Teaching Math, for all to learn By: Molly Heidtke

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! 

Sheridan- Noteblog Week 2

I see many connections between the readings in the Cognitively Guided Instruction book and the math used in my field placement. The field placement that I am is in a first grade class and I observe math every day that I go in. Math is a huge part of the curriculum in my school because the school that I am in, Colt Elementary is an early education program. The school is kindergarten through first grade. The readings (chapter 4) talked about using counters, or other tangible objects in order to solve multiplication and division problems. The students in my class are mostly working on addition and subtraction programs, but sometimes multiplication or division problems are thrown into their math worksheets. They are used to using their counters and solving problems using this type of manipulative. I feel this is very useful because the students are actually seeing what is happening with the numbers. My class is also starting to use grouping my tens. In chapter 6 they were using larger numbers in their examples than we use in our classroom. For example, an example in chapter 6, page 78 is: “The school bought 6 boxes of markers. There are 24 markers in each box. How many makers are there all together?” Most of the students in my placement do not have enough knowledge to solve a problem like this. They need more work on grouping with groups of tens. Last semester in my placement, students were just starting to use the tens-frame to look at numbers 1-10. This week, they are starting to use two tens-frames to look at numbers 1-20. Some students are struggling with the concept that if one of the tens-frames is completely full, that means that there are ten counters in the spots. Some students still count each individual spot in both frames, instead of counting on from ten and then moving to the second tens-frame. I do feel like most of the students in my placement have basic addition and subtraction problems down, and I’m curious to see how the students do when we move to multiplication and division problems.