Reflection on Introduction to Statistics

Students have many difficulties in an Introduction to Statistics course.  I have observed that

• the number of definitions to know in order to understand material is daunting.

• the concepts are seemingly abstract and this creates an obstacle when it comes to using them to solve problems.

• in the statistical inference unit, there are many sampling distributions that tend to blend together and students treat each one like the previous one.

Luckily, I have had the opportunity to teach this course four semesters.  Each semester I have modified content in order to improve the course so that students may find joy in the class rather than torment.  Some of the ways in which I do this are

• skeletal notes.  As I discuss in my CoAT portfolio, the skeletal notes are created so as to accommodate many learning styles.  Students who tend to take Intro. to Stats do not plan to continue with math, which says to me these are students do not learn best with traditional mathematics teaching.  Therefore, they need a different approach.  These skeletal notes have been parried down to only the essentials of a chapter.  See an example for more detail.  

• classroom activities.  I have a handful of activities I use each semester, and they may be borrowed from other texts or online blogs, such as a sampling design activity, or I may design them myself, such as a probability activity.  For these activities to work, though, students must have read the section prior to class.  These activities are designed to help students understand better what they have already "learned".

• semester long project.  I understand the need for students to explore statistics firsthand, so I have them work on a project.  The purpose of this project is for students to ask a meaningful question, design a survey and collect data (or find data from a reliable source), analyze the data, and come to conclusions.  Obviously, this is daunting for students who are fearful of mathematics.  To ease this anxiety, the students are put into groups of 2 - 3.  In addition, I provide guidance at each step.  I provide two examples, one in which the students used an existing data set and another in which the students collected their own data.

  • First project.  The students ask "What is the relationship between sex of turtle and the size of its carapace?"  They want to examine the relationship between a quantitative variable and a categorical variable.  We see they turn the quantitative variable into a categorical variable, however, by splitting it up into small, medium and large (this has significant issues, but many professional statisticians do so and get published; that is, my students are well on their way to success).  Once these students have their categorical variables, they choose to use the Chi-square test in order to determine whether there is a relationship between the variables.  This project demonstrates this group's understanding of the material they have learned.  In addition, they have a honest and proper analysis at the end, stating they have no concrete conclusions.  This did not stop them from doing further research into classification methods which could potentially be used to determine the sex of unlabeled turtles.

  • Second project.  The students ask "What is the preferred dessert of Simon's Rock students?"  This questions doesn't seem to have much depth, but the students make their case from a business perspective.  These students demonstrate their awareness for issues such as voluntary response bias, and they correctly identify their variables as categorical.  In addition, the calculations made are correct.  The survey questions, however, are very wordy and the purpose of each question is unclear given what the students claimed they wanted to accomplish.  The project template states proposals must be approved by me.  Unfortunately, it does not state that survey questions do.  Because of this lack of validity for survey questions, the analysis involving confidence intervals also seemed weak.  This is quite alright!  The students recognized their issues, and even stated at the end more research is necessary and how they might have improved their study.  This, in of itself, is a significant lesson.

In addition to my own material, I have searched for outside sources that will aid a student's understanding and satiate the curiosity of more enthusiastic students.  It is unclear whether students utilize these resources.

• Help for the struggling student:

  • supplemental material to increase student understanding -- Youtube videos addressing topics in class that are frequently ones students have difficulty understanding: sampling distributions, confidence intervals, and hypothesis testing. 

• For the enthusiastic student:

  • critical thinking about statistical inference content, such as p-values and confidence intervals.

  • media related to course content, e.g. The Stanford Prison Experiment staring Ezra Miller.

  • an article uncovering truths with statistics: the infamous freshmen 15.

While I have spent many hours developing the curriculum for this course,  I frequently invite students to give feedback on the class.  I have provided an article on statistics education, in which a professor interviews students about their position on their education.  It is important to be willing to have open and honest conversation with students on how I might improve the course, and I use this article as the beginning of this conversation.  This article allows students to think about their education and how it is they learn best.  I have only had one conversation with a student who did read this particular article.  In addition to this article, I provide many one-minute quizzes where students state what it is they have learned.  There is a longer survey provided at mid-term.

In the future, I intend on improving the course with the following

• provide more examples of effective statistics projects.  While the template for the project has outside examples, students may actually look at samples if they come from Simon's Rock students.  That is, I may take the projects from past classes, with permission of their authors, and give them to students.

• encourage students to view the supplemental material by requiring response journals

• make class more discussion based by increasing the number of in-class problems.  This is difficult because there is so much to cover in 55 minutes, but I can certainly try.

It has been privilege to teach this course, and I know many students are having a positive experience.  I hope I can continue to help students learn statistics in this way.