Curricular Proposal: Modularity

Objectives

To have children gain a beginning understanding of the powerful idea of modularity as it applies to problem solving: the idea that complex problems can be solved by solving simpler sub problems.

To have children gain an understanding of this by thinking through and implementing a solution to a particular programming problem using MicroWorlds logo.

To have children reflect on and document their work along the way (including what worked and what didn’t work) as well as document at the end a description of their program broken down into the steps needed to accomplish the overall programming task.

Rationale

Children are continually confronted with complex problems in school which they need to solve. Rather than teaching them rules for problem solving in the abstract or showing them step by step how specific problems can be solved, they would benefit from environments where they are able to construct their own understanding of rules for solving problems. The activity of creating a computer program to “solve” a programming problem is one means where children are given the opportunity to do this. By reviewing the process whereby they arrived at their final solution they gain an understanding of how the original problem they were presented with related to the actual smaller problems along the way that they needed to solve in order to come up with their final working solution.

Standards

Problem Solving
“Problem solving is both a means of developing students’ knowledge of mathematics and a critical outcome of a good mathematics education. As such, it is an essential component of the curriculum. A mathematical problem, as distinct from an exercise, requires the solver to search for a method for solving the problem rather than following a set procedure. Mathematical problem solving, therefore, requires an understanding of relevant concepts, procedures, and strategies. To become good problem solvers, students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships, and solve problems in both mathematical and everyday contexts.”

Process

The steps in my curricular activity will consist of the following:

1. Play turtle. The children will play the game “turtle” where I give them verbal commands, forward 2 steps, right 90, etc. and have them carry out the commands and then figure out what shape they have “drawn” with their bodies. They can then each take a turn of playing this with each other.

2. At the computer, I will demonstrate the commands, fd, bk, rt, lt in logo and then allow the children time to explore with these commands as they wish.

3. Play a game in logo to learn how to move around the screen. I will create a project with 4-5 planets placed at different spots of the screen. Using the commands they learned in step 3, I will challenge each child to “visit” each one of those planets with their turtle using the least number of commands.

4. Have the children each create a definition using the commands in step 3 to draw a square, rectangle, triangle and circle.

5. project - Have each child design an animation using at least 2 shapes. This will include creating a background scene using the graphics editor in logo and then defining the 2 procedures to implement their animation. I will show them an animation I created initially and then demonstrate the basic animation techniques.

Design notebooks: At the beginning of this curricular activity, I will give each child a design notebook to record their work both using pictures and words and any math calculations they may need to do. I will ask them to use the notebook to record:

a. any figuring out they need to do
b. record any problems they encounter
c. record how they solved those problems
d. anything else they may wish to record regarding the activity

4. After they have finished their projects, I will have them document in their notebooks their complete “solution” (the breakdown, what problems needed to be solved (programmed) and then combined to accomplish the programming project) by referring back to notes they have made previously in their books. I will also ask each of them to verbally describe their projects, including how they felt about the activity.

I will work with 2 children in the 2nd grade over two 3-4 hour sessions. Session 1 will cover steps 1 and 2 and session 2, steps 3 and 4. Each child will be working on their own computer, however I will encourage them to discuss and share their ideas and solutions, ie work collaboratively as much as they wish.

Materials

2 Macintosh computers with MicroWorlds logo installed
Notebooks
pencils

Special Considerations

Given that I will be working with 2 second graders and I am not sure of their capability using logo, I will adjust the difficulty level of the project as needed. Both children I will be working with have a lot of experience using computers (for their age) so I am hoping the prospect of learning to use the computer in a new and potentially exciting way will maintain their interest level throughout the activities. If not I will have to adjust the amount of time involved in the project accordingly. Also since the girls are only in 2nd grade, their experience with recording work in notebooks is limited. If it turns out that this aspect of the project is too time consuming and tedious for them, I will resort to having them do the explanation part of the notebooks verbally and I will tape record it or record it myself in a separate notebook. Since we will be involved with the activities for 3-4 sessions, I will plan a break every hour to move around physically and have a small snack.

Evaluation
I will use the following criteria to evaluate the success of this curricular activity:

1. The children understanding of the concept of modularity as evidenced by their final descriptions and documentation of their programming tasks.
2. The children’s interest and involvement in the activity.
3. The children’s understanding of the logo concepts presented.

Documentation

I will document this activity as follows:

1. The children will each document their own work in a notebook.
2. I will observe and make notes of their progress as they are working.
3. I will take screen shots to document their projects along the way.
4. I will tape record certain pertinent dialogues along the way as well as each child's last description of her project. This will enable me to participate in their dialogues and still keep a record, as well as have a record of their final descriptions.
5. I will take a few pictures of the girls using a digital camera.