Module 12

Coordinate Grids

List the websites that you explored and discuss which ones you would use in your own classroom? Discuss the advantages and disadvantages of using online programs in the classroom? 

http://www.shodor.org/interactivate/activities/GeneralCoordinates/
http://www.beaconlearningcenter.com/weblessons/GridGraph/default.htm
http://www.shodor.org/interactivate/activities/MazeGame/

I liked the maze game as an activity to do in the classroom. All the websites were fun and incorporated points on a grid different ways. The disadvantage of the maze game is you can select any points on the grid to make a maze. You are not having to locate specific points. The beacon learning center game does require you to figure out points 1-5. The sight however is not very kid friendly.

Did you find any websites that you like? What were they?

Miras, Reflections, and the Kaleidoscopes

After you’ve completed all the activities, take a picture of the boy on the swing set showing how you were able to successfully use the mira. Have you ever used a Mira before? Did you find any part of this problematic? How did this build on your understanding of transformations? Discuss the ideas from the article that you will take with you into the classroom.

This was my first mira activity. I had never used one before. I had trouble getting the mira just right to make an accurate reflection. These activities were very fun. It helped me better understand transformations by having to perform them. In the article they mention that for students to have a better understanding they must learn more than the definitions. I think that the activities discussed in the power point and article can give the students a visual representation of the word reflection.

Was the mira hard for you to do? Have you done anything like this?

Case Studies

Respond to the following questions in your Blog:

1. What ideas about measurement do the children in Barbara’s class (case 12) bring to school before they are taught about it?

The students were discussing the size of the box and emphasized on the box being big. They then started comparing themselves to the box. The pointed out the box was bigger than certain students.  The students were asked how they could measure the box at school, and the students began using objects in the class to measure the box. They tried bins, a chair, and books.

2. Many children struggle with the idea that the larger the unit, the fewer the number of units needed to cover a length. Go through the cases by Rosemarie (case 13) and Dolores (case 14) to identify how different children are making sense of this issue.

In case 14 Dolores, the students were given the scenario of two boys measuring a room. One got 30 steps and one got 43 steps. Students had varying conclusions like one miscounted, one took longer steps, and one had bigger feet. All the students had different understandings. on case 13 Rosemarie, the students wanted to measure the distance using hand and feet. They made the connection that they could not use hand and feet. They must use things the same size to get the right measurement.


3. In Dolores’s case, line 245, Chelsea notices that Tyler and Crissy both measure the width of the basketball court as 62 “kid feet.” Why didn’t everybody measure the width as 62 kid feet? What discrepancy is Chelsea noticing? What is Henry noticing? How are their observations related to the issue that arises in Sandra’s seventh-grade class (case 17)?

Not everyone had 62 because of the varying shoe size and mistakes made. One student mentioned when comparing the measurements that some of the measurements were the same or close together. Later Chelsea made the conclusion that people with bug feet take fewer step.

How would you demonstrate to the students that the different lengths mean the unit they are using are different sizes?

4. The children in cases by Mabel (case 15) and Josie (case 16) are working out the use of standard tools for measuring length. Specifically, the children in both classes discuss how to place the tool and how to read the number of units. What do the students have to say about these two issues? What do they understand about measuring with accuracy and precision?

They discuss using a ruler to measure objects. If the object is longer than the ruler, you have to use several rulers. If you do not have a more rulers, then you can out your finger and move the ruler. The students also discuss that when using your finger as a place holder, it can alter your length a little because of your finger. If you have to do this several time, it may make a big difference in length.

5. By comparing the cases from second, third, fourth, and seventh grades to Barbara’s kindergarten (case 12), can we identify ideas that, by the older grades, are understood by the children and no longer warrant discussion. What are some issues that still lie ahead for Barbara’s students to sort out?

The older group discussed measurements using various terms and were able to understand how to measure objects with different types of units. The younger group needs to work on their vocabulary and how to describe objects when comparing sizes.

For further discussion

A fellow teacher says that he cannot start to teach any geometry until the students know all the terms and definitions and that his fifth graders just cannot learn them. What misconceptions about teaching geometry does this teacher hold?

This teacher is relying on the fact that students need to know definitions. You shouldn't strictly rely on the students vocabulary knowledge. In the article, the author mentions "Geometry is more than definitions; it is about describing relationships and reasoning".

Did you have a different misconception? What do you recommend when teaching geometry? Definitions?

Now that you’ve had some time to explore the world of geometry, how has your view of the key ideas of geometry that you want your students to work though changed? 

My view has changed. In school, I remember learning definitions. It wasn't until later grades was I required to show what each term meant. I think that the best way to learn and understand geometry, you have to show students examples while teaching the definitions. Working with just definitions and minimal examples can be confusing, especially for lower grades.