Investigating Triangles

Using one of the instructional frameworks in Module B and one (or more) of the digital technologies in this lesson, create a concise lesson activity that addresses this misconception.

This week’s material fit in well with my week at school which was spent investigating and constructing triangles with my grade 6 class. The students in my class are eager and able and I wanted to challenge them to combine their knowledge of angles, measures and shape. An example question would look like this: In triangle PQR line PQ measures 7cm, angle P is 35 degrees and angle R is 47 degrees. Find the lengths of the other sides and how large the last angle is by drawing a diagram. I gave each group rulers, protractors and compasses and the investigation phase was great – it worked very well! But when it came to going over our work I found using my interactive whiteboard a bit clumsy, as I was rotating the ruler and it was difficult to measure. I didn’t even know how to get a compass up and could have to switch between my IWB and my white board, using homemade compasses and protractors. It wasn’t that smooth of a lesson! I kept thinking to myself that I wish there was a simulation tool that the girls could use to stretch and manipulate their diagrams and understanding. Srinivasan et al. (2006) argue that in order for simulations to be effective they must be pitched at the right level. If the simulation is not challenging enough, or on the other hand too challenging, then it will not going to have the intended benefits. The digital technology that I explored this week was Geometers Sketchpad and I could completely see how this would have enhanced my triangle investigation. I have designed a lesson based on the similar concept of triangles I did this week in my classroom, but also included the T-GEM concept.

Generate

• Start the lesson with in the same way with pencils, rulers, compasses and protractors.
• Ask, if we have two angles and a side given to us, how can we figure out the remaining measures and angles of a triangle?
• Students work collaboratively to investigate.
• Discuss findings and methods as a class, but the teacher should not say if any answers are correct or incorrect at this point.

Evaluate

• Students to go on Geometers Sketchpad in groups and work though the same questions on the platform. If it if one of the first times using the platform, the teachers could give a brief introduction to the platform and demonstrate how some of the tools work.
• Each group should now compare the answers they have when they used physical tools and when they used the simulation. Are their answers the same or different? Did they use the same method/steps to find the answer?

Modify

• Teacher to use IWB to display and work though questions on Geometers Sketchpad.
• Discuss findings as a class.
• Discuss the students opinions about using the simulation and reflect on the benefits and drawbacks of both.

One drawback of Geometers Sketchpad is that it is quite expensive and you would have to use it frequently, throughout the entire school, to justify it. I personally find geometry and shape concepts more difficult to teach, as it’s difficult for children to visualise certain concepts. Sinclair and Bruce (2015) argue that geometry in general more gets little attention, particularly at in primary school. They claim that although the importance of spatial reasoning is growing, the fact that geometry affects many other areas of mathematics and thinking hasn’t fully caught on yet. Could simulations be the way forward for teaching geometry to young students?

References

Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM, 47(3), 319–329.

Srinivasan, S., Pérez, L. C., Palmer, R. D., Brooks, D. W., Wilson, K., & Fowler, D. (2006). Reality versus Simulation. Journal of Science Education and Technology, 15(2), 137–141.