The sheer amount of convergence tests can overwhelm students. Our courseware breaks down the information for students and provides error-specific feedback through the Explain Error tool.
Explain Error is available in the Practice mode to anticipate and diagnose common errors. When a student makes a mistake, the courseware shows them specifically where and how they went wrong in order to turn the mistake into a learning opportunity. Let’s take a look at a sample problem.
Sample Problem
The student is asked to solve the following problem in Lesson 10.2: Infinite Series.
A spring is attached to a platform so that it is hanging down vertically. A 1-pound weight is attached and released. The tension in the spring is such that it extends 12 inches and then rebounds up 9.6 inches, 80% of the original displacement. If the oscillations continue down and up in the same manner, i.e. the spring is extending and recoiling a length equal to 80% of the previous displacement, what is the total distance the weight has traveled when the spring reaches equilibrium? Write the exact answer. Do not round.
Students who enjoy solving puzzles will enjoy this type of problem, but there are a few common mistakes they can make. We offer feedback for these errors:
Explain Error #1
The student mistakenly thinks the spring extends and recoils the same amount before the 80% reduction in displacement occurs on the next cycle. This doubles the correct answer.
The student selects the Explain Error option to learn more:
Explain Error #2
The student identifies the crucial components of the geometric series modeling the problem, but makes a mistake when using the formula to calculate the sum.
The student selects Explain Error:
Explain Error #3
The student fails to add the first displacement of 12 inches to the total displacement. This is an easy mistake to make if the student identifies a = 9.6 and r = 0.80. Note that this error can be avoided if the student chooses a = 12 and r = 0.80.
The student selects Explain Error:
After having made any of the three mistakes above and then reading the explanations corresponding to the errors, the student is highly likely to make the proper correction and calculate the desired answer. In Hawkes’ Practice mode, the student can go back and resubmit a different answer:
Interested in seeing more of the calculus question bank? Contact us today at info@hawkeslearning.com or 1-800-426-9538 to get free access to the student courseware!
News from the Nest 
That’s a useful problem, but it is not really the type of issue with convergence tests that my students have. They have trouble telling which test to use and how to remember the hypothesis and conclusion of each test.