# The Concept of Change in Mathematical Reasoning

Instructor: Lynne Hampson

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

In this lesson, we will discuss the concept of change in mathematical reasoning, defining and comparing the math reasoning of yesteryear to the reasoning of today.

## What Does it Mean to Change Mathematical Reasoning?

Change in Mathematical Reasoning is not likely to change the answers to math questions that have always been considered correct; the solution, sums, or products are still the same. The change comes in how learners can relate to math, and it focuses on increasing the ability to learn computation in a new and more profound way. The decade a person has lived in or is presently living in affects the shift in thinking that relates to this change.

## Change in Reasoning From Then to Now

The pedagogical goal for math education is no longer what students can memorize or repeat. The focus now relates to how students take what they learn and apply it to their everyday lives. These new ideas on teaching involve math as a part of life in a way by which learners can make reasonable decisions for themselves. In the past, directions were explained verbatim and students were scored on their ability to memorize and regurgitate.

For people born between the early 1980's and the early 2000's, an older philosophy of teaching promoted instruction that used a teacher/blackboard approach. The teacher would stand at the front of the room and write on the board, explaining the steps used in solving a problem. If a student was good at memorizing or taking notes to be used later for study and memorization, they did well with this type of learning. However, this is not to say that students retained the information or used it in real world settings, such as applying decimal addition to money skills.

Through educational psychology and an emphasis on HOW students learn, there has been a change in the way math is taught. This change will be ongoing (as with time, all things change). The last several years have brought about many new ideas about how students learn. Teachers are now taught to move away from the 'you-listen-and-I-speak rule' and instead become a facilitator of problem solving.

Around the early part of the new century, teachers were being encouraged to cultivate a different type of learning environment. Students have moved further away from memorization of math skills and have moved into a role where they work together in groups or on their own to figure skills out for themselves. Formulas, rules, and equations are still used, but teachers are trying harder to explain why these formulas work in certain instances, and why they don't work in others.

## From Sit and Listen to Learning Through Play

A child's ability to sit still and listen used to be, and even now sometimes is, a big part of their achievement in school. Sitting still and paying attention is viewed as a huge plus for any kid trying to learn in a classroom, but is it possible they learn more when they are actually moving? We often hear that children's favorite times are recess, phys ed., or lunch!

Studies have actually shown that students learn better when they can use not just their minds, but also their bodies, to learn. Many published papers support this philosophy. Howard Gardner, a Harvard theorist and cognitive researcher, developed a theory of multiple intelligence which proved scientifically that kinestetics (learning through movement) can enhance student achievement.

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