Teaching Materials for Benjamin V. Holt
To give the reader a good sense of my course materials and the philosophy out which they are born, I shall present examples of the kind of materials I use in my courses which are representative of the structure which most of my courses follow. While any one of my courses is suitable for the purpose of illustrating my overall philosophy and methodology, I shall give the reader a tour of my "Math in Society" (MTH 105) course.Should the reader wish to see any of my other courses and their accompanying materials, they may view the the main page of my course website following the "Courses" link in the menu bar at the top of this page.
The following link will open a new tab with the MTH 105 Homepage and all of its links.
MTH 105 Homepage
The reader will notice that that there are links to each graded item including: All of the above items are addressed in the Course Syllabus which describes the implementation of my teaching philosophy in the classroom. In addition to a description of each of the graded item in the above links, the syllabus informs students of the weight of each graded item which make up their course grade. Finally, last page of the syllabus gives the course schedule of topics for each day of the course.
Homework
Each homework assignment is pass or fail and consists of a random selection of $10$ textbook-like questions which are randomly generated by the course website. To pass an assignment, a student must answer $80\%$ or more of the questions correctly. In order to avoid steep learning curves, and to make the system as user-friendly as possible, each question is multiple-choice with usually $8$ similar looking options.The reader will notice that the first homework assignment is a quiz on the above syllabus.
One advantage to this approach is that it provides a form of feedback; if the student works out a problem and doesn't see their answer among the possible options, they know that they must go back and check their work. It's an opportunity for growth and self-correction. Another advantage is that it is entirely objective in assessing whether or the objective(s) of the question have been met or not.
Of course, such a pass/fail notion doesn't always allow the instructor to understand what the student is missing. I will address this later on.
One of the biggest advantages of using software which I can share with my students online is that students may attempt any homework assignment as many times as they need in order to pass. Once they do, they are informed that they have passed the assignment as seen below:
When the student clicks on the button, they receive the following message along with their pass code:
At this point the student uploads the code into Canvas, I verify its authenticity, and then the student receives credit.
Exams
Each exam consists of multiple-choice and open ended questions also generated by the website. The advantage of the multiple-choice scheme is outlined above.The Exam Simulator allows me to share with my students how I create their exams since I really do use the course website to generate each exam.
Each exam consists of $20$ randomly-chosen and randomly-generated multiple-choice questions which test basic knowledge of two topics ($10$ questions per topic). All exam questions come from the homework.
Repeated use of the exam simulator allows students to practice and become more familiar with the standard of a high-stakes assessment and to monitor their progress as their simulated grade improves.
Problems of the Week (POWs)
Problems of the Week are designed to challenge students by posing a non-standard problem which goes well beyond the more routine problems encountered in homework. Just as importantly, the POW emphasizes the student's ability to write mathematics.The student's grade depends not only on the correctness of their solution, but also on how well the student explains their process in solving the problem. Moreover, the quality of a student's presentation is also a large part of the grade. Students are not allowed to simply scribble out a solution on tattered, fringey paper with with mistakes crossed out in ink.
The POW is the venue where students put forth their most polished work. For some students this means writing out their work very neatly by hand, for others it means using a word-processing program with electronically generated figures. Whatever works best for the student is fine, so long as they explain their process well with a generous dose of language.
Class Notes
My class notes are all online. For my MTH 105 course, the reader may view the topics to be covered at the following link:Class Notes
The reader will notice that at the top of every page of my class notes is worksheet corresponding to the topic being covered. For example, when we cover Expected Value (Long-Term Averages), there is a link to the Worksheet on that topic near the top of the page. Students complete this worksheet as (which is a random selection of homework problems) in groups and present their solutions to their peers. Students know that they may download the worksheets in advance, and some students simply access them with their phone or other device.
Video Lectures
For both my online face-to-face courses, I record video lectures. The reader may view videos for select MTH 105 topics here:Video Lectures
For my face-to-face sections, I require students to watch the lecture corresponding to the topic of the before class. When students come to class prepared, I am able to engage students more fully in class with group work and activities which enhance the ideas present in each video lecture.
Dynamic Ideas Require Dynamic Illustrations
As mentioned in my teaching philosophy, one of the great advantages of using web-based technology is that dynamic ideas can be illustrated dynamically. I will now share several examples.One example, when covering the topic of long term averages, is illustrated by the following link,
Long Term Averages of Repeatedly Rolling a Die.
Although a process may be random, the long-term average of the face value of rolling a fair, six-sided die will always settle in to $3.5$ eventually. I encourage the reader to try this by repeatedly pressing the button and watching the long-average approach $3.5.$ (Note: after pressing the button once, the reader may simply hold down the "Enter" key to simulate each roll faster.)
Another of my favorites is an illustration of the meaning of a 95% confidence interval for a population proportion.
Confidence Interval of a Population Proportion
With repeated random samples (visible to the user), the true population parameter (also visible) falls within the confidence interval (also visible) approximately 95% of the time. The reader is encouraged to follow the above link and try it for themselves. (Note: after pressing the button once, the reader may simply hold down the "Enter" key to simulate each roll faster.)
Although the following links aren't associated with my MTH 105 course, I decided to include some other dynamic illustrations below of which I am especially proud:
- Left and Right Riemann Sums Approaching the Exact Area Under a Curve (Repeatedly hit the "More Rectangles" button.)
- Difference Quotient Approaching the Exact Slope of Tangent Line (Repeatedly hit the "Plot" button.)
- Gallery of Statistical Visualizations