After
going over the readings for this week’s class, I was really intrigued by the
Falkner and Kabiri articles. In Children’s Understanding of Equality: A
Foundation for Algebra, Karen Falkner, Linda Levi, and Thomas Carpenter
discussed how many children are very closed minded when it comes to the meaning
of the equal sign. Many of the
students from the article believed that in an algebraic equation, the equal
sign only means the answer. This
is of course false in a problems like 8+4=_ +5. In the article the authors state, “even kindergarten
children, however, appear to have enduring misconceptions about the meaning of
the equal sign” (Carpenter, Falkner, & Levi, 1999, p.233). This shows that this misconception is
rooted early on, so in grades as early as preschool and kindergarten, it becomes
imperative to teach the right thing.
I believe this article ties in very well with the article by Mary Kabiri
and Nancy Smith titled, Turning Tradition
Textbook Problems into Open-Ended Problems.
If
we as teachers can create more open-ended problems not only will our students
expand their thinking, but concepts like the equal sign, will have more than
one meaning. In the article the
authors state, “Often, when teachers plan instruction for their student’s, they
focus on the middle achievers…However, many problems can be made more
open-ended and accessible to a wide variety of student abilities with minimum
effort” (Kabiri & Smith, 2003, p.186-187). They go on to explain that this can be done simple by taking
traditional textbook answers and adding an “additional dimension” where more
than one answer is possible. So
far in my placement, I have not seen many open-ended questions in math,
however, I am excited to see if I can somehow incorporate these type of
questions into my lesson plan to see how the students react to a new style of
questioning.
I had a very similar reaction to the, Children’s Understanding of Equality: A Foundation for Algebra, reading. It seems that Mathematics carries with it the idea that there is one clear path and solution to each problem. Teachers that I have observed in various placements tend to center their math lessons around drills, repetition, and worksheets. While these methods can help students learn math facts it is most definitely a very dry, meaningless way to teach students math. I think so many people struggle with math simply because they are only being taught one way to look at and solve problems. Using this way of teaching prevents students from inquiring and engaging in math activities. Each student learns differently so a group of 30+ students cannot possibly be expected to effectively learn one to solve a problem.
ReplyDeleteAdmittedly, before taking this class I hadn't really considered the idea of teaching math using open-ended problems. Based on my own experiences, math has always seemed like a question and answer type of subject in which the teacher tells the students how to solve a problem and the students' progress is assessed on whether or not they correctly answer each problem. As you can imagine this puts a lot of pressure on both the teacher and student. But, by creating open-ended questions I think students will feel more confident to try problem solving their own way, and teachers will feel better knowing students are able to foster their own learning. Even in the Kindergarten setting I am placed in right now, it always amazes me how much better the students are at explaining simple ideas to their peers than I am. As mentioned in the article, sometimes students learn better by listening to each others explanations rather than the teachers, so in providing open-ended questions we are allowing students to explore those different pathways.
I, too had not thought much about the difference between open ended questions and close ended questions before this class. As Caitlin said, I have always seen math as more of a questions and answer subject, where the teacher explains a topic and expects the correct answer from the students. This puts loads of pressure on both the teachers AND the student. I think that if students were presented with more open ended questions and allowed to work through them with their peers they would greatly benefit from this type of self education. I was working with some students in my kindergarten placement yesterday on a pattern worksheet that some of them struggled with. Most of the students who didn't understand simply asked me to help, but basically wanted me to do the sheet for them. It was after this that I had some of the students who did understand the sheet help the students who didn't. It was nice to be able to see the students helping each other figure out a difficult problem.
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