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 graded items 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 $8$ 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.
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.
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 them.
Repeated use of the exam simulator allows students to $1)$ practice and become more familiar with the standard of a high-stakes assessment and $2)$ to monitor their progress as their simulated grade improves.
Data Showcase Discussions
Over the course of the term in both my face-to-face and online sections, students are asked to collect data on some numerical aspect of their life which can be measured daily and which the feel comfortable sharing with the rest of the class.Some examples of acceptable data to collect include:
- The amount of sleep a student gets each night.
- The number of texts a student sends each a day.
- The amount of time spent playing video games per day.
- Discussion 1: Everyone introduces themselves to the class and makes a guess for what their true average is for the variable they are measuring.
- Discussion 2: Students post their current data set while performing a rudimentary analysis using descriptive statistics.
- Discussion 3: Students post their current data set (with more data) while performing a rudimentary analysis using descriptive statistics.
- Discussion 4: Students post their current data set (with even more data) and give a $95\%$ percent confidence interval for the true average of the variable they are measuring. They observe if the interval contains their initial guess from Discussion 1 or not.
- Discussion 5: Students post their current data set (with even more data) and test the hypothesis that their guess is the true average. They conclude whether their initial guess was plausible.
Also, by collecting data about their own lives, the results of the analysis become more relevant visceral. Students also learn how collecting data can help them challenge their a own intuition or assumptions about a situation by collecting and analyzing data. This way of thinking helps students more critically evaluate information and facts they encounter in their daily lives.
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.
The above enables me to work directly with students during class time, which is spent either doing activities such as data collection, extra-credit quizzes, or even completing completing pass codes. For the latter, I am able to observe and fill any gaps in a student's understanding. In total, this course structure allows me to build community and trust with my students by working with them directly.
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