From the angles video and case studies, I saw just how hard it can be for some students to define exactly what an “angle” is. I can’t say that I was really surprised by this, because to be honest, I would probably have a difficult time trying to come up with a justifiable definition as well. It’s funny, we use mathematical terms all of the time, but I think we rarely examine them to the extent that we saw in this video and read about in our case studies.

I also noticed that many children seem to confuse the length of the sides of an angle, or the edges of a shape, to an angle. I think it’s important to make sure your students understand that the actual length of the sides or the length of the edges of a shape have no correlation to do with the actual degree of an angle. I can still draw an obtuse angle, with “little” sides.

Both the video and case studies demonstrated students thinking “out of the box” as well though. For example, in the video, one little girl was trying to make the point that angles don’t have to be created from straight lines. I also thought it was exceptional how she pointed out that a straight line doesn’t need to be drawn vertically or horizontally, but can also be drawn at a slant, diagonally. Just because you draw a diagonal line, doesn’t mean that it’s not straight.

Many of the children also tend to use their hands when describing an angle, and although I think this typical for many students to “talk with their hands”, I also think having students draw their interpretations is sometimes better (as young kids tend to fidget). And as we saw in the video, when they used both of the hands to demonstrate, they didn’t have a hand left to point out the angle they were trying to create!

I also found it interesting that a lot of students are able to identify the bottom angles in a triangle, but forget about the “top” angle. In the case studies, the teacher noted that she thought this was because the bottom angles look more like the examples of angles that students are typically shown. I never thought about that before, but I think it’s really interesting. It’s kind of like our old case study, where students didn’t recognize an obtuse triangle as a triangle because it didn’t look like the isosceles triangle they were used to seeing depicted as a definition of a triangle. I guess that’s why it’s so important that we provide our students with several unique images, and make sure that they understand the definition of the different geometric terms as well.