This weeks reading primarily focused on new ideas to
teaching math. In the reading “Children’s understanding of equality: A
foundation for Algebra.” The author discusses the importance of having a
thorough discussion of the algebraic principle and the placement of the equal
sign. I found this article to be very interesting in the sense that my second
grade class is learning the idea of the placement of the equal sign and filling
out a problem to make it equal on both sides. Unfortunately I was not able to observe
my teacher, teach this to the students, but I found it very relatable that
students need to learn these ideas at a young age. When I was introduced to
algebra in middle school, I was confused on how to balance an equation and I
think by introducing this idea to elementary school students, they will be more
successful in later years.
The second idea that was based off this weeks reading was
the idea of allowing students to come up with their own idea of solving a
problem and also using open-ended questions to further trigger their previous
knowledge on problem solving. I observed the idea of allowing students to solve
their problems their own way last semester in my placement. The students showed
several different ways that they came up with how to add 16+7. Some students
showed that they used their hands, some drew on their papers and others just
showed how they wrote out the problem (horizontally and vertically). I thought
it was interesting that the teacher allowed for all students to show their findings
of solving problems and found that to be rewarding to all students and the
teacher, in the sense that the teacher has a better understanding of how each
student solves their problems. Allowing for the teacher to help the student if
they get stuck.
Overall, this weeks readings allowed for me to explore new
ways in teaching math. I plan to use open-ended questions as a math teacher as
well as take most of Reinharts ideas in ways to help students explore how they
would want to solve a problem. One main idea from his article that I found it
very interesting was when he said not to carry a pencil around, looking back at
my mathematic experience, teachers would walk around and basically solve the
problems for the students rather then allowing them to figure it out
themselves. The next time I am in the classroom I plan to help students without
doing the work for them!
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ReplyDeleteI like the idea of having students come up with solutions to problems on their own. I feel like math is a subject that is tough for some students. The solving of math problems really show that all students think differently. Some students are visual learners, and sometimes it might be hard to incorporate visuals into teaching math. It is very important to incorporate visuals in teaching math for those students who need it. I think it is so important, especially in the early stages of school, for students to explore different ways to solve problems. Although I think it is important for students to solve problems on their own, I think it is important for teachers to teach different ways to come up with answers. Students might only use one method because it is the only one they know. If the teacher uses many different methods of problem solving in her teaching, students can explore different methods and find which one works best for them.
ReplyDeleteIn the article, "Never Say Anything A Kid Can Say" by Steven Reinhart, the teacher talks about how she had to change her teaching to suit her students. She explained that she knew the content well and could deliver the content to the students, but the way that she was doing it was not helping the students. The teacher in this article was focusing more on product rather than process. She wanted to switch the focus of her math teaching from coming up with one specific answer, to reflecting on the process that occurs when figuring out an answer. The students were encouraged to ask questions and express how they were solving a problem. This method helped the students with learning the math content.
I like the idea of working on groups to solve math problems. When I am in placement, whenever I observe math, the students always work independently at their desks. Sometimes they copy off of each other, and sometimes they don't do the work. I feel like if the students worked in groups, there would be more pressure for the students to complete the work. They can also get insight into how other students in the class solve certain problems. One focus of the Reinhart article is, "require several responses to the same question." When working in groups, students will have to come up with multiple ways to solve a problem. If students are working independently, they may not be able to solve the problem in different ways. If they are working in groups, they can come up with many different ways together.
Reading these articles made me think of math instruction in a much different way. I think that if my teachers in elementary school taught me to think about math processes and different ways of solving math problems, I probably would have been more successful in math, and liked it more.
The idea or strategy that I took away most from the readings was the thought of making math open-ended. One of the most frustrating things for me when it came to math was the fact that there was always one right answer and, in most instances, one correct process. I understand that math is just a subject that will have one specific concrete answer but it does not always have to be presented this way. In the Kabiri and Smith article, “Turing Traditional Textbook Problems into Open-Ended Problems”, they introduced problems that allowed for the students to come up with their own equations or problems from the numbers and directions that were provided. Providing these types of questions let the students come up with their own way of solving a problem. For me, the most important sentence out of the entire article was, “it is the approach that is open-ended” (Kabiri and Smith, pg. 187). The way I comprehended this was that, teachers do not always need to provide questions that are open-ended, although they are beneficial and having a good mixture of open-ended and traditional questions would be ideal. Traditional questions can be given as long as the teacher allows for children to have an open-ended approach to solve the question. Students need to be able to find a style that fits their own and if that is allowing them to solve a question different from the teacher’s way, than so be it. It is important that students learn different problem solving skills, it will only be beneficial to teach them more ways to solve a problem than less.
ReplyDeleteWith this open-ended idea in mind, it leads to all the other articles and ties them all together. In the article, “Never Say Anything a Kid Can Say” talks about how it is the process of coming up with an answer rather than the specific answer itself. Promoting an open-ended approach to a problem allows for the process of a problem to be the focus rather than the correct answer. Also, if a teacher takes on this approach, it does not allow them to just answer the questions for the students if they need help on a problem. They will be more focused on helping the student obtain the steps of solving a problem rather than looking for the correct answer.
These ideas are all very important to remember when teaching math in elementary school. From my own experience, it is so meaningful to have math be a subject that students enjoy and have fun with in elementary school or else they will not like it throughout the rest of their schooling.