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I am currently teaching a high-school student, 1st grade Social Science. He is weak in mathematics. My initial strategy was to explain basic concept but with high repetitions, so that he can have a strong foundation. Initially, I gave "Solving 1 Variable Linear Equations".

It has been 4 months (2 hours a week in 1 day), and we have discussed up to "Solving Inequalities with Square Roots: $\sqrt{2x-3} = x + 1$... etc." Until recently, I give him an easy problem of solving 1 variable lin.eqn, which we have discussed many times before, and he still has not got strong understanding of the concept. He keeps asking easy stuffs like : "$-2 + -4 = -6$.. right?" or "$2 + x = 3(\frac{x}{2} + 3) \implies x = 3(\frac{x}{2} + 3 - 2)$...right?".

How to solve this problem?

What I have tried:

  • Using markers with different colors to indicate different terms so that the written solution looks clearer.

  • Told him to become independent with respect to me as tutor. To get used to mathematics and read the book.

  • Repeat exercises of basic concept (1 var. linear equation) many times.

  • I also often give extra hours.. (up to 3 at most)

Impact:

  • He is improving, but not enough to get good marks (or even average). If I continue the method, there could be two possibilities : either he will be good in the long term, or... not.

  • But still does not show good understanding of the concept. Very stiff, it seems that he thinks mathematics as instructions that have to be memorized.

Particular Questions:

  • Should I go back to the very basics, teaching arithmetics, understand brackets, etc..? What book or article is good for this..?

  • From my experience, I understand mathematics not through tutors but by reading math books. So, is it better to teach the student: how to read math books?

Thanks.

Arief
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    "−2+−4=−6.. right?" -- which is right. But I see you mentioning the constant need for reassurance, which may be caused by the pedagogy and by the fact that many schools simply have no textbooks to flip back some pages to find needed info. These students are not used to work with textbooks. This is an acquired skill. – Rusty Core Nov 30 '18 at 17:16
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    Possible duplicate of How to teach a student algebra who misses too much previous knowledge? – shoover Nov 30 '18 at 17:37
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    Can you say a bit more about your specific context? I'm not sure what "1st grade social science" is. – kcrisman Nov 30 '18 at 18:49
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    On a different note, perhaps the fact the student is from social sciences is not as relevant as the actual ability level, but it's possible you are asking for motivational questions that would help the student get better, in which case you might want to try some supply/demand/price/etc. functions (revenue is often quadratic in basic models) or even minimax game theory stuff. The math is pretty simple, but it provides reasons for needing to solve these. – kcrisman Nov 30 '18 at 18:51
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    Concentrate on drill, not explanations. Don't try to reach him, Just condition him. Give him feedback on how he does on drill (keep some score). Don't go all the way back to arithmetic, but instead use the prealgebra work as a chance to practice some arithmetic in passing. Keep the problems relatively simple until he is up to speed. Do linear problems, not sqrt, for now. Don't do unpaid hours. – guest Nov 30 '18 at 19:56
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    You can do small expllanations as you go. But jus keep drilling. Don't be derailed by the "he doesn't get it". Some people learn from conditioning, first, not logic. Especially for weaker students. – guest Nov 30 '18 at 20:23
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    For single variable solving, the key is to do it mechanically, in same order (group/add/divide or whatever) and always showing all the steps and painfully doing same thing on each side (NOT moving something from one side to the other but adding or subracting same amount to allow a cancelation). The problem is you smart people assume everyone is like you and don't realize some of us dummies need things to be more mechanical. Especially at first, gaining familiarity. – guest Nov 30 '18 at 20:26
  • "he thinks mathematics as instructions that have to be memorized." Maybe that is (a) not that bad and (b) true if you replace instructions by rules. There is no point in proving things like collecting like terms by applying axioms and the commutative law. – Jasper Nov 30 '18 at 21:50
  • @kcrisman here, the high school has two majors: Natural Science (studies Physiscs, Biology, Chemistry, Math, ...), and Social Science (studies History, Ecocomics, Math,...). – Arief Dec 01 '18 at 03:42
  • @guest I have been teaching that way. But, like RustyCore said, until now the student still needs constant reassurance and very awkward (not fluent). This is after many repetitions of solving 1 var. Lin.Eqn for about 2 months – Arief Dec 01 '18 at 03:45
  • @kcrisman my question is different, I also aks about good book and article for teaching math fundamentals, and also ask will it be better if I teach the student how to read math books instead of just explaining math concepts. Even the title is also different – Arief Dec 01 '18 at 03:50
  • Maybe he is hopeless. You can't save them all. – guest Dec 01 '18 at 04:57
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    @RustyCore and guest, could you post answers, also? – Tommi Dec 02 '18 at 08:48
  • I noticed some of the answers seem geared to a young child. This might be because you have the words first grade and the answers are for first graders. I suggest you rewrite high school student 1st grade social science as high school student with a major in social science. – Amy B Sep 13 '20 at 06:02

3 Answers3

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I noticed that you said that he needs reassurance and many of the comments suggest that he needs drill. I would therefore encourage you to use Khan Academy. You can set up an account with you as his teacher. This will give you an opportunity to assign practice in skills in a specific time frame and see his progress. More importantly, he will have immediate feedback and reassurance which he seems to need. He can also review concepts with short videos which might be considerably easier for him than learning to read a math book.

As for math as an algorithm (i.e. a set of instruction) vs. understanding concepts, I don't believe it is one or the other. There is a spectrum in which we combine understanding with doing things by rote. Some examples - although I have deep understanding of many concepts, there are many times when I am not thinking about the concepts of why an algorithm works, but just plugging away at an algorithm. Some examples include: long division, taking the derivative of various polynomials, using the Pythagorean theorem etc. You should explain the concepts but there should be emphasis on algorithms and how to do things. Most of us can't do math without these rules, formulas, and algorithms.

There should also be emphasis on how to check work. For example, plugging your answer back into the equation to see if it works. Doing this will also give immediate feedback.

Weak students often need significant driling to fully get order of operations. I would emphasize that with your student.

Hope some of these suggestions are helpful.

Amy B
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To me, it seems like, maybe the child has a fear of mathematics. We can help him out by innovating the teaching methods. For example,

1. Make the class interesting, with objects, presentations

Some theme-based presentations designed with contents focussing on logic development can help. This may also engage a child to solve a problem interestingly. Teaching a child how to deal with numbers

2. Introducing to topics in a new way!

We can give exposure to a topic with the help of real-world examples/applications, or by conducting some fun activities. Introducing topics in such a manner can work in two ways: first, the students would be eager to learn. Second, they'll understand why the topic is being introduced.

Rutva Babaria
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We can help a child by giving some tricks to solve things. For example, if a student is confused while performing operations on negative numbers, we can take the help of the number line. Let's see how!

Q: What is the addition of $-3$ and $-2$

What you can do in this case is: Draw a numbed line with $(-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6)$ The second step, ask the child what are the two numbers we have and what number he/she wants to take first. suppose he/she answers, $-3$, Then explain that we have to jump $3$ units in a negative direction. And adding $-2$ means going $2$ more steps in the negative direction. which will lead to -5 (required answer).

  • Few more Examples :

And for the equations with variables, here's another way :

Q: Find the vale of x : $2x+5=1$

Solution :

$2x=(1-5)=-4$
$∴x=(-4/2)=-2$

These are the easy steps for 90% of the students but for the remaining 10%, we have to explain why $5$ is subtracted from $1$ on the other side. We can explain this by explaining balance examples. For example, a weighing scale has $2x+5$ apples on one side and one apple on the other. And $=$ is the equal level between both sides. To balance you took five apples from both sides but, the side where we have $1$ apple will become $-4$ because you took one apple but you have to take $4$ more apples!! And further you divide both weights by $2$.

You can explain the concepts with the easiest examples you have. This will help a child to understand why we solve problems in this manner.

Rutva Babaria
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