Module Twelve

Coordinate Grids

The websites that I explored were: 

Gregs Grid Graphs- I thought this site was a good one. It has the student first figure out the coordinates by matching the letters to the coordinates. The it shows the points with letters and the students need to write out the coordinate. One thing I notices though is that it states that the coordinates are written with parentheses but when the site has you write out the coordinates it doesn't allow enough typing to do so. This could confuse students in the long run and not use parentheses. 

Stock the Shelves- I think students would think this is a fun game to play. It makes you be completely accurate on clicking your points, if you are even a little bit in the box and not on the center of the 2 lines it counts it wrong. This is something that students could do to practice to make sure they are understanding where coordinates are. This also includes negative coordinates so it would probably be better for students who have had a little time working on coordinates not students just starting. 

Math 6 Spy Guys- I like how this one includes a lesson before allowing the students to do the fun activities. This way if students are having issues they have something they can go back to and look at for help. The "math fun" activity is something that I think the students would find interesting. I'll admit it took me a little bit to understand what it was asking me to do. This activity would have to be done in pairs. You could also do this activity without a computer. I'm not really sure what it has to do with coordinates though. 

I would probably allow my students to use the first 2 activities I listed as I think they could really learn from them and they would have fun with it. Advantages of using online programs in the classroom is it gives the students extra practice and also gives them something to do if they finish their work early. Disadvantages are the students might not actually be doing their work like they are suppose to and there is really no way to grade if they are doing it correct or not. 

Did you look at any of the same websites I did? If so, what were your thoughts on them?

Miras, Reflections, and the Kaleidoscopes

No, I have never used a Mira before. I dont ever remember even seeing one before. I had a little bit of difficulty with using the mira as if you moved if just a little it made a big difference in what you were looking at. I really liked how in the one worksheet it asked us to draw what we thought it would look like and then use the mira and draw what it looked like and then compare the two. I think this is something that would really help students understand transformations. 

I thought that the activities in the article were all very informative for the students. I think allowing students to do activities like this would help them to better understand the concept them just looking at pictures of images that how been transformed. 

What did you think of these activities?

Case Studies

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 in Barbara's class are able to compare two objects to one another and state whether they are bigger or smaller than one another. When Barbara asked her students of ways to measure the box they said with a measuring stick (described like a ruler to me) and a tape measure. They also showed that they knew when measuring you have to start at one end and go to the other. 

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 13 the the students are having a hard time understanding why the teacher will take a less amount of steps to complete the length even though her foot is the biggest. They think that because Miriam took the most steps that means she has the biggest foot, which is wrong she actually has the smallest. 

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 62kid 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)?

They are noticing that the width can be different depending on who is measuring it because not everyone's feet are the same length. Also since they are walking a pretty far distance it could be really easy for the students to miscount. These observations are related to the ones that arise in Sandra's class because they all walked the same length but some of different answers. 

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?

In both of these cases the students begin to figure out the best ways to measure items and the best units of measure to use. They also began to understand that in order to accurately measure something you need to use units of measure that dont change. They also realize that they need to measure from the start to the finish to get an accurate measurement. 

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?

I believe that in each grade level the students learn more and understand more about measurement. Having the students do activities like their teachers had them do and talk about the different concepts helps the students to better understand measurement. I think measurement is a concept that each time students talk about it they will learn more and go more in depth on how it needs to be done and the best ways to complete it. 

What did you learn from these case studies about teaching measurement?

For Further Discussion... 

Every student learns at their own time and pace. You can't wait for all your students to understand something before moving onto the next part. Many times students will learn to understand a term or definition more when they have examples to look at and see what they actually mean and how they actually work. Instead of focusing so much on the students understanding terms and definition teach the students about geometry using hands-ons activities, it will help them to better understand the terms they might of not been understanding before. 

Before exploring the world of geometry I really thought it was all about shapes and that was it. Boy, I was wrong. I now see that geometry is so much more. From perimeter, area, coordinates, etc. Learning about geometry can be really fun for students as there are so many hands on activities for them to do. I still am not a wiz at geometry and will probably always struggle with it but learning all these fun activities to help teach it has made it a lot more enjoyable. 

Has learning about geometry in this class changed what you think about geometry?