Project Math Access DVD 02 - Intermediate Grade Levels- Part 06
Transcript Start
Audio Description: Part six; teacher interview.
STICKEN: Tara, Ijust have some questions about what you've done with Ali.
TEACHER: Okay
STICKEN: Relating to the abacus...
TEACHER: Sure
STICKEN: And I'm wondering, what method Ali is using when she uses the abacus?
TEACHER: Ali is using the Logic Method, for a number of reasons. One of the reasons is that she‘s able to conceptualize that the addition and subtraction, it‘s related, not only with Unifix cubes, but she‘s also able to transfer that over to the abacus. So with those type of skills and that type of ability, I went ahead and tried it and she‘s doing great with it. She is a chit-chatter; that‘s why we call her chatty Barbie. The only time she doesn't talk though is when the wheels are turning, and so I've really kind of worked with her to talk through it, you know, you want to subtract 40, but you can‘t so you subtract 100. And that has improved for her.
But I've found when I work on the abacus, with the Logic Method, I really have to have the child secluded, in a quiet area, where there's not a lot of other commotion, because it really, the thought process that goes with it requires a lot of explicit attention. And that's why I chose the Logic Method with her, and it's worked out pretty well. She gets confused sometimes with whether we're adding or subtracting, but overall I think she does have a good understanding of the relationship between adding and subtraction.
STICKEN: So, in summary, because All has a facility for numbers and understands what she's actually doing in the operations of math, she's able to use the Logic Method without much difficulty.
TEACHER: Right.
STICKEN: Describe a student for whom you would not use the Logic Method, but rather Secrets.
TEACHER: For a student I would choose to use Secrets would be a student that had some difficulty understanding the relationship between addition and subtraction, had some difficulty with the whole “why" in general. I found that if they can't answer “why", even just with reading and it doesn't, they can't answer “why" with math, then it's very difficult to go on to the Logical Method.
I may use it for a student that has strong rote skills. Now All does have strong rote skills, but I felt that she was able to go ahead and take it one step further to the Logic. I might use it with a student who had strong rote skills, but has more difficulty answering the “why", implementing that higher level thinking, that it requires to do the Logic. So the candidates that I'm using currently have very strong rote memories, but the “why" is a little vague with them. But they have the basic concept of subtraction and addition; that is there. But just how the two come together and how it's related on the abacus and how it's related to a 5-base system, It's really a lot to throw at a kid and so I kind of make that decision on a case-by-case basis, looking at the child, whether or not all of these things can come together. It doesn't for every child; it's just a case-by-case basis.
STICKEN: So when you choose to use Secrets, it's used as more of a mechanical way of calculating.
TEACHER: Yes, kind of like howl learned math when I was younger. A lot of times when math is taught I think, it's like the same way, the same process year after year after year and other methodologies and other understanding of it I think is important. Like with the particular students that I have that I use the Secrets with, I don't rely just solely on that. We also use a combination of Unifix cubes and the calculator. And they've also been introduced to the horizontal and the vertically presented math, just to know what it is and to have and understanding. But the relationship, I think, is much more difficult for them to conceptualize, with the 5-base versus the 10-base, and so forth and so forth.
STICKEN: Do you see an advantage if a person is capable of the Logic Method, is there an advantage to using Logic over Secrets and if so, what is the advantage?
TEACHER: I think there is a big advantage because number 1, it's not so mechanical, there's more of an understanding of what they're doing and number 2, it's very related in a 5-base method to carrying as we do in print. So the relationship that is there, although the student that we just saw, I don't think is quite there yet doesn't realize that wow, there is this big relationship, it's very similar to what we do in print. But I definitely think there's an advantage because there's just more thinking, there's more thinking behind it and it's not so you do this, you do that, you do this and don't ask why and just keep going. If the why, if the child can understand the why, you betcha, I'm gonna enforce it and explain and try to get them to conceptualize the relationship between print and braille, which is difficult, to say the least.
STICKEN: Now if someone is not capable or at a point where they're able to use the Logic Method, so they're using Secrets, and it's mechanical, what do you see as the advantage of using the abacus at all, instead ofjust using the calculator, which is also mechanical?
TEACHER: That is a very good question and I've pondered that many times. What's going to be more feasible in life, you know, down the road? And I think with the age that I'm working with that has not panned itself out yet. I think as these children get older and are exposed to more situations and experiences, that will pan out. But, at the age I'm working with, I'm probably almost guilty of overwhelming them: abacus, calculator, Unifix cubes, the calculator on the Braille Lite, the list just goes on and on and on.
But at this point, I think they are at an age where that has not panned out. I think the advantage at this age is it's a nice tool, if they can go on and handle it, and you know wherever you're at, you're not always going to have, what do you do if the batteries die on the calculator, you know, those kinds of things that come into play. Same thing with the Braille Lite, if it dies or it needs to be charged, we still have to use a Braillewriter, we still have to go back to, it's like a basic, kind of paper and pencil, is kind of howl look at it, how you and I need the paper and pencil, I think that's how I feel kind of about the Braillewriter and the abacus, too. These are essential tools.
And a lot of the technology that we have today, it's very useful and it has its implications, but if we don't learn on paper and pencil first, and we go to type, it's confusing to us. And just to have those instilled as those basic tools, I think is important. How it pans out, you know, no one will know in the long run, what this child will use in their daily life, but to have the tools, at least instilled, and the experiences with them, I think is important as youngsters, as they are now.
STICKEN: Have you seen any growth in understanding of number theory with the kids who are using Secrets, where they're able to move towards the Logic Method, or at least, has the abacus facilitated a greater understanding of the math processes?
TEACHER: Yes, recently I saw this. In my mind, I was pretty convinced that this particular child was going to be Secrets, Secrets, Secrets. But recently I saw him kind of make ajump that, “oh, okay, this is why". And I hate to just jump into Logic if they can't understand the why and you hate to just give them Secrets and they're just going to be Secrets, but I think what I've seen with this child, it definitely has facilitated and definitely he's gotten to the point now where he doesn't look at them and has figured out, “oh, but I want to add 1, but I don't have 1, so 5 minus 4 is 1". That is starting to take place, but you can't just expect the child to just pull that out of thin air. You know, where does that come from and why. I think that takes some time and is a developmental milestone I think is bringing all the information together. But I would say definitely, yes, the Secrets have facilitated making that jump to Logic.
STICKEN: So there's kind of an “aha" moment and you attribute, at least in part, using the abacus...
TEACHER: Definitely, well, it's kind of like us too when we learn, we just cross out and carry and the “why" really isn't there. But then later, you're like “oh". I think same thing with the abacus, they kind of have that dawn, , it dawns on you later, that moment and I think definitely that plays in, definitely.
STICKEN: Have you worked with any kids who you see as incapable of using the abacus or you think it's inappropriate to use the abacus?
TEACHER: Not at this point. Very briefly, as an itinerant, I worked with some children that also had low vision though, that I thought would definitely be calculator users. But again, I think it's just a case-by-case look at the child and everybody gets on the same page and determines where this child will be, because the abacus can be difficult, definitely. If it's questionable, you know, try, try, try, that's always my theory, try it and see how it goes and if that doesn't work then maybe go to the calculator, but I think that it's not something just to discount right away, I mean you don't know until you try with a student.
STICKEN: What do you see as the bottom-line, baseline kinds of aptitudes or skills that a student would need in order to use the abacus?
TEACHER: Well, I think they need a very good understanding of place value and I kind of have accentuated that with the lesson, too, with the different compartments for the different values of each column. I think they need a good understanding of counting, skip-counting, the ability to manipulate the abacus and also hand placement. I recently started multiplication with a student; that is absolutely important. And not wanting to jump the gun and get ahead. But it seems trivial, but where that left hand is and where that right hand is as abacus gets more complex, is absolutely essential, absolutely essential to think about where your left hand is and where your right hand is and the multiplier and the multiplicand and your answer.
So I think, so the fine-motor skills need to be there, the understanding of place value, obviously counting, skip-counting, and I also think it can be started early, but where they're at in the math curriculum. Now as you probably noticed, this particular lesson that Ijust have done, All had gone on in the math program; she has gone on, but I don't feel she's quite ready on the abacus yet. . I want to make sure we've got the addition and the subtraction. But considering that she is at the end of 2"“ grade, I think she's right on target with the subtraction with the carrying, the beginning multiplication is usually where they end up at the end of 2"“ grade and she's right on target. And with all the other tools and all of the braille and all the other components, I think it is reasonable to expect some may be a little bit behind, with all the things that have to be synthesized and brought together, but, like I said, she's moved on and she knows it in braille and knows how to write it but not necessarily on here yet.
STICKEN: Now your students are 2"“, 3"‘, and 4”‘ grade, and most of them come from a resource room that's Kindergarten and 15‘ grade. Do most of your students come with basic abacus skills?
TEACHER: Yes, they do.
STICKEN: And so assuming that it's introduced to them in Kindergarten, they certainly don't understand place value or skip-counting or any of those things, but the abacus is used for instructional purposes to help them understand those concepts? to help them understand those concepts? No, not at all, it's used in conjunction. Sometimes it does require specific instruction with just that, just focusing on the abacus, but I don't see it as a separate entity at all, no.
STICKEN: Just to expand on an earlier question, can you think of the characteristics of a student who would, in your view, not ultimately benefit from the time spent learning abacus and would be better off skipping abacus all together, what would that student look like? And I'm thinking in terms of cognitive skills, not motor skills, obviously they have to have the fine-motor skills to be able to move the beads, but...
TEACHER: I think it does go back to cognitive and if the ability to understand the 5-base system, this is 5, this is 50, this is 500, whereas this is 1, if the basic ability to understand the abstract representation of the numbers, if that isn't there, I would hesitate to move on. However, if there's an understanding there and they're doing okay with Secrets, with addition and subtraction, I would keep trying, at least with the 4 basic operations to see where this could go. Because I think it's just got a lot of potential. You put it in your pocket and you go out into the community and you need to know a simple problem and it's right there. That's a fine line I think though, where to stop. But I don't think it should just be chucked out completely all together. If a kid is 100% academic and they come in, yes, Iwould be pushing it, definitely.
STICKEN: Okay, but how about the kids who are in afunctional curriculum? Do you think there's any application at all for kids in afunctional curriculum?
TEACHER: I think that there is, but I think eventually they'd probably wean off of it and go to a calculator. I mean, I don't know, I don't have those older kind of kids in those vocational, kind of functional curriculums, but I would try it, ifl had like a high school student that was vocational bound, functional bound; I would try it and see, you know, how far they've come, what kind of abacus instruction they've had, but if it wasn't working, then I would go to calculator. But that's kind of where I fit on it; I would always try it first, I think, no matter what. I think everything is a kind of, you have to, you know the assessment and the teaching part just go hand-in-hand. Can they move on, well let's look at this, can they do this, in order to go on to the next skill. I really think those kind of go hand-in-hand. And although it's not formal, you're constantly assessing as you go along, because you just see it when you're working with the kid, what they're doing and what kind of problems they're having. But I would always try it, I would always try it because I think it's very valuable and I think it lends itself to understanding some of the concepts of math more rather than just the calculator where you punch and go.
STICKEN: Great. Thanks.
TEACHER: Thank you.