Week 6 Blog Post
For my one focus student, I used an example from a playground to illustrate a math concept. Students were beginning a lesson on solving inequalities and equations, and the math concept that I wanted them to all grasp was always making sure to perform the same operation to both sides of the inequality/equality.
Since all of the students in my class just went through elementary school and are familiar with various playground objects, I used an example of a see-saw to illustrate the concept of keeping two sides of an equation in balance. I asked students to picture themselves sitting on a see-saw with a smaller cousin/sibling/etc. on the other side. This would imply that the student was on the ground, and the smaller cousin/sibling/etc. was in the air. I then asked what would happen if they were both wearing 5 pound backpacks, and removed the backpacks at the same time.
This was to illustrate that as long as we added or removed the exact same amount of weight from each side of the see-saw, the relationship between the two sides wouldn't change. This concept was then translated into its math equivalent, and I spoke with the student about the importance of always performing the exact same operation to both sides of an inequality/equality.
I also wrote all academic terms that were being used in the lesson on the board, and left the definitions up for the entire class period while the students were working on the exercises.
This actually seemed to work very well - when students were working through the exercises, they all referred back to the see-saw illustration to justify why removing the same quantity from both sides of their equations was OK to do. They also referred to the academic terms on the board, and used them in discussions with each other. The focus student I was paying particular attention to actually used the see-saw illustration to justify his answer to a question I asked him involving subtracting "x tiles" from each side of an inequality.
Looking back, I do wish we'd moved on from the see-saw analogy, and using algebra tiles, a little faster. It seems like students grasped the illustration well, and grasped using algebra tiles well, but started to get confused when they were faced with purely algebraic inequality/equality solving. This confusion slowly dissipated as we continued to practice solving inequalities and equalities algebraically.
Since all of the students in my class just went through elementary school and are familiar with various playground objects, I used an example of a see-saw to illustrate the concept of keeping two sides of an equation in balance. I asked students to picture themselves sitting on a see-saw with a smaller cousin/sibling/etc. on the other side. This would imply that the student was on the ground, and the smaller cousin/sibling/etc. was in the air. I then asked what would happen if they were both wearing 5 pound backpacks, and removed the backpacks at the same time.
This was to illustrate that as long as we added or removed the exact same amount of weight from each side of the see-saw, the relationship between the two sides wouldn't change. This concept was then translated into its math equivalent, and I spoke with the student about the importance of always performing the exact same operation to both sides of an inequality/equality.
I also wrote all academic terms that were being used in the lesson on the board, and left the definitions up for the entire class period while the students were working on the exercises.
This actually seemed to work very well - when students were working through the exercises, they all referred back to the see-saw illustration to justify why removing the same quantity from both sides of their equations was OK to do. They also referred to the academic terms on the board, and used them in discussions with each other. The focus student I was paying particular attention to actually used the see-saw illustration to justify his answer to a question I asked him involving subtracting "x tiles" from each side of an inequality.
Looking back, I do wish we'd moved on from the see-saw analogy, and using algebra tiles, a little faster. It seems like students grasped the illustration well, and grasped using algebra tiles well, but started to get confused when they were faced with purely algebraic inequality/equality solving. This confusion slowly dissipated as we continued to practice solving inequalities and equalities algebraically.
I absolutely love this analogy! Using analogies to explain math concepts is severely underrated. I'm definitely going to use this idea in my own classroom. Maybe to connect the analogy to the math, you could represent an equation like x + 2 = 23 as a see saw, where you have 1 backpack and 2 pencils on one side of the see-saw, and 23 pencils on the other side. This could help bridge their understandings, I think, as long as they already know that x and 2 are not "like terms," while 2 and 23 are like terms. I can imagine it would be hard for students to connect this to division though. For example, if they had a problem such as 5x = 15, it's hard to visualize splitting up one see-saw into 5 smaller ones. If you started with adding/subtracting problems, and then build up to multiplying/dividing, maybe the transition from the see-saw analogy to the problem-solving could be smoother.
ReplyDeleteDear Ken,
ReplyDeleteThank you for sharing your successful ideas for bridging the academic knowledge gap for your students in math.
I love your text-to-world connections that you made with your students by using the see-saw example. That is something they could all relate to and it sounds like it really helped them visualize the concepts you were teaching.
You are smart to write the academic terms (and their definitions) on the board for students to access throughout the lesson. I can see where that would be very helpful!
I appreciate your insights into making content more accessible for all of your math students, Ken! They are lucky to have you!
Sincerely, Julie Elvin