The Dynamic Classroom: Teaching and Learning Mathematics with Technology

We are forewarned that there will NOT be 7 presenters, as was originally advertised. Five of them could not come, so we are down to two presenters. We are also told that all of the information that is covered in the presentation either already is or will be posted on this site.

Ihor Charischak is the project manager of CIESE (pronounced "sees") and presenter.

Part 1: Set the stage. Ihor lets us know he sets up the presentation into three parts: Set the stage, do an activity, do the debriefing. In other words, it seems like preview/warmup, then complete the objective, and summarize and see if the students achieved the objective.

Knowledge domains:
1. Ability to use tech resources. Geometer's Sketchpad, spreadsheet apps, web-based microworlds and applets, graphing and green glob, and other software. He also mentiong digital whiteboards, which he shows a slide of a teacher using NLVM. HE next mentions TI-Navigator (he does not seem to like the TI-84). It is interesting to hear him talk about a resource he does not seem to like. It is nice to hear views like this, though, as he may be biased against it, but he still mentions it.
2. Create technology-oriented learning environments. Use a computer to model for the whole class. Use computers in small groups. Use a computer lab.
3. Personalizing the curriculum. It's more than just a textbook. It is a guide for content, learning, teaching, and assessing.
4. Math background and attitude towards learning math. The teacher must have a passion for teaching and learning math. If the teacher is enthusiastic, so will the students.
5. Pedagogical strategies and discourse. Break out of the "telling habit" and move toward asking the students to help guide toward discovery. This opens up to conversations and debate about math.
6. Assessment strategies. You have to meet the standards, but you know you're reaching the students if they're still talking about it after they leave the class or the lesson is over.

These are the domains that Ihor believes makes up a dynamic classroom.

Part 2: Do the activity (in story form). Now we are referring to the site for the presentation. We starts out with the sign problem. Common responses are:

1. the total should be 6,122
2. There should be a comma between 1 and 8 in 1802
3. The answer should have some kind of units

This is a classic example of what's wrong with many word problems. The students did not sit and look at the problem to make sense of it. They went into what I like to call "automatic mode," where they automatically do something without first thinking.

Then we look at the bus problem. Most kids give an answer with a decimal, but do not figure out that they're dealing with buses and need a whole number of buses, rounding up. However, students who visually represent the problem have no problem figuring out how many buses are necessary. What does this tell us about how students think? What does this tell us about how we should teach?

Fraction darts: as we look at this example, Ihor wants to show the game. However, he did not link to it from his presentation, and there is poor communication between Ihor and the gentleman running the computer. It would be great to have an interactive whiteboard, or at least a better setup for being able to use the computer with the presentation. As we are looking at the game, we see that equivalent fractions are able to be presented within the game (i.e. 5/8 = 10/16). Ihor mentioned about how students figured out that if they added one to both the numerator and denominator, it would move the dart up slightly. Also, by playing around with other relationships shows how to devise different ways of working with fractions.

I have to wonder if this presentation was rehearsed ahead of time, as there are many things that are stalling getting the info to us. This leads to a good lesson. As you incorporate more technology into your classroom, it is imperative to practice and test out what you are doing.

Next, we look at a dice-rolling simulation. Again, we are having a problem with using the computer...Why did he not check his power supply before beginning? Anyway, there is a dice-rolling simulator on the TI-84, as well, in the ProbSim app. I use it quite a bit, and there are other simulations within it. You can vary the number of rolls, sides of the dice, etc., and it will keep track of the outcomes for you. If you roll two dice, you will see a certain outcome arise. A nice way to explain this is by creating a matrix that keeps track of the sum of the two dice, and you will see that 7 has the most possible outcomes, while 2 and 12 have the fewest.

Next we look at the pizza problem. This is a variation that I think we have all seen in Algebra courses. We see the variation between toppings, sizes, etc. Looking into the end of the problem, the people who run the site ended up making this a piecewise function, where everything levels off after 5 toppings.

The jinx problem is one of those classic "math magic" problems, where no matter what you start with, you get an answer of 13. All it gives is an algorithm where the final answer will be 13. The main idea behind Ihor speaking about this is stating that most students don't know what a variable actually is. AMEN to that! I agree with that, and it is one idea that I constantly stress in class.

As I am following along with this presentation, I think to myself that this would be great to share with pre-service teachers to help ignite this type of teaching for use as they develop their own methods for teaching.

Finally we look at Green Globs, which allows students to explore how equations work. They are able to discover about linear and nonlinear equations.

Part 3: The debriefing. What did we learn today? I learned that I would have gotten as much out of just going to the website as by sitting through this session. It's not that it wasn't necessarily a good presentation, it was just not anything new to me. Again, this needs to be aimed more at pre-service and novice math teachers.