• On Teaching Trigonometry: Graphing Trigonometric Functions (Part 2)
    Mathematics

    On Teaching Trigonometry: Graphing Trigonometric Functions (Part 2)

    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.   OUTLINE Programming a computer to graph trigonometric functions Selecting a programming language and libraries Python Python library: Matplotlib Python library: Numpy It's time for graphing! Questions about the computer-generated graphs   SUMMARY: We talk about how you can show your students to program a computer to graph trigonometric functions. We use the Python programming language as an example.    If you need to see Part 1 of this article, you can access it here. Showing your students how to graph trigonometric functions, using different techniques,…

  • On Teaching Trigonometry: Graphing Trigonometric Functions
    Mathematics

    On Teaching Trigonometry: Graphing Trigonometric Functions (Part 1)

    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. OUTLINE Domain and co-domain Motivating graphing of trigonometric functions Now it's time for graphing Sine and cosine It's time for practice Tangent and cotangent It's time for practice Secant and cosecant It's time for some games Use of technology to graph trigonometric functions Graphing calculators Geogebra Maple Wolfram Alpha And more...   SUMMARY:  We talk about how to introduce your students to graphing trigonometric functions.    After you’ve explained to your students that the sine and cosine are functions from the real numbers to the real…

  • On Teaching Trigonometry: Trigonometric Functions and the Unit Circle
    Mathematics

    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.   OUTLINE Non-acute angles Generalizing the sine function Tangent, secant, and so on Now the unit circle The sine as a function on the real numbers 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,…

  • On Teaching Trigonometry: Angles and the Right Triangle
    Mathematics

    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.   OUTLINE A good start with angles A note on practice Augmented Reality Motivating the right triangle Cosine, cotangent, and cosecant It's time for practice  On proof 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…

  • On Teaching Trigonometry: Introduction
    Mathematics

    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…

  • Technologies for Teaching Mathematics
    Technology

    Technologies for Teaching Mathematics

    If you are a teacher or tutor and sometimes find it difficult to help your students or tutees understand some mathematical concepts, there are some fascinating technological tools designed to alleviate your challenges. GeoGebra AR GeoGebra is a website that has apps that can be used as scientific and graphic calculators and can be used to do other computations, such as solving polynomial equations. Recently, GeoGebra has incorporated augmented reality in some of its apps. So students can have a live demonstration of some fascinating math topics right through their phones. Sometimes, students can find it difficult to graph functions of two variables because they can find it hard to…

  • Technologies for Teaching
    Technology

    Technologies for Teaching

      For related products, scroll to the end. ↓↓↓     You’re likely on the hunt for new technologies to use in the classroom that’ll take your student’s education to the next level. New tech in education is released all the time. And with a busy teaching schedule, it’s often hard to find the time to research what’s worth yours and your students’ time. To help you bring some of the great new education technology released in the past few years, we’ve done the research for you. What follows are three of the top new releases making waves in education. Google Tour Creator You may already be using Google’s amazing…