Math projects (Assignment # 3)

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0Bz450c6VLSIYMzNjNmFhMzktZTlhMC00MGY1LTljN2QtODFjODA2NTc5OTA0&authkey=CIbS65oE&hl=en

Comments on Creativity, flexibility, adaptivity, and strategy use in mathematics

This article brought an interesting question to my mind. How much of what we have learned could help or hinder what we learn next? Our previous knowledge could effectively help in constructing a new knowledge and our nature as human beings is to build new knowledge on what we’ve already learned and retrieve information from the past to help us understand the present situation. At the same time, previous knowledge could obscure what we are ready to accept and learn. We become bounded with what we know.

How much is too much?

When our mind is cluttered with knowledge, we sometimes miss the obvious and when we are used to complexity, we forget about simplicity. I connect that to how sometimes kids solve a new problem in a very creative way just because they do not have any previous knowledge regarding that problem.

The French author Antoine de Saint-Exupery says:  “Grown-ups never understand anything for themselves, and it is tiresome for children to be always and forever explaining things to them. “

As a teacher, I believe that some basic knowledge about a topic is required. Yet, I need to take advantage of what my students don’t know and have them spend a big part of their time in a mathematics classroom exploring ideas and using heuristic problem solving. I want to encourage their creativity and their ability to challenge some rules and break some limits. In my classroom, I want to see fearless young mathematicians.

Word Problem

The problem

Ryan left the science museum and drove

south. Gabriella left three hours later

driving 42 km/h faster in an effort to catch

up to him. After two hours Gabriella finally

caught up. Find Ryan's average speed.

Is it practical?

I think it could be practical but I don’t like the idea of speeding to catch up.

Is it imagery memorable?

The presence of a picture would help the student visualise the distance to calculate the average speed.

Can it be solved with the given info?

Yes, let’s assume that Ryan speed is x then the distance they travel is:  5 x = 2( x+ 42)

X = 28 km/h

Can it be interpreted in more than one way?

It was not clear if Gabriella left the science museum to catch up with Ryan or maybe her home in that case the distance would not be the same...

It was not clear if Gabriella was driving faster than Ryan or faster than usual...

Would the kids be able to interpret it as intended?

Since I did interpret it in a different way the kids for sure would think about that too

Is there anything strange about it?

Yes, my question here: was Gabriella on a highway because unless Ryan was driving 8 Km/h Gabriella was driving above speed limit....

Another thing, I did not understand why Ryan had to travel south would the direction he took change anything in the problem solution??

How would you change it?

I would make the problem clearer

Ryan left the science museum and drove on the highway towards home.

Gabriella left the science museum three hours later, taking the same highway, driving 42 km/h faster than Ryan in an effort to catch up to him.

After two hours Gabriella finally caught up.

Find Ryan's average speed.

Two columns problem solving

https://docs.google.com/leaf?id=0Bz450c6VLSIYYjhlYzBjODQtNTNhOS00MjM5LWJhYjctNzdjOWJmZmQ1ODFl&hl=en&authkey=CIjp5p8K

Practicum stories

My first story

I really enjoyed being in classrooms with kids. But what happened is that I was not able to look at a class as a whole but as individual students and even as individual human beings and thinking that each kid has a story. They are sons and daughters and they come with a background and a history. Before I started my practicum,when I imagined classrooms, I thought of classrooms as whole group and was thinking about how will I manage a whole group of students? How will I teach a whole group of students? But now I realized that this is not how I am going to see the students I am going to teach. I was not able to see them as a group of students. actually I was not able to see them as just students, I saw more than that. I was surprised by my way of thinking and asked my self Why?  and the only reason I had was, maybe because I am a mother and I saw my own kids in every one of them. 

My second story

Most of the teachers in the school use a traditional approach to teaching. My idea about teaching is very different and far from traditional. I was worried when it is my turn to take over a class that is not mine and introduce a different method of teaching, such as games and group work, I might loose the attention of the kids and lose control especially because they are not used to those methods. Yet, I was determined to try my way and it actually worked. The kids where very excited about the new method and got engaged in the activity. To get their attention, I need only to switch the light on and off few times. I was surprised that the kids were able to adapt to the new method so quickly and that gave me the confidence and courage to do it again.