Testing Tutorials in Upper-Division: An Example from
Quantum Mechanics
Gina Passante, Paul J. Emigh, and Peter S. Shaffer
Department of Physics, University of Washington, Seattle, WA 98195-1560
Abstract: The Physics Education Group at the University of Washington has been developing and testing Tutorials in
Physics for use in upper-division courses on quantum mechanics. Like Tutorials in Introductory Physics, these materials
are intended to supplement instruction in lecture-based courses, with a focus on improving student conceptual
understanding. We describe the overall impact of the tutorials on student learning in a junior-level quantum mechanics
sequence at the University of Washington. Our findings indicate that students at all levels (by academic performance in
the course) b enefit from the use of tutorials. Moreover, on co urse evaluations, students have overwhelm ingly ranked the
tutorials as being helpful to their learning, with the highest ratings coming from the highest performing students.
Keywords: physics education research, quantum mechanics, upper-division, tutorials, student understanding
PACS: 01.40.Fk, 01.40.G-, 03.65.-w
INTRODUCTION
Quantum mechanics is often considered one of the
capstone ideas in a physics degree. The underlying
concepts are becoming increasingly relevant across a
broad range of fields. There is mounting evidence,
however, that even majors often complete their study
unable to reason correctly about certain foundational
ideas [1-3]. As has been found in studies at the
introductory level, many difficulties seem to be
independent of lecturer, textbook, or university [4,5].
To help address this problem, the Physics
Education Group at the University of Washington
(UW) is developing a set of tutorials (Tutorials in
Physics: Quantum Mechanics [6]) for use in upper-
division courses on quantum mechanics. The approach
we have used is one that has proved effective in
introductory physics courses. Like Tutorials in
Introductory Physics [7], the tutorials on quantum
mechanics are a supplement to lecture instruction that
aim to improve student learning by focusing on
specific conceptual and reasoning difficulties. They are
being created through an iterative process of research,
curriculum development, and assessment.
In upper-division courses, however, the number of
students and the opportunities for data collection are
much more limited than at the introductory level. In
addition, the different course structures and
expectations of students, teaching assistants, and
instructors can impose additional constraints. In this
paper, we discuss some of the differences we have
encountered and describe methods that we have been
using to assess the overall impact of the tutorials.
CONTEXT FOR RESEARCH AND
CURRICULUM DEVELOPMENT
The structure of the tutorials on quantum mechanics
is similar to what has been discussed in previous
articles describing Tutorials in Introductory
Physics [8]. Each tutorial sequence consists of a pretest
(typically taken by students online); a tutorial section
in which students work together in small groups
through a tutorial worksheet; and a short tutorial
homework that is graded by teaching assistants. The
sequence is followed by post-test questions that are
given as a regular part of each course examination.
Each tutorial pretest is administered before the
relevant tutorial, but after lecture instruction on the
corresponding material. They typically take between
15 and 25 minutes to complete and are multiple-choice
with explanations of reasoning. The post-test questions
constitute about one-third of each of the two midterm
exams and one-fifth of the final exam. The pretest and
post-test questions are never identical. We refer to
questions written to assess the tutorials as “tutorial
exam questions” and the remaining questions (written
by the course instructor) as “lecture exam questions.”
At UW, the quantum mechanics course has
traditionally had three 50-minute lectures (or two 1.5
hour lectures) and one 50-minute recitation each week.
The recitations are led by graduate student teaching
assistants (TAs). Over the course of this study, tutorials
have gradually replaced TA-led discussions during
certain weeks. Students receive participation credit for
attendance; however, at times as many as half of the
students may not attend.
