Stephens and Clements (2015) discuss the importance of students having sufficient background foundational knowledge before exploring and utilizing simulations. Simulations help to motivate students and create excitement, but students need to understand that there is a difference between reality and simulation which was discussed by Srinivasan et al. (2006). This lesson will be using the T-GEM framework and an interactive activity from Illuminations. Using interactive manipulatives are helpful for learners as it allows these students to work at their own pace, self-discovery and exploration. The activities can be adapted to the individual learner with the support of the teacher if needed. Further using technology allows for an engaging and interactive learning experience for students. It’s also important for student to be able to connect curriculum to real life scenarios, and technology allows students to make these connections.
https://illuminations.nctm.org/Activity.aspx?id=3510
G-Generate:
Exploration is key for students. This will allow students to ask questions they may have, and connect previous knowledge with knowledge they are gaining through self-discovery. Students will be able to practice the relationships between equivalent fractions and match each fraction to its location on the number line.
Students will use the interactive activity to explore. They will select “Build Your Own” option. Here students will be able to explore creating equivalent fractions by dividing and shading either circles or squares.
With students, go over key terminology and foundational concepts.
What are fractions?
What is a number line?
What is the numerator and what is the denominator?
What are the various ways to represent fractions?
Where do we use and see fractions in our everyday lives?
Students will generate a hypothesis regarding the relationships between fractions and how to create equivalent fractions and the relationship on the number line.
E-Evaluate:
During this stage, the teacher can pose questions that may not follow students’ hypotheses as this will allow students to evaluate the relationship. Teacher will also use equivalent fractions and have students create additional equivalent fractions. Here, students will have to use their numeracy skills to solve these questions.
M-Modify:
Teachers will ask students to represent fractions in lowest terms. Here students will have to use their multiplication and division skills to determine this relationship and apply their knowledge. How will students use their foundational knowledge and apply it to this activity.
Questions for students:
Can all fractions be reduced to lowest terms? What are the main “benchmark” fractions?
Can one fraction have many equivalent fractions? How can you show this visually and numerically?
How does multiplication and division relate to fractions? How are number lines useful to describe fractions?
Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.
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.
Amanda,
I loved how you tied so many things together in this post to show how all these theories can work together as one cohesive unit. By reading through your lesson, it’s clear how each section can help students question, consider, and test, making them all active learners and involved in the learning process.
One thing that I have to wonder, though, and this is by no means an attack on your lesson which I think is very well done, is if anything is lost by having students manipulate the fractions through a simulation instead of physical manipulative. Do you think there are any learners who may struggle to make the connections with the concepts since they are purely visual and not physical pieces? I remember the wooden pie pieces when I was learning fractions really brought the ideas home for me since you have the ability to stack them on top of each other and see how many added up to another one. I know the assignment this time was to use a visualization and I can see some students really enjoying manipulating the online version. I just wonder if we lose anything by making it not fully tangible.
With that said, I really like the questions you included in the lesson, especially the ones about benchmark fractions. That was a great way for students to anchor their exploration and make sure that they were fully understanding and verbalizing the learning that was happening.
-Jonathan-
Hi Jonathan,
Yes I agree that students should have the option of using hands on physical manipulatives!I should have added that component to my lesson. I teach struggling learners so my lessons are very differentiated. For example, for a lesson, I can have up to 6 students who all learn differently and in this case they would have the option of using simulations or physical manipulatives. Thank You
Hi Amanda,
What a great idea to get students to explore using an online simulation to understand fractions better. I really like the fact that you emphasize on the basic definitions in the evaluation part of your T-GEM.
In addition to the above, I really liked one of the questions you posed in the end:
Can one fraction have many equivalent fractions? How can you show this visually and numerically?
I think it is really important to ask our students to create something of their own and this is exactly what you are offering by posing such questions. It is one thing to be spoon-fed “good” teaching where a teaching uses online simulations to help students visualize their learning but it is important to take learning one step further, which is to encourage students to be in-charge and make something of their own. In this case, students can show their understanding in a visual way.
Thank you for sharing.
GK
Thank you for your comments Gursimran!
Do you enjoy using online simulations with your high school students? How do you integrate simulations within your practice?