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Physics Education Research at Maryland Abstracts |
Maintained by
University of Maryland PERG
The Robert A. Millikan Award Lecture--Building a Science of Teaching Physics:
Learning What Works and Why
Edward F. Redish
Plenary invited talk, AAPT meeting, Lincoln, NE, August, 1998
With the explosive growth of technology in the workplace and with our sister
sciences of biology, chemistry, and engineering reaching a vigorous maturity,
we have to rethink the role of physics instruction. New situations present both
challenges and opportunities. Is it sufficient for us to continue to treat education
as a fundamentally local problem, with each of us finding our own limited solution,
perhaps propagating it with a textbook? Or is there some way to use our scientific
tools of observation and analysis as a community to build a more global, more robust,
and more transferable understanding of why and when physics instruction is effective?
In this talk I will explore how physics education research leads to a deeper
understanding of what we are trying to do in physics teaching, to new methods of
delivering instruction, and to new ways of evaluating what our students are learning.
A Comparison of Pre- and Post-FCI Results for Innovative and Traditional
Introductory Calculus-Based Physics Classes
Jeffery M. Saul, Richard N. Steinberg and Edward F. Redish
AAPT meeting, Lincoln, NE, August, 1998
As part of an evaluation of primary and secondary implementations of
four different curricula, we collected and analyzed pre/post FCI1 data
from over 2000 matched2 students at eight undergraduate institutions.
In particular, we looked at the Hake factor3 (the fraction of the possible
gain) for both the overall FCI and for questions explicitly addressing
Newton's third law for each of the four curricula. We found that the average
fractional gains for classes taught with Tutorials in Introductory Physics4
(35% ± 3% std. error), Group Problem Solving5 (34% ± 1%), and Workshop Physics6
(41% ± 2%) were significantly better than those for traditional lecture classes
(16% ± 3%). Similar results were found for the Newton's third law cluster.
The overall results are consistent with Hake's3 but avoid some of the experimental
design difficulties incurred by soliciting results post hoc.
1 D. Hestenes, M. Wells, and G. Swackhammer, Phys. Teach. 30 (3), 141-159 (1991).
2 Here, matched indicates that only results from students who took both the pre and post FCI are included.
3 R.R. Hake, Am. J. Phys. 66 (1), 64-74 (1998).
4 L.C. McDermott and P. S. Shaffer, Tutorials in Introductory Physics (Prentice Hall, Upper Saddle River NJ, 1997); E. F. Redish, J. M. Saul, and R. N. Steinberg, Am. J. Phys. 65 (1), 45-54 (1997).
5 P. Heller, T. Foster, and K. Heller, in AIP Conf. Proc. 399, 913-934 (AIP Press, Sunnyvale NY, 1997);
6 P. Laws, Workshop Physics Activity Guide (John Wiley and Sons, New York, 1997).
Factors Affecting the Drop-Out Rate of Female Engineering Students
Apriel K. Hodari, Jeffery M. Saul, Edward F. Redish
AAPT meeting, Lincoln, NE, August, 1998
Women drop out of engineering and physical sciences at a much higher rate than men.1
However, reasons for this differential are not well understood. Previous studies have
not found that performance (as measured by grades) or other likely factors adequately
predict whether (or explain why) some students stay while others drop out.2 The
Physics Education Research Group at the University of Maryland has been evaluating
introductory physics classes by studying students' cognitive expectations using the
Maryland Expectations Survey (MPEX)3 and their conceptual understanding using
the Force Concept Inventory (FCI).4 We will present FCI and MPEX data correlated
to gender and persistence to probe whether cognitive attitude or conceptual
understanding is correlated with the gender differential in drop-out rates.
1 E. I. Holmstrom, Best & brightest: Education and career paths of top science
and engineering students, Report to the Alfred P Sloan Foundation (Commission on Professionals in Science and Technology, 1997).
2 E. Seymour and N. Hewitt, Talking About Leaving (Westview Press, 1997).
3 E. F. Redish, J. M. Saul, and R. N. Steinberg, Am. J. Phys. 65, 45-54 (1997).
4 E.F. Redish, J.M. Saul, and R.N. Steinberg, Am. J. Phys. 66, 212-224 (1998).
Seeing the Invisible: A new quantum tutorial with LED's
Lei Bao, Edward F. Redish, and Richard N. Steinberg
AAPT meeting, Lincoln, NE, August, 1998
Students often have problems understanding important concepts related
to the structure and properties of conductors and semiconductors.1
One of the most difficult concepts to relate directly to physical
observables is the idea of energy bands and how they affect the electrical
characteristics of the material. Students usually don't have previous
experience with these issues and often get disoriented when they first
encounter the concept. For an upper-division first course in quantum
mechanics for engineers, we have developed a tutorial2 and an interactive
lecture demonstration3 using LED's that address these issues.4 The
tutorial and the results of the instruction will be discussed.
1 L. Bao, R. N. Steinberg, and E. F. Redish "The student microscopic
model of conductivity", AAPT summer meeting, 1998.
2 L C. McDermott et al., Tutorials in Introductory Physics (Prentice-Hall, 1997).
3 D. R. Sokoloff and R. K. Thornton, "Using interactive lecture demonstrations
to create an active learning environment", 35:6 (1997) 340-347.
4 Our work is based in part on some similar work done for high school
students by Zollman, Dean, et al., Visual Quantum Mechanics Project, Physics
Education Research Group, Kansas State University.
A Diagnostic Test to Investigate Student Use of Multiple Models of Mechanical Waves
Michael C. Wittmann, Edward F. Redish, and Richard N. Steinberg
AAPT meeting, Lincoln, NE, August, 1998
As part of a continuing investigation of student difficulties with the physics
of waves, we have developed a short diagnostic test that investigates student
understanding of topics in mechanical waves, including propagation, superposition,
and sound. The questions were chosen after extensive research showed that
students were having common difficulties in many different areas of wave physics.1
We refer to the model used by many students to describe wave physics as the
Particle Pulses Mental Model (PM). In this talk, we describe the PM and the
diagnostic test. Student performance before and after modified instruction
will also be discussed.
1 M. C. Wittmann, R. N. Steinberg, and E. F. Redish "Making Sense of How
Students Make Sense of Mechanical Waves," University of Maryland preprint (1998).
The Hidden Curriculum: What do we really want our students to learn?
Edward F. Redish
Plenary invited talk, APS/AAPT Meeting, Columbus, OH, April, 1998.
We are are rarely explicit about what we want our students to learn in
introductory college or university physics. We often say we want them to
"learn problem solving", but we usually have in mind complex, expert
problem solving skills. In practice, we usually test for algorithmic
problem solving and pattern matching skills -- something quite different.
I refer to this gap between what we want and what we do as representing
a "hidden curriculum". At the University of Maryland, the Physics Education
Research Group has been exploring some of the components of the hidden
curriculum -- concept learning and cognitive attitudes towards physics.
Our results, and the results of other physics education research groups,
are beginning to clarify the nature of the difficulties with traditional
teaching methods and to demonstrate some effective ways to improve our instruction.
Conceptual Understanding, Expectations, and Research-based Curricula or:
Are Reform Physics Curricula Worth The Effort?
Jeffery M. Saul, Richard N. Steinberg and Edward F. Redish
AAPT Regional Meeting (Chesapeake Section), Annapolis, MD, November 1997.
The study of student difficulties in the introductory physics class has led
to the development of several new curricula designed to improve what students
get out of the introductory course. These curricula vary both in approach and
in the effort and commitment required of the instructor and the institutions.
As part of the Maryland Physics Expectations (MPEX) project,1 we have given the
FCI and MPEX survey to undergraduate classes at 10 schools using either traditional
lecture instruction, University of Washington Tutorials, University of Minnesota
Group Problem Solving, or Workshop Physics. Because of the all-laboratory
approach, Workshop Physics is one of the most demanding research-based curricula
both in terms of equipment and facilities as well as the complete overhaul of the
course and the change in teaching style required of the instructor. The MPEX and FCI
results from the Workshop Physics classes will be compared with the results from
classes using the other curricula.
1 E. F. Redish, J. M. Saul and R. N. Steinberg,
"Student Expectations in introductory Physics,"
Accepted for publication in the American Journal of Physics.
Identifying
and addressing student difficulties with the physics of sound,
M.C. Wittmann, M.S. Sabella, R.N. Steinberg, and E.F. Redish,
AAPT meeting, Denver, August, 1997.
The Physics Education Research Group at the University of
Maryland has been conducting research into student understanding of sound.
Using pretests, individual demonstration interviews, homework questions,
and exams, we have followed the development of student conceptual understanding
of the nature of sound and the mathematical descriptions they use to describe
their knowledge. Our results show that students have serious conceptual
difficulties understanding the longitudinal wave nature of sound and are
often unable to write or interpret equations that describe their conceptions.
We have developed curriculum materials to address their difficulties using
video-analysis tools with videos of candle flames perturbed by low frequency
sound waves. Preliminary results show that these materials help both to
improve students' conceptual understanding and their application and interpretation
of equations.
Student
performance on traditional exam questions in two instructional settings,
M.S. Sabella, R.N. Steinberg, and E.F. Redish,
AAPT meeting, Denver, August, 1997.
In the past few years, researchers have demonstrated that
interactive engagement methods can help students build fundamental physics
concepts in the introductory university physics course. While it is sometimes
assumed that building strong concepts will help students solve problems,
transfer of learning from one domain to another is difficult and cannot
be taken for granted. The UMCP Physics Education Research Group has been
comparing two instructional approaches in the engineering physics course
at UMCP. One class has traditional problem solving recitations while the
other has McDermott style tutorials. We have probed student problem-solving
by giving both classes identical exam questions. Improvement can be observed
in some contexts. We will also describe how we have attempted to address
concept-to-problem transfer issues by giving the students "bridging problems"
that link basic concepts to traditional problems.
Student
difficulties with vectors in kinematic problems,
E.F. Redish and G. Shama,
AAPT meeting, Denver, August, 1997.
Students in introductory physics often have difficulties
with the concept of vectors. We have observed and analyzed student performance
in a small class of first-semester algebra-based physics at the University
of Maryland. Students were observed in tutorials and during in-lecture
discussions, and their homeworks and examinations were analyzed. All of
the students made errors in the meaning and use of vectors in kinematic
problems. We conjecture that their difficulties result from a mental model
of motion that retains the full path as the description of the motion,
and that contains inappropriate rules for extracting average or overall
features from this full description. We refer to this mental model as path
dominated. An exam question designed to test this hypothesis was delivered
to 135 students. In this problem, approximately ½ of the students
made errors that may be explained as a result of path-dominated misconceptions.
Student
expectations, Workshop Physics, and the MPEX,
J.M. Saul, R.N. Steinberg, and E.F. Redish,
AAPT meeting, Denver, August, 1997.
Many students enter introductory physics with counterproductive
attitudes and beliefs about physics. Traditional instruction had little
or no positive effect on these attitudes and beliefs at three large state
universities as measured by the Maryland Physics Expectation (MPEX) survey.
However, students in Workshop Physics (WP) at Dickinson College (1) had
more favorable expectations at the beginning of the class than students
at the state universities, and (2) showed significant gains in their cognitive
expectations clusters at the end of the first semester, while students
at the universities showed mostly losses. In order to see whether Dickinson's
results are due to WP or to the higher selectivity at Dickinson, we have
given the MPEX survey to students in WP classes at seven schools. We will
compare the results at the WP schools with results obtained in classes
at state universities and with students at Dickinson.
Student
misconceptions on classical issues at the boundary of quantum mechanics,
E.F. Redish,
invited talk, APS/AAPT meeting, Washington, DC, April, 1997
Although quantum mechanics (QM) makes a substantial break
from classical mechanics, both in its structure and its concepts, QM relies
heavily on understanding classical ideas. Since students are known to have
serious difficulties with many classical concepts, even after instruction,
some of the difficulties they encounter in learning QM may be associated
with weaknesses in their classical conceptions. The Physics Education Research
Group at the University of Maryland has identified a number of student
difficulties with classical prerequisites that make it difficult for them
to interpret traditional quantum instruction. Approaches that might help
them overcome these difficulties will also be discussed.
Identifying
and addressing student difficulties with mathematics when learning physics,
R.N. Steinberg,
invited talk, APS/AAPT meeting, Washington, DC, April,
1997.
For the past several years, the Physics Education Research
Group at the University of Maryland has investigated student difficulties
understanding the role of mathematics in learning physics. The context
has ranged from introductory physics for teachers to undergraduate quantum
mechanics. At each level, we have found that many students are unable to
apply mathematical tools instructors assume they know (ranging from graphs
to differential equations) to the physics they are learning. In this presentation
I will give an overview of this research and describe how we use it as
a guide to curriculum development.
Probing
student understanding of introductory physics: Techniques and implications,
R.N. Steinberg,
invited talk, given at Ohio State University, February,
1997.
In developing and evaluating new curriculum and instructional
strategies for the physics classroom, the importance of considering the
details of student understanding of the subject is becoming widely recognized.
The physics education research community has been developing multiple techniques
of probing what beliefs the students are bringing into the classroom and
the influence of instruction on these beliefs. In this talk, I will present
some of our work in the Physics Education Research Group at the University
of Maryland on how we probe student understanding, how we evaluate our
probes, and how we interpret and apply the results.
Measuring
student expectations in university physics: The MPEX survey,
E. F. Redish,
invited Talk, AAPT meeting, Phoenix, January, 1997.
If we want to have a larger fraction of our students learn
physics than is presently the case, we have to understand what distinguishes
successful from unsuccessful students. Students not only bring to class
their prior understanding of physics concepts, they bring assumptions about
the nature of physics knowledge, what they are to learn, what skills will
be required, and what they need to do to succeed. These "expectations"
affect not only how students interpret class activities, but the type of
understanding they build. To probe the distribution and impact of these
expectations, we have created the Maryland Physics Expectations (MPEX)
Survey, a set of statements with which students are asked to agree or disagree.
Observations of more than 2000 students at a dozen institutions in first
semester physics classes show that many students have expectation misconceptions.
Furthermore, the first semester class tends to deteriorate rather than
improve these expectations.
TA
training as an evolving process,
Jeffery M. Saul,
invited
Talk, AAPT meeting, Phoenix, January, 1997
Many beginning graduate student TAs do not receive training
as undergraduates to teach orcommunicate physics to non-majors. In addition, physics education
research has found that while graduate student TAs are good at mathematical problem solving,
some have difficulty applying basic
physics concepts and using these concepts to explain phenomena
without equations. To better
prepare our new TAs at the University of Maryland, we have
increased pre-semester TA training
from two days to a week over the last three years. However,
based on physics education research,
implementation of new TA training programs at other schools,
and my own experience, I believe
more can and should be done to develop TAs with better teaching
and communication skills. In this
talk, I will discuss how TA training has changed, evaluate
the current training, and make some
suggestions for TA training in the future.
Student
difficulties with energy in quantum mechanics,
E. F. Redish, Lei Bao, and Pratibha Jolly,
AAPT meeting, Phoenix, January, 1997.
The Physics Education Research Group at University of Maryland
has been studying student learning of quantum mechanics. Our previously
reported research shows that student difficulties exist with classical
concepts that are prerequisite for learning quantum mechanics. In this
talk, we report detailed studies of student difficulties in quantum mechanics
arising from confusions with the classical concept of energy. Students
are confused on some detailed issues concerning energy and energy diagrams
such as the possible value of total classical energy, the meaning of discontinuous
potential energy diagrams, and the quantization of energy levels in the
quantum case. We have also found new induced confusions on classical issues
that are created by students misinterpreting quantum concepts. Proposals
for instruction to deal with these issues will be discussed.
Student
performance on multiple-choice diagnostics vs. open-ended exam questions,
R.N. Steinberg and M.S. Sabella,
AAPT meeting, Phoenix, January, 1997.
Multiple choice diagnostic tests are becoming increasingly
popular in the physics education community to measure student understanding
of basic concepts. Further research is needed to assess the effectiveness
of this use. We have developed open ended examination questions that correspond
to several items on the most widely used diagnostic, the Force Concept
Inventory (FCI).1 The questions were included on final exams
of introductory calculus-based physics classes at the University of Maryland.
The FCI was administered during the last week of the semester in these
classes. Correlation between student performance on the FCI and the complementary
exam questions will be discussed.
Student
difficulties with math in physics: Giving meaning to symbols,
E. F. Redish, R.N. Steinberg, and J.M. Saul,
AAPT meeting, College Park, August, 1996.
Although there have been studies on student understanding
of the nature of science and science process, there has been little work
on the implication of the role of student understanding of the symbology
of physics on educational practice. We have seen a variety of difficulties
that correspond to students having an incorrect understanding of the role
of math in physics. Students can often perform mathematical operations
correctly in the context of a math problem, but be unable to perform the
same operations in the context of a physics problem. Students often have
little appreciation for or understanding of the rich meaning carried by
a symbol. We have seen a number of different kinds of failures of this
type and will give examples and a preliminary classification of student
difficulties with assigning meaning to the mathematics in a physics context.
Student
difficulties with math in physics: Why can't students apply what they learn
in math class?
J.M. Saul, M.C. Wittmann, R.N. Steinberg, and E.F. Redish,
AAPT meeting, College Park, August, 1996.
Research in mathematics education has revealed evidence that
many students' knowledge of mathematics is fragmented into unconnected
procedural pieces. As a result, students have difficulty applying what
they have learned in math class in other contexts such as introductory
undergraduate physics. We will present several examples from interviews
and exams of students in the introductory calculus-based course at the
University of Maryland.
Identifying
student difficulties with the propagation of mechanical waves,
M.C. Wittmann, E.F. Redish, and R.N. Steinberg,
AAPT meeting, College Park,
August, 1996.
The Physics Education Research Group at the University of
Maryland has been conducting research into student understanding of mechanical
waves in our introductory calculus-based physics courses using student
interviews, examination questions, and a free response diagnostic test.
We have observed a number of common student confusions in the area of waves
on elastic strings. Based on our research, we have developed student centered
instructional tutorials using interactive video tools on the computer.
We will demonstrate some of these materials and discuss their effectiveness.
Student
difficulties with quantum mechanics,
Lei Bao, Pratibha Jolly, and E.F. Redish,
AAPT meeting, College Park, August, 1996.
We investigated student difficulties in learning quantum
mechanics in introductory calculus-based physics and a third-year quantum
course at University of Maryland. A series of pre-tests and post-tests
were used to test their understanding of atomic structure and their ability
to interpret the meaning of quantum wells, energy levels, and orbitals.
Some common conceptual difficulties were identified and analyzed. We found
many students confuse the energy representation with a description of position.
We developed a student-centered instructional tutorial addressing this
issue based on previous work of the Kansas State Group. Two additional
tutorials were created to help students build the concept of wave function
using M.U.P.P.E.T. simulations. We will report on the effects of the tutorials
as evaluated by analyzing final exam questions.
The
bouncing ball: An MBL demonstration of the period doubling approach to
chaos,
Lei Bao,
AAPT meeting, College Park, August, 1996.
The subject of chaos is one of considerable activity and
interest in physics today. Simple examples that permit students to get
an early introduction to this subject are particularly important. In this
paper we will present a chaos-demonstration experiment where a computer-based
data acquisition system is used in the traditional bouncing ball experiment.
The bifurcation and period doubling process can be clearly demonstrated
with the computer which allow us to easily both create a graphical display
and carry out detailed calculations. A simple physical model of typical
bouncing ball orbits is analyzed and compared with the experiment results.
Possible implementations of such topics in an introductory physics course
is also discussed.
A comparison of student expectations
in introductory calculus-based physics,
J.M. Saul, R.N. Steinberg, and E.F. Redish,
AAPT meeting, College Park, August 1996.
Part of the "hidden curriculum" we have for introductory
physics is to improve student understanding of the nature of physics and
the relation of physics to the real world. Students often enter the course
with epistemological beliefs and attitudes about physics and learning that
are incorrect or counterproductive. The impact of a course on these items
is rarely tested. We use our Survey of Student Expectations and interviews
of students to see how classes affect student beliefs and attitudes during
one year of introductory calculus-based physics. Data from traditional
classes, and research-based curricula such as Workshop Physics, Group Problem
Solving, and Tutorial classes will be presented
Student
difficulties understanding the role of mathematics in introductory physics,
R.N. Steinberg, J.M. Saul, M.C. Wittmann, and E.F. Redish,
APS/AAPT meeting, Indianapolis, May 1996.
Understanding mathematical formalism and relating it to a
physical situation plays a critical role in learning introductory physics.
Although there has been a great deal of research into student understanding
of mathematics, very little has been reported in the context of learning
physics. At the University of Maryland, the Physics Education Research
Group has been conducting research into student understanding of the role
of mathematics in introductory physics. In this presentation, we will describe
difficulties students have recognizing the relationship between equations
and the physical situation they represent in the context of oscillations
and mechanical waves. Results are based on the analysis of examination
questions and individual demonstration interviews.
Student
difficulties with superposition of mechanical waves,
M.C. Wittmann, E.F. Redish, R.N. Steinberg,
AAPT Regional Meeting, March, 1996.
The Physics Education Research Group at the University of
Maryland has been conducting research of student understanding in physics.
We have investigated student understanding of mechanical waves in our calculus-based
physics courses. Our methods include the analysis of free response conceptual
questions, examination questions, and interviews with the students. Examples
of our results include student difficulties with the speed of waves and
with superposition. Based on this research, we have developed new, student
centered instructional materials using interactive video tools on the computer.
Evaluation of Student Expectations in Introductory University
Physics and Development of the Expectation Survey
Jeff Saul and Edward F. Redish
MEETING
AAPT meeting Spokane, August, 1995.
Student expectations and attitudes towards the nature of leaning
and physics can have a counterproductive effect on what they learn
from course activities. To study coursewide distribution of student
attitudes, we have developed a Likert-style survey. Previously, we
reported use of the expectation survey to measure the distribution of
student attitudes both coming into the course and as a result of the
course itself. Results from over 800 students at five institutions
will be discussed with an emphasis on the students' constructivist
attitudes and their view of the linkage between physics and reality.
Particular attention will be given to precourse population distributions
and correlations between student attitudes and success in the course.
We will also report on studies of the reliability of the survey from
interviews and repeated surveys. Issues which have turned out to be
difficult for students to interpret will also be discussed.
How much MBL do you need to get good results?
Edward F. Redish and Jeff Saul
AAPT meeting Spokane, August, 1995.
Thornton and Sokoloff1 have demonstrated that persistent student
difficulties with the reading of velocity graphs can be overcome
using two two-hour laboratory sessions. The results are very robust
and have been tested at many universities with many different lecturers.
We have reproduced the bad results obtained without MBL despite a strong
attempt to "teach to the test" in a lecture format. We have reproduced
their good results using MBL in a one-hour McDermott-style2 tutorial.
We have also obtained very good results on the FCI Newton-III cluster
with another one-hour MBL tutorial.
1 Thornton, R. K., and D. R. Sokoloff, "Learning motion concepts
using real-time microcomputer-based laboratory tools", Am. J. Phys. 58 (1990) 858-867
2 McDermott, L. C., and P. S. Shaffer, "Research as a guide for
curriculum development: An example from introductory electricity. Part I:
Investigation of student understanding", Am. J. Phys. 60 (1992) 994-1003; erratum,
ibid. 61 (1993) 81.
The Distribution of Student Expectations and Attitudes
in Introductory University Physics
Edward F. Redish and Jeff Saul
AAPT Meeting, Orlando, January, 1995.
Student attitudes and expectations towards the nature of physics and the nature
of learning play an important role in what they choose to learn in a University
Physics course. Detailed studies of a small number of individual students indicate
that they may have attitudes that are strongly counterproductive to their learning
what their teacher intends from assigned activities.1 In order to study the
distribution of student attitudes more broadly, we have developed a Likert-style
survey. This has now been distributed to a large number of students in a variety
of classroom settings. Preliminary results from pre- and post-testing will be presented.
1. Hammer, D., "Two approaches to learning physics", The Physics Teacher
(December 1989) 664-670; and "Defying common sense: Epistemological beliefs in an
introductory physics course", Ph. D. thesis, University of California, Berkeley (1991) unpublished.
The Role of Examinations in Changing Student Attitudes
towards Physics and Learning Physics
Edward F. Redish
AAPT Meeting, Orlando, January, 1995.
Students in the introductory calculus-based physics class often have poor attitudes about
the nature of physics information and about their approach to learning physics. Many feel
that the physics learned in class has little connection to their personal experience or
to the real world. Many feel they either "get" the material or do not. They rarely have
the idea that the first piece of information that comes to their mind may not be correct
or appropriate. Since students pay little attention to advice if it does not appear
on exams, we have developed a style of examination that accentuates these two elements.
Questions include: (1) representation-translation short-answer questions that are easy
if one is thinking about a real world example - and almost impossible otherwise; (2)
estimation questions; (3) problems that include problem-building and problem-evaluation
elements. Exams are paired with make-up exams to encourage students to evaluate their
understanding. Examples will be given and results from surveys and interviews will be
discussed.
Comments and questions may be directed to
E. F. Redish
Last modified 10 May 2001