WitCH 40: The Primary Struggle

This is one of those WitCHes we’re going to regret. Ideally, we’d just write a straight post but we just have no time at the moment, and so we’ll WitCH it, hoping some loyal commenters will do some of the hard work. But, in the end, the thing will still be there and we’ll still have to come back to polish it off.

This WitCH, which fits perfectly with the discussion on this post, is an article (paywalled – Update: draft here) in the Journal of Mathematical Behaviour, titled

Elementary teachers’ beliefs on the role of struggle in the mathematics classroom

The article is by (mostly) Monash University academics, and a relevant disclosure: we’ve previously had significant run-ins with two of the paper’s authors. The article appeared in March and was promoted by Monash University a couple weeks ago, after which it received the knee-jerk positive treatment from education reporters stenographers.

Here is the abstract of the article:

Reform-oriented approaches to mathematics instruction view struggle as critical to learning; however, research suggests many teachers resist providing opportunities for students to struggle. Ninety-three early-years Australian elementary teachers completed a questionnaire about their understanding of the role of struggle in the mathematics classroom. Thematic analysis of data revealed that most teachers (75 %) held positive beliefs about struggle, with four overlapping themes emerging: building resilience, central to learning mathematics, developing problem solving skills and facilitating peer-to-peer learning. Many of the remaining teachers (16 %) held what constituted conditionally positive beliefs about struggle, emphasising that the level of challenge provided needed to be suitable for a given student and adequately scaffolded. The overwhelmingly positive characterisation of student struggle was surprising given prior research but consistent with our contention that an emphasis on growth mindsets in educational contexts over the last decade has seen a shift in teachers’ willingness to embrace struggle.

And, here is the first part of the introduction:

Productive struggle has been framed as a meta-cognitive ability connected to student perseverance (Pasquale, 2016). It involves students expending effort “in order to make sense of mathematics, to figure out something that is not immediately apparent” (Hiebert & Grouws, 2007, p. 387). Productive struggle is one of several broadly analogous terms that have emerged from the research literature in the past three decades. Others include: “productive failure” (Kapur, 2008, p. 379), “controlled floundering” (Pogrow, 1988, p. 83), and the “zone of confusion” (Clarke, Cheeseman, Roche, & van der Schans, 2014, p. 58). All these terms describe a similar phenomenon involving the intersection of particular learner and learning environment characteristics in a mathematics classroom context. On the one hand, productive struggle suggests that students are cultivating a persistent disposition underpinned by a growth mindset when confronted with a problem they cannot immediately solve. On the other hand, it implies that the teacher is helping to orchestrate a challenging, student-centred, learning environment characterised by a supportive classroom culture. Important factors contributing to the creation of such a learning environment include the choice of task, and the structure of lessons. Specifically, it is frequently suggested that teachers need to incorporate more cognitively demanding mathematical tasks into their lessons and employ problem-based approaches to learning where students are afforded opportunities to explore concepts prior to any teacher instruction (Kapur, 2014; Stein, Engle, Smith, & Hughes, 2008; Sullivan, Borcek, Walker, & Rennie, 2016). This emphasis on challenging tasks, student-centred pedagogies, and learning through problem solving is analogous to what has been described as reform-oriented mathematics instruction (Sherin, 2002).

Stein et al. (2008) suggest that reform-oriented lessons offer a particular vision of mathematics instruction whereby “students are presented with more realistic and complex mathematical problems, use each other as resources for working through those problems, and then share their strategies and solutions in whole-class discussions that are orchestrated by the teacher” (p. 315). An extensive body of research links teachers’ willingness to adopt reform-oriented practices with their beliefs about teaching and learning mathematics (e.g., Stipek, Givvin, Salmon, & MacGyvers, 2001; Wilkins, 2008). Exploring teacher beliefs that are related to reform-oriented approaches is essential if we are to better understand how to change their classroom practices to ways that might promote students’ learning of mathematics.

Although teacher beliefs about, and attitudes towards, reform-oriented pedagogies have been a focus of previous research (e.g., Anderson, White, & Sullivan, 2005; Leikin, Levav-Waynberg, Gurevich, & Mednikov, 2006), teacher beliefs about the specific role of student struggle has only been considered tangentially. This is despite the fact that allowing students time to struggle with tasks appears to be a central aspect to learning mathematics with understanding (Hiebert & Grouws, 2007), and that teaching mathematics for understanding is fundamental to mathematics reform (Stein et al., 2008). The purpose of the current study, therefore, was to examine teacher beliefs about the role of student struggle in the mathematics classroom.

The full article is available here, but is paywalled (Update: draft here). (If you really want it …)

It is not appropriate this time to suggest readers have fun. We’ll go with “Good luck”.

UPDATE (28/7)

Jerry in the comments has located a draft version of the article, available here. We haven’t compared the draft to the published version.

37 Replies to “WitCH 40: The Primary Struggle”

  1. https://cutt.ly/PsTTqS3 leads to a pdf which has on it “This is the final draft of the paper, and contains the text as it appears in the actual published article. It can be freely distributed.” So a legit copy.
    I look forward to reading the thing. Well, perhaps I look forward to struggling to read the thing.

  2. I read it. It seemed fine, I guess? One thing that I missed was anything relating to empathy and emotions. Personally, if I’m intending to allow students to “struggle”, I would take into account how they are feeling. If they are already anxious, it’s probably not a good time to deliberately confuse them. Also, I think explicitly expressing an willingness to be patient as a teacher can help students feel okay about taking time to understand things.

    (It’s very likely I’m missing something because I have heard of some of these authors but not read anything by them before.)

      1. I did, but I guess I skipped over things. Reading the quotes from teachers shows that some use the word “struggle” in an everyday sense and just kind of freely muse about it. Then the researchers think of it in their more branded Productive Struggle sense when they code responses. As such it seems that the ‘positive’ responses indicate those that have been trained to use the word in a specific way, rather than indicating actual differences in teaching. Is that the crap?

        1. s-t, it is classic Gish gallop. To understand all that is wrong with the article, and just how awful it is, you have to read it and you have to decode it. I’m sorry, but “skipped over things” won’t work.

          I’m not saying this is your job, or the job of other commenters. I think demanding that would violate some Human Rights convention. But that’s the problem with almost all education research. It is almost impenetrable, and unless you work really hard, you can’t really get to see to what extent it is old-hat, or useless, or meaningless, or, as in this case, actively damaging.

          1. It seemed to me like research into the effectiveness of their marketing – they have been trying to create a certain change in the curriculum and marketing it through their professional learning workshops. Then this research is testing to see how many teachers had received their message, and finding out how they had interpreted it. I didn’t get the sense that this article was meant to be useful to teachers. Now I will wonder how it is damaging.

  3. Two initial thoughts:

    1. “Embracing struggle” is talked about as if it is a new idea. I don’t think this is true.

    2. The article is focused on teacher beliefs. Beliefs. (I mean, it is partially funded by a Catholic Diocese and Catholic Education organisation, so… makes sense.) Sorry, but I don’t really care what a teacher believes; aren’t we professionals?

    1. Thanks, Glen. On your first point, it’s a question of what they mean by “struggle”. But yes, to the extent that it is not crazy, it is definitely not new. On your second point, you are sort of correct, but the article makes clear what they did is much more insidious than the title suggests.

  4. ” That is, most teachers in this study believed there is inherent value in the process of allowing students to struggle, independent of any apparent progress students are making with the problem at hand.”

    Ohhh, now I get it. You see, what I should have been doing this whole time is giving my students impossibly complicated problems to do, extra bonus points if the problems are unsolvable or I’m asking them to prove something that is false. Having them get frustrated with my ridiculous questions is definitely of inherent value. To optimise struggle, perhaps I should also cancel all classes and just send them problems to do by carrier pigeon. On that note, let me also write them all in ancient Greek, and backwards, with every third character replaced by the poo emoji, because that will definitely lead to some struggle with inherent value.

    How silly I was in carefully catering learning experiences before.

      1. What they are doing is using their considerable clout to push the idea of focusing on struggle, especially when they are training teachers (they explicitly say this).

        While my comment is not really serious, the point I’m trying to make is that while struggle (or wrestling with ideas, taking time to think things through, working at something for a while, whatever you want to call it) is a typical thing that happens when teaching, focusing on it as an end-goal (“I taught well today because my students struggled a lot”) can kill the learning experience.

        1. Glen, of course I didn’t take your comment literally. But when they write “struggle” they mean “productive struggle”, and they note aspects such as “supportive classroom culture”.

          1. Yes I’m aware of the jargon and the slogans… I don’t think it affects the point I’m making. Teacher training is already deeply problematic. What does this focus on struggle actually do to support the learning of mathematics? They might as well be talking about teaching kids to run 100m in 10 seconds.

            The focus should not be on struggle. Who cares what teachers believe about struggle. The important thing is how they teach, how they run their class, how they interact with students. How do they impart knowledge in their discipline, how do they ensure that their students actually learn.

            Students struggling is a side-effect of learning. Learning anything! There is nothing deep to be said about it being present. If it is absent then you have issues. But also, if students don’t ask questions then you have issues. If students don’t talk much, you have issues. If students don’t go to the toilet…. then you have issues. Maybe we can write articles and do studies and re-write our teacher training to address these. Maybe we can make a little priority list for teachers to carry in their back-pocket to make sure each of these things are happening in their classroom.

            1. Yes, of course. Obviously I’m playing Devils’ advocate in the comments. Pretty much literally: I think what these people are doing is evil.

              I’m just pointing out that they genuinely think they’re doing something more sophisticated than throwing kids in the deep end.

  5. My first thoughts – it reads like a lot of the “Maths Ed” academic papers. Lets come up with a new word for an old idea and give a few people careers out of writing academic papers to each other about it all.

    The sample size seems incredibly small for a meaningful argument. I suppose one could call it a “case study” which would be fine, except the conclusions are suggesting something a lot more powerful.

    I’ve had a rough go with some of the stats presented in the paper, but being a qualitative study I didn’t get very far!

    1. Thanks, N8. I’m not so sure it’s an old idea. It is unclear from the article, but I suspect it is a new evil. And, yes, the universal flavour of the declarations for such a small sample is ridiculous. It’s even more misleading than that, in a manner s-t has noted. I wouldn’t bother with the stats: they’re undoubtedly correct, but why would anyone care about them?

      1. Considering that they put the participants through their own special training module on the importance of struggle

  6. Hmphhh My students have been getting ample opportunity to struggle for years – in every assessment I give them. I always knew more after walking out of an exam than when I walked in, so I like to share that experience ….

    More seriously, I think every teacher gives his/her students a chance to ‘struggle’: You write a question on the board and ask students to have a crack. You wander around looking at what they’re doing and give encouragement, a helpful nudge/suggestion or a clip round the ear as required. Then you work through the question with the students after an appropriate amount of time has passed.

    As Glen says: “The important thing is how they teach, how they run their class, how they interact with students. How do they impart knowledge in their discipline, how do they ensure that their students actually learn.”

    Knowledge and experience can’t be given, it has to be earned. This so-called ‘struggle’ is one of many standard techniques used by every teacher for doing exactly the important things that Glen has noted.

    Strangely enough, I agree with Glen:

    “Embracing struggle” is talked about as if it is a new idea. I don’t think this is true.”

    and N8:

    “it reads like a lot of the “Maths Ed” academic papers. Lets come up with a new word for an old idea and give a few people careers out of writing academic papers to each other about it all”

    If all these so-called educational experts stopped publishing, progress in quality teaching would be set back by exactly 1 day.

    1. Thanks, JF. (Why is it strange you agree with Glen? Apart from his weird ideas on integration, he’s pretty smart.)

      Of course you and Glen are correct, that this “have a crack” notion of struggle is completely standard, about as new as Socrates. But I’m not convinced that’s all these guys are on about. I can’t see that the article links to their propaganda, but I think there are plenty of code words in the article to indicate that they are doing something different from “have a crack”. And, remember, the article is about primary school.

  7. Think I’m going to be sick. Is primary school really called “elementary” in the “education studies” world (in Australia!!)?

    1. You forget, Craig. These nitwits are seeking relevance in countries beyond Australia (but yes, the ‘Americanisation’ of the language is very distasteful).

  8. ‘Reform’
    ‘Critical learning’
    What a weird use of language.
    Next reform in the struggle of critical learning may well be that some numbers are more equal than others.

  9. It would be interesting to see how students develop ideas about how to add 1/2 and 1/3 together.
    God forbid a “teacher directed procedure” be told to them to help them out.
    What would a decent teacher know about anything to do with mathematics and learning it?
    I feel these constructivist and problem based learning type papers and academics really devalue any knowledge that a teacher can bring to students learning mathematics.

    1. Good teachers know when explicit instruction should be given and when to let students try on their own. So in the case of adding fractions, I usually do an explicit example or two with my Specialist students and then ask them to have a go at 2/7 + 3/5, say, on their own. Then we look at it together after a couple of minutes. All the while, I’ll cruise the room and offer encouragement, advice or a clip behind the ear.

      The problem with many constructivists is they only have a hammer and so see everything as a nail.

      I haven’t had a good read of the article yet (I save my masochism for Sunday evenings) – I hope it’s not pushing some thinly disguised form of ‘learning through [the struggle of] exploration’.

  10. The authors link the paper to the work of Dweck (2007) which I have read. It has been a best-seller. However, I found that it was like many self-help books: based on research, littered with many anecdotes, but does not tell me much that I did not know (cf. “The complete book of running”, “The 7 habits of highly effective people”). But people buy these books in droves.

    Back to the paper. I read through the paper by Russo et al. which is set in a primary context where I have no experience. It reminded me about other research that concluded that secondary mathematics text books in Australia do not offer students challenging exercises. A typical chapter goes like this. Here is a mathematical idea; now some examples to illustrate the idea; then some exercises to be solved which are exactly like the examples. On completing the chapter, there will be a test (available through the publisher) that will contain problems exactly like the exercises. Not much in the way of challenge here. I have seen this pattern many times.

    We have seen the recent changes that are about to come to the NSW curriculum; I would not be surprised if we see the same in Victoria. From this paper by Russo et al., I infer that primary teachers would support offering more opportunities to challenge their students. That’s comforting.

    I am a keen chess player – but not particularly talented. I just love the experience of sitting at the board and thinking hard for a couple of hours. The joy of pure thinking. I would like to convey this feeling to students.

    Good night (morning actually).

    Dweck, C. (2007). Mindset: The new psychology of success. (Updated ed.) New York, NY: Random House.

    1. Terry, the awfulness of current secondary textbooks is entirely irrelevant. As for your inference, it’s the kind of thinking that made P. T. Barnum rich.

  11. I looked through the above criticisms of the paper by Russo et al. Here is a summary of some of them and my comments.

    Struggling is not a new idea. True; cf Percy Cerutty; https://en.wikipedia.org/wiki/Percy_Cerutty

    Some students might not respond well to a struggle today. True. Teachers should endeavour to be aware of external issues that may be affecting individual students and respond accordingly. I doubt that the authors would disagree.

    One can overdo this. True – but I doubt that this is what the authors intend.

    Sample size is too small. Having read a bit about sample sizes, I’d say that sample sizes should be justified in any research project that goes through an ethics committee, and I assume that this project did go through the process. When I served on such a c’ee for many years, I would always ask the researchers to justify their choice of n. This is a mathematical problem!

    All good teachers know this. Probably true. It is often (but not always) the case that research backs up what experts at the coal face know already.

    The authors use jargon from the US. The paper is not published in an Australian journal, and I imagine that the authors wrote for an international audience.

    Written by constructivists. Probably true. Now I do not put myself in this class, but I have often wondered what the term means. I discussed this with people who classify themselves as constructivists. (Some of my best friends etc.) I have read papers on the topic. And I still don’t know what it means.

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