This week I decided to use the T-Gem model to create a lesson on mixed numbers as a way to build on students knowledge of fractions. In a fractions unit before moving onto mixed numbers students should have a strong understanding that a fraction is part of a whole. When students begin to learn about mixed numbers and improper fractions they often struggle to see what they mean conceptually as they have spent so much time learning that fractions are part of a whole.
As Stephen and Clements (2015) mention, before using any simulations students should have adequate background knowledge. Therefore, I added a simulation activity in the Evaluating Knowledge and Modifying Knowledge sections. The first activity in Generating Knowledge is a way for teachers to assess what students know already about mixed numbers and how to represent them, followed by an activity where the class can unpack what they mean together. Next is when they move to apply what they learned in the simulation activity followed by a reflection.
Srinivasan et al. (2006) discuss how simulations are compelling and can help motivate students but you cannot simply tell students that simulations are the same as real life. Students need to be able to apply their knowledge in real-life contexts as well. Therefore, to build on these activities, I would blend more simulations using programs like Mathletics and Khan Academy with hands-on materials like fraction towers, fraction circles, etc. Once students reach a strong conceptual understanding, my ideal summative tasks would involve a real-life application such as using money.
References:
Srinivasan, S., Perez, L. C., Palmer,R., Brooks,D., Wilson,K., & Fowler. D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 137-141.
Stephens, A. & Clement, J. (2015). Use of physics simulations in whole class and small group settings: Comparative case studies. Computers & Education, 86, 137-156.
Stephens & Clement (2015) commented that “teachers were surprised that there appeared to have been no pre/post advantage for students in the small group condition. This was true even though small group participants had had the advantage of hands-on experience with the simulations, the time for each and every student to raise questions with group mates and with the teacher, presumably a more relaxed atmosphere in which shyer students could speak up, and the increased engagement the teachers reported for the small group work” (p. 148). I liked how you made students work in groups and then individually with the simulations. Was this an intentional strategy on your part? Also, I was wondering about your thoughts on the pedagogical effectiveness of small groups.
Cheers!
Gordon
Hi Gordon,
It was intentional but for different reasons. With the age group that I work with (ages 8 &9), I find it hard for them to work together efficiently when going online and participating in simulations. They are still working on their teamwork, collaboration and group decision making skills so often when they work online together one person tends to take over and do the work, or neither. I find it very useful, however, for students to problem solve and collaborate together with hands-on materials. Their communication is very effective and productive.
Hi Sarah,
I really appreciated that you used both hands on manipulatives (in this case tangerines) as well as a simulation, to help your students with the concept of mixed numbers in your lesson plan. I think all of these activities would help students to build on their knowledge and actually visualise something being more than one whole. One aspect of PhET that I found very helpful was the different levels within each simulation. This makes differentiation easy – students could be on a task that suits their ability but all using the same technology! I find fractions to be one of those topics where there are some students who take much longer to grasp it. Do you imagine that you may have some students still a step behind or on a different level of the PhET simulations?
Thanks for your post!
Kathryn
Hi Katherine,
I would definitely imagine that some students would still be behind, and others more advanced. I am very fortunate to work at a school with a Learning Enhancement Team LET). Therefore, if students are struggling the LET teacher will work with these students and perhaps modify the lesson or assist them with it. Additionally, for the students who are advanced, an LET teacher will often pull them out and give them an enrichment activity.