Leanne Grillet, Senior Director of Outreach at American Printing House (APH) and Professor at Florida State University shares her expertise in a common mathematical tool
Alex: Hey Everybody! Welcome back to another episode of Teaching Tips Tuesday. I am profoundly excited and admittedly a little nervous for our guest today. We have Leanne Grillet–she is the Senior Director of Outreach at APH (American Printing House) and a Professor at Florida State University, one of my professors in fact. Leanne taught me nemeth, the abacus, we did a lot of stuff about just kind of planning for tbi life and I am thrilled to have you out today.
Leanne: Well thank you so much I am really happy to be with you Alex.
Alex: Thank you! And I also understand you are a doctoral candidate.
Leanne: [blushes] I am, I have taken the long road and doing a class this semester and I have finally hit the stage of working on my dissertation.
Alex: And if I’m not mistaken that dissertation is about one of these-the abacus [holds up an abacus].
Leanne: It is about the abacus and really about the professional development so that teachers feel confident about teaching the abacus to their students.
Alex: All right! Well that is our topic for today, the abacus. So can you first tell the folks at home what is an abacus?
Leanne: [chuckles] Well an abacus is an ancient counting tool and the abacus that people probably think of immediately is a 10-bead 10-column abacus where you can count up to 100. They often went vertically across and you saw them in elementary, preschool, kindergarten classrooms–many times rainbow colored. That’s not the I’m talking about. I’m talking about an abacus that has specific beads and has specific methods for using complimentary numbers to understand and compute not only addition and subtraction but multiplication and division. It can do square roots, it can do complex-you can do fractions, there’s all sorts of things you can do on the abacus but people don’t necessarily think about it that way because in America we traditionally think of that preschool abacus. So the Abaci we have available actually at APH but sometimes you can find them in other places. Uh we have beginning abacuses–or abaci–[holds us a beginner 2 column 9-bead abacus] that just has, uh, nine beads in each column. Not ten, but nine beads in each column and two columns–this is the beginner [gestures at abacus]. While it’s no longer available it is out there, people still have these. What we moved to–with recommendation from teachers–is to the expanded beginner abacus [puts beginner 9-bead abacus down to switch with 2 column 9-bead abacus] which is the three columns of nine beads. If you think about it the only numbers that you can hold in one column are the numbers zero through nine, so having a tenth bead and one column makes absolutely no sense–we don’t write a ten that way.
Alex: [nods in agreement]
Leanne: We write a 10 by putting a 1 in the second column or the tens column and a 0 in the ones column. So this really matches our numbering system–our decimal system well. And these can be used to add, subtract, they can even be used to multiply and divide though I will suggest something else if if you’re going to go that far.
Leanne: The other nice thing about it is one-to-one correspondence. that beginning of learning numbers and understanding what they mean. Also, these don’t get lost meaning they’re all stuck on that wire bead, they’re not going to pop off and roll around on a student’s desk. It has felt backing so once the bead has moved it takes a little bit of work to move it again which is good when students are trying to feel where they are on the abacus, but, again, you don’t lose these. They’re not counting beads that get stuck all over the place, they have a specific space and a specific column so we’re not trying to organize columns in a virtual, vast realm of space–this is really set, so there’s the plus one. Now, the Kramer abacus–built by Kramer–is the one that has one bead on a top of each, and then a separation bar, and then four beads below, and then there’s a way that you calculate that top bead is worth five, and this goes so on. But this goes all the way up to trillions and if you put two abaci together it goes even further, so this is kinda the traditional abacus that’s been around since the 1950’s. And, so again, felt backing beads are a little bit harder to move; if your beads are easy to move you need a new abacus. One last abacus, we also have–the large abacus–which is the Kramer abacus [holds up Kramer abacus to beginner abacus to display size comparison] is just–
Leanne: Bigger. Great for students who have a hard time manipulating beads that they have can’t feel as well, and some advantageously blind adults find this a little bit easier. I have also found this helpful for teaching and then bringing it down to the student level on the Kramer abacus. So that’s really what it-what an abacus is, it’s for counting but it’s for doing–you can do complex math if you learn how.
Alex: The easiest way I’ve explained it to classroom teachers is instead of our kids handwriting out their [holds up abacus] math problem, this is them handwriting out their math problem.
Leanne: [smiles and nods in agreement]
Alex: And of course there’s nemeth to do that, but to do the actual computational step [pats abacus] it can all belong on there.
Leanne: It is, there’s nothing wrong with learning the–the paper pencil algorithms, and of course our students who are braille students do that paper pencil algorithm on a braille writer so it’s like saying “oh go use a typewriter” or a computer keyboard to try to do your multiplication of four digits times two digits. And if I even told you to do that on your computer right now you’re gonna go “yeah right, not doing it” because it’s hard, it’s similar, but if there’s an importance that should still be learned. This just speeds the process up after the student has the understanding of what that means. There’s–this is the paper pencil and the quick method for your student to complete these and don’t think that just because the student is, um, blind, that they’re the only ones that should use this. Sighted students-especially in other countries, use this. So your low vision student–this is a great way to help hold the numbers up the same column, how many students have you that kind of move a column over on accident? Use the abacus, nothing wrong with it.
Alex: All right! So we have kind of already touched on this as we were talking about this but if it’s your doctoral thesis you must be pretty passionate–
Leanne: [smiles with glee in agreement]
Alex: about-about the use of the abacus so could you explain to us, why-why are you so passionate about it?
Leanne: So, I think, as a whole we’ve started to understand that, that math is a part of the STEM curriculum–the science, technology, engineering, and math. And many people kind of focus on the S, T, and E–especially if there’s a fear of math and for students with vision loss, math can actually be kind of a challenging concept to grasp. [stammers] The abacus actually introduces our students to early math concepts and number operations where they can get that one-to-one correspondence and true understanding of number sense, addition, subtraction, multiplication, and division. It builds something called procedural fluency. Many times when we talk about fluency people think of reading, like you can read fluently, put it into math, we can-we can flexibly and accurately and efficiently determine our computations, our answers. And that’s what the abacus does–it gives them that fluency. You don’t–well, you can have fluency with the braille writer–it is a labor-intensive fluency. It just isn’t as fluid, so this helps our students with vision loss gain that procedural fluency and work through those problems and it’s accessible, and it’s a manipulative, and again, I say vision loss–it doesn’t matter what their loss of vision is–even if it is low vision, this works as well. So, [stammers] that’s really it. Um, historically we know that our people with vision loss weren’t perceived as individuals–to have an interest in science, technology, or math, nor even an inclination to pursue those, but at APH we actually know this is counterintuitive–
Leanne: To what we experience with this community. S0, that’s why we are having this some of this focus on the abacus and learning it.
Alex: Excellent! Uh, well something you said kind of brought me back to your class actually when you mentioned the-the fear of math you talked about how [stammers] you had us raise our hand and say who doesn’t like math? I raised my hand when you said that and you said that we could never tell our kids that because then that’ll start building the idea that math is a thing–is an option that you can not like and that’s not what we want our kids to learn. [stammers] So that just really brought me back to Florida State.
Leanne: So you can find it hard or challenging–there’s nothing wrong with hard and challenging. We go through those things in life.
Alex: [Shrugs shoulders and nods in agreement]
Leanne: But, conquering that is a really important piece and if we start young, some of that love is gained from young use in math. And some of our students of our students are not exposed to numbers, especially our students with extremely low or no vision because we are surrounded by numbers visually on a clock, on a microwave, uh, punching in a temperature on a stove, on an iron if you still iron. Even [stammers] the numbers throughout a grocery store–just think of how many numbers you see and how our student’s don’t get this exposure, so we have to artificially add it to their environment.
Alex: [Nods] Now, there are a lot of challenges around the country for our other things we focus on, we have CaneQuest, we have CaneSkills, we have the braille challenge for braille–I understand yours. You’re heading an initiative for something like that with the advocates.
Leanne: I am! So, I’ve had this little brainchild in my head for a number of years now that I wish there was a math competition for something similar to the braille challenge. I have loved what the Braille Institute has done in motivating students to learn braille and to build their skills. And I wanted to be able to have something similar, so APH wrote a proposal for a grant to the Simon’s foundation, uh, to the Science Sandbox, and, and asked, and we actually asked for a variety of things but the thing they were most interested in was the few sentences I wrote about this little idea of the Abacus Bee and they loved it so much they said “we want to support you in doing this”. And so we’re doing a pilot program this year for an Abacus Bee which is an abacus competition so many people think of Bee as in a spelling bee, bee just really means a competition. So don’t think that we’re asking you to spell math, this is truly, uh, solving addition, subtraction, multiplication, and division problems with reading them in either large print, mammoth braille, or UEB braille, as well as an auditory competition–just listening and solving it. And while we call it the Abacus Bee–and the abacus is an important piece for our students to use–there is nothing against mental math, and many people who become skilled in the abacus actually create physical and mental pictures of an abacus and actually complete math problems mentally. So, there’s no requirement that you use an abacus, but you may not use any type of paper pencil method–
Leanne: so you cannot pull out the braille writer and try to solve the problem–
Leanne: You can’t pull out a pencil and paper and try to solve the problem, you need to do either the abacus or mental math to be able to do it.
Alex: Okay! That also reminds me of being blindfolded in your classroom and solving math problems on my absence–that really takes me back.
Alex: All right, well thank you so much for coming on today and telling us all about this [pulls out and points to abacus] wonderful, mathematical tool. I have one last question for you and that is what is your favorite part of your job?
Leanne: Ugh, my favorite part of my job is actually providing professional development, teaching and training, and working with vision professionals, but also parents or paraprofessionals or those who surround the student–whatever age that student is. Even if they’re a 40-year old I want to surround them, I want to provide that professional development to those teachers and people so that they feel they’re giving that, uh, consumer or student the best opportunity for a successful career in life. So, watching that professional development happen and someone taking away knowledge that they feel they can make a difference in someone’s life.
Alex: All right, that is an excellent answer! Well thank you again so much for being on this episode of Teaching Tips Tuesday with us Leanne.
Leanne: Thank you so much and if you aren’t a part of the Abacus Bee this year in our pilot program–because there’s only a few locations–stay tuned, come join us next year!
Alex: All right, well I look forward to seeing it all across the country and I look forward to seeing everybody at home on our next episode of Teaching Tips Tuesday. We are now on our every other week schedule so I won’t see you next week, but the week after that, uh, have a lovely rest of your week and we look forward to seeing you again next time.