently good, although there has been something of a backlash in recent years, sparked in many cases by the obvious fact that many students, even third level students, seem to lack basic skills, especially in mathematics. This seems to be a worldwide problem (except perhaps in Asia) but was not always the case.

The basic idea behind inquiry/discovery methods is that by tackling ‘real world’ problems, “constructing their own knowledge” in the process, students develop a deeper understanding of the mathematics required to solve those problems. (Presumably the belief is that knowldege and skills acquired by solving real world problems transfers to other problems so, in a sense, discovery learning eventually ‘eats itself’.) Apart from the fact that ‘understanding’ is a difficult concept to define, the precise role of teacher guidance in inquiry based methods is often hard to nail down. It seems to vary from almost no guidance to so much guidance (‘enhanced inquiry’) that is difficult to see how this form of teaching is any different from traditional methods.

Now I’m just an engineer who is not an expert in pedagogy but the impression I get from reading the education literature is that, at the very best, methods of learning that are not teacher-led are unproven. Indeed, there is absolutely no consensus as to how best to teach, not only mathematics, but almost every single subject. So despite what camp you are in, traditional or progressive, you should tread very carefully when you get into the realm of educational policy and curriculum reform. And if you are a ‘progressive’, you need to be extra careful because the extraordinarily creative and innovative 20th century, and the first decade of the 21st, was built on the foundations of traditional education and traditional methods should be discarded only in the face of extraordinary evidence. To me, that is the only intellectually honest way to proceed. Otherwise, you will just end up doing large scale experiments on children. This is what we have done in Ireland with the Project Maths initiative which, despite claims that it is evidence-based, has sparked a large degree of concern amongst genuine and thoughtful educators, especially at third level. These are people with no axe to grind but who are leaving exam board meetings depressed at the extent of failure in mathematics modules. Many bemoan the lack of very basic skills shown by second and third year college students. The general feeling amonsgt third level lecturers is that whatever way students are learning mathematics at school, they are not acquiring the basic ‘grammar’ of the mathematical language to the extent that this grammar is imprinted in their long term memory, freeing up their short term memory for all of that critical and creative thinking that we want them to do. It is very hard to see how discovery methods will fix this problem.

But the existence of pedagogical camps is a problem because very often people see what they want to see when they examine research. Confirmation bias and motivated reasoning are rampant. A really good example of this was a recent article by renowned maths educator, Jo Boaler, in which she claims that some recent PISA results could be interpreted as showing the superiority of inquiry methods over more traditional methods in which learning basic maths facts and rules ‘off by heart’ is a key component. (She singled out Ireland for particular criticism despite the fact that  our PISA ranking is higher than many countries of whose methods she approves.) Her article has been thoroughly demolished by Greg Ashman, an English (i.e. from England) teacher and blogger based in Australia. (I had previously raised my own doubts about her interpretation of the data.) I don’t know a huge amount about Boaler but I plan to read her work in more detail so that I can arrive at some sort of informed opinion. I have to say, though, that her response to the PISA data worries me. It seemed to me to be ideological.

The signs are, what with the huge emphasis on fairly nebulous skills as opposed to knowledge in the new Junior Cycle, that the Irish education system is going to go down the ‘progressive’ route and my view is that this will be disastrous, especially if there is a large emphasis on discovery methods. I think we need to remember Newton’s famous statement: “If I have seen further, it is by standing on the shoulders of giants”.


Further Reading

  1. The case against minimal guidance



  1. Being intellectually honest in education



  1. The case for fully guided instruction



  1. Why knowledge is important for critical thinking



5.Seven Myths about Education


  1. Why learning basic maths facts is important



  1. The cognitive niche – or why human beings might find maths hard! (See the section on “Emergence of Science and Other Abstract Endeavors”)


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