What are the key ideas of geometry that you want your students to work through during the school year?
During the school year I would start by having my students recognize all of their shapes by naming them first. After students were able to visually recognize their shapes I would want for them to be able to draw them, describe them, and label them. Once the students understood the shapes and their attributes I would want my students to then start to learn the terms of ray, line segment, angles, planes, and all the other geometric terms that they will be exposed to during their time using geometry. I feel like teaching the students these terms would help them in learning how to to measure angles as well as be able to tell the difference in isosceles, right, and obtuse angles. The students also need to be familiar that their are 2-D shapes as well as 3-D shapes and that although 3-D shapes favor 2-D shapes the way you measure them will be different. The process of learning geometry is like any other subject. You have to start with the basics and build upon them for students to understand the full concepts you are trying to teach them.
Thinking About Triangles:
How would you structure this lesson for students in an elementary classroom?
I think the way that the lesson was structured in the video was actually pretty to the point and was able to teach a strong lesson. I enjoyed how Dr. Higgins started out by getting students involved in the lesson by having them to look around the classroom and write down the different objects that they saw that were triangles. I would then lead a whole class discussion and have them to share the objects that they found and explain how they knew that the objects were triangles. I would then do the same thing Dr. Higgins did in her PowerPoint of having the students to think of words that started with "TRI" and have them to discuss what those different words had in common. I would then instead of moving the the geoboard activity as shown in the PowerPoint I would teach/review with students what an equilateral, isosceles, and scalene triangle were. When students were familiar with those terms and refreshed on them I would move to the geoboard activity and follow the same questions that were addressed in the PowerPoint lesson. I would then have the students to cut out their shapes they had recorded, find a partner, and group their triangles by similarities. I would have the students to discuss why they grouped their triangles like they did and also have them to find differences within the groups. The students may take a while to grasp all of the concepts and as the teacher I may have to alter my lesson to make sure all students understand. If I felt like the lesson was not going as planned when I introduced it I would stop it, rework it, and teach it again the following day.
What parts did you have issues with? Did you need to revisit some vocabulary words to
remind yourself of their meanings? If so, which ones?
I luckily did not have to revisit any vocabulary words because the triangle terms have always stuck with me throughout school...working with triangles was one of my favorite parts of geometry! I did have an issue tho in forming many right triangles without repeating any. I was able to only form 4 on my geoboard and put them on paper and I would love to see a visual of where all 14 triangles were to go. I found it to be difficult to not recreate the same triangles more than once as well. Maybe if the geoboards were bigger it would have been easier to create more?
Van Hiele Levels and Polygon Properties Article:
I found the article and the PowerPoint to be very interesting because I was not familiar with the levels until I viewed the PowerPoint and read the article. I do not think I have mastered what the levels are but I have gained a better understanding for sure. The PowerPoint talked about how most students that we would be working with would be in the 0-1 level and I can actually see that when working with the students I have in the past year.
The activity that was in the PowerPoint was one that I enjoyed and one that I would not mind doing with my students (if I was in upper elementary grades). I feel like the students would really enjoy it and be satisfied with themselves like I was when I was able to get the shapes correct. Knowing what I know now after looking at the PowerPoint, doing the activity here and above, and reading the article I feel more confident in teaching geometric ideas to my students. I understand now that it is in fact a process and that students need to learn their basic concepts and build upon them to be successful in geometry as they would in other areas of mathematics. In my classroom I hope to be able to make learning geometry a fun thing for my students as well as making sure they are grasping all concepts along the way.
For Further Discussion:
The van Hiele levels can be applied to geometric thinking concepts by concept or to one’s overall
thinking about geometry. How would you rate your own thinking? Does the level vary or remain fairly
consistent across the subject matter? For example, are you at different levels working with the
concepts of two-dimensional or plane geometry than working with three-dimensional or solid
geometry? Explain.
I would rate myself at a level 3 of: deduction. Level 4 of rigor I feel like is someone who is extremely proficient with their geometry skills and I do not feel like that necessarily applies for me. I feel like my level stays pretty much the same throughout the subject level except if someone was to put an extremely hard formula for me to decipher in relation to a shape. I may be able to recognize the formula and the shape and know what answer you are asking but not necessarily know how to find the answer. As long as I am familiar with what is put forth in front of me I would say that I would remain the same.
It seems to me like you had the same basics ideas of geometry as I had before this module began. I also believe that learning the shape names are one of the first parts of geometry. Geometry is all about shapes and their attributes and therefore students need to be able to identify basic shapes before they can identify more complex shapes. How would you teach basic shapes to students? I know that most kindergarten students should know these shapes already, but what if they did not? How would you teach them?
ReplyDeleteI also talked about teaching the geometric plane and angles and lines. At what grade level do you feel that these concepts should be introduced at? Do you think we should teach students the angles and how to measure angles before we teach them about the geometric plane and types of lines?
I also felt like the activity in teaching triangles was a really good one, and I would do it similarly. I liked how before you started to do the geoboard triangles, you would review the definition of each type of triangle. I feel like if we do not do this, then some students might just sit there confused because they do not know what we are talking about as a teacher.
I really enjoyed doing the attribute activity as well. It was fun and I was always excited when I got the answer correct. Do you think there is a way for us to use this same activity but with younger student?
I had never heard of the Van Hiele model either. I was really interested to hear about it for this reason. After hearing about it, I realized I have also seen it in the schools. How has learning about this model changed your thinking about how you will teach shapes in your class?
Hope you had a good fall break!
To teach basic shapes to students I would start by having a large visual to hold in front of the class, give the students the name, and its attributes. For example: this is a triangle. A triangle always has 3 sides. Teaching students angles I feel like may could be started in third or fourth grade but with the basics of right angle, obtuse, and acute angle. Students would need to know the basics on angles before they could work with them. I believe the geometric plane should wait until after teaching students about he angles but I feel like types of lines could be taught either before or after. I would not say "the same" activity for younger students but a similar one. We could have students to form triangles of different sizes (like in the powerpoint where no two triangles could be the same) and not give them exact names to follow by like: scalene triangle and so forth. Having students to do that may could lead into a small discussion of the different types of triangles. Also, an activity we may could do with younger children would be to have them to form different shapes of different sizes with the geoboards. In knowing what I know now I know that when teaching shapes it is a process. Students must learn the basics before they can more forth into harder concepts.
ReplyDeleteHope you did as well!
That is exactly how I taught my kindergarten student shapes last year when I was tutoring in the ed lab. He did not know basic shapes and would just guess at the names. I had shapes and would show him the shape and explain the attributes.
ReplyDeleteI also agree that I would teach the names of angles probably in fourth grade. I also think that the basic names of line segments like parallel and perpendicular could be introduced after this. I think I started to learn about the geometric plane in sixth or seventh grade.
I like the triangle activity. I feel like it gives students a way to practice making triangles. With the geoboards I would also have the younger grades making shapes, but I would use this as a way to help them remember shape names or review them. Like I could say, make a circle and students would soon find out that on a square geoboard, a circle is not possible to make a circle.
I am excited to know that you did that in your kindergarten classroom...makes me feel better about my ideas. Thank you for your feedback...it is always informational and helpful!
ReplyDeleteI just posted a lengthy message on here and somehow deleted it before it posted. Let's see if I can do it again...
ReplyDeleteThe triangle activity can be used as in introduction to different triangles which means you'd teach the vocabulary through the different phases. Though if it is a follow-up activity, reviewing the vocabulary does make sense. The activity with the van hiele levels is actually intended for the primary grades though the language I used is at a higher level. You can actually use the activity with any grade level.