• Mathematics,  Premium

    On Teaching Trigonometry: Trigonometric Functions and the Unit Circle

    Note: Thoughts expressed in this article are solely those of the author(s). Any advice given in this article may not work in all situations.     SUMMARY: We talk about how to introduce your students to the general notion of a trigonometric function defined for any angle, acute or not, and we talk about how to use the unit circle to define trigonometric functions.   After you’ve spent some time practicing with your students and give them some time to work on exercises on their own, you may need to move on to other topics. Now that you’re done working with evaluating trigonometric functions on an acute angle, it’s probably…

  • Basic,  Mathematics,  Premium

    On Teaching Trigonometry: Angles and the Right Triangle

    Note: Thoughts expressed in this article are solely those of the author(s). Any advice given in this article may not work in all situations.     SUMMARY: We talk about how to start introducing your students to the trigonometry of the right triangle and to remind them of the importance of practice.   By now, many of your students may be all excited about trigonometry. You’ve managed to persuade them that it is worth to put the efforts to comprehend the technicalities that you will explain to them. But you will also need to remind them of the importance of prerequisite knowledge. To effectively communicate the technicalities to your students,…

  • Basic,  Mathematics,  Premium

    On Teaching Trigonometry: Introduction

    Note: Thoughts expressed in this article are solely those of the author(s). Any advice given in this article may not work in all situations.     This is the first in a series of articles about ways that one could teach trigonometry: On Teaching Trigonometry: Angles and the Right Triangle On Teaching Trigonometry: Trigonometric Functions and the Unit Circle On Teaching Trigonometry: Graphing Trigonometric Functions (Part 1) On Teaching Trigonometry: Graphing Trigonometric Functions (Part 2)   We will not assume a specific setting in which the teaching will take place. So what we will say may be applicable to classroom settings or other settings. Also, we will not necessarily assume…

  • Mathematics

    Why Math?

    You may have had bad memories from mathematics at school, or maybe you liked it and stayed curious about it or even work in a related field. But in any case, you may ask yourselves: why research in mathematics is important? You may think that we already know all we need to know in mathematics as we are already able, for instance, to make the sophisticated computations required to successfully send a rocket into space to explore other planets. You might be surprised, but continuing research in mathematics can and will change our lives. And even save lots of human beings. How could mathematics save lives? A few years ago,…