Teaching a student who refuses to learn

Question

How to deal with a student who refuses to learn?

I've met a few of those over the years as a a private-class math teacher. They don't want to learn anything about the subject. Some of them are just not motivated, some have serious gaps in their past education, such that whatever I'm teaching makes very little sense for them.

They offer resistance to being given explanations, as if everything (or most of what) I'm saying is unnecessary and excessive. They are usually only permissive of the solution to problems that are known to be on their school's exams, and prefer step-by-step instructions free from any context/theory/mathematical properties.

To give some context:

I usually deal with either very young students who have some respect for older people authority (and come to think of it, this still exists), or pre-admittance exam students, who have well accepted the fact that they need to learn the subjects they are being taught.

But recently, I've been teaching this college student from a humanities field who needs to pass a class on high-school level mathematics. He's older than I'm used to, and confident he'll never need math in his "real" life. Hence, the problem I've been used to face reached a whole new level.

Things I usually do, but aren't working:

1. Instruct the student to show some important result (such as proving Pythagorean theorem), the proof being written by his own hands usually puts a whole new meaning to theorems and formulas.

2. Give application examples about finance (because everyone is usually interested in money).

3. Explain that understanding things makes it easier to remember and harder to forget.

4. Explain that other subjects/classes will require knowledge in mathematics.

EDIT There have been a few very good answers, but some of them and a few comments made me realize another point: Yes, I get that I usually can teach only the step-by step solution as a short term solution, this should allow the student to pass the test.

The problem I'm struggling right now is that over ten years worth of teachers have used this kludge with this student already. The result is that I'm expected to make a college student be able to solve high-school level problems while being oblivious to elementary school math and refusing to learn it.

Think about this: The student needs to pass tests on arithmetic progressions and trigonometry, but forbids you to explain how to simplify fractions or solve first degree equations.

Answer 1

This is not an answer, but an assertion that what you are experiencing is not something new. Here are some quotes from a 1993 article of an Estonian math prof, who moved to the U.S. in the early 1990s, so the problem is at least thirty years old. Some say that the commoditization of universities started from the Reagan times.

This quote is not directly related to your student's situation, after all the author's students studied some watered-down version of calculus, not high-school math, still I think the general idea applies.

I guess, the blame can be distributed between subpar school math programs, inadequate preparation of school teachers, constant pressure of high-stake tests, as well the students' expectation that good grades by themselves are a measure of success.

Bold in quotations is by me.

When I had taught in Russia, I was thanked for teaching my students to be humans, to behave reasonably in unusual situations. But I met a lot of resistance from some of my American undergraduate students, especially when I tried to give them something unexpected. On tests they wanted to do practically the same as what they had done before, only with different numerical data.

It is a common opinion that the United States of America supports democracy. Democracy always was connected in my mind with good education for all people, and I knew that American thinkers also believed in this connection. Thus, when I came to this country, I expected to have rich opportunities to teach students to think critically, independently, and creatively and to solve non-standard problems without hindrance from authorities.

But ... when I started to teach so-called "business calculus" to undergraduates, I got into absolutely new situation. All my ideas about teaching students to think became completely out of place. Never before had I seen so many young people in one place who were so reluctant to meet challenges and to solve original problems. All they wanted were high grades, and they wanted to get them with a conveyor belt regularity.

I found out that every technical calculation, which I was used to ignoring, was a considerable obstacle for my students. It took a considerable amount of time for me to understand how poor they were in basic algebraic calculations. ... I had to learn by trial and error, how much of elementary mathematics was taboo in the business calculus course. Not at once I realized that I was lecturing about exponential functions to students who were not required to know about geometrical progressions. ... Another mistake made by me was to include a trigonometrical function in a test problem. I could not imagine that students who take "calculus" were not supposed to know trigonometry, but it was the case.

At one of my lectures of business calculus, when asked why I gave problems unlike those in the book, I answered: "Because I want you to know elementary mathematics." I expected to convince students by this answer. In Moscow a university student who was told that he or she did not know elementary mathematics got ashamed and checked into the matter immediately. Elementary mathematics was normally taught to children who looked like children. Now imagine my astonishment when right after my answer an imposing train of well-grown adults stood up and tramped out. They decided (correctly) that they could graduate from the university without knowing elementary mathematics. And that they would easily find a lecturer who would teach them from the text.

The basic principle of market economy is that everybody tries to get as much as possible paying as little as possible. Nothing wrong with this when paying for goods. But some students apply the same rule to learning: they seem to think that they BUY grades and PAY for them by learning. And they try to pay as little as possible.

The advantages enjoyed by Americans are the results of real competence and real efforts of previous generations, whose heritage is now getting devalued as a results of the bureaucratic character of the education system. And someday ignorant people with degrees and diplomas may want power according to their papers rather than real competence.

Answer 2

If you are a private tutor, hired by an undergrad or adult student, or hired by the parents of a student in 6-12 (middle school/high-school), then I'd suggest that when you meet with a "client" as a potential tutor, that you develop a contract with the student and/or parents to make clear your expectations: what is the minimum level of participation/effort that you expect of the student you may agree to tutor? Making this explicit ahead of engagement, then, allows you to determine when the "contract is broken" if such participation and effort does not materialize.

The "things you usually do" are spot on. The only thing I would add is working from the beginning, to evaluate each student, inform each tutee (and/or their parents) of how you plan to address their needs, and what you need in return from the students (and/or their parents). Hence the "contract" I suggest.

In addition, try as early as possible to build a "team" mentality with the tutee: spend a few minutes, particularly at the start, trying to get to know the students you are tutoring, what they are passionate about (helps with respect to using applications in your tutoring), so you can present yourself as being there to help them accomplish their goals. Offer yourself as a "coach", someone there to help them better their performance. But, explain to them that you can be most helpful to them, and are willing to spend the time and effort to help, but it won't work only they too commit some time and effort (training). Try to convey to your students that making mistakes in NOT a problem: the best of mathematicians make mistakes! Sometimes a formerly unsuccessful student wrt math may appear completely disinterested in math, and like "it doesn't matter at all to them". Most of the time, that attitude has emerged, defensively, after previous shaming, or lack of success in earlier math classes. Instead, many such students focus on and build their self-esteem around being a great athlete, or dancer, or artist, or musician, etc.

Sometimes, for pre-college students, they might not be yet able to relate to your efforts wrt #4. Try to show how math can be interesting to them, right now: use football stats, or a book like "How to lie with statistics", or budgeting (similar to your financing example) for something they are currently passionate about (clothes, concerts, a new smartphone, sports equipment, vidio games, dates, etc.).

It is clear, from your post, that you care about your work, and want very much to help the students you work with. That's a huge plus for you. But you have the right to negotiate the "terms of engagement, as much as the person paying you has. The best teachers/professors I've ever had the pleasure to work with expected A LOT from students, but their expectations were reasonable, and they also brought to the table patience, dedication, excitement, and encouragement.

[Added]: I should also suggest that in the "contracts" you set up with clients, for both your benefit, and the benefit of the student you will potentially tutor, that you write a sentence or two emphasizing that it is possible that there may be no immediate results of your work with the student: Often times, a lot of time has elapsed between when the student was struggling, and when tutoring begins. Hence, immediate results (in homework success or passing a test) after one or two or three teaching-sessions is likely unrealistic. But success in renewed hope and effort from the student is an even more positive outcome for the future success of the student.

Answer 3

This is how most students perceive math tests. Whether it's fair or not, this is the perception and it is the normal response to a broken math education system.

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Imagine you are a teenager and your driving test for your full license is in a week. The Department of Motor Vehicles is massively understaffed, so if you fail, you can't book another test for a year. You hire a driving instructor to help you with step-by-step instructions for parallel parking, how to not forget to shoulder-check before changing lanes, etc. But when you go for your driving lesson, you're instead told to learn about the static vs kinetic friction of tires on the road, mechanical engineering principles that underlie the internal combustion engine, and civil engineering theories about traffic. When you resist and ask for step-by-step instructions you know will be on the test, your driving instructor responds:

"...the proof [of civil engineering traffic formulae and Newton's Laws of Motion] being written by [your] own hands usually puts a whole new meaning to theorems and formulas."

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Obviously, you and I know that real math, by definition, requires understanding, while safe driving only requires good physical habits. The student, though, may have experienced nothing but pseudo-math (100% step-by-step instructions) for more than a decade. In their minds, the proof of the irrelevance of abstractions is the fact that they're not tested or incentivized, the same way a driving test excludes conceptual applications of Newtonian physics.

Given how prevalent this sad misperception is, one must blame the math education system, years of bad teaching and awful testing. So, keep in mind when you say that you want them to "understand", to know why symbolic mathematical statements are true or false, they may have no idea what you're talking about while facing enormous incentives to just focus on step-by-step instructions. In their minds, every moment you spend on Pythagorean Theorem proof is meaningless, ivory tower gibberish akin to learning the history of petroleum engineering research the day before the only driving test they can book for the next year. The idea that understanding will help them in the long-run is just incredibly foreign and "obviously" false, an irrational leap of faith that requires doing worse on an imminent, high-stakes test. In fact, they may have experienced the opposite of this many times! Some will have tried to seek deep understanding, only to fail (because of prior knowledge gaps), then gotten burned on a test where rote memorization would have earned them a higher grade.

Against such entrenched delusion ("Math is just steps and rules!") and terrible incentives ("The math test is just steps and rules!"), it's no surprise that your arguments for deep understanding don't have much effect.

I'm not going to BS you and say that I have a great solution for this. I've talked to dozens of teachers, been to countless math education workshops and conferences, read zillions of books and websites, etc. and am unaware of anybody who claims to have solved this problem, especially when one doesn't control how abstract the assessments are.

The closest thing to a solution I've come up with is the following toolbox. It often does not work because students are missing years of prior knowledge and the teachers' math tests are such #$@&*, but it's the best I've got.

• Empathy. Tell them the story of the driving test and do so with great passion and anguish. Tell it better than they could. Earn an Oscar for your storytelling. Ask them if it's a fair comparison of their experience, motives, and incentives. This will massively boost your credibility while making them feel much more understood. (If you don't like the driving analogy, you could also make one up where a consultant insists an employee spend a ton of time on tasks for which the boss does not pay them or promote them for, when the annual review and promotions are in a week.)
• Safe Grades. At this point, they may be a little more open to things you have to say. Tell them they've been doing grammar exercises while you want to teach them poetry. Ask them what minimal grade they'd need to be earning before being willing to explore other aspects of math. Ask them how hard they're willing to work to achieve that Safe Grade.
• Deal or No Deal? If that willingness is way beneath what you consider necessary to earn the safe grade, then tell them to find another tutor. You're here posting on Mathematics Educators Stack Exchange, suggesting you are more caring and skillful than average, but that caring and skill is not necessary to help students rote memorize for tests. Tell them to move along. If they are willing to earn that Safe Grade, then giddy up! Get that over with ASAP, then you'll have time to do real math. :)

P.S.: Use statistics to convince students that they'll need math. "We're all going to get sick one day. What should you know about medical research? You seem to care about politics. How do you know if policies are working?"

Answer 4

Well, there is a recent and excellent book about this question: Why Students Resist Learning: A Practical Model for Understanding and Helping Students by Anton O. Tolman, Janine Kremling and Anton O. Toman.

The authors say resistance in learning may be a joint consequence of several factors, including resistance from teachers and schools. Here is a resistance framework proposed by them:

Metacognition is a very effective tool to help people with their resistance, accordingly the authors.

Answer 5

My advice is to accept 3/4 of a loaf. Tailor your instruction to cover exactly this:

"solution to problems that are known to be on their school's exams, and prefer step-by-step instructions free from any context/theory/mathematical properties."

This is really still useful content to cover and better than nothing.

Also, I wouldn't kill yourself in terms of work and maybe charge a little higher, since it is more of a hassle for you.

He's an adult learner who just needs the minimum in this darned math class to support humanities stuff he likes better. Just get him through. It should not be your objective to instill some turnaround in his attitude towards math. Heck if he just progresses and has some basic wins, that may slightly improve his attitude towards the subject.

The one thing I would not tolerate is disrespect or refusal to take training (after a discussion on his objectives and an attempt to coach him in that direction). If there is still a problem at that point, then just cut him loose and tell him to try someone else.

P.s. Think of this as very similar to personal training in the gym.