need help with a third grader

I don’t have time for the long detailed reply this deserves right now. Basically, take your time and get it right. There’s no value in a fast mistake. Get the foundations first, build the structure on top later; we all know what happens to the house built on sand.

I have made some long posts on math; email me at [email protected] and I will see what I have copies of to send you. And please keep emailing me because I have organization issues of my own!

Start with a basis in understanding using concrete materials. Don’t get too in love with a given material. Make sure the kid understands before adding symbols and working on paper. But be sure you do get to the practicing calculations.

Be sure the kid understands lower level math (in this case number concepts, adding and subtracting single digit nos.) before going on to more difficult concepts. Math is very sequential and if you lose it early you aren’t going to somehow make it up later. Don’t assume a certain level. Really check it out.

That’s sort of a general way to approach it anyway.

—des

And don’t assume she understands the math concepts or is even developmentally ready to. You may have to back ‘way back and start building, especially if she’s been surviving on rote memory adn depends on that strategy, and will have to learn to think about what those symbols mean and *why* different steps are taken.

thanks for all of your help : ) I am told she uses Touch Math. I have been recently trained in it, but have never seen it used nor do I know if it is useful. Any thoughts? Thanks

A lot of people speak highly of Touch Math here. I have a student who has been trained in the dot-counting pattern used by Touch Math, and it does seem to help him. It’s one of those things that can be a useful tool for small but significant skills, namely addition and subtraction facts in this case. However she will still need the “big-picture” thinking skills beyond this.

WHen I taught middle school LD classes, I was amazed the year I got a group of students who could actually do basic addition and subtraction, reliably and correctly. It freed me up to *teach* more advanced things. When I noticed thye were all touching the numbers when we did board work, and touching them in the same places, I asked… it was touch math. It didn’t really slow ‘em down (and, as Victoria says, who needs fast mistakes).
However, there is a danger that students will do that kinesthetic routine at the expense of developing any number sense; there are math folks who rant and rail against it. I have begun to suspect that it’s the same kind of fear as that of the folks who think that somehow, if I *teach* phonics, students are prevented from loving the stories they are now able to read. Yes, I *could* teach it in such a manner, and enough people obviously have been so I need to take active measures to make sure it doesn’t happen, but letting fear of doing that prevent me from teaching necessary skills would be equally egregious.

my student needs to learn her mult. facts to 25 and her mother has told me the previous tutor would teach them and she would forget them the next day. i have seen touch math for mult. and divid. and have found it hard to understand for myself. what are some strategies to help this youngster? thanks again.

i noticed that with touch math she has the ability to add easily and quickly but she seems to lack number sense. she can’t count by twos past 10. these are just my first day observations.

Welp, knowing the tables to 25 is a bit past the norm — where is this & who’s making that demand? Generally up to 10 is what you actually need for fast calculating (you can use those to do further ones), though culturally lots of folks teach them to 12.

What are the “Them” that are forgotten the next day? ONe of the most common errors in learning the tables or any facts is to skip the learning and go straight to “practice.” LEarning is done a little at a time, and um, sometimes it takes more than a day. Practicing a few each day until they aren’t forgotten before adding more and/or giving up and deciding you can’t is a very effective method of learning things.
http://www.resourceroom.net/math/index.asp has several links with ideas for learning them, including some sample chapters from a text and workbook designed to help folks who struggle with them.
That could be news to somebody who expects the student to know ‘em up to 25; are there other, perhaps unreasonable, expectations for quantity and quality of learning? Generally if you try to lift 100 pounds, you’ll try 40 times and decide that you simply can’t do it. If you start smaller and build, though — oh, and build in SUCCESS — then iwhat seemed impossible becomes possible.
One of the lessons of learning big things is to learn that what looks impossible probably isn’t — but if you keep getting dumped with more things that aren’t seen through to success, you learn the opposite lesson (that you can’t do what is expected) and it’s easy to incorrectly conclude that you’re damaged goods because of it.

Maybe she meant up to the no. 25, ie 5X5?

I think it is a funny way to think of them. Seems more logical, imo, to teach them in sets that are easiest to hardest, ie
1s, 2s, 5s, 10s, 0s.
Then maybe 3s, 4s, 9s.
By this time, you know most of them and you fill in the gaps.
But I guess you could teach 0s to 12; 1s to 12; 2s to 10x2; 5s to 5x5

Then do 3s to 3X9; 4s to 4x6; 9s to 9x3
etc.

—des

Yup, that’s how “Tools for the Times Tables” does it — starts with 0 & 1, then 10, then … I forget the exact sequence, pro’ly 2 and 5 and 9, then 4 and 3 adn then 6,7,8.

I answered a lot of this in a private email, but here are some more thoughts.

Definitely time to work on number sense and base ten system. If you don’t know what 25 is and what it looks like and why it isn’t the same as 52, well, the rest is water off a duck’s back.

Make haste slowly. Follow Sue’s advice and work on getting one thing right instead of fifty things wrong. One thing right in a day — 180 new facts learned in a year, a habit of success, good self-esteem, and confidence to learn the next things. Fifty things wrong every day — a habit and expectation of failure, low self-esteem, and the classic math anxiety. The most common word you should be saying in a tutoring session is “Good!”.

Des — I wouldn’t want to work on the multiplication tables in a piecemeal fashion like that; fear it would cause more confusion. If you learn 3 x 6 and 4 x 6 and 5 x 6, well, when you forget 6 x 6 you can work it out by adding on another 6. It helps a lot to have a pattern and a structure to hang on to. Students who like patterns but forget details can learn to use the pattern, and students who have difficulties seeing patterns need to practice and learn how they work.

The whole point of multiplication is to have a *quick* and *automatic* way of dealing with bunches of things — otherwise we’d just add. A counting system such as Touch Math just has to be slow. OK as a tool for introducing the idea, but afterwards you want to automatize because that is the point of the affair anyway.
When dealing with multiplication there are at least three numbers to keep in your head — the multiplier, the multiplicand, and the product. If you try to count groups, the multiplier is the counter (how many groups) and the multiplicand is the countee (how many in each group, to be counted repeatedly), and then you *also* have all your partial sums as you work up there — 5 x 8, let;s see, 5 goups of 8 things, one two three four five six seven *eight* — once, nine (one finger) ten (two) eleven (three) twelve(four) thirteen (five) fourteen (six) fifteen (seven) *sixteen* (eight )— twice, seventeen (one finger), … this gets to memory overload awfully fast!!
Yes, count and add to see the patterns at first, definitely. And make sure addition is well understood, which I strongly suspect it isn’t. But then, work on quick recall as a time and work saver. Work on it gradually, a bit at a time, and try to get it right and solid the first time. As the previous experience proves, imitation and regurgitation without a good knowledge base is a waste of time, she would have been better off spending the time learning Japanese haiku. Learning implies retention and transfer, or else it isn’t learning.

>Des — I wouldn’t want to work on the multiplication tables in a piecemeal fashion like that; fear it would cause more confusion. If you learn 3 x 6 and 4 x 6 and 5 x 6, well, when you forget 6 x 6 you can work it out by adding on another 6. It helps a lot to have a pattern and a structure to hang on to. Students who like patterns but forget details can learn to use the pattern, and students who have difficulties seeing patterns need to practice and learn how they work.

Oh gee, I guess I really did give the impression that I might think that was a good idea (doing times to 5x5 and stopping). It was my thoguht that that was the intension of the approach (stopping at 25). I don’t agree that it is a good idea. You *could* do it but I don’t agree with it. I think it makes sense to teach the easier patterns first (ie X1, X 2, x5, X10) but I don’t think it makes much sense to stop at some random no. like “do them til you get to 25”. Just go up to 10, so you do the tables to 10 (ie up to 10x10). You could go up to 12 but I don’t see that you have to.
I’m sorry I didn’t clarify that.

—des

hello everyone. i should have been more clear, des you are right, i meant up to 25, ie. 5 X 5…the biggest product would be 25.

i guess what bothers me when working with her yesterday was that she has absolutely no number sense. she doesn’t understand how to count by twos. i worked on patterns with her yesterday and it took her some time to find the pattern in 5, 7, 9, 11. she at first thought the numbers increased by five. when watching her add using touch math, i noticed she had the right answers which is great, but there seems to be no real understanding as to how it works, or the concepts behind it if that makes sense. i also asked her if 20 is the same thing as 20 + 7. she had no idea and i confused the poor thing.

i know her mother will be wanting her to learn the mult facts with the product to 25, but i feel that i need to work on her understanding it first. i don’t want to confuse her anymore. i normally work with 8th grade math, so i want to make sure i am doing my best for her. you all definitely know a lot and i appreciate all of your help.

i will take all suggestions!!! i don’t want this sweet, little girl to hate math! Or feel failure because she doesn’t know her mult. math facts.

I strongly recommend taking some time to talk to the mother and to get her on board with the idea of getting things solid and correct. Explain to her that you want to make sure the child *remembers* the facts, or else it’s a waste of time, and obviously the approach used before was worse than useless, so you are going to use different ways to get things stuck in memory. Once she loses her fear that the kid will fall further and further behind (a reasonable fear given results to this point), she will work with you and not against you.

I have remembered the workbook I am using with kids who need basic number sense and math facts; it’s called MathSmart — the big thick “complete” version, available in stores like WalMart, probably also on Amazon. It doesn’t have enough reasoning and problem solving to be really complete, but it is useful as a resource for practice, practice, and more practice. I work with the pennies and the book, about two pages in twenty minutes each session with my little Grade 2 girl last year. I started by reviewing parts (not all) of the Grade 1 book, and towards the end of the year we “graduated” into the Grade 2 book. My Grade 3 boy reviewed the Grade 2 book also; I don’t remember if we got into the Grade 3 book or not; we were doing multiplication tables in one or the other (there’s a lot of overlap which is good for remediation). I’d suggest getting the books for Grades 1 and 2 and maybe 3 and telling both mother and child that this is “review’ so it should be fairly easy and you will move through it quickly, then do two or three pages a day. You can skip the very introductory Grade 1, but start right in with the easiest additions. The practice and examples help build number sense, and succeeding at a couple of pages of exercises a day develops a positive approach to math, which I am sure this kid is really lacking. Another thing you can do, I do often, is to do a couple of pages of review in Book 1 and a page of new (multiplication) in Book 2 or 3 every day — the review builds the basic skills and confidence and the kid goes into the new with a successful approach. When the mother sees all this math being done she will also relax a bit more. And keep those pennies on hand, use them whenever a concrete problem comes up. And if the child is an eraser addict, work in pen so some writing gets done in a reasonable amount of time.