Need advice for algebra tutoring

[Frozenwolf150]

I wasn't sure whether this should go here or in the Science, Mathematics, & Technology section, since hardly anyone ever visits this section, but I suppose it's relevant.

To explain my situation, I may once again be in a position to tutor another student in Algebra. Long story short, he needs it the class to fulfill his graduation requirements, but has been unable to achieve a passing grade after two attempts. I already tried tutoring him this past summer, but apparently that along with the extra help he'd been getting at school were not enough to help him grasp it. He's not a poor student, as he excels in foreign language and humanities subjects, but math is not something that comes easily to him.

I don't quite know how best to convey basic algebraic concepts to someone for whom math has always been a weakness, especially when math was always easy for me. I took Algebra back in the 8th grade (when I was 13 years old) to give you an idea of how much of a difference there is between the two of us. In other words, I can't relate to where he's coming from or see it from his point of view. I tried to teach him 'by the book' using his textbook, I tried explaining the material in my own words by way of my own methods, and we worked through a number of sample problems, but apparently none of this helped.

This is essentially my question. What would be the best way to teach Algebra to someone who's struggling with it?

I have not yet volunteered for the tutoring job again just yet, because I wanted to get some feedback first.

 

[Uncayimmy]

A friend of mine in school was very smart. He was a fantastic debater. Very sharp. Kept abreast of current events and was able to connect the dots. He was a political science major in college.

Yet he had to take remedial math...and struggled with it.

My ex-wife was an elementary school teacher. I remember helping out now and again with fourth graders who could talk your ear off using grammar and vocabulary appropriate to their age. Yet every year it seemed that there was one kid who simply could not put those thoughts down on paper. It was like there was a crossed wire.

I'm not saying this kid is like that, but you should be aware that some people have mental blocks towards certain subjects despite reasonable "intelligence" and effort. if he he is he may be better off with someone with professional experience who understands this.

That said, in my experience I have found that if someone is stuck despite their best efforts, getting them to teach you is a good approach. Start a few levels below where they are stumped. They might feel silly explaining something they think is easy, but it's a good place to start. Maybe you'll see where the kid missed something. Hopefully you'll see how he approaches and understands what he already knows, which will give you a chance to use the same approach with what he doesn't know.

Good luck. Keep us posted on his progress if you accept the gig.

 

[quixotecoyote]

Start from the beginning with elementary school concepts like 2+_=4

Make sure he gets the concepts and isn't misunderstanding things.

I had such a hard time getting my head into math because my father used too many code metaphors trying to explain variables to me, and I spent my initial classes trying to figure out why the code kept changing, since obviously if we find that when 2+x=4 then x equals 2, yet obviously 2+x=5 means x can't equal 2, so there has to be some secret trick that makes x change that no one can explain in a clear way and why is everyone looking at me like I'm an idiot and why is my dad calling me an idiot and why do I need this **** anyway so **** you and **** your tutoring, find some other chump to harass......





Sorry, brought back some memories there.

 

[Frozenwolf150]

Allow me to clarify about the age issue. We both attend the same college, and he needs to pass Algebra to get his degree in teaching. He's older than I am, and I'm already somewhat old for a college student, since I've had to stop and resume my education due to medical issues.

That said, in my experience I have found that if someone is stuck despite their best efforts, getting them to teach you is a good approach. Start a few levels below where they are stumped. They might feel silly explaining something they think is easy, but it's a good place to start. Maybe you'll see where the kid missed something. Hopefully you'll see how he approaches and understands what he already knows, which will give you a chance to use the same approach with what he doesn't know.

Good luck. Keep us posted on his progress if you accept the gig.

That had occurred to me, but I never had a chance to try it. Thanks, if I go ahead and volunteer, I'll be sure to keep this in mind. I remember that one of my English teachers way back in high school said that the best way to learn something is to teach it to others (with the least effective way being the lecture format).

Start from the beginning with elementary school concepts like 2+_=4

Make sure he gets the concepts and isn't misunderstanding things.

That could work if I explain that Algebra, and pretty much all types of math, use the same basic concepts in different ways. For example, I've found that the hardest part of Calculus is actually all the algebra and arithmetic it involves.

Sorry, brought back some memories there.

Heh, not a problem. Now I know not to take your father's approach of making things more complicated than they need to be.

 

[Ixion]

Well, as you have had some experience tutoring, I will share my experience here. I have tutored kids as young as 10 up to seniors in high school, mostly in mathematics. I have tutored basic arithmetic, algebra, geometry, and calculus. I volunteered for the job (sort of...I was paid, but it was never more than what would have covered gas expenses).

I don't have tons of trouble with mathematics, but it does take me longer than those more mathematically inclined. Like you, I have found that math is based on similar concepts, and that usually screwing up calculus problems was due to errors in my algebra/arithmetic. I am better with geometry/trigonometry than algebra, probably because I am more of a visual learner.

I think it is important to go slowly and make sure the student understands one concept before moving on. Not so much that they get frustrated and want to quit, but enough that if the concept comes up, they can identify the concept, apply the math, and move on. I also try to approach the problem from several directions. I believe people learn in different ways, so I have my students write out the problem, draw a diagram illustrating the problem (this can get interesting in algebra), and read the problem out loud. This appeals to visual, auditory, and kinetic/experience learners. Most people incorporate several methods of learning, but might favor one. Until I can see how my student learns best, I use the three most common methods. Another thing I have found is that if the student really isn't getting the concept, 1)try approaching the concept from another direction (this could require you thinking outside the box a bit to find another way of explaining it) 2)Help the student identify the exact portion of the problem they don't get. This is not accusatory, and some people that have trouble with math may find this frustrating, as they have trouble explaining exactly which portion confuses them, or why it does. This is like Quixotecoyote explaining the reasons variables confuse him. Once you have found the culprit, then you can begin to work at fixing the problem so it becomes understandable.
I would also begin the first 10-15 minutes of a new session reviewing what we did the week before, and working on it more if they were still having problems.

Finally, one more thing I want to emphasize about my experience is that positive reinforcement goes a long way. I would discuss the student's homework and/or quizzes and exams, and praise them for what they got right, rather than what they got wrong. Inevitably, they would bring up what they didn't get right, and I would respond that those were areas we would just have to work harder on. People like praise and rewards, young and old. If I thought they did a particularly good job, I would reward them with something. It wouldn't be something big, but the reinforcement seems to help secure the concept in their brains. "Oh yeah, I got ______ because I remembered when to solve a quadratic equation." It also helps because people that are having trouble with math concepts have already convinced themselves that they will never be able to do math because they did poorly in the past and were only reinforced with bad grades and/or people yelling at them.

As far as my experience went, of the 5 students I tutored, all of them improved their grades. 3 of them went from failing to B's and high C's. One went from D's to A's. One went from C's to B's. Of course, A's are preferable, but improvement is improvement. You can only do so much per tutoring session, so don't expect to work miracles either. Setting realistic expectations for you and your student can help a lot. You are not going to help if you try to get them to learn a ton in a 3 hour cram session. A tutoring session of 1-2 hours is best. I hope I am not coming off as patronizing, as that is not my intent. I know you have experience tutoring before, and I hope my experiences help you make this decision. I think your friend may be able to find help, if the right kind of tutor comes along. If you think it will be too difficult or not worth your time, suggest to your friend to check with the college. Many colleges have learning centers or tutoring centers to help students and may be able to find someone that can help your friend if you cannot. Math departments often post tutors to help struggling students. Good luck!

 

[willy k]

I also have extreme trouble with algebra. Algebra is like Ambien for me, just a little bit and I'm asleep! I'm deeply interested in physics and cosmology but I just can't learn the language of mathematics.

I've also been a keen observer of "teachers." Most (80-90%) of the people who's job title is "teacher" lack two essential qualities, knowledge of the subject and the ability to teach. Limited knowledge of a subject is only a small detriment, the lack of ability to teach is a huge impairment.

What many "teachers" do instead of teaching is to tell students what they know. Telling a person what you know is not teaching. I'll give you of an extreme example of this . I and two co-workers were sent off to a class to learn a CAD programming language. The teacher was an acknowledged expert in the software. He was just spewing out all sorts of information about the software one day and half of the class were just sitting there in utter frustration. Someone said something like, "we don't have any idea what you are talking about," to which he replied, and I quote "It's easy if you know how!" Several of us just threw up our hands and groaned in disgust.

So that is an example of what you shouldn't do. Don't tell your student what you know, it's totally irrelevant.

Another thing that you've already found is that teaching "by the book" can be worse that useless.

In my own case I realized one thing that makes learning algebra very difficult is the tendency to give multi-part or "clever" problems to solve. I told someone who was attempting to tutor me that "word problems" were not a good way to teach me because they are actually two very different problems. Obviously part one is to derive a formula and the second part is to utilize the formula to solve the second part of the problem. Just because you can do it and just because every freaking textbook does it this way is not a good enough reason to do it. Make them two separates lessons, when the student understands each technique separately they might be able to combine the two without anxiety.

I'm about spent. One other thing that might help is to let the student explore without you saying things like "that's not important." Let the student go off on tangents.

 

[Skeptical Greg]

I'm sure you have Googled this, but just in case this one didn't come up or catch your attention --

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/

Has been a great help to me getting my son through 1st year algebra .. And I am learning a great deal as well..

It advances through several levels, including college ..

P.S.

Seeing willy k's post above - and in light of the tutoring site I listed - I can also say my son's algebra text book from school is useless ..

 

[Travis]

You tie them to a chair and tell them to solve for X and if they don't do it in 15 seconds you start electroshocking them.


Oh wait you want advice on "algebra tutoring" nor "algebra torturing."


Well, I sucked at math and the only way I ever got algebra was when it was demonstrated visually and had context and wasn't just formulas to memorize.

 

[quixotecoyote]

You tie them to a chair and tell them to solve for X and if they don't do it in 15 seconds you start electroshocking them.


Oh wait you want advice on "algebra tutoring" nor "algebra torturing."


Well, I sucked at math and the only way I ever got algebra was when it was demonstrated visually and had context and wasn't just formulas to memorize.

I remember when they were trying to teach us to factor polynomials with that 'monkey method' because the teacher thought he could teach us visually. As soon as someone told me about FOIL I stopped having problems with that, but I never could see that goddamn monkey.

 

[Fredrik]

My advice is to explain all the obvious details too. For example, tell him that the reason he can add the same number to both sides of an equation is that the equality sign means that what you see on the right-hand side is actually the same number as what you see on the left-hand side.

Start from the beginning with elementary school concepts like 2+_=4

Make sure he gets the concepts and isn't misunderstanding things.

I had such a hard time getting my head into math because my father used too many code metaphors trying to explain variables to me, and I spent my initial classes trying to figure out why the code kept changing, since obviously if we find that when 2+x=4 then x equals 2, yet obviously 2+x=5 means x can't equal 2, so there has to be some secret trick that makes x change that no one can explain in a clear way and why is everyone looking at me like I'm an idiot and why is my dad calling me an idiot and why do I need this **** anyway so **** you and **** your tutoring, find some other chump to harass......

Yes, this is the sort of thing I had in mind. Explain that the phrase "solve the equation yada yada" means "this time your job is to find all the numbers that you can substitute for x in this equation without making it false".

Explain that the reason why ab=ba is that the size of a rectangle doesn't change if you rotate it 90 degrees (draw a picture), and that the reason why (a+b)+c=a+(b+c) is that you can think of each letter as representing an instruction about the number of steps you should walk in some direction. Explain that -x can be interpreted as an instruction to walk x steps in the opposite direction.

When you show him how to solve an equation, show every step the first few times, e.g.

x+5=2. Add -5.
(x+5)+(-5)=2+(-5). Use the fact that addition is associative.
x+(5+(-5))=2+(-5). Use the fact that -x is the inverse x.
x+0=2+(-5). Use the fact that 0 is the identity element (that adding 0 has no effect).
x=2+(-5). Do the last sum.
x=-3

(You probably shouldn't use the terms "inverse" and "identity element" unless you're teaching him group theory ). Don't talk about this as "moving the 5 to the right-hand side" until he's comfortable doing this.

 

[Skeptical Greg]

Wow Fredrik ! That is really some good info I can use..
You would make a great Tutor ..
Thanks.

 

[Paul C. Anagnostopoulos]

My advice is to explain all the obvious details too. For example, tell him that the reason he can add the same number to both sides of an equation is that the equality sign means that what you see on the right-hand side is actually the same number as what you see on the left-hand side.

Indeed, there are three concepts that you gotta understand in order to do algebra.

The equal sign means that the expression on either side is the same number.

As long as you do the same thing to both sides, you'll maintain the equality (more or less).

A variable is a name that stands for one or more numbers you don't know yet.

When you show him how to solve an equation, show every step the first few times, e.g.

x+5=2. Add -5.
(x+5)+(-5)=2+(-5). Use the fact that addition is associative.
x+(5+(-5))=2+(-5). Use the fact that -x is the inverse x.
x+0=2+(-5). Use the fact that 0 is the identity element (that adding 0 has no effect).
x=2+(-5). Do the last sum.
x=-3

My son is dyslexic and has some trouble with math. Here's how he would write that problem when he first started algebra.

x + 5 = 2
  -5    -5
x + 5 - 5 = 2 - 5
  combine
x     = -3

Speaking of dyslexia, is your student dyslexic? Why don't you have a chat about number lines and adding/subtracting signed numbers to see if he has it straight. Trust me when I tell you that reading:

6 - 2

but thinking:

2 - 6

can cause problems.

~~ Paul