Chapter 3 Reflection

What are the key ideas presented in chapter 3?

• connecting meanings and relationships to addition, subtraction, multiplication, and division
• addition and subtraction are connected
• subtraction names a missing part
• addition names the whole in parts
• multiplication takes counting in groups, multiplication is repeated addition
• multiplication and division are connected
• division names a missing factor
• models can be used to solve any mathematical problem
• models can be used with any problem or any number size
• you can use models to make number sentences make sense

How do these ideas inform your understanding of teaching numbers and operations?

The ideas set a foundation and give a deeper meaning and understanding to teaching numbers and operations. The chapter also metioned that addition is not "put together" and subtraction is not "take away". As a teacher I must remember that children should not have limited definitions or understandings for addition and subtraction because later they will have trouble understanding that addition and subtraction can be used in different forms. Connecting problems to children's lives and keeping the problems in context is very important. The ideas presented in chapter 3 helped open my eyes to new and different ways to solve math problems other than the traditional ways I learned. I must keep in mind that the children do not have the mathematical skills that I have developed, and solving problems in different ways and thinking about different ways to solve problems can help me facilitate students more efficiently. I liked how the text highlighted avoiding key words. When I was in elementary school, I was always taught to look for key words. After reading the explanations as to why key words should be avoided, I now understand why I should not stress using key words. Problem analysis and explanations are very important in mathematical processes. Explanations can be particularly helpful in understanding why a student solved a problem a certain way or how he or she got an answer to a problem.

Week Three Reflection

Your reflection question for this week relates to chapter 2. How does the information and the tasks presented in chapter two connect to the videos of lessons you viewed as part of challenge 5?

Much of the information and tasks presented in chapter 2 have to do with subitizing and quick number recognition. The tasks allow for math tools to be used. The tasks also allow for exploration and independent problem solving for all students. The tasks require more than just talking about numbers; they require children to analyze numbers and objects and compare them. The ideas and tasks presented provide a foundation for mathematical processes that can be used with larger numbers and computation of numbers.



What task (activity) in chapter two was most interesting to you? Why?

I liked activity 2.9 the Dot Plate Flash because the dot plates seem like they would be easy to make and use. Students could make their own and drill each other in a center to help develop pattern recognition skills. The dot plates can be used at any time of the year and any time during the day. They require little clean up and would not be a distraction to others if others were working on something different.

Week Two Reflection

How did each article help further your understanding of your topic area?

subitizing-instantly seeing how many
perceptual subitizing-recognizing a number without using mathematical processes
conceptual subitizing-viewing number and number patterns as units of units

• Subitizing is more accurate than counting
• Counting does not imply the understanding of numbers
• Subitizing is a precursor to counting
• There are two types of subitizing: perceptual and conceptual
• Some argue that subitizing cannot be taught

Subitizing is a very unfamiliar word to me. Subitizing is crucial in helping children recognize patterns, understand numbers, conserve, and understand arithmetic and place value.

• Children need to know how to decompose numbers
• Reasoning helps with working with large numbers
• Composing an decomposing are important for understanding parts and whole
• Dots and patterns should be used in a quick image format
• Seeing and describing quick images helps with flexible thinking and sharing of ideas
• Quick image activities are not a replacement for concrete activities
  

Quick image activities can help with number fluency. Students will learn more about number patterns and combinations through quick image activities rather than counting by ones to solve problems.

• Students should invent and examine ways to solve problems on their own
• Tasks make all the difference in students' abilities to solve problems
• Students should be given the chance to explore on their own rather than watching a teacher
• Students form their perceptions of subjects by the kinds of tasks they do
• Tasks should allow for reflecting and communicating
• Tasks should allow for students to use knowledge and skills they already possess
• Tasks should allow students to use tools; tools should be suitable

Tasks should allow for students to explore and think for themselves. Students will not be interested or completely compotent in math if the only way they learn math is by watching the teacher solve problems on the board. Students need to explore on their own and come up with their own ways and strategies to problem solve.

The articles showed me different ways to help enhance students' learning in math. I agree with all of the articles in that it is important that students learn to solve their own problems by first gaining an understanding of numbers and symbols. If students do not have the basic knowledge of numbers, symbols, and patterns, they will not know how to efficiently problem solve. Teachers need to do less teaching on the board and more scaffolding and mentoring to help children learn and explore math by making up their own ways to solve problems.