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An introduction to Formulas, concepts and ideas in Math education.

Practical theoretical concepts visualized at 6th – 7th grade level

(DNS 2001)

Index I. Introduction

The importance of math education lies in the simple fact that all we see around us can be explained or understood with the help of math, mathematical formula’s and mathematical models.

Relating the abstract concepts of mathematical formulas and models to real life represents a bigger challenge then the aforementioned would imply.

When teaching math, students repeatedly ask, whether this or the next concept has anything to do with real-life and a second question is the always returning question of why is something (concept, idea or definition) like that.

Within this synopsis we want to show and proof that mathematical formulas and concepts at grade 6-7 level can be done in different and interesting ways.

The emphasis is here on giving proof, hands-on education, visualization of concepts enhancing the retention rate and practical use of theoretical concepts.

On the other hand math has another function as well, namely enhancing and developing the logical reasoning skills and enhancing awareness and observational skills.

Teaching math has to include two areas of understanding, namely;

· Calculation competence.

· Understanding the ideas behind the numbers, shapes and explanations given.

When children learn math they need to play with real objects and explore real problems that interest them.

II. Why teach math

Mathematics is useful for everyday life, for science for commerce and for industry because it provides powerful to the point and explicit means of communication and because it provides means to explain and predict.

It develops logical thinking and reasoning and could have [for some] æsthetic appeal[1].

Problem solving is ‘key’ in being able to do all other aspects of mathematics. Through problem solving, children learn that there are many different ways to solve a problem and that more than one answer is possible. It involves the ability to explore, think through an issue, and reason logically to solve routine as well as non-routine problems. In addition to helping with mathematical thinking, this activity builds language and social skills such as working together.

III. Defining the area

We have chosen to write about the introduction of the concepts of , the Pythagoras’s theorem and different geometrical concepts like triangles, parallelogram and squares. We made this choice because these different areas include calculations of all kinds, formulas that need explanation and the possibility of reproducing objects. Additionally we have the possibility of including all students through the different activities.

According to State Requirements[2], the students at 6-7 grades should get acquainted and work with:

o Expansion of knowledge of ‘whole numbers’ towards the concept of ‘all numbers’

o Coordinate system, including the connection between numbers and drawings

o Investigation of the underlying connection, formulas and concepts within the four different areas in math

o Drawing, measurement and calculation

o Measurement of circumference, surface and volume

o Methods of deciding surface (area) at the hand of geometrical observations

o Methods in order to register and have overview over results of investigations

o Description of data and information with the help of tables and diagrams and the ability of processing these with the help of electronic means (computer & calculator)

o Working with EDB; computers-programs & competence in working with computers.

Within the following teaching plans, and ideas, these requirements are met and worked with. But first we will present our pedagogical and didactical considerations.

IV. Pedagogy and Didactics in Math teaching

The first thing to recognize and acknowledge is the fact that the starting-point in math teaching (and for what that matters all teaching) has to be the student. This implies a student centred approach. Taking the starting point in the student gives the possibility to relate the subject matter to be taught to prior knowledge[3] of the students, and it lies at the basis of teaching differentiation.

We firmly believe that theory & practice go hand-in-hand; it is therefore desirable to implement this concept in the learning situation.

A fact supporting this theory is the fact that, according to research done[4] by the National Training Laboratories in Bethel, state of Maine and by Bandura[5], the retention rate for students can be measured through activities such as:

o Lecture

o Reading

o Audio-visual

o Demonstration

o Discussion

o Practice by doing

o Teaching classmates (peer-to-peer)

In this schema no. 1