There are a number of advantages that teaching math without teaching algorithms can bring. One that is outlined in Warrington's essay is that students learn to construct knowledge and find meaning in sophisticated areas that are difficult to truly understand. This is brought about through the careful creation of an environment where students are not afraid to discuss with each other and think for themselves. Students are allowed to be creative and are not "shackled by rules and conventions" that limit creativity. This was illustrated in the experience of Warrington giving the class the word problem about chocolate-covered peanuts.
Disadvantages of teaching math without teaching the algorithms are abundant. As Warrington presented each new question to the class, she would allow for as much discussion as was necessary for the students to get the right answers. If this was done in all classrooms, much material would have to be cut due to lack of time. I do not think cutting necessary topics from the curriculum is an ideal choice of action. A second disadvantage of teaching math without teaching the algorithms is that only the truly interested student will learn and participate. I do not feel every single student in this sort of classroom setting would be fully engaged or comfortable in thinking completely independently, and this could become frustrating and trivial for a number of students. Algorithms and easier to hold on to, and the less-creative mind may have an easier time getting through the course materials with them.
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I agree with the advantages you mentioned. I think that when students aren't given algorithms from the get go, they are more willing to expand their thinking which leads to the development of discussing ideas with one another.
ReplyDeleteI think a disadvantage that could be included is when students aren't told right methods or answers, they may end up developing a framework of misconceptions and false ideas as did Benny.
I really liked your disadvantages. You explained and illustrated them well. And I agree with you. I did wish for more advantages listed with more information from the paper.
ReplyDeleteAnother advantage that could have been included was that students are able to develop independence and autonomy like the girl who disagreed with everyone else. I thought that was fascinating. I do like how you took a different take on the article and strongly advocated the disadvantages.
ReplyDeleteWow, is there really only one advantage to this method of instruction and an "abundant" amount of disadvantages? It seems that you did not value Warrington's instructional method very much. While I am very comfortable with disagreement and value students being able to form their own opinions, I sometimes worry that students don't give new ideas or experiences a chance before they reject them. I would encourage you to think a little more about what might be valuable in this type of teaching, if for no other reason than to further shape your ideas about what you hope your students will learn and be able to do when you have your own classroom.
ReplyDeleteI agree with you that if this was the method of instruction for the whole year, some things would have to be cut from the mathematics curriculum. I also agree that some students may not engage with this type of instruction, but that is also true for other forms of mathematics instruction. The current way of teaching mathematics leaves whole classrooms of students disengaged by the time they reach high school. Do you think this way of teaching might engage more students in the long run?