Mental Math T-GEM

My posting for this week involves the T-GEM cycle and the interactive “Make a Ten” activity from PhET. I believe this would be particularly helpful in the lower elementary classroom, as the way in which the visualization is organized, and the speed in which one can manipulate numbers makes it ideal and quicker to use than traditional manipulative tools. This simulation shows an example of how “…computers might be the best educational option for our students” (Finkelstein et al., 2005), using layering of numbers and essentially makes it an online and more improved/technology integrated version of the Numicon tools. Essentially, it provides a model-based inquiry for math manipulatives, but it’s responsiveness works much faster than using the physical pieces. While the articles I read closely this week were more geared towards the sciences, I found that much of the content could be applied to this mathematics simulation as well, as it deals with pattern detecting and creating rules. Xiang and Passmore write, “There has been increased recognition in the past decades that model-based inquiry (MBI) is a promising approach for cultivating deep understandings by helping students unite phenomena and underlying mechanisms” (Xiang & Passmore 2015), which I think applies to this tool.

Here’s the link to the simulation.

Generate:

• Students explore and play around with the simulation. Then, they look for as many different ways as they can make equation or number sentence for two numbers that have a sum of 10. Then 15. Then 20. Then 50.
• Students collect information about numbers and the patterns then can detect individually.

Evaluate:

• Students are grouped into threes and discuss their findings with their classmates. Collectively, they turn those patterns into relationships and rules for mental maths strategies.
• Students collate their rules and move around the class to have a look at how many of their rules match up with others in the classroom. Students take note of rules that looked different from their own.

Modify:

• Students review and test out each others’ rules, making room for comments and being ready to explain their thinking.
• Students go through the cycle again, assessing their strategies with subtraction, and looking for commonalities

As Finkelstein et al. write, “We do not suggest that simulations necessarily promote conceptual learning nor do they ensure facility with real equipment, but rather computer simulations that are properly designed are useful tools for a variety of contexts that can promote student learning” (Finkelstein et al., 2005). This tool is one such simulation that enhances student learning.

References:

Xiang, L., & Passmore, C. (2015). A framework for model-based inquiry through agent-based programming. Journal of Science Education and Technology, 24(2-3), 311-329.

Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physics Education Research,1(1), 1-8.