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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.

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    $\begingroup$ "−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. $\endgroup$
    – Rusty Core
    Nov 30 '18 at 17:16
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    $\begingroup$ Possible duplicate of How to teach a student algebra who misses too much previous knowledge? $\endgroup$
    – shoover
    Nov 30 '18 at 17:37
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    $\begingroup$ Can you say a bit more about your specific context? I'm not sure what "1st grade social science" is. $\endgroup$
    – kcrisman
    Nov 30 '18 at 18:49
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    $\begingroup$ 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. $\endgroup$
    – guest
    Nov 30 '18 at 20:26
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    $\begingroup$ @RustyCore and guest, could you post answers, also? $\endgroup$
    – Tommi
    Dec 2 '18 at 8:48
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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.

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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.

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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.

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