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I am curious about the effects of certain phrasings in educational contexts, particularly in mathematics. In fields like physiotherapy, using phrases like "it's just lifting your leg" can seem dismissive and fail to empathize with the patient's experience. Similarly, in education, saying "it's just using the chain rule" might undermine the student's challenges.

Are there any studies or research that explore the impact of such seemingly trivializing language in the context of teaching mathematics? How does this language affect student perception, motivation, and understanding of mathematical concepts? I am looking for references about this topic. i've done an animation trying to explain the context: https://youtu.be/vnhK3bTVYLk

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    $\begingroup$ Doesn't this just involve a literature search? :) $\endgroup$ Jan 17 at 15:46
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    $\begingroup$ What search terms have you tried on scholar.google.com ? $\endgroup$ Jan 17 at 16:17
  • $\begingroup$ What did you find in your ERIC search? $\endgroup$
    – shoover
    Jan 18 at 21:29
  • $\begingroup$ I am closing this question because you seem to be asking the Math Ed site to do a literature search for you. This is not what the SE network is for. Once you have done your own literature search, you are welcome to post here to clear up any confusion you might have. $\endgroup$
    – Xander Henderson
    Jan 22 at 18:40
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    $\begingroup$ Nominating to reopen. "Are there any research about ..." is a common type of questions here, and they are usually well received. Sure, it would be better if the OP shared what they tried, but that's no reason for closing. You may be irritated with the OP's perspective, but the questions is interesting and received useful answers. $\endgroup$
    – Kostya_I
    Jan 24 at 18:32

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You can find one such study here:

  • Kroeper, K. M., Muenks, K., Canning, E. A., & Murphy, M. C. (2022). An exploratory study of the behaviors that communicate perceived instructor mindset beliefs in college stem classrooms. Teaching and Teacher Education, 114.

Take a look at Table 1 on page 5, for example.

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Hypothetically, a study researching the effect of a single word ("just") within a complex educational context would fall under the heading of a psychological priming effect.

In some sense, these studies are easy to do. But the problem is, these kinds of studies are infamous for being poorly designed, very subjective, easily biased by researchers, not generalizable to real-world classrooms, and routinely fail under larger replication attempts.

Psychologist and Nobel laureate Daniel Kahneman wrote a letter to the community in Nature in 2012, saying this:

As all of you know, of course, questions have been raised about the robustness of priming results. The storm of doubts is fed by several sources, including the recent exposure of fraudulent researchers, general concerns with replicability that affect many disciplines, multiple reported failures to replicate salient results in the priming literature, and the growing belief in the existence of a pervasive file drawer problem that undermines two methodological pillars of your field: the preference for conceptual over literal replication and the use of meta-analysis. Objective observers will point out that the problem could well be more severe in your field than in other branches of experimental psychology, because every priming study involves the invention of a new experimental situation.

For all these reasons, right or wrong, your field is now the poster child for doubts about the integrity of psychological research.

While it's unlikely that any research exists on such a fine-grained linguistic issue in math education, if any such research exists, we should definitely not trust its findings, nor expect that its findings would be useful in real classrooms.

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In my experience (obviously anecdotal, but take from it what you will), it all comes down to whether you're dismissing the struggles of the student (i.e., "why is this not easy for you") vs the complexity of the problem (i.e., "the problem looks intimidating until you realize this key insight that makes it more routine based on what you already know").

For instance, suppose a student is struggling to use the chain rule to compute $\dfrac{\textrm d}{\textrm dx} \left[ \sin (x^2) \right].$ In that case, it would be unhelpful to say "it's just the chain rule" because that's what they're trying to do.

But now imagine that a student has learned the chain rule and is comfortable applying it, and you're teaching them implicit differentiation. To show them how to compute $\dfrac{\textrm d}{\textrm dx} \left[ y^2 \right],$ you might say something like

I know it looks weird because there's no $x$ in that expression being differentiated. However, if you just write $y$ as a function $y(x),$ then it's easier to see that this is ultimately just boils down to a straightforward application of the chain rule: $$\dfrac{\textrm d}{\textrm dx} \left[ y(x)^2 \right] = 2y(x) \dfrac{\textrm dy(x)}{\textrm dx} = 2y \dfrac{\textrm dy}{\textrm dx}$$

In this case, the point the phrases "if you just," "it's easier to see," and "a straightforward application" is to highlight key insights that can be used to reduce the complexity of the problem. You're trying to convey that a change of perspective can make this problem feel less intimidating and more routine to the student based on what they already know.

That said, it's easy to overestimate the prior knowledge of the student, which can lead an expert to think they're dismissing the complexity of the problem when they're actually dismissing the struggles of the student.

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    $\begingroup$ I would also note that this is helpful for mathematicians as well! When a paper says "an easy application of Cauchy–Schwarz gives us the bound..." it can prevent us from hours of banging our heads looking for a more complicated reason. $\endgroup$ Jan 18 at 19:46
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    $\begingroup$ Chemist here. As students we translated the language of one professor roughly like this: "trivial" -> ca. 2 pages paper and pencil. "obvious" -> 1 page "as one can easily see" -> maybe 4 pages? $\endgroup$ Jan 18 at 20:08

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