Math Misconceptions and Considerations HSG-SRT.C.7 & 8
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Why is my decimal answer marked wrong? The words exact value often means “don’t use a calculator”. Students are expected to know the exact values of the trigonometric ratios for a 30 ° , 45 ° , and 60 ° angle. Misconception:
decimal form
radian mode
When students are not familiar with right triangles and trigonometry, they tend to rely heavily on their calculators when doing computations. This will yield incorrect answers for the following reasons: the answer is in decimal form instead of radical form or the calculator is in radian mode instead of degree mode. What to do:
After learning about special right triangles in standard C.6, students can easily derive the trigonometric ratios in radical form using the special right triangle formulas.
Is that the angle of elevation or the angle of depression? The angle of depression is always a great setback for many students. The angle of elevation is so easy and then almost in a careless nature they often wrongly assign the angle of depression. Misconception:
Students incorrectly identify the angle of depression as the acute interior angle in the triangle. What to do:
Have students draw the horizontal line of sight. This will help them to recognize that the angle of depression is the angle formed between the line of sight and the hypotenuse.
I can find missing angles the same way that I find missing sides. Depending on what students are asked to find in a right triangle, they may need to utilize the inverse trigonometric functions. Misconception: Up to this point, students have had a lot of practice setting up trigonometric ratios and solving them. When students are introduced to the inverse trigonometric functions that are used to find angle measures, they may forget how and when to use them. Also, when using the inverse trigonometric functions, students will tend to refer to them as “sine to the negative one power�.
What to do:
Building on student’s understanding of using inverse operations to solve equations may be a good strategy to introduce inverse trigonometric functions. Also, making some type of association between finding angles and using inverses may prevent confusion. For example, the fact that angle and inverse both begin with a vowel whereas side and function both begin with a consonant. Additionally, be sure to use proper terminology when discussing inverse trigonometric functions.