# Math teacher looking for modeling tool

1. Sep 29, 2007

### Quantumduck

Hello,
I am a High school algebra teacher looking for a modeling tool for algebra tiles. I have four sources of online "virtual" manipulatives, but none of them do what a set of algebra tiles on an overhead can do.

First there is the National Library of Virtual Manipulatives. http://nlvm.usu.edu/en/nav/category_g_4_t_2.html

The problem with that model is that it has no negative 1. I can use the X and Y to do positive and negative variables, but there is no way to model (x-1)(x+1). That is essential in using Algebra tiles.

Next there is http://www.shodor.org/interactivate/activities/ or Interactivate which has no algebra tile modeling, but huge amounts of other math models.

There is also http://www.x-power.com/Flash/Tools/AlgebraTiles.html or Xpower. They are a pay website, but the color background is black. Ever tried to keep High School students awake in a darkened room so we can see red on black?

Finally there is Dr. Strader's website: http://strader.cehd.tamu.edu/Mathematics/ . He has the Java source code available to manipulate the what he has, but I don't know java to reprogram it to just allow me to choose the equations.

So, I am asking for help. Does anyone know of any modeling tool that would allow a teacher to stand at the smartpanel and actually model algebra tiles and have the kids do the same equation on their desks with the tiles?

Help! And thank you for any suggestions! I am trying to instill a whole new generation of kids loving math!

2. Sep 29, 2007

### ice109

i don't understand the point of this?

3. Sep 29, 2007

### D H

Staff Emeritus
Algebra tiles appear to be a mechanism for making simple algebra more understandable. Out of curiousity Quantumduck, are these used for teaching basic or gifted and talented algebra? (I went to school with the dinosaurs; I think my high school had two overhead projectors total.)

Qduck, you might be addressing the wrong crowd in this forum. We do have a few K-12 teachers here, but most of us are college students, professors, or non-teaching professionals. Have you tried your question on a forum aimed at teachers?

4. Sep 29, 2007

### Quantumduck

Yes I have. Unfortunately, most high schools don't have the technology to display the modeling. They use the overhead projector and colored plastic tiles to do the modeling.

As to the question of who the students are, they are normal high school students. Algebra tiles are a way to differentiate instruction in the teaching of math concepts, specifically "like terms", binomial multiplication, trinomial multiplication and factoring trinomials into binomial terms.

They are highly effective at all levels of algebra education, but the shift from "old school" to technology has not caught up.

If someone has a straightforward resource on learning Java programing, I would be up for that. I have the source code from one person's site, and I could modify it to suit my needs (If I know Java Programming!!! Big IF).

Thanks for all your suggestions and questions. I appreciate them all.

5. Sep 29, 2007

### ice109

no offense but this seems soooooo dumb to me. are you wanting to do this because your students don't understand what you're trying to teach them or because this is how you prefer to teach them? i fail to see why this would at all be necessary for teaching this stuff.

6. Sep 29, 2007

### symbolipoint

The use of actual physical items can help certain students understand the symbols and expressions in a realistic practical way. The actual tiles can be manipulated, which is more difficult if done in software form; but if a software program is available, then this brings the potential to show several students at once while they sit at their seats. The actual physical tiles should be easier to manipulate than tiles only in software.

Hey, QuantumDuck, did you yet find any program that allows you to actually rotate the tile pieces?

My own sensibilities are that a good drawing can or should work well, and no computer technology be needed.

7. Sep 29, 2007

### D H

Staff Emeritus
Don't knock it. I can see how techniques like this could be quite beneficial to average students. Symbolic techniques lead to deeper understanding and work fine with gfted and talented students. Basic students (the ones who graduate high school without even knowing how to count money) need help. Boys, in particular, need help. We have an impending crisis because boys are going on to college in ever smaller numbers and dropping out of high school in ever larger numbers. The current school structure does not suit the natural psychology of boys. We tag them far too many boys ADDH, but many of these supposed ADDH boys are just acting naturally. Boys tend to be visually oriented. View these visual techniques as a good thing.

8. Sep 29, 2007

### ice109

i still don't understand. i looked at the algebra tiles webapp on the first page he linked to and from it i get the impression that whole point is to make the xs and ys appear as objects, which they are though. a monomial is an object, i don't understand why that needs to be belabored with a tile.

9. Sep 29, 2007

### Quantumduck

Thanks for the support to you and to DH. The use of modeling in bridging the gap between the concrete thinking of younger ages and the more abstract thinking required to do algebra is essential. Especially when we are dealing with 13 and 14 year old kids (ie. Freshman Algebra in high school.)

The goal of this is for me to be able to model to a class, while they do the same thing at their desks with actual pieces. Then I give them some problems and they model the problems with their pieces. Then I give them so problems that can not be modeled (numbers are too large, they don't have enough tiles) and they then have to bridge the gap from concrete to abstract.

The bridging actually very difficult for some learners to achieve. Asking them to jump from adding, subtracting, multiplying and dividing numbers to then dealing with doing functions with X and X^2 is not easy. They will add the X and X^2 because they both have X's. Then they will get X^3, because they know something has to happen with the X's.

I have thought of just going with a drawing program straight up. The hard thing about that is then you have to 'draw' 6 different types of shapes / color combinations and do multiples of them all very quickly. Difficult to do in the classroom.

Thank you for all the suggestions (even the challenges!)

10. Sep 29, 2007

### Quantumduck

Because you are an adult with a firm grasp of the ability to do abstract thinking. If you go talk to a 13 year old kid (typical age of an 8th grader or freshman in algebra I) you will find they don't have that ability to think abstractly. They are very concrete in their thinking.

Numbers relate to things. Negatives are weird, because they don't. X's are placeholders for any number. But we can still do things with them even though we don't know what it is. How does that happen?

These are abstract thinking patterns that you and I take for granted. A 13 - 14 year old learner needs something to help bridge that concrete / abstract divide. We only need to use them for a few classes at the beginning of adding and subtracting expressions, multiplying binomials, and factoring trinomials. Those few days are the difference between a whole classroom of lost learners, and three lost learners.

11. Sep 29, 2007

### ice109

i'm sorry this boggles my mind. i refuse to believe that the students need this. i really think you're underestimating them.

adolescents graduate to abstraction ~11-12. pre algebra is taught to many students in middle school.

edit

i went to a crappy elementary school and i remember solving a linear system in 3rd grade. and i'm dumb so i solved it guess and check.

Last edited: Sep 29, 2007
12. Sep 29, 2007

### D H

Staff Emeritus
Do a google search on algebra tiles. That's how I found out what these things are.

13. Sep 29, 2007

### Quantumduck

I beg to differ, but obviously I should defer to your significant grasp of educational theory. I teach 180 kids (six classes) of algebra, so could you come to my school and give inservices on how to educate the learners better? I obviously could use your significant knowledge of high school educational practices.

14. Sep 29, 2007

### D H

Staff Emeritus
Really. Have you noticed how math scores are plummeting in the US compared to other countries? Have you noticed all the nasty statistics on a growing divide between educated and less-educated? Between boys and girls? Have you noticed the growing tendency toward anti-intellectualism and pseudoscience in this country?

Qduck, go for it.

Does anyone have suggestions on how to learn Java? An alternative is Ruby, which is very easy to learn. I don't know if Ruby has any graphical capabilities.

15. Sep 29, 2007

### Quantumduck

Thanks DH. I will go to the Barnes and Nobles this weekend and get a Java book. It seems that if I need a tool, I am going to have to build it myself. I have no problem doing that!

16. Sep 29, 2007

### ice109

let's take a look at how they teach algebra over seas then. i don't think that people overseas are all have average iqs higher than here either. i think these crutches are exactly the reason scores here are plummeting. i'm not an elitest either, i'm all about educating everyone but

if they're adding monomial and binomials it's because they've been poorly defined for them.

and considering negative numbers just what will the tile $-1$ look like? you'll bring it close to $x$ and not only will it dissapear but $x$ will shrink as well? how concrete is that?

Last edited: Sep 29, 2007
17. Sep 29, 2007

### D H

Staff Emeritus
ice109, you are not contributing to this thread. The polite thing to do would be to bow out.

Qduck, if you need to learn a new language I recommend Ruby over Java. Ruby is a very friendly and easy to grasp language. Did I mention that its free?

A fifteen minute starter on Ruby: http://tryruby.hobix.com/

I don't see any algebra tiles in Ruby, but this http://puzzlemaps.rubyforge.org/ is educational software in Ruby that incorporates graphics.

18. Sep 29, 2007

### Quantumduck

Thank you very much for your opinions on teaching in the US.

You make some blanket assumptions, such as "because they've been poorly defined for them." You certainly must have heard the one about "when you assume things". Take out the You when you say that one.

In other countries, they use things like Algebra tiles to help learners understand the concepts. Gee, I guess that is why we started using them too. IT WORKS.

As to how the negative and positives interact.

A positive X is green. A negative X is the flip side, and it is red. Anytime you have two opposite colors (units are generally tan, red, X^2 are blue, red, and X's are green red) you get a zero pair. Why? Well -X +X = 0. They don't shrink, they add to zero because that is they are additive inverses of each other, and when you add the inverses you get the additive identity.

See, we use those big words in class, and now they are not just concepts to grab out of thin air and hope it sticks in their brain, I can have something solid and tangible for such definitions as identity, inverse, commutative, associative and distributive properties.

Yes, they didn't have this 'new fangled stuff' when we were in math class. But it works. It works in a matter of hours instead of days and days of memorizing facts and boring drill and kill. It works because it helps them understand the concepts on tests. It works because they are able to understand the words with something in addition to me telling them.

I am sorry you can't understand that. I offered you the chance to come to my district and share your expertise on secondary teaching methods with me and my department. Will you accept?

19. Sep 29, 2007

### Quantumduck

Thanks DH, I will check it out tomorrow. I appreciate your help.

20. Sep 29, 2007

### ice109

of course i accept but it's not really feasible is it.