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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 "Probability & Statistics" (STAT 243Z) 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 STAT 243Z Homepage and all of its links.

STAT 243Z 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 $70\%$ 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 $7$ 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.

I am also working on a Question + Solution Generator for most problems in the homework. Here is a sample of what I have so far.

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 Practice Page 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 from the homework. So, since all exam questions come from the homework, students know what is expected of.

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.

Data Collection and Analysis Project

Data Collection and Analysis Project is designed to challenge students allowing them to:
  1. pose a non-standard problem which goes well beyond the more routine problems encountered in homework and
  2. is grounded in their personal experience. Just as importantly, the project emphasizes the student's ability to write and articulate mathematical and statistical ideas.

Class Notes

My class notes are all online. For my STAT 243Z 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 Mean (Expected Value) & Standard Deviation of Random Variables, 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 STAT 243Z 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 random sample faster.)

Other dynamic illustrations of statistical ideas can be found here:

Gallery of Statistical Visualizations

Free Software

I would also like to point out that web-based technologies have enabled me to create software which students might otherwise have to pay for. In particular, I would like to highlight the Holt.Blue Statistical Software Suite which enables students to easily perform many common statistical procedures without having to purchase an expensive software package, and without having to make a significant investment of time to learn free, but less intuitive, packages.

In Summary

Although these materials do not make up the entirety of what I do as an educator, I can say that incorporating technology into my teaching has completely transformed how I teach and deliver content to my students. It has also given me a supreme advantage in illustrating dynamic, yet subtle, ideas such as the behavior of confidence intervals over repeated sampling, as well as limit ideas from calculus. Moreover, I am able to provide my students with free, accessible tools, such as software, which they need to be successful in my courses.