Brad's Readings

By The Unit or Square Unit

Intro:

• This article poses a very interesting question to the students. They ask "For the school carnival, sponsors will pay for advertising their products on signs. How can the school make the most money: by charging the sponsors by the square unit of area or by measuring the perimeter of the signs and charging by the linear unit?"

Why Area and Perimeter are Difficult?

• Students put borders on things or cover something with paint. However, the true meaning of common terms are not understood by students.
• Students struggle to grasp the non constant relationship between perimeter and area.

Class 1

• Presented the question above to students with examples
• Examples all had area of 100, but perimeters varied
• Students also talked about units used to measure different things correctly

Class 2

• Measured different objects irregular and regular to compare perimeter and area numbers
• Students realized the concept of objects more like a square have less perimeter

Class 3

• Much the same as the other two classes
• Proposed the question of how to find the area and perimeter of a shoe print accurately.

Importance of Lessons

• The longer the shape the greater the perimeter
• The area can be the same but the perimeter different
• The more balanced the sides the bigger the area.

Summary Quotes

"Some procedural knowledge is always necessary to do mathematics efficiently, and short ways of computing perimeter and area by adding or multiplying are worth knowing. However, children also need to develop conceptual knowledge of the fundamental properties of these topics."

"Some educators might argue that discovering the relationship between perimeter and area is an extension activity - a pursuit for more advanced argue that such relationships are essential to mathematics. All children should have the opportunity to work with problems for which the answer is not immediately evident..."

Why Do Some Children Have Trouble Learning Measurement Concepts?

This article was mainly written about 1st graders:

• It found that 1st graders can learn a great deal about measurement, though Piaget's theories don't suggest so.
• Most benefit comes from concrete instructions and evaluation.
• Experience, experience, experience... is most beneficial

Integrating Measurement Across the Curriculum

A big thing from this article I took was the fact that measurement is in every subject and tested for. However, the other subjects have some sort of instruction and measurement is just expected to be understood. The article recommends the following which will probably benefit us the most.

• Students should have varied experience with measurement tools
• Integrating across subjects
• Students should communicate measure processes and results
• take advantage of real world connections
• take advantage of special occasions ex. olympics