Expert answer:Reflection -Instructors reasons for choosing probl
Expert answer:Answer each of the following questions based on your reading “Instructors’ reasons
for choosing problem features in a calculus-based introductory physics course” by Yerushalmi.(attached)1. The end of the introduction suggests that readers “reflect on how these problems are similar
or different to the problems they use, and then try to articulate their reasons for favoring
particular problem features.” Write your reflection based on that prompt now. How are these
problems similar or different to what you use? What are your reasons for choosing particular
problem features? 2. The paper reveals that instructors seem to have different criteria for how they choose
problems for any situation and how they choose problems for exams. Do you have different
criteria for choosing problems based on whether the problems are part of a homework
assignment, in-class assignment, or test? If so, what is your reasoning? 3. What are the strengths and weaknesses of this study? What do you think a good follow-up
study would be?
physrevstper.6.020108.pdf
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PHYSICAL REVIEW SPECIAL TOPICS – PHYSICS EDUCATION RESEARCH 6, 020108 共2010兲
Instructors’ reasons for choosing problem features in a calculus-based introductory
physics course
Edit Yerushalmi and Elisheva Cohen
Department of Science Teaching, Weizmann Institute of Science, Rehovot 76100, Israel
Kenneth Heller
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
Patricia Heller
Department of Curriculum and Instruction, University of Minnesota, Minneapolis, Minnesota 55455, USA
Charles Henderson
Department of Physics and Mallinson Institute for Science Education, Western Michigan University,
Kalamazoo, Michigan 49008-5252, USA
共Received 14 March 2010; published 25 August 2010兲
This study investigates how the beliefs and values of physics faculty influence their choice of physics
problems for their students in an introductory physics course. The study identifies the goals these instructors
have for their students, the problem features they believe facilitate those goals, and how those features correspond to problems they choose to use in their classes. This analysis comes from an artifact-based interview of
30 physics faculty teaching introductory calculus-based physics at a wide variety of institutions. The study
concludes that instructors’ goals and the problem features they believe support those goals align with researchbased curricular materials intended to develop competent problem solvers. However, many of these instructors
do not use the beneficial problem features because they believe these features conflict with a more powerful set
of values concerned with clarity of presentation and minimizing student stress, especially on exams.
DOI: 10.1103/PhysRevSTPER.6.020108
PACS number共s兲: 01.40.gb
I. INTRODUCTION
Three central goals are presented in the educational literature for using problems in the introductory physics course as
a means of: 共1兲 helping students construct physics knowledge 关1,2兴, 共2兲 helping students develop generalized
problem-solving skills 关3兴; and 共3兲 introducing students to
the nature of scientific culture 关4兴. The form and content of
those problems directly impact what students learn in the
course, especially when problem solving is the primary assessment tool. Ideally, specific problem features would emphasize the learning goals of the course. For example, multistep problems that avoid explicit physics cues 关5–7兴 can
focus students on the underlying physics concepts useful in
that problem situation. Such problems promote the integration of conceptual knowledge and the skills of planning and
evaluation. Because of their complexity, these problems often require guidance and feedback 共coaching兲 to allow the
novice student to progress 关8–10兴. Another example is qualitative problems that are used to help students construct their
conceptual understanding by requiring predictions and explanations. These problems prevent students from simply manipulating formulas 关11,12兴 to arrive at a solution.
This paper presents a study designed to determine what
problem features physics faculty value, whether those features are consistent with their goals for their introductory
physics course, whether they use problems with those features in their course, and the extent to which their valued
problem features and goals are aligned with those in the educational literature. The study involves an analysis of inter1554-9178/2010/6共2兲/020108共11兲
views with 30 physics instructors who were given 5 alternative problem versions 共Figs. 1 and 2兲 and asked about their
preferences regarding the use of these problem formats and
the reasons underlying their preferences. The instructors
came from a variety of institutions: large state research universities, primarily undergraduate state universities, primarily undergraduate private colleges and community colleges.
The information from this analysis can help curriculum developers in designing problems that will be both valued and
used by instructors, and help professional development leaders address instructors’ concerns regarding problem formats.
It may also help instructors reflect upon their goals for using
problems and whether their problems support the goals of
their teaching.
FIG. 1. “Core problem” that instructors were asked to solve
prior to the interview.
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PHYS. REV. ST PHYS. EDUC. RES. 6, 020108 共2010兲
YERUSHALMI et al.
FIG. 2. Four problem variations that instructors were shown during the interview.
To frame the results discussed in this paper, we suggest
that readers begin by looking at the alternative problem versions 共Figs. 1 and 2兲, reflect on how these problems are similar or different to the problems they use, and then try to
articulate their reasons for favoring particular problem features. Assume that these problems are designed for a
calculus-based introductory physics class.
II. BACKGROUND
Research-based curricular materials that emphasize problem solving are intended to move students toward more expertlike behavior. It is recognized that one year of physics is
not enough time to cause students to become expert problem
solvers. The goal is to move them from novice behavior into
an intermediate state that is sometimes called competent
problem solving 关13兴. This section provides a brief overview
of how experts approach problem solving and what problem
types are best suited to help students develop these expertlike
approaches.
A. How do experts approach problem solving?
Experts devote considerable time to first analyzing a problem qualitatively and describing the situation in terms of
physics principles 关14–18兴. Novices, on the other hand, often
use surface features to characterize a problem 关19,20兴, such
as an inclined plane or free-fall problem. Expert problem
solutions have a strategic approach 关21兴 rather than the novice approach of plugging numbers into formulas. Experts
plan the process of searching for a solution by identifying
useful subproblems and relationships guided by physics prin-
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INSTRUCTORS’ REASONS FOR CHOOSING PROBLEM…
ciples. Novices, on the other hand, perceive each solution
step as an independent entity 关22兴. Experts also use the
problem-solving process as a learning opportunity, reflecting
on their solutions to refine their understanding of the related
concepts and principles, an aspect missing in novices 关23兴.
B. What problem features are best suited to develop an
expertlike approach?
In order for students to develop expertlike approaches to
problem solving, the problems they are asked to solve must
require such approaches. In particular, they should require a
qualitative analysis, planning, and reflection. Unfortunately,
the types of problems most accessible to physics instructors,
those in textbooks, frequently lack these characteristics and
can often reinforce detrimental novice approaches. Examples
of such problems are those without a context, or a context
that uses a previously encountered surface structure. In addition, complex problems are often broken down into predetermined parts, thus bypassing the students’ need to practice
essential strategic skills. Textbooks do give students many
useful exercises, but these alone will not move a novice toward expert problem solving, nor do they usually enhance
conceptual learning 关24,25兴.
Alternatives to such types of problems exist. These emphasize one or more of the problem-solving skills in which
novices are weak. Examples are Context-Rich Problems 关5兴,
Experiment Problems 关26兴, Real-world Problems 关27兴, and
Thinking Problems 关28兴. These problems typically are presented in a real-world context, require more than one step to
solve, are not accompanied by diagrams, and may contain
either more or less information than is needed to solve them.
They require students to practice making decisions by analyzing the problem situation, identifying the physics concepts needed to solve the problem, decomposing the problem
into subproblems as needed, planning the execution of the
solution, and evaluating the results of the solution.
Some curriculum developers also advocate the use of
qualitative problems that are constructed to bring out student
difficulties understanding fundamental physics concepts.
Such questions are used to carefully build from student alternative conceptions to correct conceptions such as in Tutorials 关29兴, to stimulate discussion such as in Peer Instruction
关12兴 or to make students explicitly reflect on their thoughts
such as in Troubleshooting Tasks 关30–32兴.
Much is known about efficacy of these alternative types
of problems 关5,6,10,33,34兴 and the weaknesses of problems
typically found in textbooks 关23兴. Nevertheless, textbooktype problems continue to be selected by introductory physics instructors for practice and exams in their courses.
III. DATA COLLECTION AND ANALYSIS
An artifact-based, structured interview of physics faculty
provided the raw data for this study 关35兴. This section briefly
describes the background of the physics instructors who participated in the interview, the data collection procedures, and
an overview of the data analysis.
A. Interview participants
The 30 physics faculty in the interview sample was approximately evenly divided among four groups based on
their type of institution: Community College 共CC兲, Primarily
Undergraduate Private College 共PC兲, Primarily Undergraduate State University 共SU兲 and Research Oriented State University 共RU兲. They were randomly selected from a pool of
107 tenured or tenure-track faculty in Minnesota who had
taught an introductory calculus-based physics course within
the last 5 years and could be visited by an interviewer in a
day trip from the University of Minnesota, Twin Cities Campus. All but two instructors were male. Their teaching experience as well as their experience teaching the introductory
calculus-based class ranged from a few years to a few dozen
years.
B. Data collection
The structured interview protocol used in this study asked
instructors to compare a series of concrete instructional artifacts, similar to those they were likely to encounter in their
teaching environment, and to make judgments about them.
Comparison among artifacts encouraged introspection while
using natural language and avoiding leading questions. Three
types of instructional artifacts were used: problem statements, instructor solutions, and student solutions. Each interview took about 1.5 h to complete. A video camera recorded
both verbal and visual responses. Written transcripts were
made of the interviews and checked as necessary with the
original video and audio recordings. In this paper we focus
on one part of the interview 共typically lasting 20–30 min兲 in
which instructors were given four different variations of a
core problem. Prior to the interview, each instructor was
given the core problem as “homework” 共see Fig. 1兲 and was
asked to solve it. The core problem was taken from a final
exam for the introductory calculus-based physics course at
the University of Minnesota. It was designed and approved
by a group of four physics faculty who taught the course. Its
solution requires several important physics concepts 共e.g.,
linear and circular kinematics, dynamics, and energy conservation兲, and students could potentially work the problem in
different ways.
The four variations of the core problem are shown in Fig.
2. They differ in the reasoning process they require the student to engage in while solving them. For example, Problem
C is phrased as a story, deals with real objects, does not
include a diagram or hints, and requires the student to divide
the problem into subproblems. Problem A, on the other hand,
is divided into subproblems, includes hints and a diagram,
and is phrased in an abstract form. To allow for a rich set of
ideas to emerge from the interview, none of the problems
were designed to be an ideal example of its type.
The interviewees were asked to examine the problem
variations. They were first asked: “Please describe how these
problems are similar or different to problems you give to
your students. Please explain why you use the problems that
you use.” If necessary a probing question was added: “Do
the problems you give students look different in different
situations 共lecture, homework, exam, beginning or end of
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YERUSHALMI et al.
course…兲? How and Why?” Later on they were asked: “Different ways of asking problems require different things from
students. Comparing these problems to the homework problem, are there things a student needs to know or be able to do
when solving these problems that are not required in solving
the homework problem? Do you see any things that the
homework problem requires that you have not yet mentioned?”
C. Data analysis
For each interviewee we constructed a table representing:
共a兲 the features the instructors identified in each problem; 共b兲
their stated use of problems with these features, 共c兲 their
preferences regarding each feature; and 共d兲 their reasons for
their preferences. Reasons were categorized and, as described in the next section, often included instructional goals.
Each transcript was analyzed by a pair of the authors 共EC
and either EY or CH兲. Small discrepancies in the classification of statements were resolved between that pair and larger
differences were resolved jointly by all the researchers. The
classifications were reviewed by all of the authors.
Once the analysis was completed for each of the individual instructors, the data were compiled to determine the
valued problem features, the instructors’ goals, the extent to
which the valued problem features were used, and differences between instructor responses from the four different
types of institutions.
IV. RESULTS
The study results are presented in the four sections below.
The first two sections describe the most common problem
features identified by the instructors, and the instructors’
goals for using problems in their introductory physics course.
The third section describes how the instructors’ value specific problem features based on whether they believe the feature promotes or hinders their goals. This section also describes the instructors’ usage of the valued problem features.
Finally, the last section describes why many instructors do
not use problem features that they believe promote their
goals and use features that they believe hinder their goals.
When the faculty examined the four problem variations
共Fig. 2兲, seven problem features were most frequently mentioned. The numbers in parentheses after each named feature
indicate how many instructors mentioned the feature.
共1兲 Qualitative 共27 instructors兲. The problem does not require a calculation. This feature was usually mentioned in the
context of problem D: “There’s no calculation involved…
just understanding increase, decrease, label them” 共I11, PD
关Instructor 11, Problem D兴兲; or “ …it requires the students to
think more qualitatively…. Without resorting to a formula.”
共I9, PD兲
共2兲 Multiple Choice 共26 instructors兲. The students choose
from among given answers. This feature was usually mentioned in the context of problem B.
共3兲 Broken into Parts 共25 instructors兲. A complex problem
is broken down into several questions that the student answers sequentially. This feature was usually mentioned in the
context of problems A and D.
共4兲 Real-world Context 共22 instructors兲. The problem
statement has a context that simulates situations that students
identify as realistic. This feature was usually mentioned in
the context of problem C or the core problem.
共5兲 Wordy 共21 instructors兲. The problem statement has irrelevant words that might obscure the underlying problem.
This feature was usually mentioned in the context of problem
C.
共6兲 Given drawing 共18 instructors兲. The problem statement includes a picture that explains the situation. This feature was usually mentioned in the context of problem A.
共7兲 Complex or Multistep 共10 instructors兲. The problem
solution requires the student to connect several elements of
the situation or different physics principles. This feature was
usually mentioned in the context of problem C.
A. Instructors’ goals
When faculty examined the different problem variations,
they often had a preference for some problem features over
others. Many of these preferences were related to learning or
teaching goals held by the instructors. The two learning goals
most mentioned by instructors as influencing their preferences were developing students’ physics understanding and
developing students’ ability to plan and explore solution
paths.
Learning Goal 1: Developing students’ physics understanding 共27 instructors兲. Almost all of the instructors related
specific problem features to the development of student understanding of physics content. For example: “… and so
that’s a nice set of questions which requires the students to
think about the physics principles behind this problem.” 共I1,
PD兲
Learning Goal 2: Developing students’ ability to plan and
explore solution paths 共26 instructors兲. Almost all of the instructors also related specific problem features to the development of students’ problem-solving skill in planning and
exploring solution paths. For example: “Again, I find one of
the premiere kinds of problem-solving abilities I try to strive
for is this notion that a person can read a physical circumstance, and bring together the notions on their own …I’m
hoping that they can put the ideas together themselves.” 共I2,
PA兲; and “… a bit of thinking process, of course, to formulate the steps.” 共I3, PC兲; and “They have to know what the
question is and then they also have to be able to define the
target variable.” 共I4, PD兲
Instructors also mentioned three types of teaching goals
supported by particular problem features. These were motivating students, monitoring students’ thinking, and leading
students 共or not leading them兲 through a problem.
Teaching Goal 1: Motivating students 共21 instructors兲.
Many instructors thought that the problems they asked students to solve should serve a motivational purpose, most
commonly invoked by using real-world contexts. For example: “Well, a lot of students don’t see the purpose in any
of this stuff. It’s too academic, right. They’re 关problem C兴
trying to show you that what we’re asking you to do relates
to the real world and may have some consequences, may
have some practical benefits, right. And then if the student is
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INSTRUCTORS’ REASONS FOR CHOOSING PROBLEM…
Supports
Legend
30
25
Use
20
FIG. 3. 共Color兲 Legend for problem features in Figs. 4–10.
on board, thinking that, yeah, this is useful stuff, right. Then
maybe they’ll put their mind to it and actually solve the
thing.” 共I5, PC兲
Teaching Goal 2: Monitoring students’ thinking 共15 instructors兲. Many instructors thought that problems should allow them to better understand their students thinking. For
example: “I am more inclined to have them work out the
problem so I can look at the details of what they tried, how
they tried to solve it.” 共I1, PB兲
Teaching Goal 3: Leading or not leading students through
a problem 共22 instructors兲. These instructors focused on the
extent to which teaching should aim at leading students
through reasoning processes. All of them thought that problems should lead students through a chain of reaso …
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