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.