Primary Geometry Lesson

Srinivasan, et al. (2006) describe the learning process as described by the learner’s prior knowledge, ability and motivation.  The amount of load placed upon the students working memory by a learning task, “cognitive load”, enhances or diminishes their individual learning experience.  Not only do educators need to account for this appropriate cognitive load, they are also searching for effective tools to motivate students.  Some of the factors influencing student motivation include: challenge, fantasy, curiosity, novelty, interest, and importance/value.  Additionally, educators search and explore digital technologies and/or virtual simulation to further enhance the learning experience.  As described by Finkelstein, et al. (2005), these digital tools provide visual representations of hidden concepts.  Effective digital tools/simulations are designed to be highly interaction, engaging, highly visual, build explicit bridges between students’ everyday understand of the world and its underlying physical principles, and make physical models visible.

The below unit plan takes Sinclair and Bruce’s (2015) findings that “students perform quite poorly on a wide range of geometry tasks” (p. 319).  They found that almost every country based their primary school geometry curriculum on the study of two-dimensional shapes.  They reason that educators fail to see that geometry provides the basic meanings of mathematics: representations, models, visualizations, analogies and physical materials).  Incorporating the digital, social, inquiry and visual nature of each of the instructional frameworks from Module B, my goal is to create a unit that is engaging and motivates my students with playful tasks and exploratory lessons.

 

Topic: 3-D Geometric Shapes

Grade: 2

 

Motivation/Hook: Accessing previous knowledge

• While holding up models of a 3-D shape:
  • What does this shape remind you of?
  • What shapes do you see?
  • How are they connected?
• Scavenger hunt: Can each table group please find me two items in the classroom that has this shape? How did you know these were the same?

 

Familiarity:

• In pairs ask students to group the shapes without providing any criteria for alike shapes.
  • Why did you choose these groups?
  • How are these similar or different?

 

Teacher Guidance:

• Introduction of edges, faces and vertices (shape attributes)
• During group discussion, provide each student with the shape for students to twist and manipulate (visual and kinetic interaction)

 

Technology Integration: Virtual Manipulation

• Example tools provided by Sinclair & Bruce (2015)
  • Kidpix, Piece Puzzler, Geometer’s Sketchpad, Cabri-geometre
• Shape manipulation through tough screen and dragging
  • Is it the same shape if a stretch it? What if I rotate it?

Research has indicated that young students are more creative and create more complex and prolific patterns when using virtual manipulation than when using concrete materials.  This may be because the shapes can be snapped into position and stay fixed (you can stack to spheres on top of each other without them falling over) (Sinclair & Bruce (2015).

 

Applying Understanding

• Students use the above tools to design and create a 3-D character or object
  • Why did you choose these shapes? How would these shapes stay together?  What different sizes did you choose?
• 3-D printer to bring their vision to life (aided by an older buddy class).

 

 

 

Finkelstein, N. D., Adams, W. K., Keller, C.J., Kohl, P.B., Perkins, K. K., Podolefsky, N. S. & Reid, S. (2005). When learning about the real world is better done virtually: a study of substituting computer simulations for laboratory equipment. Physical Education Research. 1(1), 1-7.

 

Sinclair, N. & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education. 47(1), 319-329.

 

Srinivasan, S., Perez, L., Palmer, R., Brooks, D., Wilson, K. & Fowler, D. (2006). Reality versus Simulation. Journal of Science Education and Technology. 15(2), 137-140.