This Course at MIT

This Course at MIT pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

Course Overview

This page focuses on the course 18.05 Introduction to Probability and Statistics as it was taught by Dr. Jeremy Orloff and Dr. Jonathan Bloom in Spring 2014.

18.05 is an elementary introduction to probability and statistics for students who are not math majors but will encounter statistics in their professional lives. Topics include basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.

In Spring 2014, class sessions emphasized active learning, with students engaging in concept questions, discussions, board problems, and computation using R. Outside of class, students used the MITx platform for interactive reading questions and problem set checkers.

Course Outcomes

Course Goals for Students

The primary goal of the course is for students to become more sophisticated consumers of probability and statistics. After this course, students should be able to understand the statistics they encounter in research literature, be able to critique papers or experimental setups, and work with a statistician to analyze data.

Students who are interested in becoming statisticians themselves can build a solid foundation in probability and statistics through this course but should plan on additional coursework for thorough and comprehensive preparation.

Possibilities for Further Study and Future Careers

Most students who take the course plan to become physicians, engineers, or researchers in fields other than mathematics, in which they will encounter probability and statistics. This is the terminal mathematics course for many of the enrolled students.

 

Instructor Insights

In the following pages, Dr. Orloff and Dr. Bloom discuss additional aspects of 18.05:

 

A Day in 18.05

Class sessions were extremely active and student-centered, with a mix of lecture, concept questions and discussion, board problems, and demonstrations and simulations. This section uses one sample class to give a glimpse of the rhythm of 18.05.

Timeline

The progression of the class is shown in the timeline below. Click on any color block to watch that portion of the class in the video below.

 

Each in-class activity type is pictured in an image gallery with descriptive commentary from Dr. Jeremy Orloff and Dr. Jonathan Bloom. In the key below, click on an activity type to see the corresponding image gallery.

Displays the color on the preceding graph that represents .Four students sitting at a table look up at a projector screen that is showing a comic.Class introduction: Announcements and overview
Displays the color on the preceding graph that represents .n instructor stands amidst seated students. The screen on the wall shows a slide with a math problem for the students to work on.Board problem: Extended problem that student teams collaborate on at whiteboards
Displays the color on the preceding graph that represents .An instructor points at a projector screen showing a slide and addresses students, who are sitting at round tables.Lecture: Brief lecture reviewing content covered in readings
Displays the color on the preceding graph that represents .Students seated at round tables raise their hands. One projector screen shows a slide and one projector screen shows a set of dice.Demonstration or simulation: Instructor-led demonstrations or student experiments with dice.
Displays the color on the preceding graph that represents .A multiple-choice question is shown on a projector screen. Students use handheld clickers to submit their answers.Concept question: Multiple-choice question that students respond to via handheld clickers
Displays the color on the preceding graph that represents .Discussion following concept or board questions
 

Resources for Sample Class (Class 11–Bayesian Updating: Discrete Priors)

Flash and JavaScript are required for this feature.

> Download from Internet Archive (MP4 - 136 MB)

> Download this transcript - PDF English - US

> Download English - US subtitle (SRT)

This video features the happenings of a full 18.05 class session.

 

Curriculum Information

Prerequisites

Calculus I GIR . The following versions of Calculus I are on OCW: 18.01SC, 18.01, 18.01, 18.013A, and 18.014.

Requirements Satisfied

Offered

Every spring semester

The Classroom

  • A 3d visualization of a large rectangular classroom, with 13 round tables each surrounded by 9 chairs. Projector screens and white boards lines the walls.

    Photo 1 of 2 Click for next classroom.

    The class met in a classroom equipped for Technology-Enabled Active Learning (TEAL). The classroom includes 13 round tables, each of which seats up to 9 students. The seating arrangement invites collaboration and discussion, which are key in 18.05 (Image courtesy of Mark Bessette).

  • Groups of students work at white boards around the classroom; three projector screens display the same math problem. The center of the room is filled with round tables that are surrounded with chairs. Numerous projectors and cameras are mounted from the ceiling.

    Click for previous classroom. Photo 2 of 2

    The walls of the classroom are lined with white boards and screens. Cameras and projectors are arranged such that slides and live activity at any white board can be captured and projected onto screens around the room. Desktop computers were available but were not used.

 

Assessment

The students' grades were based on the following assessment elements:

 
The color used on the preceding chart which represents the percentage of the total grade contributed by reading questions and in-class questions. 10% Reading questions (graded for correctness) and in-class clicker questions (graded for completion).
The color used on the preceding chart which represents the percentage of the total grade contributed by problem sets. 25% Problem sets; lowest problem set grade is dropped.
The color used on the preceding chart which represents the percentage of the total grade contributed by the first exam. 15% Exam 1
The color used on the preceding chart which represents the percentage of the total grade contributed by the second exam. 15% Exam 2
The color used on the preceding chart which represents the percentage of the total grade contributed by the final exam. 35% Final exam
 
 

Student Information

On average, 48 students take this course each offering.

Breakdown by Year

Mostly juniors, some sophomores, some seniors.

Breakdown by Major

The students enrolled this semester were primarily life sciences majors. There were a fair number of students who planned to become doctors, researchers, or engineers. Math majors who are interested in probability and statistics tend to take 18.440 Probability and Random Variables. Electrical engineering and computer science majors who are interested in probability and statistics tend to take 6.041 Probabilistic Systems Analysis and Applied Probability.

Typical Student Background

Students tend to be upperclassmen. They enter the class as mature students, prepared to do work and manage their time. In addition, many of the students have already had exposure to reading research or even doing research, and so they can place a lot of these ideas in a context that’s familiar to them, especially when it comes to medical research.

The only prerequisite for this course is single-variable calculus. Students with a stronger mathematical background often find this course easier.

Ideal Class Size

Given the current staffing arrangement and classroom, the ideal class size is up to 75. The classroom is intended for up to 100 students. With 75 or fewer students, there’s ample room for everyone to get up and work on the white boards without feeling cramped. A class size of less than 75 also allows the instructors and students to get to know each other. With too few students, the classroom might feel way too big.

 

How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

Lecture and Active Learning

3 hours per week
  • Two sessions per week, each lasting 1.5 hours; 27 sessions total
  • Attended by all students
  • Included brief lectures, demonstrations, and frequent opportunities for student participation: concept questions, discussion questions, board problems. These time types are described in image galleries linked from the timeline key for A Day in 18.05.
 

R Studio

1.5 hours per week
  • One session per week, lasting 1.5 hours; 10 sessions total.
  • No new math content was introduced.
  • Students used R, a free statistical software package, via the user interface RStudio, to apply statistical tools, visualize data, and explore concepts through simulations.
  • Real-world examples were frequently incorporated.
  • Students used and modified pre-written code to build their conceptual understanding of the week’s topics.
 

Out of Class

7.5 hours per week
  • Readings and reading questions before each class meeting
  • Nine problem sets, due on non-class days so that students wouldn't forego class readings in order to complete problem sets.
  • Preparation for exams
  • Optional office hours on Thursdays, Fridays, Sundays, and Mondays
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
2 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
3 No classes throughout MIT. Problem set due. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
4 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
5 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture session; exam held. Lecture and Active Learning: 1.5 hours.
6 No class session scheduled. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
7 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
8 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
9 No class session scheduled. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
10 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
11 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
12 No classes throughout MIT. No classes throughout MIT. Problem set due. Lecture and Active Learning: 1.5 hours. Studio session; exam held.
13 No class session scheduled. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
14 Problem set due. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. R Studio.
15 No class session scheduled. Lecture and Active Learning: 1.5 hours. No class session scheduled. Lecture and Active Learning: 1.5 hours. No classes throughout MIT.
16 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT; exam held. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when lecture sessions are held. Lecture and active learning
Displays the color and pattern used on the preceding table to indicate dates when exams are held. Exam
Displays the color and pattern used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the color used on the preceding table to indicate dates when R Studios are held. R Studio
Displays the symbol used on the preceding table to indicate dates when assignments are due. Problem set due
 
An instructor stands and speaks to a classroom of students. A dozen students are pictured, sitting around two round tables. Projector screens show a comic and a set of dice.
An instructor writes on a whiteboard while students look on. The instructor is captured by a ceiling-mounted camera and live-streamed on screens around the classroom.
A histogram shows that in response to the question, “Which treatment would you choose?,” 3% of students chose the answer “cured 100%,” 45% chose “cured 95%,” and 52% chose “cured 90%.” An instructor stands at a whiteboard while students sit at a round table. The instructor is filmed by a ceiling-mounted camera and the recording is live-streamed on screens around the classroom. Alternate screens show a slide.
Small groups of students gather around whiteboards and work together on solving math problems. Small groups of students gather around whiteboards and work together on solving math problems. The students work directly on likelihood tables that are projected onto the whiteboards. An instructor and a student work together at a whiteboard. An instructor points at a slide on a projector screen as seated students look on.
An instructor balances a ruler with weights on his finger, as students look on.

Course Team Roles

During Spring 2014, there were two lead instructors and three teaching assistants in the classroom at all times. Much of class time was devoted to board problems, during which all five members of the teaching staff circulated around the classroom and worked with students. The course was generously staffed during the 2013 and 2014 offerings to support the transformation in curriculum and pedagogy. From 2015 onwards, the course will likely have a smaller staff.

Lead Instructors (Dr. Jeremy Orloff and Dr. Jonathan Bloom)

  • Designed the course syllabus and structured the course
  • Prepared nearly all course materials, including readings, problem sets, lecture slides, and R studio materials
  • Led each class session, gave brief lectures, conducted demonstrations, and worked with students on board problems

Teaching Assistants (Ruthi Hortsch, Erika Trent, and Dr. Peter Kempthorne)

  • Supported all class activity, particularly student work on board problems
  • As a statistician, Dr. Peter Kempthorne advised the lead instructors on teaching related to statistics and was key in developing the R studios.

Graders (undergraduate students)

  • Graded the nine problem sets for the course