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Teaching | Brian Sherson

## Teaching Statement View teaching statement in PDF format.

## Differential Calculus

I have most frequently taught Differential Calculus (MTH 251) as the instructor on record at Oregon State University. As a graduate student, I taught Differential Calculus for the first time Summer 2009, after my first year as a graduate student, then taught the class every spring thereafter for the rest of my time as graduate student. Returning for the 2016/2017 academic year, I taught MTH 251 in every term, primarily in large sections. As such, I have developed many different problems and exercises for the course, a few of which are shown below. I have also given consideration to new ideas in teaching and assessment, and with my increasing experience with programming, I have been developing tools that students can use in learning Differential Calculus. A couple of examples are shown below.

### The Derivative Machine

The Derivative Machine (credit for the name goes to Professor Tevian Drey) is a web-based tool that I wrote in May 2017 to show students the steps in computing the derivative of a function. It supports implicit differentiation (except for solving for $dy/dx$ after the differentiation) and related rates by allowing the user to indicate variables that are dependent on the variable of differentiation. It reveals explicity when Chain, Product, Quotient, and Linearity rules are invoked in the computation, while it labels all power rules, exponential rules, logarithmic, exponential, trigonometric, and inverse trigonometric derivatives as “Terminal Rules.” As I was also teaching Vector Calculus I that term, I also opted to implement the Multivariable Chain Rule as well.

While the Derivative Machine is ultimately a calculator performing the differentiation for the student, my intent is for students to use it to check their work, while at the same time get them use to proper use of Leibniz notation.

The Derivative Machine currently relies on SAGE. Due to changes in SAGE since May 2017 that now render the Derivative Machine prohibitively slow, the tool is currently being rewritten to no longer rely on SAGE.

### Skills Checklist

With the permission of our department head, I chose to offer two different grading schemes to students in Spring 2013. The first scheme, of course, is the traditional grading scheme based on raw scores on exams, quizzes, and homework. The alternative is that students show proficiency on items on a checklist given to them on the first day of class.

There are are eighteen skills on the checklist, each of which are graded on a three-tier grading scale: Unsatisfactory, Satisfactory, and Proficient. Students are given credit on the checklist through the same exams and quizzes that they receive scores for in the traditional grading scheme. One key difference, however, is that students are given the opportunity to improve their scores on the checklist through reassessment. Students are permitted to take up to two make-up quizzes on items of their choosing (up to ten points worth on each quiz). Since many quiz items are likely to be seen again on midterms, and all items can potentially appear on the final exam, students can also expect to improve scores on exams as well. Furthermore, scores were non-decreasing. Students did not have to worry about regressing from a P to an S.

Other than giving make-up quizzes, the only extra effort needed in grading was in deciding upon a U/S/P score for a checklist item. This was usually a quick decision by looking at the raw scores on the applicable problems on exams and quizzes. Furthermore, the three-tier scoring meant being forgiving on minor computational errors that did not otherwise detract from a student demonstrating knowledge of a skill.

The effect I found is that many students were motivated to do well. They were given direction, and knew what to work on when it came to final exam time. Indeed, many students opted to focus on the final exam problems they needed to do well on to score well on the checklist, and did not have to stress over their overall final exam score.

This is a grading scheme I would like to visit again some time. However, the class was a small section, and some extra planning may be needed if this is ever to be done in a large section. The one change I would make is to remove the non-decreasing nature of skills checklist at the final exam. While I have not made a final decision, one idea I have is to reassess students on a fixed number of skills checklist items, regardless of how many items they have already mastered previously. Students would then specify which skills they wish to be reassessed on. Skills Checklist MTH 251 Spring 2013 Syllabus

### Sample Problems

#### Related Rates

1. A rocket is fired straight up into the air. By the time the rocket is 300 feet off the ground, the rocket's upward velocity is 60 feet per second. Meanwhile, a bystander is observing the rocket, and is standing 400 feet away from the launch pad. How fast is the distance between the bystander and the rocket changing? (Assume the ground is level.)
2. Two cylindrical swimming pools (of different sizes) are being filled at the same time at the same volume rate. Assume the smaller pool has a radius of five meters, while the larger pool has a radius of eight meters. If the water level in the smaller pool is rising at half a meter per minute, how fast (volume rate) is water filling the pools? How fast is the water level rising in the larger pool?
3. Suppose a horse is trotting along a hyperbolic path $x^{2}-y^{2}=16$ in the $xy$-plane, where $x$ and $y$ are given in meters. Assume a bystander is standing at the origin with a camera, rotating to keep a fix on the horse. If the horse is at the point $\left(5,3\right)$, and the camera is rotating at half a radian per second, what is the speed of the horse?
Note: The speed of the horse is given by$s=\sqrt{\left(\frac{dx}{dt}\right)^{2}+\left(\frac{dy}{dt}\right)^{2}}.$

#### Applied Optimization

1. A rectangular plot of land is to be enclosed by a fence that costs \$4 per foot, and also divided into three smaller rectangular regions by internal fence that costs \$3 per foot. The three partitions will all have same dimensions. If the total area of the rectangular plot is to be 75,000 square feet, what are the overall dimensions (width and length) that minimize the total cost of the fencing, and what is the minimum cost?