In Erlwanger's article, he makes the point to his readers that using Individually Prescribed Instruction (IPI) is not successful when trying to help young students understand mathematics. The sixth grade subject, Benny, is a smart child. As he studied the rules that go along with fractions, he found patterns that were not necessarily correct. For example, since he knew 3 +5 is equivalent to 5+3, then he carried that communitive property over to say that 1/2 is equivalent to 2/1, which is not true. When there is no teacher there to explain why this does not work, Benny has no reason to believe he is doing anytyhing wrong. Right along with this reasoning, when Benny gets the correct answer, he doesn't know why it is correct. He tells Erlwanger that his answers are graded just by a key, and even if the answer is true it will get marked wrong just because of the key. This instills in Benny the idea that mathematics is just applying rules to try to get the same answer as the key, rather than explaining to him that the answers are right, and a teacher can show him why and how. A student-teacher relationship is necessary for students to progress in correct and accurate mathematics as well as to help the students learn to enjoy math.
It is imperative today to keep up this student-teacher relationship to prevent students from "plugging and chugging" with incorrect procedures. This goes right along with the instrumental verses relational understanding, and, in this case, the instrumental understanding does not even consist of the correct rules, let alone the correct understanding of how and why the rules can be applied. If young students today are not given the guidance they need at the early stages of mathematics, then when more concepts are tuaght to them they will not have any foundation to build upon and so their understanding will decrease rather than increase. Our responsibility as educators is to help students learn mathematics, and the only way we will help them is if we are personally teaching them.
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I totally agree that it is important that students and teachers have a good relationship in order for the students to better understand the material. It is important that the teachers are aware of their students and how each student is doing in the class. I was just wondering what this relationship would consist of. What sorts of things should a teacher do so that the "Benny" incident is no longer repeated?
ReplyDeleteNot to leave you the same comment as Haley but I also agree with you that having a strong student-teacher relationship is crucial to the success of students. Like you said Benny was a smart kid but still came up with the wrong answers. I think it would have been beneficial to include in your post what educators should be doing to prevent this. What type of evaluation and correction could happen in the classroom to help students gain a correct understanding?
ReplyDeleteI think you make a valid point in stressing the importance of teacher assistance in math classes. It is very important for students to understand why procedures work the way they do, especially as they advance to higher level math classes. I don't know if I agree with you on the point that this causes their understanding to decrease, rather I think it disallows progression of understanding.
ReplyDeleteYou did an excellent job of presenting the issue of teachers connecting with the students. I agree that teacher student contact is very important but I wished I could have read more of how to accomplish this.
ReplyDeleteI really liked how you mentioned "plugging and chugging." If students don't have the proper teaching they will resort to this method of guess and check. How much should the teachers personally teach them? How much individual time should the students be allowed?
ReplyDeleteYou have a good, solid topic sentence.
ReplyDeleteI thought the last sentence of the first paragraph was a good insight that Erlwanger wanted to get across. I might have introduced that in the beginning of the paragraph as a main point that Erlwanger was writing about.