Teaching

Selected Mathematics Classes

History of Mathematics

My History of Mathematics has several goals. First, it introduces students to the history of most concepts taught in the middle- and high school curriculum. Second, it continually emphasizes the important humanistic and cultural components to the history of mathematics; we regularly discuss the relationship between mathematics and politics, religion, and the arts. Finally, the course provides students with an introduction to the history of mathematics as an academic research discipline. If you’d like to know a lot more, I’ve written a book chapter (to appear in. ) about this final aspect of the course, along with other advice and experience for new teachers of the history of mathematics.

Introduction to Statistics

Course overview

One of my favorite classes to teach is CWU’s introduction to statistics course (Math 311 / 314). The course provides students with an introduction to descriptive statistics, random variables, confidence intervals, and hypothesis testing. Instead of teaching a long list of tests and procedures, the class introduces only a few (linear regression, t-tests, proportion tests, and chi-squared tests), and it focused on helping students understand the underlying mathematics and reasoning behind these tests.

I strongly believe that in a first stats class, “less is more”, and that once students have a firm theoretical grasp of hypothesis testing, learning more advanced techniques is much easier.

The practice of teaching statistics

Many stats educators have pointed out the value of using real-world data (and not just toy datasets) in class. The GAISE Report has also emphasized this practice. My beginning stats students are introduced to real-world data in their first course – often on the first day. Some of my classes have worked on data gathered by faculty or graduate students at CWU. Other classes have worked with local government agencies. One particular highlight was a year in which the students analyzed data for our county’s Food Access Coalition, and presented their findings formally to the FAC board at the end of the quarter.

Statistics: Advanced Concepts and Methods

Course overview

I have worked as a paid statistical consultant for several projects over the last decade, primarily in the groups devoted to medical research. In my two-term “Advanced Stats” sequence, I try to introduce students to all the skills they need to do this work, and therefore to all of the basic skills they will need to apply statistics to problems in research or business.

I cover topics in multiple linear and logistic regression, ANOVA and two-way ANOVA, non-parametric statistics, and modern permutation and bootstrapping methods, but also spend some time and effort learning data manipulation skills.

The practice of teaching advanced stats

There are two main features which characterize my practice of teaching advanced stats: real-world data and communication.

All students spend their two quarters working alone or in a small group on a set of real-world data collected by a stakeholder with an interest in their findings. Usually students work with faculty members in other departments at Central Washington University. In several instances, the students have made significant findings, and this has sometimes led to my students’ co-authoring publications with the researchers who collected the data.

Our class spends some time in the first quarter learning to present statistical findings clearly and accurately in writing. During the second quarter, students go through a “public speaking boot camp” with a focus on the presentation of technical results to non-experts. At the end of the quarter, students prepare talks, engage in self reflection by practicing the talk in front of the class and later watching a video of their performance, and then give their talk to an audience outside of the class.

Selected Honors Classes

The Douglas Honors College is a marvelous environment in which to teach. Classes are small, the students are some of the most dedicated with whom I've ever worked, and the classes all have an interdisciplinary component, which helps to keep them fresh and fun.

The first of these is my attempt to create an Honors class which will help students understand several fields of science, and more importantly, to see how these fit together.

From Galaxies to Cells: Making Sense of the Universe

The overall design of the course is this: We ``zoom in'' on the cosmos by starting with the largest thing there is (the universe itself), and trying to understand it. We repeatedly discover that things are too complicated for us to understand unless we zoom in, and focus on a smaller piece of what we have been discussing. This will lead us, at each stage, to a new branch of science.

Our journey consists of eight large steps.

Cosmology and the Stars: The big bang, cosmic background radiation, the structure of galaxies, basics of stellar evolution, measuring distances and temperatures of stars. We complete a computer lab modeling stellar evolution, and (some years) an observational lab on the night sky. Eventually, we decide that it's too difficult to understand all the stars, so it might be best to zoom in on just one.

The Solar System and the Planets: Formation of the solar system, the nature of the sun, and a tour of the planets, with an emphasis on how they differ from each other. Eventually, we decide that it's too difficult to understand all the planets, so it might be best to zoom in on just one.

Geology and the History of the Earth: Earth cycles, plate tectonics, stratigraphy. The history of the Earth. Perhaps surprisingly, we discover that we can't understand the history of the Earth without understanding the history of life.

Evolution: The fossil record, natural selection, sexual selection, mass extinctions, and the history of life. Eventually, we decide that we can't understand national selection without knowing how traits are passed between generations.

Genetics: Mendelian genetics, Punnet squares, and sex-linked traits. Molecular genetics and DNA (including studies of chromosomes and “crossing over.”) Eventually, we decide we can't really understand this without knowing more about DNA itself.

Molecular and Cellular Biology: Structures of the cell, cell replication, and proteins; gene expression and the Central Dogma of molecular biology. The structure of DNA. We realize we can't fully understand DNA and proteins without knowing something about chemistry and the atoms which comprise these molecules.

Chemistry: Atoms -- how we know they exist, and how elements are discovered. We recreate the construction of the periodic table to better understand atomic properties. Basic theory of chemical bonds, and the behavior of electrons in atoms and molecules. We discover that we can't really understand atomic interactions without understanding the basic principles which govern the atomic and subatomic worlds.

Fundamental Physics and Quantum Mechanics: A tour of the subatomic world; difference between nuclear particles and leptons. Behavior of electrons, including the theory of energy shells. The quantization of the universe. We use the quantization of electron energies to understand emission radiation, and finally answer questions about stellar distance from the unit on stars. We close by using these distances, together with what we know about the structure of matter, to understand (in part) the big bang.

It’s About Time

The History of Science