In Math 2204 I have finally entered the realm if Unit 4... with simplifying trigonometric expressions as our starting point. Students in the academic stream traditionally find this topic very difficult. I have tried numerous strategies with students, none of which I have found reduced their difficulty or more importantly reduced their anxiety level with this portion of our curriculum. So this year I am trying something new... using TI-Nspire CAS handhelds. Here's why!
The process of drawing unit circles, drawing the triangles (45, 60, 30), correctly labeling the point on the unit circle and then simplifying an expression that uses those values requires multiple steps before a correct value can be obtained. If a student makes a mistake anywhere in this process, the final answer is incorrect. That can be very frustrating, for anyone let alone academic students. I was thinking that if a student can check their work as they are going through this multi-step process, them maybe there will be a reduction in anxiety and learning will take place... with some risks taken along the way.
So why the TI-Nspire CAS? Simple! The TI-Nspire CAS will generate exact values for trigonometric expressions when prompted to do so. Sin(120) in degrees will give root3/2. So when using unit circles and angles of rotation to find Sin(120) we used the handhelds to produce the answer first and then used our knowledge of unit circles, rotations and special triangles to generate the correct answer. In this situation students were eager to generate the answer and answer questions in the process to generate it manually without technology.
Interestingly when we came across a solution that had root6/3 in the answer but our workings manually resulted in root2/root3, students checked that both were equivalent. It led to the question why. That led to students recalling the concept of rationalizing the denominator.
In both examples knowing the answer and having the ability to check seemed to reduce their anxiety with this part of the curriculum. It is still early but the use of TI-Nspire CAS seems to be helping. I will know for sure when I require some evaluation to be submitted. That is coming soon.