"Benny's Conception of Rules and Answers in IPI Mathematics" is a journal written by Elrwanger. In this article Elrwanger spends time with Benny, a student of this IPI program. He notices that Benny has misconceptions of rules with fractions and decimals. For example, Benny thought 2/10 was equal to 1.2. Through questioning Benny, Elrwanger found that Benny had made up rules. This reasoning Benny had made pointed out that students need a relational understanding and a strong one from the very beginning. If they don't have this understanding, then they can become lost and make up their own rules. Benny must not have fully understood a concept, so he made up a rule by himself. Benny had been doing this program since from 2nd-6th grade and he had a lot of misconceptions to unlearn and had a lot of new conceptions to learn.
Relational understanding is really key from the beginning, even now. It is hard to change a student's ideas about a concept once they have made up their own rules, and especially if they have been using this rule for many years, like Benny. I feel it is necessary to really get with the students and make sure they fully understand something. I remember my teachers teaching an idea/concept and then we had a worksheet to enforce the concept. To see if we had understood the concept, they would go over our worksheets herself. A lot of my teachers tried hard to make teach relationally because it is easier to come up with concepts, then having to memorize them all. If you don't give students a good base from the beginning, it is going to be really hard for them to build off of misunderstood information.
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I definitely agree with you second paragraph and can totally relate. Whenever I had a bad math teacher I would try to get a new one as soon as possible. Sadly in Benny's case, he didn't have that option.
ReplyDeleteIn your first paragraph though I didn't really find a topic sentence and felt more summary than anything else. Especially with your short sentences it felt like, comment. stop. comment. stop. etc. Though then like I said before your second paragraph was much better. Thanks
I agree with Kyle that your second paragraph is really nailing a modern-day problem in mathematics education. The teacher is really what makes or breaks a math class and it is their job to teach so that the student understand. They shouldn't just be a means to get the equations.
ReplyDeleteThe only problem I ran into with your blog was that I didn't know what the main point was until about halfway through the first paragraph. My suggestion is to make the topic sentence tell what the whole paragraph will be talking about.
You have a lot of really great ideas about how to make sure that students understand the concepts behind the procedures being taught. I think it is a great idea to be close with the students to make sure they are really understanding the reasons and concepts of why certain operations and procedures are done. I got a little confused with all the uses of the word concept. I felt like concept was being used for two different things. Great blog!
ReplyDeleteI agree with your perspective on math teaching today being about worksheets. I had the same experience. I would have liked a stronger topic sentence in your second paragraph as well as firmer points to hit; then using examples to back it up.
ReplyDeleteYour specific examples of Benny's misconceptions are great!
ReplyDeleteI would have gotten to the main point a little sooner in the first paragraph.