# ALEKS Archives - Eva Varga

## How Imaginary Numbers Led Us to Dual Enrollment

November 29, 20161

Over the past couple of years, Geneva has been struggling with math, a subject she has always enjoyed. She was working through Advanced Algebra with Life of Fred and despite my best efforts, I just couldn’t help her when she got stuck.

To be honest, I don’t recall ever learning about imaginary numbers and I just couldn’t grasp it. I was frustrated and she began to lose her confidence.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25.

Can you explain this in simple terms? Fortunately, we discovered Mr. D Math in the spring and through his weekly instruction, her confidence and enthusiasm were restored.

As the new school year approached we contemplated continuing with Mr. D but when her girlfriend shared that she would begin dual enrollment coursework at the local community college, Geneva opted to do the same. She thereby took the math placement exam in August with no preparation whatsoever and even taking the summer off (our first “true” summer vacation).

She placed into Algebra 1 (Math 60) – just where I would have predicted based on what I knew of her skills. The way the course was designed, she would be working with a software program called ALEKS at her own pace. Her instructor informed her that if she completed the coursework and passed the final exam by midterm, she could then begin the next class, Algebra 2 (Math 65).

At the close of the term, she will have finished two consecutive math courses. Delightfully, as she completed them both within the 10-week term, we will only have to pay for one and yet both will appear on her transcript.

Our dual enrollment experience has {thus far} been very successful. Join me again on Saturday when I share a peak into our 4-year high school forecasting.