No, inquiry learning will not keep kids in maths class


Another day, another article in The Conversation. This time, researcher Jill Fielding-Wells and Kym Fry argue that inquiry learning is the solution to students enrolling in maths course at Years 11 and 12. It is not.

The authors claim that a key reason students do not take-up maths at Year 12 is because “they believe maths is too hard, too guarded by a rigid set of rules and not applicable to real life.” I agree with the first point. If students believe it is too hard then that requires us to ensure that we teach them by the most effective means possible. As they improve at mathematics, they will find it less hard and become more motivated. This logic is the inversion of the usual calls to make mathematics more engaging in order to motivate students so that they will then achieve.

Maths really does have a rigid set of rules. If this is not to the taste of some students then we cannot do much about it. And why do we hold school maths to a standard where it has to be relevant to the real world? The real world can be pretty mundane at times. How is art relevant to the real world? How is writing a story relevant to the real world? Should we insist seven-year-olds replace fairies and dragons with corrupt local politicians and broken washing machines? Should we tell children not to bother learning to draw because you can take pictures with your iphone?  I suspect complaints about the relevance of maths stem from the perception that maths is hard and the way people rationalise the fact that they have not mastered it.

I definitely do not think that having a long and tedious discussion of how many pizzas are needed to feed the class, where everyone has a chance to express their opinions in the possible absence of mathematical understanding, is an effective way of achieving such mastery. Yet the authors think this is a valid approach because:

“Inquiry more closely aligns with the real work of mathematicians. In practice, mathematicians identify, or are approached with, a problem. They must decide on the maths they can use to solve it. Then they come up with a procedure, solve using the mathematics and monitor the outcome.”

School children are not professional mathematicians. There is a difference in the level of expertise here. Why would we assume that the most effective way of teaching maths would be by trying to copy what expert mathematicians do? Paul Kirschner has written about this strange conflation which he describes as confusing epistemology – how new knowledge is discovered about the world – with pedagogy – the best methods for teaching well-established knowledge to novices.

It does not matter which approach looks most like what professional mathematicians do. It matters which approach is most effective.

To demonstrate the supposed effectiveness of inquiry learning, the authors draw on a most unconvincing review article which, as part of its abstract, describes how, “references are given with explanations or possible reasons for the results that are not always consistent and, at times, even contradictory.”

These results are pretty easy to explain. You usually get a boost for any intervention when compared with a control because the control is usually business-as-usual. Teachers and students cannot be blind to whether they are getting something new or the same old same old and so you initially see some gains through a kind of placebo effect. And yet inquiry learning has been relatively inconsistent at pocketing even such modest gains.

This is because inquiry learning ignores what we know about the mind. It ignores that we have very limited working memories, that new academic knowledge has to pass through working memory and so we need to limit and control want we wish students to pay attention to in the first steps of learning, otherwise we will overload them. This is why providing models and worked examples is effective. This is why confronting novices with an open-ended problem embellished with arbitrary and distracting real-world details is not effective.

Not only will such instruction be ineffective, it is likely to be frustrating and potentially demotivating.

This is probably why research into the practices of effective teachers shows that they tend to fully explain new concepts from the outset, model key process and initially guide student practice. This is also probably why data from the Programme for International Student Assessment (PISA) shows that inquiry-type approaches correlate with worse PISA scores in maths and science.

No, inquiry learning is not the solution. It would probably make things worse.

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33 thoughts on “No, inquiry learning will not keep kids in maths class

  1. Chester Draws says:

    At my school the students really like explicit instruction. They get quite shirty if you move towards inquiry learning and similar, away from explicit methods. We also have a larger progression through to Year 11 and 12 Maths than most similar schools.

    I know it’s anecdotal, but it’s anecdotal based on a couple of thousand students.

    If inquiry learning was really the way forward, it would have triumphed long ago. It’s not like it’s not been tried by lots of people in lots of places. So claims that it is “the cure” are very unpersuasive.

  2. “It would probably make things worse.” What probability would you say?

    You provide Rosenshine’s evidence and PISA correlation evidence (which is not gr8 evidence). Yet, this contradicts the What work Clearing House Evidence -which gives it’s strongest rating to “asking deep explanatory questions”.

    Who do i believe? And probably the more important question, Why?

    Willingham at least says it is way more complicated,

    “… laboratory studies show that repetition helps learning, but any teacher knows that you can’t take that finding and pop it into a classroom by, for example, having students repeat long-division problems until they’ve mastered the process.

    Repetition is good for learning but terrible for motivation. With too much repetition, motivation plummets, students stop trying, and no learning takes place. The classroom application would not duplicate the laboratory result.”

    • Chester Draws says:

      Yet, this contradicts the What work Clearing House Evidence -which gives it’s strongest rating to “asking deep explanatory questions”.

      This is unrelated to inquiry learning. The issue at core is: do we ask deep questions at the start of the topic (inquiry learning) or the end of the topic (explicit teaching).

      • The WWC does not make that distinction of asking before or after a topic. Asking explanatory questions is totally related to inquiry learning. The WWC state, “In these experiments, students are randomly assigned either to conditions that encourage deep explanations or to comparison conditions that expose the students to the similar content, but without the process of building explanations.” (IES, Practice Guide, p. 41).
        “but, without the process of building explanations” is easily aligned with direct or explicit instruction.

        They go further highlighting the need for Inquiry based methods,
        “to stimulate inquiry is to give them a problem that challenges their beliefs, that stimulates thought at their zone of proximal development, or that creates cognitive dissonance through obstacles, impasses, contradictions, anomalies, or uncertainty. ” (IES, Practice Guide, p. 42).

        The stimulus to inquiry could be given before, in the middle or the end of an instructional session. A further problem is, what is an instructional session anyway? Is it the hour lesson, or a week of such lessons , or a month or a year?

        Most of the time in the research it is a short time. For teachers though, it is a series of times.

        Perhaps, an inquiry approach is motivational at the start of say a 4 week exploration of a topic, explicit is needed in the middle, and revision and interleaving and creativity is introduced at the end. Who knows?

        There are also many problems with definitions here, which is highlighted by Greg, in a post about the explicit vs direct instruction. Most of the research does not deal with these nuances. That’s why i’m concerned when definitive judgements are made about Inquiry Based Learning, “It would probably make things worse” or from Hattie “a disaster”.

        The WWC shows most of the educational evidence is not good quality and it contradicts the certainty showed by other key figures, in particular, the EEF, Hattie, and now the cognitive load theorists. Although, I tried to point out that, at least, Willingham recognises the complexity of this.

        The overlap of inquiry, explicit, direct and problem based is way too complicated for anyone to say either method is better than the other.

        A deep explanatory question for teachers is, Why do evidence summaries of the key Evidence bodies (Hattie, EEF, WWC, Deans for impact, Rosenshine, OECD, …) differ and contradict so much?

  3. Hi Greg. Most of my teaching is essentially inquiry based, but you suggest the research into effective teachers shows that ‘they tend to fully explain new concepts from the outset, model key process and initially guide student practice’. And I do that. Inquiry isn’t in opposition to explicit instruction. You use both. Here is the concept. This is how it works. Now show me what you can do with it…

      • So you are suggesting the students don’t need to show me what they can do with the concept?! Wow. So I tell them what to do. How to do it. Then do it for them…sounds like a perfect way to improve test scores. Forget about learning.

      • Great article. And I think we are on the same page. Chunk the info. I guess we need to be careful about prescribing one cure for all. Learning is complex. Students are complex. What works in one Maths class may not work in the class next door, let alone down the street. For me, though, application is key. Don’t tell me what you know. Show me what you can do with what you know. Be that Maths. Science or PE.

    • If ‘most’ of your teaching is ‘essentially enquiry based’ then it can’t be explicit instruction at the same time.

      They can’t be learning a thing AND showing you what can be done with it at the same time (unless what they are learning is trivial).

      • I’ll revisit this. Most of my teaching is explicit instruction. Most of the learning that happens in class is inquiry based. They show me what they can do with what they have learned. Happy to chat more, but remember not all teachers teach the same thing. My context is most often Food Technology. PS. Its not trivial…but some might argue that.

    • Matthew says:

      Im not convinced that learning is all that complicated or that it varies so much from one location to another that general principles cant be applied. Its is similar to sports, some sports require training that some people dont like to do, or are not good at doing, but if you want to get better you just need to buckle down and get on with it

  4. Jay Jam says:

    Teachers should know that advice provided by Jill Fielding-Wells and Kym Fry is in direct contradiction of the evidence summarised in the NSW Government’s Centre for Education Statistics and Evaluation teaching guidelines “What Works Best”. Some relevant key points are cited below. The guidelines are widely distributed and promoted by CESE.

    “Key points
    • Explicit teaching practices involve teachers clearly showing students what to do and how to do it, rather than having students discover or construct information for themselves.
    • Students who experience explicit teaching practices make greater learning gains than students who do not experience these practices.”

      • Chester Draws says:

        the NSW “What Works Best” is in direct contradiction with the largest independent education evidence base, the USA Education Dept’s , “What Works Clearing House”.

        Where please? I see KIPP at the top of Mathematics, and that’s hardly inquiry learning.

        I’m not convinced the USA Education Dept in “independent” btw. Why are they more independent than Hattie?

      • Why are they more independent? Well there is a panel of around 20+ academics rather than one guy – Hattie. There is not a commercial conflict of interest like Hattie. Their material is not connected to a commercial company like Hattie (Cognition, Corwin, Pearson…) they don’t sell books or services their guides are free.

        The contradiction is in a number of areas-

        The WWC guide is here -https://ies.ed.gov/ncee/wwc/PracticeGuide/1

        1. THE NSW guide details 7 strategies. The WWC summary details the evidence is not gr8 for any of these individual strategies. The WWC does not even list – expectation, welfare, explicit instruction, …

        2. the WWC lists ‘asking deep explanatory questions’ as one of the strongest evidence bases. This is an inquiry based approach as distinct form an ‘explicit’ approach.

        The NSW guide lists “expectation” as a key strategy, it bases this on Hattie’s notion of ‘self-report grades’. I’ve detailed a number of analysis of the 5 meta-analyses Hattie used here – https://visablelearning.blogspot.com/p/self-report-grades.html

        None of the 5 meta-analyses are investigating “expectation”. Please read them, it will show you how dodgy this evidence base is.

        Whilst using Hattie to justify ‘expectation’, NSW uses other evidence to justify ‘ well being’. Yet even in Hattie’s evidence many of the factors of ‘well being’ are lowly rated or even negatively rated, e.g. Welfare – see here – https://visablelearning.blogspot.com/p/diet.html

      • Chester Draws says:

        The WWC guide looks quite good. It has:

        “2 Interleave worked example solutions with problem-solving exercises”. That’s pure explicit instruction. It really couldn’t be more so.

        “5b Use quizzing to promote learning. Use quizzes to re-expose students to key content..” Again, not inquiry learning, but what explicit teachers do constantly. I use quizzes a lot, and I dislike inquiry methods.

        That the last item is “9 Ask deep explanatory questions” doesn’t exclude explicit teaching. Indeed they recommend “Posing these questions during instruction is usually most useful after students have mastered the more basic factual content relating to a topic”, which is an endorsement of explicit learning. Inquiry learning is asking questions before full factual content is taught.

        So I don’t see that the WWC is at odds with explicit teaching at all. Indeed, I read it as endorsing it.

      • I did not say the WWC was at odds with Explicit teaching, Jay Jam used the NSW 7 “what works best” to provide evidence inquiry does not work. I presented the WWC guide which has strong evidence that aspects of the inquiry approach does work – asking deep questions. I also provided other reasons the WWC contradicts the NSW guide, but you’ve just ignored those e.g expectations is on the NSW guide but does not appear on the WWC guide. That contradicts the notion of “what works best”.

        Two of the tenets of the Scientific method are Reliability (replication) and Validity (are studies measuring the same thing). Most Educational research fails on both of these. So there should be at least some cause for hesitation about drawing strong conclusions, like the NSW guide has done.

        The NSW guide is also based on Hattie’s effect sizes and there is a strong evidence base showing the way Hattie and EEF present those are highly problematic.

        I think a variety of teaching approaches work, as i tried to outline in the way you would teach a sequence of lessons over long time period.

        The NSW guide bases it ‘explicit teaching’ on Hattie’s “Direct Instruction” and quotes Hattie’s effect size as the evidence. Your notion of explicit teaching is different from Hattie’s direct instruction – ask Greg points out there are at least 5 different versions of direct instruction. Also, there are many different forms of inquiry and explicit approaches. There is a lot of overlap and that’s a major problem for designing research.

        None of the 7 what works best (based on their definitions in the NSW guide) appear on the WWC guide. Although explicit teaching does appear in their Maths guide. But their definition of explicit teaching is different to yours.

        Interleaving worked examples can be an aspect of a whole range of different methods including Inquiry & problem based teaching.

      • Chester Draws says:

        I did not say the WWC was at odds with Explicit teaching, Jay Jam used the NSW 7 “what works best” to provide evidence inquiry does not work. I presented the WWC guide which has strong evidence that aspects of the inquiry approach does work – asking deep questions.

        Asking deep question is not — I’ll repeat this so you get it — NOT related to inquiry approaches.

        I followed the WWC guide and it says, with regards to asking deep questions: ““Posing these questions during instruction is usually most useful after students have mastered the more basic factual content relating to a topic”, Inquiry methods ask the questions at that start (you know, so they inquire) in order to stimulate learning of the factual content.

        You seem to have decided that explicit methods are only surface learning, and don’t involve asking questions at a deep level. That simply isn’t true. The distinction is that explicit methods asks the hard deep questions only after ensuring the students know, and have practiced, all the skills required first.

        You are arguing against a straw man. I don’t know any teachers who don’t like to ask deep questions (albeit I know a few that aren’t very good at it). Where we differ is when in the sequence of teaching we ask those questions. And that is a vital difference.

    • You don’t have to be condescending & belittling, I understand your point.

      Their practice guide does not make the precise recommendation of asking questions in the order you say. The guide implies those questions can be asked at any time of the learning process. They say-

      “Ask questions that challenge students’ prior beliefs and assumptions, thereby promoting more intensive and deeper reasoning.” They then say,

      “An example of a potentially thought provoking question in a middle school science classroom would be “Why is it good for a forest to periodically have forest fires?””

      This is an inquiry based approach.

      You seem to have a very specific definition for these approaches, you have not addressed my point that the research does not have a consistent set of definitions for these.

      • Chester Draws says:

        No, it isn’t an “inquiry approach”. It’s merely asking questions. What kind of teacher doesn’t ask questions?

        An explicit approach might be to talk about what forests are, how they are managed, what undergrowth is, how fires start (and how they are put out), and generally ensure students would have the required terms fully understood before asking “Why is it good for a forest to periodically have forest fires”. If nothing else, an explicit teacher would ensure that the students knew the word “periodically”, which most of them would not.

        An inquiry approach might be a brief discussion on forests, followed by the question, and then told to go and research it and report back an answer.

        Greg has several times listed on his blog a consistent set of definitions for Explicit Instruction. https://gregashman.wordpress.com/2017/03/15/what-is-explicit-instruction/ I pretty much go with that.

        I wouldn’t like to give a firm definition of inquiry learning, partly because it is different things to different people, but we could go with this one: https://www.edutopia.org/blog/what-heck-inquiry-based-learning-heather-wolpert-gawron

    • Greg’s definitions are useful. But, you seemed to agree with my major argument that the definitions for all of these is different. In the research, it is all different too. So I am arguing no-one can make definitive claims. Even Greg admitted in a previous post,

      “Despite what some may claim, I am aware of no evidence that explicit instruction is good for the recall of basic facts …”

      • I’m not sure what the rest of the sentence means – “…but that some alternative is needed to reach more highfalutin goals.” I think you are talking about deeper learning?

        But surely, the important part relevant to this particular set of questions, is the first part of the sentence.

      • The point I was making is that some people argue that explicit teaching is effective for teaching students to regurgitate facts but that inquiry learning or similar approaches are better than explicit teaching for developing students’ critical thinking skills or creativity or problem solving or deep understanding or whatever. All the evidence I have seen is that no such difference exists. Explicit teaching is superior for teaching facts and it is superior for developing critical thinking skills etc.

  5. If the real world of high school students did involve compelling math problems we might expect the need to motivate them to study math would not be an issue.
    It doesn’t. You can operate quite well without much skill at math until you want to study something that requires it.

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