RESPONSE: The author broke down his presentation into three different sections. After a brief introduction on the importance of Multiple Representation, he started his first section with the eight widely used representational systems used in the teaching and learning of mathematics. He followed with clear examples of three different types of representations, using the multiplication of mixed fractions as his example. And finally, in section three he gives the ten reasons to use Multiple Representations in the Teaching of Mathematics.
After reading several dry and boring articles on Multiple Representation, I found this presentation to be very clear and easy to understand. His mixing of visuals with the way his presentation is broken down was excellent way the different representations interact.
FIVE GOALS OF SECONDARY MATH EDUCATION
I must preface my goals by stating that I am new to the profession. I have a structural engineering degree and about twenty –five years as a project manager in the construction industry. I have spent one year teaching eighth grade algebra in the School District of Philadelphia. I am therefore coming from a less academic more career oriented approach to the goals of secondary math education.
- I was somewhat surprised, that the majority of students in my class suffered a weakness in the fundamentals of mathematics. Addition, subtraction, multiplication, division, fractions, decimals, percentages. The first goal should be, no matter the duration of time incurred, that all students be able to master the basics outlined above. Without a solid foundation, the struggle to understand more complex mathematical concepts will be frustrating and overwhelming.
- Another essential goal would be for the student to solve mathematical word problems. In other words, the ability of a student to use their mathematical skills in solving everyday practical problems. These problems do not have to be complex problems found in physics, but problems as simple as finding cost, interest, etc. The ability to develop problem solving strategies. They need to be able to visualize, describe and analyze situations in mathematical terms.
- Understand patterns, relations and functions. Specifically being able to generalize patterns using functions.
- Students should understand the fundamentals of algebra, geometry, statistics, probability and discrete mathematics and how they interplay.
- Understanding numbers, ways of representing numbers, relationships among numbers and number systems.
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