There are a many advantages to Warrington's take on teaching division of fractions to her students. One is that it develops a relational understanding before it even introduces an instrumental understanding. The students never attempted to "flip and multiply" because that wouldn't have made sense to them yet. Another is that the students estimated before they actually tried to get the right answer so they new an approximate range that their real answer should be in. This also shows that they were developing a relational understanding. Another plus to this technique is that Warrington didn't tell her students if they were right or wrong and let them lead the discussion in class, whether it was in small groups or the whole class. This allows students to feel safe in the classroom and let them share their ideas without the fear of being wrong because no one actually knows if they're right or wrong.
There are disadvantages to this technique as well. One is the fact that it takes a lot of time to go through this kind of discovery process with every kind of mathematics that you come across. In some cases, it would be so much faster to slap an algorithm on the board and call it good. Another disadvantage is that if there's one student who understands right away, they kind of inhibit other students' learning because they are not given the time to figure it out completely on their own. I know if classes that I've been in that sometimes I just wait around for one of the "smart kids" to bust out an answer, sometimes because I have no clue what's going on but sometimes because I'm just lazy.
9 years ago
I agree with both your advantages and disadvantages. I know in the long run it is better for the students to teach them constructionally i am just worried that it will only benefit the 'smart kids' as you said.
ReplyDeleteI agree that making students estimate first really helps with a relational understanding of fractions. Up until this class I haven't even really thought what dividing fractions was really all about.
ReplyDeleteSomething I have been wresting with is whether it is okay that only the "smart kids" are the ones benefiting from it. Maybe that is okay because the other students are using a crutch no matter what so maybe it helps those students that really do have a passion for math. I haven't decided if I agree with what I just said yet.
Great job using topic sentences and backing your advantages and disadvantages.
ReplyDeleteLearning concepts this way also saves time because students understand the concept, so they don't have to take the time to relearn it every time they need it, and they can apply it to new situations.
I think that Warrington waits to give all her students time to think before she has people start explaining. However, I agree that some students will wait for someone else to solve it. But I think students would be more likely to think for themselves in this classroom than they would in one where they knew the teacher would give them the answer and procedure.
Yes, I totally agree with you disadvantages, especially the part about waiting for the smart kids to figure out the answer! I thought this was very well written but I think it would have been nice to maybe include why the students not using the invert and multiply rule shows that they had a relational understanding.
ReplyDeleteI really like the point you made about students feeling "safe" in the classroom. I think that this is integral to providing the kind of environment in which thinking, not just answer chasing, can actually happen. If the students feel that their ideas are just as valid as anyone elses, then they are going to be more willing to contribute their own ideas.
ReplyDeleteAs for dealing with the "smart" kids and their followers, I am tempted to use a certain applicable saying - "You can lead a horse to water..." If a child is determined not to think, they will always be able to find a way.