[kenberg]

An acquaintance, let's say a friend but we don't get together often, contacted Becky (my wife). She is probably in her 40s and wants to get some math help. She asked what Becky would charge for tutoring. Becky said no charge but asked what sort of thing she had in mind, thinking maybe this was for work related issues. It wasn't. She just wants to be better at math, fairly basic math.

More power to her and Becky is very willing to help, but it seems that the first effort should be to set some sort of goals, choose some text or online resource, that sort of thing.

By contrast, Becky helped a teen-age girl with math some years ago. The girl's mother was homeschooling to protect her daughter from learning about evolution but the school system insisted that she learn some math and the mother didn't know any. So there was a clear objective. The girl had to get through the math exam and there was a syllabus.

The woman who now has contacted Baecky mentions fractions, basic geometric concepts such as area, that sort of thing.

Any thoughts? I know of the Khan Academy but that seems to be organized for a person going from start to finish for a full year in, say geometry. Something different is wanted. This person doesn't need to know where (or if) the three medians of a triangle intersect. But understanding that if the side lengths are all doubled then the area is quadrupled might be worthwhile.

It is stunning how often a normally intelligent person is floored by simple mathematical ideas. I am all for an adult wanting to do something about it but setting some realistic goals seems sensible.

Any ideas?

[lamford]

 kenberg, on 2015-March-06, 10:40, said:

An acquaintance, let's say a friend but we don't get together often, contacted Becky (my wife). She is probably in her 40s and wants to get some math help.

I am surprised that you do not know your wife's precise age ... (although I am told by some grammar experts that it is ambiguous)

[Trinidad]

I would just order a book. (Perhaps she even has a book already.) I would say that if she is willing to pay for the tutoring (which she will get for free), she should be willing to pay for a book.

I could think of e.g. Geometry for Dummies

Rik

[kenberg]

 lamford, on 2015-March-06, 11:09, said:

I am surprised that you do not know your wife's precise age ... (although I am told by some grammar experts that it is ambiguous)

Before posting I noticed this but I decided it was close enough and left it alone. Becky is 56, albeit in base twelve..

[kenberg]

 Trinidad, on 2015-March-06, 11:35, said:

I would just order a book. (Perhaps she even has a book already.) I would say that if she is willing to pay for the tutoring (which she will get for free), she should be willing to pay for a book.

I could think of e.g. Geometry for Dummies

Rik

She would happily pay for a book, I am sure. Maybe the dummies series would be right. Somehow I am more favorably inclined to an attitude of Math for perfectly intelligent people who somehow never got this stuff early on. In this case she was, on the basis of her sixth grade performance, put in an advanced math class. It made no sense then it went from bad to worse.. I won't guess at how this happened, but I know that it does.

[hrothgar]

Hi Ken

All of the major standardized tests out there have study guides of one form or another, most of which have sample tests.

I would recommend that the women who wants to learn wanders down to a Barnes and Nobles or some such and starts perusing the various sample tests, starting at the simplest and moving toward the more advanced. Once she hits one tht gives her significant trouble, she should buy the book. In turn, this will give Becky a good idea what sorts of things to focus on.

Alternatively, see if you can find a sample exam that the daughter will be responsible for passing...

[kenberg]

 hrothgar, on 2015-March-06, 14:34, said:

Hi Ken

All of the major standardized tests out there have study guides of one form or another, most of which have sample tests.

I would recommend that the women who wants to learn wanders down to a Barnes and Nobles or some such and starts perusing the various sample tests, starting at the simplest and moving toward the more advanced. Once she hits one tht gives her significant trouble, she should buy the book. In turn, this will give Becky a good idea what sorts of things to focus on.

Alternatively, see if you can find a sample exam that the daughter will be responsible for passing...

My fault, I was speaking of two different events. The problem with the daughter was some time back There was a syllabus, she followed it, she passed. She was a normal adolescent (well, that is probably an oxymoron) so keeping her on task was a bit of a problem, but she passed.


The current case is a 40+ (age not size) woman wanting to improve here own math skills. There is no immediate need for any particular skill, so it is all a bit vague.

However.

Since my posting, Becky looked online at Khan. I take some credit for this since she had not thought of Khan before I brought it up. She liked what she saw, although she didn't see any exercises. So she browsed online and found some, and has sent of the Khan link to the woman and asked her to look at this and see if it sounds good..


I think that there is a real need out there. Becky was at the Y the other day and a couple of the women were lamenting their difficulties with helping their kids with Common Core Math. At least part of this, I am guessing, is the attitude "The kids are not being taught as I was taught, therefore it is wrong". Not everyone has trouble with it. The woman who cleans our house has a ten year old daughter who loves her math class and is doing fine in it. Her parents are definitely not nerds. There are more than a few parents, and others, out there who get the vapors at the first appearance of fractions.

[barmar]

 kenberg, on 2015-March-06, 14:53, said:

I think that there is a real need out there. Becky was at the Y the other day and a couple of the women were lamenting their difficulties with helping their kids with Common Core Math. At least part of this, I am guessing, is the attitude "The kids are not being taught as I was taught, therefore it is wrong".

I wonder how many of these parents were taught "New Math" back in the 60's and 70's, and their parents had similar complaints.

However, I just learned from the wikipedia article that New Math was only popular briefly (coincidentally when I was in grade school). I wonder if that explains why I frequently encounter people on StackOverflow who don't know many of the basic concepts that I think of as something everyone should have learned long before they started computer programming. Like a couple of days ago I criticized someone for not knowing the difference between integers and fractions.

[cherdano]

 barmar, on 2015-March-08, 13:57, said:

Like a couple of days ago I criticized someone for not knowing the difference between integers and fractions.

I can assure you that knowing the difference between integers and fractions was always a learning goal in math education...

[Trinidad]

 kenberg, on 2015-March-06, 14:02, said:

Maybe the dummies series would be right. Somehow I am more favorably inclined to an attitude of Math for perfectly intelligent people who somehow never got this stuff early on.

I haven't read this dummies book, but I think the dummies series is OK in general (and not for dummies). So don't let the title of the series put you off.

To illustrate how misleading book titles can be:
For years I refused to buy "Why you lose at bridge" by S.J. Simon, no matter how good people said the book was. The reason: I was winning at bridge, so the book was obviously not for me. Finally, I decided to buy it anyway and I can safely say that I recommend it for people who win at bridge too. It is the best bridge book ever written.

Rik

[kenberg]

 Trinidad, on 2015-March-08, 16:48, said:

I haven't read this dummies book, but I think the dummies series is OK in general (and not for dummies). So don't let the title of the series put you off.

To illustrate how misleading book titles can be:
For years I refused to buy "Why you lose at bridge" by S.J. Simon, no matter how good people said the book was. The reason: I was winning at bridge, so the book was obviously not for me. Finally, I decided to buy it anyway and I can safely say that I recommend it for people who win at bridge too. It is the best bridge book ever written.

Rik

I recently finished We Were Liars. I highly recommend it, even to truth tellers.

I'll report back on this project later. I have hopes for it.

[Cascade]

 kenberg, on 2015-March-08, 17:48, said:

I recently finished We Were Liars. I highly recommend it, even to truth tellers.

I'll report back on this project later. I have hopes for it.

Murderous Maths is a series designed for children but I am sure would work with adults. Its biggest fault is that it is British so money etc is in pounds not dollars other than that it probably is fine anywhere.

[mike777]

"An acquaintance, let's say a friend but we don't get together often, contacted Becky (my wife). She is probably in her 40s and wants to get some math help. She asked what Becky would charge for tutoring. Becky said no charge but asked what sort of thing she had in mind, thinking maybe this was for work related issues. It wasn't. She just wants to be better at math, fairly basic math.

More power to her and Becky is very willing to help, but it seems that the first effort should be to set some sort of goals, choose some text or online resource, that sort of thing....."


At this point we are not even sure what the goals are. They may not be all Math is my guess.


to only assume Math goals I am going to bet will often be wrong. this is difficult but the teacher I hope will be open to non Math goals.

Let the client set goals...not the teacher. Again I am betting the goals may not include Math.

[Zelandakh]

As someone who has done some maths tutoring I will say that one of the big advantages of this format rather than a class is precisely that you can tailor examples to the student. Two examples: I had a male student who was "forced" to have tutoring by his parents - making questions related to football (eg what angle do you have to shoot a penalty to hit the top corner?) helped a great deal in raising interest; then there was a female student who was bright but lacked confidence - the key here was taking the subject she found the hardest and installing a new, simpler approach that was less confusing for her then the standard class method. The point is that tutoring should not be a "one size fits all" process.

That said, there may be some parallels to the female student mentioned above. One approach would be to find out which of the topics gives her the most fear and tackle that first. Everything that comes thereafter will feel more comfortable. A perhaps even better way forward might be to combine the subjects to exaplin the concepts together. For example, you might start with a 2x2 square (ideally on a square board or re-writable pad with squares) and use that to discuss area. Then split into 4 smaller squares and move onto quarters. Then more difficult cases.

Really though, the first thing to do is sit down with her and find out what the issues are. After that it will likely be a lot easier to work out the best approach. It might be that working through a book course is a good strategy; my experience is that this is actually rare in comparison with a more targeted approach though.

[kenberg]

I was once hiking with an intelligent and successful guy who asked my help in understanding why negative 2 times negative 3 is the positive number 6. I am not sure how well I succeeded. He knew that it was true because he had always been told it was true, but it made no sense to him.

becky and Janet are still trying to work out a schedule, I imagine that they will. But J looked at some material on the Khan Academy on fractions.
Example: You are given a horizontal line with hash marks. A hash mark has a zero underneath it and then there are several equally spaced hash marks to the right. The fourth one over has a 1 beneath it, the eigth one over has an 8 beneath it and so on. An orange dot on the line can be moved to the right or left with the mouse, and the directions are to place it on the hash mark that represents 7/4. This troubled her, but in an unexpected way. To place the dot, you just start moving 1,2,3,4,5,6,7 and stop. But she asked if 7/4 was really a number. She would use 1 and 3/4. Using 7/4 upsets her. She is quite sure that it is not right to do so.

Upon reflection, I can perhaps understand. If I stop by the fish market, I would never ask for 7/4 of a pound of flounder. If all you are going to do is to order a certain amount, you order it as 1 and 3/4 pounds or maybe a pound and 12 ounces, but not as 7/4 of a pound.

But: Suppose we know that 4/7 of the people at Disneyworld are under the age of 12, suppose we know that there about 3000 kids there under the age of 12, and we want to know ow many people are there. We multiply 3000 by 7/4. Yes, we could multiply by 1 and 3/4 but it seems to be more direct to just say multiply by 7/4.
It's a general practice. If some state has 2/3 the area of Maryland, then Maryland has 3/2 the area of that state. If the temperature is 36 Farenheit degrees above freezing then it is 5/9 times 36 Centigrade degrees above freezing. If it is 20 Centigrade degrees above freezing then it is 9/5 times 20 Farenheit degrees above freezing.

The lesson is that both 7/4, and 1 and 3/4, describe the same number, but which presentation is preferable depends on what you are going to do next. If you plan to cook some fish, 1 and 3/4 will work fine and the guy behind the counter won't look at you as if you were speaking in Greek.

A story that I still recall some 50+ years later:
A friend was teaching a night class in pre-calc and I agrees to sub for him one night. After class one of the students came up to see me and it went like this:

Student: You look like a reasonable guy. Can you tell me why you can't subtract fractions the same way you add fractinos?

Me: Huh?

Student, waving hand in air to indicate imagined numerators and denominators: When you add fractions, you take this number and multiply it by this number over here, then you take this other number and you multiply it by this number, then you add these two numbers and place it here. Then you take this number and multiply it by this other number and you place it here. Why can't you subtract fractions the same way?


Me: Well, first you put the two fractions over a common denom [This was as far as I got]

Student, jumping in: Look. I am a practical man. I don't have time for math theory. What I want to know is why you can't subtract fractions the same way you add fractions.

Me (hoping to soon go out for a beer): Well, you can.
You take this number and multiply it by this number over here, then you take this other number and you multiply it by this number, then you subtract this from that and place it here. Then you take this number and multiply it by this other number and you place it here.


Student (smiling): Thank you. And they tell you that math is all obvious.


Anyway, I am looking forward to this adventure.

[Trinidad]

I guess you meant:

 kenberg, on 2015-March-09, 07:05, said:

Example: You are given a horizontal line with hash marks. A hash mark has a zero underneath it and then there are several equally spaced hash marks to the right. The fourth one over has a 1 beneath it, the eigth one over has an 8 2 beneath it and so on.

 kenberg, on 2015-March-09, 07:05, said:

The lesson is that both 7/4, and 1 and 3/4, describe the same number, but which presentation is preferable depends on what you are going to do next.

That, to me, is the essence of math. The rest is just a big tool box with tricks.

• To understand that you can look at an object in different ways.
  
• That your problem determines how you look at the object.
  
• That looking at an object in a different way changes the way you look, but it doesn't change the object.

That is true for fractions like 7/4 = 1 3/4 = 1.75 = 175 %. But you can also rotate or flip triangles, they remain triangles. You can put sets of equations in matrix notation, they remain the same set of equations. You can do a principal component analysis on a data set, the data set is still the same. You can look at a signal in time space or in frequency space, it is still the same signal. You can express a problem in cartesian coordinates, in polar coordinates or in helical coordinates, it is still the same problem.

The more advanced you get in math, the more tricks you will learn. But it starts by realizing that you can look at every object in different ways and that YOU decide in what way you are going to look at it (the way that makes it easiest to solve your problem).

Rik

[barmar]

 Trinidad, on 2015-March-08, 16:48, said:

I haven't read this dummies book, but I think the dummies series is OK in general (and not for dummies). So don't let the title of the series put you off.

To illustrate how misleading book titles can be:
For years I refused to buy "Why you lose at bridge" by S.J. Simon, no matter how good people said the book was. The reason: I was winning at bridge, so the book was obviously not for me. Finally, I decided to buy it anyway and I can safely say that I recommend it for people who win at bridge too. It is the best bridge book ever written.

Rik

Yeah, these titles are intended to be amusing and provocative, not taken literally.

In the case of the "For Dummies" series, the way to interpret it is that the intended reader is not generally stupid, they just feel like a dummy in the specific subject area because it seems like something everyone else knows better than them. A brain surgeon or rocket scientist might still feel the need for "Home Repairs for Dummies".

[Zelandakh]

1 3/4 is called a mixed number; 7/4 is an improper fraction. Different notations for the same thing. To that you can add 1.75 and 1.75e0 plus some less common forms. What I would say is that 1 3/4 is the form you use in every day life but 7/4 is often more useful in maths, so it is a good idea to be familiar with both because it will make things simpler. Another way of looking at it is that 7/4 is not so much a fraction as a calculation but that is probably a little illogical for most people so I would not recommend going that way unless you are confident you understand how she thinks. For some though, imagining a fraction as just a special case of division removes the mystery about them. Again, find the form that works best for the student!

[barmar]

 Zelandakh, on 2015-March-09, 09:42, said:

Again, find the form that works best for the student!

This is, of course, what makes teaching a class of 30ish students such a challenge -- each student will have different strengths and weaknesses that the teacher has to try to address. With one-on-one tutoring you should be able to zero in on the specific problem areas and come up with a way to clarify them.

[WellSpyder]

You might not want to order seven quarters of a pound of fish. But what about sweets? Do you still have shops selling old-fashioned loose sweets by the quarter pound? "I'll have seven quarters of lemon sherberts, please"

Or what about thinking of currency? I might have one dollar and three quarters in my pocket. Or I might have seven quarters. I would expect to be able to buy the same things with them, though...