Module 11

Hello again everyone!

  I hope you all had a great week and are enjoying the decent weather we have been having lately. Summer is right around the corner and it's hard to believe that we only have 3 weeks or so left in the semester! This week's module was very informational as always. I have provided my thoughts and ideas about each section. The required posting topics are headed in bold red.

Tangram Discoveries--Solution

 

 

   It was really helpful to have the answers to the tangram activity we completed in the last module. While I did successfully say that the triangle had the greatest perimeter, I did not suspect that the trapezoid and parallelogram would share the same perimeter, thus making all three shapes equal in perimeter size. I am glad to see that I was correct about the square having the least perimeter because it's short length of sides. After reading the first part of the solution description, I realize that it would have been a lot easier to come up with the answer for this question if I was more familiar with the different types of shapes and their properties as well as the terminology that is used to described them. While I do know most of the words, I don't think I am familiar enough with using them to answer such questions. This activity has helped me see that I need to brush up on my knowledge of certain shapes and vocabulary.  

 

    I also provided the correct answer to the question of which shape had the greatest and least area. For some, this might have been a trick question because the answer is that no shape is the greatest/least because they are all equal in area. Similar to what I mentioned in my blog, Dr. Hargrove's solution page explains that since all shapes share identical parts, then their areas will also be identical. Nevertheless, I can see how this can be a tricky question for anybody by just looking at the shapes. If I had not put the shapes together to form he polygons, then I probably would have given an incorrect response simply because other shapes look bigger than others. Just as the solution page suggested, sometimes looks can be deceiving, even in math! Just a thought.

 

 

Coordinate Grids

 

    It was interesting to think about the idea of teaching young students about coordinate grids and mapping. I can remember learning about these things in late elementary school but recall being taught about it a lot more in middle school. As we have learned in past modules, both the Common Core and NCTM standards call for students to learn spatial reasoning skills and applying them to real life scenarios. I believe that teaching them about graphing and mapping in the early years will help them develop the skills they need to meet standards in future math courses. Children in the younger grades can even be taught certain concepts by using directional or positional vocabulary, just as Dr. Hargrove mentioned. This is really something to keep in mind for my future teaching!

 

   As instructed, I explored links on the Internet4Classrooms website and enjoyed playing through each of the games available. I think each of the activities would be great to use in the classroom with students. They are fun ways to help them become familiar with the coordinate grid system. I explored each of them but for this blog posting, I will only highlight a few of my favorite ones (excuse the blurry pictures).

 

Billy Bug 2 (#2 on list)

  I thought this was a cute activity. The objective is to move the bug to the given coordinate points on he 4-quadrant graph so that he can eat food at that spot. You click the arrows to move up and down and click FEED to check the answer. I think this is a fun way for kids to explore the different sections or quadrants of a coordinate plane.

 

 

Coordinate Geometry (#4 on list)

   This activity involves matching coordinate points with their designated points of angles and segments shown on the grid. I think this would be a helpful practice activity after students learn about coordinate geometry. Since there are specific words students might not know like "angle", "segment", and "vertex", they might be better off learning specific terminology before attempting the activity. Nevertheless, I think it can help them learn ways to find coordinates on the grid because it tells you whether or not your answer is correct.

 

 

Maze Game (#10 on list)

    At first, this game was a little confusing but once I figured it out, it was actually kind of fun. The game involves selecting a number of "mines" be randomly placed on the grid. The objective is to create lines by connecting lines from different sets of coordinates without coming in contact with a mine. I think kids can have fun trying to dodge the mines as they practice using their coordinate graphing skills.

 

 

What's the Point? (#18 on list)

   This is another activity students can use to practice recognizing coordinates with multiple choice answers. A point is plotted on the grid and then you choose the coordinate points that match. I like that users can adjust the difficulty level by plotting points on one quadrant of the grid or all four.

 

 

After working with each site and activity, I considered the questions given in the module checklist:

 

What websites did you explore and which ones would you use in your own classroom?

      I explored each of the listed websites and think the different activities would be helpful in an elementary classroom. Of the sites on the list, I really like math.com because it covers a range of mathematical subject like basic math, algebra, geometry, and more. I like how the website is broken down into different subcategories so that you can focus on a specific concept. These sections give users a first glance of a lesson then takes them through 3 other steps: an in-depth explanation, examples, and individual practice. This would possibly be a good website for students to explore to refresh their memories of specific concepts before transitioning into a new section.

     Another great website featured on the list is called MrNussbaum.com. This site allows you to explore different lessons/activities related to a variety of subjects. For the math portion, users can choose what math category to explore and the games and activities that will help them develop a deeper understanding of the concepts. I think this is one site that would really appeal to young children because the games are fun and interesting.

      I also liked exploring the Shodor Interactive website (http://www.shodor.org/interactivate/) because you can do advanced searches for activities, lessons, and discussions within specific mathematical categories. The different sections provides users with a lesson, practice activity, and options for help with additional resources. Moreover, I really like how the lesson sections offer educators tips and advice on how to teach the concept, lists the related curriculum standards, and explains how the activities can help students. Very interesting!

     

What are the advantages and disadvantages of using online programs in the classroom? 

    I think one major advantage of using online programs in the classroom is that they can help make learning fun and engaging for students. Essentially, students have some sort of control in terms of the pace in which they complete activities and in their ability to revisit specific sections as often as needed. I think learning through online games helps meet the needs of various learners and can help students develop the technology skills they will need later in life. Moreover, such programs can be accessed at home where parents and other family members can work with their children to see what they are learning in the classroom.

    Some disadvantages to this would be that online programs don't provide enough structure to the learning experience that traditional class lessons can, which can cause a loss of motivation or willingness to do the activities. Some students that don't have the necessary skills to complete an activity might not be able to fully understand an assignment. I think the biggest disadvantage is the fact that since lessons are given through videos or tutorials and not through face-to-face contact, it might confuse a lot of students. As a UNCW extension (online) student, this is a problem I encounter pretty often. It's always easier for me to understand something when it is explained in person, even if I am a visual learner. Students than might need the hands on experience to learn more effectively might not get much out of online programs that strictly use visual cues or reading.

 

 

Miras

 

  This was an interesting activity! Other than my semi successful attempt to use the Mira in the last module, I have never used (or even heard of) a Mira. I will say that this is an amazing little tool! I think this is something all teachers should consider using in their classrooms to introduce students to the concept of symmetry.  It was helpful to be guided through the Mira PowerPoint activity and learn different ways to use the tool in geometry.

 

  The first part of the PowerPoint had us using the Mira to trace the image of a boy onto a swing. I thought I did a pretty decent job even though I lost my line of symmetry because it was kind of hard to see where my pencil was going over the lines.

 

Next, I completed the activity that involved predicting how the given curlicue would look when reflected on the other side. Here is an image and description of my prediction. I said that I thought that the original image looked a little like the lowercase letter "e", so I just made the letter backwards. As you can see, I kind of messed up a little hence the eraser marks on my paper. This is where I quickly realized that I drew a translation or "slide" of the original image.

 

 

  After completing this part, I used the Mira to draw a more accurate symmetrical representation of the image. I traced the outlines of the curlicue and then shaded in the middle. It's not perfect but I think it shows that I was somewhat successful in creating a similar image with my prediction. The Mira was obviously helpful in creating a symmetrical image.

 

 

 

  This section also explored the concept of congruence. As instructed, I thought about my own definition of what congruence means:

   congruence: A characteristic that shapes have when they are equal in size and shape.

 

I was surprised that was correct in my definition because I really wasn't sure. I did use my experiences from past modules and other experiences to develop my idea of what congruence really is. The activity that accompanied this section was a little confusing at first but working with it for a few minutes helped. I had trouble rotating the Mira the way I wanted it in order to line up the symmetrical images. Nevertheless, I was able to find the same answers Dr. Hargrove shared.

 

I like the idea of having students practice the concept of symmetry by designing their own symmetrical shapes. As instructed, I drew a straight line and then developed my own half of a shape. I drew a flower-like image where I wanted the curves to resemble petals. Here is an picture of the half-drawing and then a picture of the completed drawing I did using the Mira. My picture didn't turn out as I had expected. I think it looks more like a cloud than a flower.

I then explored using the Mira to find the symmetry of shapes given the worksheets. For Symmetry sheet #1, I had some trouble finding lines of symmetry for the two parallelograms. That is why they have question marks on them. The same goes for the two shapes I couldn't find lines for in problem A1. For the question on the bottom of the page, I chose to describe the symmetry of the pentagon. I simply said that it had 5 lines of symmetry because it was a regular pentagon. A regular pentagon has 5 equal sides, thus making it have 5 lines of symmetry.

 

 

 

 

 

     The last part of the PowerPoint addressed the idea of alphabet symmetry, something that I had never really considered before. I used the Mira to find possible symmetry lines in each letter of the alphabet. I’m not sure if I have the correct answers but here is the chart indicating what I found. I also answered the questions asked within the PowerPoint. My responses are shown in the image below.

 

Questions from module guide:
Have you ever used a Mira before? Did you find any part of this problematic? How did this build on your understanding of transformations?

 

      As I mentioned before, I have never really heard of a Mira before. I think I have seen them a few times but never knew what they were or how they were used. As I worked, I did encounter a few problems trying to line up the lines/parts to trace over. Also, for shapes/images that were very close together, it was a little hard trying to position the Mira at the right angle. Despite certain issues, I love the idea of using such a tool to reinforce geometric concepts like symmetry and transformations. It was helpful to use the Mira when predicting what a reflected image would look like. In my case, the tool helped me see certain mistakes you can make when making transformation. For example, someone might think they have created a symmetrical images when they actually just did a translation or “slide”.

 

TCM Article – Reflections and Kaleidoscopes

 

    I enjoyed reading this article because it involves the idea of using a toy that children are usually fascinated with: kaleidoscopes. I think it’s great that such a lesson makes learning about math relevant to young students because it is something in which they are familiar. Moreover, I like how the detailed lesson focuses more on getting students to make predictions and discover answers using reasoning and justification. It’s great that the lesson also calls for students to practice reflections using the Mira tool.

  I thought it was really neat to read about how kaleidoscopes originated, how they are made and how they produce the unique images they do.  The directions for making the kaleidoscopes were a little hard to understand at first but I’m sure if I had the necessary materials, it would make more sense. I think the actual process of completing the activity and using the finished product would certainly help children connect concepts of symmetry and transformations with tangible objects.

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?  

  I don't think it is accurate to assume that children cannot learn certain geometric concepts until they know all of the terms or definitions. It is certainly helpful to be able to know specific words to explain something but it is not necessary to understand the concept. I am reminded of a set of case studies we read a few modules ago featuring students that struggled to put their ideas into words. While they used non-mathematical terms like "slanty" and "stretched out" to described triangles, the students still had a way of understanding what they saw and experienced. Essentially, I believe that children learn best from exploring a new concept firsthand before being given a lot of information about it.  

 

 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?

    I don't think they key ideas I wish my future students has changed too much. I still hold onto the same things but have gained a much deeper understanding of just how important teaching children geometry is. In my initial response to this question (from module 7), I mentioned that I wanted to students to really understand the concepts I teach instead of just memorize the facts like I did as a student. Having considered the necessity of learning vocabulary words, I realize that this is not as important as knowing how to apply learned ideas to the real world. My view has changed in that I now know that a child's knowledge of geometric concepts can help them develop other skills and abilities they will need in real life--like spatial reasoning.