Project Math Access DVD 02 - Abacus- Part 08
Transcript Start
Audio Description: Part eight; abacus secrets method; teacher interview.
TERRA KNOWLES: What we saw today were two students that I have in a self-contained classroom, self- contained slash resource. I've been working on abacus with them for years. Not only myself, but they came to me from a vision primary classroom where they've been working on these skills, I would say as early as Kindergarten. And now they're in 3"‘ and 4”‘ grade, so they have progressed quite a ways.
They have other things going on which made me make the decision about using Secrets. One student in particular, has some emotional slash communication difficulties, but has a great rote memory. So that was one of my deciding factors when I decided to do Secrets with him.
The other student has also a great memory, and understands the Secrets in a better context than using Logic. I struggled with to use Secrets or to use Logic, and which students do I use them with and which students do I not use them with, when do I introduce abacus, do I have to follow the curriculum exactly as it appears, all these questions that come up and there's no black and white answer to them.
So what I, myself have done, have followed the curriculum to the best ability that I can, but then in any regular ed curriculum that has the math books provided in braille, there's a lot of information presented both visually and vertically, and one print math page in the math braille book is about 5-6 pages in the math braille book, so not only are you dealing with trying to find where the heck at you are on the page and trying to get through all the visual clutter, because I was very surprised in a lot of the mainstream math books that are brailled, a lot of that visual type of clutter is on those pages. So trying to sift through all that information and get to the important part, rather than all of this other extraneous information is difficult, to say the least.
So I came to a section in the series where they started talking about addition with regrouping, subtraction with regrouping, after several other skills had been introduced and when I first started with them them I thought I would try Logic to see if they could do it. Well, for the most part, they put in a lot of effort and tried hard, but it was just very difficult for the students to understand the logical method behind it.
Now one of the fears I had with going to Secrets was that it would be rote and there would be no understanding as to what they're doing on the abacus. So one of the things that I've tried to do to avoid that is the estimation piece, before going to the abacus, using some of the problems with Unifix cubes, using some of the problems on Tactiles, many different things. This is just one piece in the whole picture of the math curriculum. And the math curriculum is a huge, not very well defined curriculum. There is a not a black and white answer to do.
Because the abacus does take time and because these students have other things going on, I have gone ahead and moved on in the series, but everyday go back and review the addition Secrets, the subtraction Secrets, how you use them. But we have started some of the other applications that have begun to come up in the series.
For a few reasons, number one, we could spend the rest of the year on doing these Secrets and I don't want them to miss some of the other math concepts that come up as the year goes on.
The Secrets are working well for them because they both have great rote memories and they have the problem solving skills to go to the sheets and get the Secret for the problem that they're working on.
Some of the difficulties that I've experienced with it is if a problem has numerous Secrets in it or if the problem, the place value, and at this age I don't want to go much beyond thousands, even if I get to that with them. They both have an understanding of the place value of the abacus, which is nice. They have not learned all the intricacies on the bottom, what some of the markers are for, for the comma, decimal points, some of the other intricacies that come with the abacus.
I try and, a lot of I think blind adults, I don't know for sure, but I think some blind adults are using calculators as a supplement. I want them to have both skills. So that's why when I'm doing the abacus, we check on the Braille Lite, we check on the braille calculator, kind of supplement all these skills.
There's so many things, but I don't want to overwhelm them, and some of the problems that I'm experiencing with implementing the abacus is that if I teach them, the Secrets that they had for addition, we have been through these many, many times and when I first started teaching them I broke down the Secrets. We spent a week on ones, we spent a week on twos, then a week on threes and if you look in a regular ed. curriculum, they don't break down addition like that and they do not break down subtraction like that. Therefore, that's where you're supplementing. Just so that they could understand the concept of when they needed to use this Secret is the reason why I broke it down and spent time with the ones, spent time with the twos, spent time with the threes.
No way would I go through all of them and then expect them to choose the right one, but they've had a lot of experience with which Secret to use when. Not so much the subtraction and that's why we stopped at twos. They are not fully through all of the subtraction Secrets. They understand the concept of subtraction, but getting it down on the abacus, we're not completely there.
I find in general that I try to keep the abacus with the curriculum, but because the dual curriculum, and there's so many things, I'm not always there. I might go ahead and continue, but not neglecting the abacus. The abacus is done everyday. I think it's a valuable tool, but it has its drawbacks and there's no definite you start here and you go there.
I have areas where I want them to be proficient before they move on. The way this resource room is set up, they're with me for 2nd, 3rd and 4th grade. So I really get to work with them and I really see the progress of them before they move on.
And if Logic is a possibility, I have other students in the class and then I kind of break down into groups and do Logic with some of the students and Secrets with the others. I like to try to do abacus kind of isolated. I have a kind of a table set aside, kind of quietly because it requires a lot of thinking on the part of the student and a lot of processing. And so I try to do abacus off and in a separate area isolated from the other students.
STICKEN: What do you feel the payoff is in taking the time to teach the kids abacus? Why is it a valuable tool?
TERRA KNOWLES: I think it's a valuable tool for several reasons. First of all, it's a lot easier than trying to teach a lot of vertical math skills on a Braillewriter. It's a lot more efficient; it's portable. You know, I really think a lot of students will probably end up going to a calculator, but what are you going to do if your battery dies and you need it, you need the abacus, to have those skills.
It goes, in my opinion, with the underlying concepts that are in math. It goes hand-in-hand. The problem, we live in a 10-base world and the abacus is 5-base. That is a problem, but they're at the age where that problem, they come across it, but they don't understand what that problem is. But I just think it's a valuable tool and it's portable and it's a computation device and without it, writing it out, carrying and regrouping on a Braillewriter, it's possible, but I mean we had some difficulties just with putting a piece of paper in. I mean just the whole process of scrolling up and scrolling down and lining up the columns, the tens columns and the ones columns.
I think another nice thing the abacus offers is it really gives a tactile definition of place value. It's really quite clear where the ones is, where the tens is and where the hundreds is, whereas if you just write out a number, it's not as clear.
It helps with the basic concepts and it's a nice tool for when those more difficult concepts come up. Because I found initially, that when I have them, I have had the luxury of seeing a student start and I've had the luxury of seeing a student with a couple years. When the students initially start, they're just like, why do I need this, because I can just do 5 + 2 in my head. But then when you're like, alright, well let's do 5, 965 + then they start to see the value of, oh, well I'd rather do that on here, than write it out, try to carry, try to regroup. Then they start to see some of the value behind what goes to the abacus.
When I first started with regrouping with addition or regrouping with subtraction, I have a tray and in the tray we discussed regrouping using Unifix cubes. We want to borrow the ten, so we're going to borrow and bring it over to the ones column. The problem with that though is, here's another problem that I've found is that when we do math vertically and visually, if we're doing subtraction with regrouping or addition with regrouping, we start in a different direction than we do on abacus. And I remember when I first started, l would have them do both. I said, okay we're going to do vertical on the Braillewriter and then we're going to do it on the abacus. It was such a headache because we're doing vertical on the Braillewriter, so we're going to work right to left, but when we come over to the abacus we're going to work left to right and they're just like, what????
So, just all those different things that go into it. I don't think the skills that are done in print conventions should be completely neglected; I think they should be at least introduced and the children know that they are there and some of the methodology that's used visually, but if it's not getting you anywhere and it's just more of a frustration, which is kind of what I found with the students that I have, that's when I started leaning heavily on abacus for some computational problems, such as addition with regrouping and subtraction with regrouping.
And normally everyday, I leave them a sheet where the problems are presented horizontally and I have them just put it into their Braillewriter and problem solve and give me the answers that they can and we go over it together. So I do like for them to have independent practice on it everyday, too, in addition to the direct instruction that we just saw here.
This is, I think, just the big problem with math for blind kids in general is because everything, 90% of it, maybe even more than that, is visual, visual, visual and the books that are formatted into braille that are available follow this visual format and if the child doesn't have the spatial skills or the exposure to it, they're like, what is this?
Just in my experience of reading through the mainstream books that are formatted into braille, just sifting through it and finding what you're looking for, in a clean cut, nice little page where you have the problems, I find it just quicker and more efficient for myself, just to braille it out and have it available for them. It's quick, it's to the point, it's the problems that they need.
The mainstream math formatted math book, I think, does have value though. I wouldn't completely discount it. But again, if there's a “thinking cloud", it's put in braille. And I'm thinking, I wonder how much time that took to draw, first of all, and then to get the braille to fit into the “thinking cloud." It's all visual. There's really, for me, I don't find the value in this “thinking cloud" that is arranged.
And a lot of times too, there'll be pictures of something and the picture will be reproduced and to me it would just make more sense to show them the real object. Multiplication with arrays, I think, in the beginning, this is kind of where I'm coming at everything is presented in arrays and it's just these dots and if you don't have have that left to right, top to bottom, that kind of systematic, spatial searching pattern, it's very difficult to follow the array. And so that's why I've started with real life Unifix cubes.
And then even then, if they do have a systematic searching pattern within the book, some of the math things are not presented in a systematic way and the way to search the page and what you're looking for and is very time consuming.
And you know, that is part of the problem too, it's just the time consuming part of sifting through the page if the spatial skills are delayed or if not knowing how to look at a page and this goes a lot with maps, too. A nightmare, you know, most of the time we're taught left to right, top to bottom, but you get some kind of pie chart, left to right, top to bottom isn't going to work anymore. Or you get bar graphs. Well, first you have to know what's on the horizontal axis and you have to know what's on the vertical axis and what it means if this bar is this high compared to this bar being lower.
And it takes a lot of time too because there's just so many spatial skills involved with mathematics for blind kids. It takes a lot of time to introduce that. I think there's definitely a link between spatial skills and using the mainstream math book. I think if the spatial skills are delayed or there hasn't been exposure and development with some of the skills, I think it's easier to use the abacus.
It still has a lot of spatial aspects to it, but it's tactually defined, it's clearly defined, the columns go from left to right, whereas in the mainstream book, the problem could be vertical, the problem could be horizontal, the problem, it could be..., if they have strong spatial skills and strong systematic scanning skills, I think it is easier to go with the mainstream math book, but if those skills, and just time factor, because our kids need a lot, our kids need a lot, and prioritizing, where is the priority, are they going to be using these types of mainstream math books when they're out of school, are they going to be using the abacus, are they going to be using a calculator, functionally, realistically, what are they going to be doing?
And I've asked myself that question with my students. My students are still at a young age, it's hard to determine what they'll be doing as an adult, but I make that decision based on what I've seen with them in classes and working with them for the time that I have them in the resource room.