Motivating students about maths

One of the long running arguments that I have been involved with is an argument about motivation. When I promote explicit instruction, it is sometimes suggested that I have neglected the role of motivation altogether. People think that it is little use showing that explicit instruction maximises learning if it puts kids off; if it’s demotivating. In commenting on one of my blog posts, Dan Meyer claimed that I, “hypothesize that learning and motivation trade against each other, that we can choose one or the other but not both.”

This is not the case. I am actually pretty interested in motivation. I just happen to have a different theory of motivation to many people. I have even gone to the trouble of creating a graphic to explain this (I have also written that I reject the dubious idea that explicit instruction is inherently less interesting and therefore less motivating than the proposed alternatives, but that’s a separate issue).

The problem is that achievement and motivation are correlated with each other and so many commentators then assume that we can increase achievement by taking steps to increase motivation; motivation causes achievement. This is often the rationale for inquiry learning initiatives (e.g. here and here). Yet we can’t be sure that it works this way around. It could just as well be true that achievement causes intrinsic motivation. This is what I tend to think. Or it could be the case that the cause acts in both directions; a virtuous circle.

A new paper has been published (thanks to @MrPABruno for the link) that offers some support for my view. It looked at the interaction between achievement and intrinsic motivation in maths in Grades 1 to 4. The discussion is full of caveats, as we might expect of a good academic paper. We can’t necessarily generalise the claims beyond the scope of the study. For instance, we should not assume that the results would be replicated in Middle School science.

Yet the findings are quite clear. “Cross-lagged models showed that achievement predicted intrinsic motivation from Grades 1 to 2, and from Grades 2 to 4. However, intrinsic motivation did not predict achievement at any time.” This falsifies a key prediction of self-determination theory. A separate finding of perhaps even greater importance was that attitudes harden very early in education and so primary school maths is critical for how students will see themselves mathematically in the future.

It would be cool if I could claim credit for great foresight but my views about this are actually based on research from the early 1970s. In Project Follow Through, students who were taught using the model that did the most to improve achievement – Direct Instruction – saw greater gains in self-esteem than students taught using models that directly targeted self-esteem.

So we seem to be building quite a consistent body of evidence.

Mathematics Achievement


29 thoughts on “Motivating students about maths

  1. Thanks for reflecting on this topic more Greg. Your insights are always valuable. I am also interested in how “productive struggle” plays into this scenario. I would hypothesize that if it is true that achievement in maths predicts intrinsic motivation, then “productive struggle” might effectively decrease intrinsic motivation due to the fact that students might view “struggle” as lack of achievement. Any thoughts?

    • Productive struggle/failure is an interesting idea and one at the heart of my PhD research. In “How People Learn,” by NAP we are told:

      “Nevertheless, there are times, usually after people have first grappled with issues on their own, that “teaching by telling” can work extremely well (e.g., Schwartz and Bransford, 1998)”

      And yet much of the research that supports this ‘usually after’ point seems to be based upon experiments where more than one factor is varied at a time, something that John Sweller, one of my supervisors, has commented on in the following book:

      The best experiments, as far as I am aware, are those conducted by Manu Kapur in Singapore. These show a positive effect of productive failure under certain circumstances.

      • suehellman says:

        I appreciate that I’m coming late to this discussion, but here’s my contribution. I think there’s often a disconnect between the way a strategy or intervention is originally conceived and put into practice, and the ways in which well-meaning imitators implement it. In the case of “productive struggle”, too often the emphasis is on the struggle. The struggle itself is seen as beng inherently productive and of value. My understanding of this term is that “productive” should mean that the struggle ends in some sort of successful resolution. Without that, the only learning (esp. for many math students) is that struggle produces unresolved frustration. When the teacher is does not ensure a successful outcome, what’s left is struggle for it’s own sake — & that’s not very motivating for most of us.

  2. Your model reflects my experience teaching my own children maths. They began with no intrinsic motivation but now they are good at maths they often say it is their favourite subject at school.

  3. Brian says:


    An interesting post. My experience also echoes your conclusions.

    I am not sure if this is going over old ground, but I believe I have seen a difference between motivation to learn and motivation to work. These seem to me to be 2 different things. I have seen students who do all the work but learn very little from the process and vice versa. Ability may clearly play a part but.

    I believe that many teachers try to motivate students to do the work which is only part of the process. Engaging in the work and learning from the work are for me seperate. Success for me brings motivation to learn and then motivation to work. I see students who need to do the work and for them that is quite a result. Again clearly, learning and working are linked.

    So while it seems likely to me that intrinsic motivation is not a reliable predictor of achievement this does not indicate that never be the case. It also seems logical that achievement will not always be a predictor of motivation. My thoughts are general whereas your research is I believe in Maths and this may also be an issue i.e. different people and different subjects.

    I will follow your thoughts as your research progresses and look for some illumination to either reinforce or disprove my suspicions.


  4. I very much liked this aspect. Motivation from good achievement is underestimated. Short pop quizzes on equation solving which, after practice, seemed very simple had exactly this aim: getting a sense of success which would motivate. Throughout the article you espouse a sense of “Or it could be the case that the cause acts in both directions; a virtuous circle.” with other research showing that both directions are at play, but achievement->motivation stronger. However, when you cite the new paper I think you go a bit too far. You state that the discussion section, as any good academic paper, throws up all kinds of limitations. To therefore claim that this paper falisifies Self-Determination Theory *and* nullifies the direction motivation->achievement is pushing it a bit too much. This certainly holds, in my opinion, for the infographic, where a succinct dichotomy is presented, where there is none. This is even apart from other points, like ‘intrinsic motivation’. In literature on ‘Attitudes towards Mathematics’ this is not the only thing.

    • The abstract states, “Cross-lagged models showed that achievement predicted intrinsic motivation from Grades 1 to 2, and from Grades 2 to 4. However, intrinsic motivation did not predict achievement at any time. This developmental pattern of association was gender invariant. Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation.”

      How is my graphic at a variance with this?

      • The limitations, the nature of ‘significance’, plus previous research you have quoted in previous blogs (or on twitter) should be enough to not suggest that the implication has one direction. Stronger, OK, but not one direction. Maybe after a replication of this study we know more. I was just surprised that you acknowledge how authors took care in formulating limitations and then are succinctly summarised in an infographic with a big red cross through one of them :-D. (In a world where people incorrectly use the ‘motivation leads to achievement’ only I can understand how you would want to emphasise the other; and research confirms this.)

      • The graphic is based on the study. It has a reference to that study in the graphic. The study found exactly what the graphic shows. I have quoted the study to you.

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