Throughout Warrington's paper, she has many advantages and disadvantages to her idea of teaching children mathematics without procedures or algorithms. One of the advantages to this style of teaching is the idea that children, when they understand how to do problems, it will have been from their own thought process and would have created thinking in their part to get to an answer. An example of this is when she would ask fraction/division problems without teaching the children the "invert and multiply" rule. This then connects to the advantage of children having part of a relational understanding of the procedures they are creating in their head. Another advantage is Warrington's idea of constructivism of teaching the children new concepts by starting with a topic or concept they've already learned. As Warrington states, this helps them understand the new concept better because they are starting with something familiar.
Besides the advantages of Warrington's style of teaching, there are also many disadvantages. One of those is her idea of children not acquiring knowledge from other people. Yes people will think about things and come up with their own consensus on a concept or topic, but they need the influence of others in order to create their own ideas. Another disadvantage is how Warrington doesn't give the children answers. The procedure on how the child got to the answer is important, but informing them of the correct one is also important so they can move onto another problem and feel like they are understanding things correctly. The last disadvantage I believe Warrington has in teaching this way is that it takes the children longer to understand a procedure when they have to create it with their own knowledge. Many children think differently than others and may not have the prior knowledge enough to create that procedure on their own. Thus, if children are taught the correctly through relational understanding, they would learn the procedure as well as why they are using it for specific concepts or problems.
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I agree that this method of teaching takes longer. Since it focuses on developing a relational understanding we've read in previous papers and from experience this takes longer to get a handle of. But I don't believe that withholding procedures is always bad. Not giving the students the answers helps all students engaged in discourse in the classroom that is healthy conversation for young mathematicians.
ReplyDeleteI really enjoyed the points that you made. I agree that it is important to teach mathematics in a step stool sort of way. Meaning that you build upon previous, solid, understanding. When reading the disadvantages, one of them that was listed was that they are thinking on their own, and creating their own ideas, and without influence of others students would struggle to come up with their own ideas. I don't feel that Warrington ever suggested that the students should work in silence and independently, I actually felt that Warrington's class offered the exact opposite, an opportunity for students to express their thinking and justify their ideas to each other. I feel the need for influence from others would be easily achieved in the classroom described.
ReplyDeleteI really agree with that figuring out concepts on their own is an advantage to teaching this way. I have found in my life that most of the things I remember best are the things that I worked through on my own. Also, there is something fulfilling about doing it yourself.
ReplyDeleteThough not entirely necessary, I think one advantage I would have added would be that through struggling and working through this assignment the students are developing their ability to think critically, and they are becoming better problem solvers. This is a crucial ability that needs to be taught in the classroom.
You brought up some clear disadvantages. I don't think Warrington doesn't believe her students learn from other people. I think this is why she has her class discuss so much, so they can learn from each other.
ReplyDeleteI think that in Warrington's classroom students will actually have more confidence in the answer then they would otherwise. They have been able to reason why the answer is correct.
I wasn't sure what you meant by your last sentence. How would one teach "correctly through relational understanding"?
I think all of the disadvantages you listed are completely viable. I do however think that there are more advantages, such as students feel comfortable discussing in front of the classroom. They would gain self confidence as they bounce their ideas off of each other.
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