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Let me know if you think the following would be better suited for academia.stackexchange. But I think some answers will be maths-specific, so I'll start with it here.

I'm a maths tutor. Up until now, when a student (ages 12 - 18) talks about maths negatively - "I don't like maths", "I suck at maths" etc, I have listened to what they had to say, but I don't have anything great to say in response. Sometimes I empathise, "yes maths is hard...", but I don't really address or talk to them about their negative attitude towards maths in a substantive way- rather I try to get the student to focus on the maths we intend to cover in the hour's long tutoring session. These situations do happen fairly regularly when I start tutoring someone new, and sometimes even if I have been tutoring them for a while. The reason my approach has been to not address their negative self-perception is partly I don't know exactly how and partly because I feel guilty that I'm basically forcing them to study maths when they don't want to - and I believe that if someone doesn't want to learn something, then I shouldn't be forcing them to.

After some reflection and reading some comments from other questions on this website, I think there is a better way to handle this situation. This would be to help them reframe their hatred of maths or self-perception of their own abilities as being poor, by starting with asking leading questions such as, "why do you think you suck at maths", or "why do you hate maths?", and then they will say something like "I get bad marks" or "I just don't understand it".

But instead of saying, "well you may have got bad marks in the past, but with effort and time you can improve your maths abilities for sure", or, "you may not understand the maths now- we need to start from the fundamentals and break it down into smaller chunks."

Sure, this is fine. But I think it could be really useful to also explain to them that, psychologically, if they keep saying to themselves, "I suck at maths" and "I don't understand maths" then that is a self-fulfilling prophecy, because: if they don't believe in themselves then they won't even try. And spending real time and effort studying maths trying is the biggest step a young student can take towards self-confidence and ultimately self-improvement.

So, is it a good idea to discuss with the student that reframing is a regular exercise they can do whenever a negative thought pops up- remember aimed at a young person - and how exactly would you explain this/discuss this with them? What exactly should you say? And, what other useful reframing exercises are there?

I have done some reframing myself with a CBT (cognitive behavioural therapy) professional for my anxiety, but I'm far from an expert at understanding how to teach someone else that they can reframe their negative thoughts and what the process of doing this entails. So my question is: how you would you explain/discuss this with someone? Would you explain it differently depending on the student's age? I suspect $18-$ year olds would be able to understand and implement reframing a lot better than $12$ year olds, so maybe a different approach needs to be taken towards my younger students?

Thanks in advance.

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    $\begingroup$ One resource that might help is a podcast called Math Therapy, where the host interviews many adults that all "hated math in school" but then turned it around and love math as an adult. All of their experiences are pretty unique so you might be able to find some good pieces of info from different guests that have appeared on there about how to reframe their negative views of math. $\endgroup$
    – ruferd
    Aug 12, 2022 at 19:02

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You mentioned two different sorts of negative attitudes: "I don't like math" and "I'm not good at math". If a student has only expressed one of those, the approach you take might be different for one versus the other. But the reasons for both are often the same: math is approached badly in school. (See A Mathematician's Lament, by Paul Lockhart.)

For the students who think they aren't good at math, your approach is lovely and if you keep researching CBT, I think you'll get good at helping them that way. (You probably know more about CBT than I do, so I won't say more about that.) My approach for students with test anxiety has been to have them listen (repeatedly) to a guided visualization I wrote that I call Math Relax. For more general math anxiety, I have them read one of the many good books for that: Overcoming Math Anxiety, by Sheila Tobias and Mind Over Math, by Stanley Kogelman are two I like.

For the students who don't like math, I'd definitely explore what about it they don't like. If the parents (who are paying the bill) are ok with some of the time being spent to deal with this bigger issue, I'd try to bring in activities that connect math with things they do like. One student I tutored liked logic. I love logic puzzles and games. His mom paid for us to do that because I thought it would help improve his attitude about math.

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    $\begingroup$ +1, good answer! $\endgroup$ Aug 19, 2022 at 16:51
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    $\begingroup$ I also recommend Mind Over Math. It's not exactly recent but Kogelman and Warren's views on math are very modern and they'd fit right in here (and who knows, maybe they do post here?) $\endgroup$
    – Thierry
    Aug 19, 2022 at 21:21
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The first point, surely, is figuring out whether, for this individual right here, the negative things they say is just a harmless ritual response, or whether there is some actual problems there.

By the harmless ritual response alternative I mean that starting to do something that requires attention, thinking and trying, more generally effort is not comfortable, and someone might express this by a phrase that puts a negative light on mathematics. But this is essentially harmless; just a part of the ritual to get in the mindset and start doing things.

I will probably make some unhappy noises before I start washing dishes or cutting the grass or various other tasks, but this does not mean you should pay attention to it and start worrying about my bad relationship to dishwashing.

Supposing it is not simply this, but there is actually some kind of emotional problem, the typical recommended way is to:

  1. Let them speak and you listen.
  2. Acknowledge that the emotions are real.
  3. Do not try to fix it by offering a recipe to follow, or other rational response.
  4. Do support them if they want to do something about it.

For going further than this I do not really have advice. But there exists plenty of literature on effective communication (also with power imbalance), and on motivation in mathematics; the stuff I have read recently include:

EIDE, Hilde; EIDE, Tom. Kommunikasjon i relasjoner: personorientering, samhandling, etikk. Gyldendal akademisk, 2017.

WÆGE, Kjersti. Motivasjon i matematikk. Universitetsforl., 2018.

There is even more material about what a safe and inviting classroom environment in mathematics is like; things like being allowed to make mistakes and drawing out multiple ways of reasoning, rather than fixating on a single correct solution or method. These might be helpful in the long run, too.

BOALER, Jo. Mathematical mindsets: Unleashing students' potential through creative mathematics, inspiring messages and innovative teaching. John Wiley & Sons, 2022.

KLAVENESS, E.; KARLSEN, L.; KVERNDOKKEN, K. 101 grep for å aktivisere elever i matematikk. Bergen: Fagbokforlaget, 2019.

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I think you are better off NOT engaging in discussion when remarks like this are made. 1. It's a distraction from the task, training on math. 2. It's an intractable argument that won't be won by some magic rationale.

As with many questions on this site, it is in the form of "how do I win this argument", but I think it is important to realize that teaching is a people management problem, to a huge degree. Different from the how do I integrate something, math problems. So, you have more options than the direct argument.

Also consider humor to deflect, but acknowledge. Yeah, it can feel that way, but after you do more problems, you'll get used to it. Or other remarks like that. Use your judgmrnt based on the personslity. But don't get sucked into some mopey self assurance crap.

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    $\begingroup$ So do you think that CBT/reframing doesn't work on teenagers? CBT/reframing works successfully for many people. And I do not think it is "mopey self-assurance crap". I think what you say (it won't work for some students) might be true for some people, but other more rational-minded students may listen to the rationale behind reframing exercises. One could argue that this is more of a therapist's role than a maths tutor's role, but it is said that a tutor sometimes has the role of a therapist... $\endgroup$ Aug 19, 2022 at 16:28
  • $\begingroup$ Don't know what that is. Just gave my answer on it's own. $\endgroup$ Aug 19, 2022 at 22:26
  • $\begingroup$ Health anxiety is anxiety about your health, and often causes panic attacks. This often happens to people who view their health as something which can suddenly get worse for no apparent reason, which is true (e.g. sudden heart attack). In the case of health anxiety, one of the things I learned through CBT is that whilst this way of viewing your health is not incorrect, a reframing of the situation - i.e. viewing the situation in another way - will reduce your anxiety about health. Specifically, doctors view people as healthy until there is a reason not to. So rather than viewing your health $\endgroup$ Aug 29, 2022 at 11:12
  • $\begingroup$ as something temporary, viewing yourself as being long-term healthy means you will worry and panic about your health less. So it's "two sides of the same coin", and it's better to see the world through the positive viewpoint. So a reframing is seeing the same situation from another, more helpful / positive perspective. That's essentially what this question is about. About if/how we should help students reframe their own negative maths experiences in a more positive/helpful way. $\endgroup$ Aug 29, 2022 at 11:12

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