Private Universe Project 4: PROBLEMS AND POSSIBILITIES

One of the key goals of mathematics education is building problem solving skills. How does a mathematician approach problem solving? What does it mean to think like a mathematician?

In this video we viewed a mathematicians work.
We observed students in a variety of problem solving situations to uncover parallels in the way that students and mathematicians solve problems.

For mathematicians solving difficult mathematical problems like this is a little like working on a puzzle or a game.

In this video the mathematician used the Towers of Hanoi to explain mathematical problems and how they are like solving a puzzle.

When a mathematician is working on a problem, they don't always know the answer.
And if you do know the answer you are not going to give a mathematician the answer, they are going to try to solve it on their own.

First thing a mathematician does is simplify the situation.
Second mathematicians look for patterns

Private Universe Project 2: TEACHERS BUILDING PROOFS

This video takes place in Englewood NJ. The principal has invited Arthur Powell, Associate Professor at Rutgers University - Newark, to work with Englewood teachers, grades K through eight. She hires Arthur Powell to implement a professional development initiative that encourages teachers and students to think deeply about problems and to justify and convince others about their solutions.

The goal of the workshop:
1) Introducing teachers to a new way of working in the classroom; having them pay careful and close attention to what students actually do and say.
2) To have teachers rethink how they view themselves in front of mathematics.

During the workshop, Arthur asked the teachers to work on combinations problems such as - How many different towers four blocks high can you make by selecting from blocks of two colors? For each solution, teachers explained and attempted to convince the others that they had found all possible towers, four high.

The main focuse of this video is getting to the idea of teaching mathematics; the improtantce to get involved in looking for justifications. The basic idea of mathematics is the idea that we can look at patterns and relationships and try to understand the underlying reasons why those patterns and relationships exist, given the particular mathematical objects. And in reasoning - in understanding why they exist - one is developing ideas of proof.

Often teachers teach to teach the lesson. It is important to teach the skills and the thinking process to help understand why things happen. Students may know how to solve a problem but it is also important to understand and be able to explain why their solution is correct.

Virtual Math Manipulative

The virtual math manipulative I picked this week is:

Fraction Bars

I felt this virtual math manipulative game would be a great way to reinforce the lessons taught using Cuisenaire Rods

Here is an example of it being used to cover the giraffe

How to use:
1) Students pick the length; then new
2) They can click on the bar they created and choose a color for that bar
3) Repeat to make other fraction bars

Lesson Plan 2: Cuisenaire Rods

I took my lesson from the cd; it its called: Cover the Giraffe

Materials:
Cuisenaire Rods; 1 rod of each color per child
Cover the Giraffe worksheet; several pages per child
Crayons
Overhead/Elmo Cuisenaire Rods and/or Cover the Giraffe transparency

Objective:
Children will cover the outline of a giraffe using a specified set of Cuisenaire Rods. They compare their work and try to identify as many different solutions as possible.

In this lesson children will develope spatial reasoning

• visualize a region as the sum of component parts


• find multiple solutions

Procedure

• Outline the shape shown on 1 centimeter grid paper. Then copy and distribute it.


• Challenge children to cover the outline using only 1 white rod, 2 red rods, and 1 light green rod.


• Establish that several different ways of covering the shape are possible.

ON THEIR OWN
Work with a partner. Each of you make your own cuisenaire rod staircase.
Now use the rods from your staircase to completely cover a giraffe that looks like this (model)
Compare your work
Record both solutions if they are different; Record just 1 of them if they are the same.
On other worksheets, find more ways to cover the giraffe. Record each way.
When done we will discuss and share as a group.

Lesson Plan 1: Cuisenaire Rods

The lesson plan I choose was from the CD.

Build a Boat

Materials:
Cuisenaire Rods 1 set per pair
1 centimeter grid paper
Overhead/Elmo to display Cuisenaire Rods
1 centimeter gride paper transparency if using overhead

Objective:
Children will create "boats" using Cuisenaire Rods. They will then make an estimate how many white rods are needed to cover the shape of their boat.
In this lesson children will:

1. Discover numerical relationships among the rods
2. Develop strategies for adding

Procedure:

Review: Ask how many white rods would be needed to exactly cover a yellow rod.

Model 5 white rods would be needed to cover the yellow rod.

Make a train of 2 yellow rods. Ask how many white rods would exactly cover this 2-car train.

Now explain today's activity/model

• Work with a partner, build a boat according to these rues:
• use at least 5 rods; but no more than 10
• make the boat lie flat
• use any colors except white
• estimate how many white rods would cover your boat
• check your estimate by figuring out the exact number of white rods that would be needed. Find 2 ways to do this
• Record how many of each color rod you used in your boat. Record the total number of white rods.
• Leave your boat in place. We will discuss as a group when everyone has finished.