Business Analytics and Decision Making

This project involved programming a Microsoft Excel Impact calculator for Research and Development tax credit decision making. As a functional program, the calculator includes a 5-stage binary logic tree for qualification requirements relative to different sub-options and elections in order to quickly compare and select the variation of maximal benefit. It also includes a fixed-base percent calculation which involves ratios of running averages of R&D expenses to gross receipts for specific years up to 40 prior tax years.

ARCHER STRATEGIC ADVISORS (REMOTE)

CHESTERTON SCHOOLS NETWORK (REMOTE)

Director of Math Education

2023-present

I am writing lesson plans and reordering the sections of topics to take a more historically approach to the highschool math sequence. I am integrating technology and visualization where needed. I report directly to the Head of Curriculum for the Chesterton Sch0ols Network. Below is a working outline of our plan:

• 1st year: Quadrivial and Analytical Geometry: This course begins with classic Euclidian geometry as taught from The Elements, before moving on to analytical geometry covering linear equations and systems, right triangle trigonometry and basic vectors.

• 2nd year: Quadrivial Arithmetic and Music: This course orients students to the important role of mathematics in western culture (beyond its current STEM focus), while still giving introductory practise in the algebraic manipulation ultimately needed for Calculus.

• 3rd year: Foundations of Calculus before Newton: The usual ”precalculus” algebra not already covered in year 2 is integrated into an exploration of the historical groundwork of Calculus as expressed in Geometry and Physics.

• 4th year: Formal Calculus After Newton: Having established an interest in and motivations for Calculus, we teach the needed practical computations and systematic foundation here.

NORTH IDAHO COLLEGE

Innovative

Curriculum

Design

I created a new interdiciplinary course titled The Mathematics and Aesthetics of Musical Tuning. To create the course I had to write much of my own book and build many of the learning tools including digital and hands-on manipulatives I needed to teach it.

I have been curious about musical instrument construction and subsequently tuning for more than twenty years. Curiosity bred inquiry and inquiry bred much reading and hours of experimental computations. Grids and grids of spreadsheets to make the eyes glaze over. But these grids were different; they were in the service of a higher goal: a means to an end. If they had become my end, an end stuck in the means, then I would not be writing this. Never in all of this was there an assignment, no carrots, no sticks, just a soul loving the beauty it was uncovering and rediscovering. The Quadrivium has a way of doing that. It is pure but it isn’t stark or discretely categorical; it is beautifully baroque. It is self-consistent, but it isn’t coldly logical. It’s a fractal peeking at infinity not a grid tallying parts.

Inspired by an ancient philosophy course I was auditing and a talk the philosophy club invited me to give, I took action.

PEARSON PUBLISHING (REMOTE)

Math Visualization Consultant

I was hired to provide expert suggestions on types, placement, and interactive content details for new animated visualizations within a new e-book edition of the award winning textbook, A History of Mathematics by Dr. Victor Katz. I also built prototypes of many of the interactives.

NORTH IDAHO COLLEGE

Why sometimes putting the cart before the horse can help beginning Calculus students develop curiosity.

As a seasoned Calculus teacher, I asked myself if there was a way to meet precalc students where they are at the onset of Calculus I. A way to entice them to lead themselves excitedly down the path towards inquiry and self-reflection. To think about how they are learning. To lead them away from the seemingly easier path of cramming merely to parrot back memorized but not understood facts. Students struggle with limits (the idea that outputs of a function sometimes hone in on a particular value as the corresponding sequence of inputs move closer and closer to a target input value.) Proving stuff that seems obvious is hard: The logic-based proof that 1+1 =2 took 100 pages.

Working collaboratively with a colleague, we shifting the teaching focus at the start of the course. Under my leadership, we reordered the typical beginning Calculus sequence (limits -- derivatives -- apps of derivatives – integrals) Following a historical cue, my colleague and I put derivatives first, before circling back to make sure the foundations of calculus are solid (limits). Running fast and loose as the first generation of calculus discoverers did is exciting. The far reaching applications and power of the methods are experienced immediately. Earlier exposure also provided motivation for why limits are important to learn.

We also implemented a school-wide initiative to actively teach students about the Psychology of Learning. Collectively the changes made big differences in student attitude, motivation to persevere, and willingness to self-reflect and alter study habits.

Calculus Sequence Reform