Reflective problem solving skills
are essential for learning, but it is
not my job to teach them
Charles Henderson
Western Michigan University
http://homepages.wmich.edu/~chenders/
Edit Yerushalmi, Weizmann Institute
Vince Kuo, Colorado School of Mines
Kenneth Heller, University of Minnesota
Patricia Heller, University of Minnesota
Elisheva Cohen, Weizmann Institute
1
Goal of this Study
Students in introductory physics are expected to learn
physics content through the process of solving problems.
• What learning skills do physics instructors believe
students need in order to learn from problem solving?
• What learning skills do physics instructors believe
students possess when they enter an introductory
physics course?
• How do physics instructors believe they can help
students to improve their learning skills during the
introductory physics course.
• Why do they believe so?
This is one part of a larger study on physics faculty beliefs and
values related to the teaching and learning of problem solving.
2
Research design
Data collection
Sample:
•6 Physics Instructors at U of MN, Randomly Selected out
of 23 that meet selection criteria: taught introductory
calculus-based physics course in the last 5 years
Semi-Structured Interview Tool:
•Based on concrete instructional artifacts
(problem statements, instructor solutions, grading)
•Interview questions: please describe how these artifacts
are similar or different to yours. Please explain your
reasons for having these artifacts the way you do
Interviews were videotaped and the audio portion
transcribed:
~ 30 pages of text/interview
Data analysis
Video- & audiotapes of
interviews (~9 hrs)
Concept Maps allow for:
• the reduction of complex
data into visual
representations
• explicit connections to be
made between ideas that
can then be tested
• Identification of shared
vs. idiosyncratic features
3
Research design
Interview transcripts
(~180 pages)
Statements
(~2400)
Concept Maps
(15 x 6 = 90)
Combined
Concept Map
(15)
4
General Result: Combined Concept Map
Perceived
external
constraints
Physicist and
instructional
values
limit
Solving physics
problems
[Fig. 2]
influence
needed for
Instructors'
actions
Students who
can improve
[Fig. 7]
help
Appropriate
knowledge
[Fig. 3]
construct
do not
construct
enough
Typical
students
[Figs. 8,9]
include
Making
Suggestions
to
encourage
Reflectively
Setting
Constraints
to
encourage
Work
[Fig. 4]
often
sometimes
Look/
Listen
[Fig. 6]
and can
then
Use
Feedback
[Fig. 5]
on
of
Appropriate
problems
[Figs. 10,13]
Providing
Resources
Individualized
responses
[Figs. 12,15]
at/to
at/to
of
Appropriate
example solutions
[Figs. 11,14]
Lectures
of
are sometimes
adapted to
For more details, see: Yerushalmi, E., Henderson, C., Heller, K., & Heller, P., Kuo, V. (2007). Physics Faculty Beliefs and
Values about the Teaching and Learning of Problem Solving Part I: Mapping the Common Core, Physical Review Special
Topics: Physics Education Research, 3 (2), 020109.
5
Role of student
To reflect on his work and compare it to that of the
instructor
Typical
students
[Figs. 8,9]
Students who
can improve
[Fig. 7]
often
Reflectively
sometimes
Look/
Listen
[Fig. 6]
Work
[Fig. 4]
and can
then
on
Use
Feedback
[Fig. 5]
of
Appropriate
problems
[Figs. 10,13]
Individualized
responses
[Figs. 12,15]
and can
then
on
at/to
at/to
Lectures
Students who succeed are
reflective
Use
Feedback
[Fig. 5]
of
of
Appropriate
example solutions
[Figs. 11,14]
Look/
Listen
[Fig. 6]
Work
[Fig. 4]
Appropriate
problems
[Figs. 10,13]
Individualized
responses
[Figs. 12,15]
at/to
at/to
of
Appropriate
example solutions
[Figs. 11,14]
Lectures
Typical students are not
reflective
6
Role of student
Examples of reflective
activities:
Examples of typical
student activities:
“Students would analyze their test
solution and maybe my test solution
to see where the major differences
are, and then try to work on it.”
“When students do HW or solve
problems it’s so tempting to just
look at solutions after working 2
minutes if you don’t know what to
do.”
“you have to discipline yourself to
say what, why did I write this down.”
“go through the strategy part of the
problem saying ‘what do I need to
know for this problem, and what are
the parameters that are specified, and
what are the things that I have to
calculate.’”
“I try to get students to think
consciously about their general
approach… not just sit and wait for
lightning bolts to strike.”
“Students spend large numbers of
hours just doing problems but not
doing them with a disciplined
approach.”
“There are many students who
make a mistake on the quiz and
say ‘well, that was a mistake’ and
then they’re not interested
anymore.”
7
Role of instructor
Instructors Suggest Reflectivity, but Require
‘Working’
Perceived
external
constraints
limit
Physicist and
instructional
values
influence
Instructors'
actions
include
Making
Suggestions
to
encourage
Reflectively
Setting
Constraints
to
encourage
Work
[Fig. 4]
Appropriate
problems
[Figs. 10,13]
Providing
Resources
Individualized
responses
[Figs. 12,15]
Appropriate
example solutions
[Figs. 11,14]
Lectures
of
8
Role of instructor
“I often tell students that if they are having difficulty
that what they should do is look at a lot of problems,
not necessarily work them, but look at the problems
and then go through the strategy part of the problem
saying to themselves ‘what do I need to know for this
problem . . .’”
“What I often say is that they have to solve problems
without looking at solutions, and if they get stuck,
talk to someone specifically about what the next step
would be, . . . so they don’t get . . . away without
thinking on their own.”
9
Instructors are Aware of the Gap!
“Unfortunately, there is a big gap between what I
would like students to do with solutions that I post
and what I'm fairly sure they are doing with them…
A large fraction of students are focusing too much
on the very problem at hand … as opposed to the
structure of the problem.”
“When I do solutions on the board during class I
hope that students just see how a professional
thinks about these sorts of things. Of course I
suspect in many cases they adopt the superficiality
of it.”
10
How Do Instructors Explain Why They
Do Not Impose Reflective Practice?
Three Perceived Constraints:
1. Workload: Instructors have limited time that they can commit to
the course.
“I think engaging students and getting them to do something,
no matter how wrong it might be, getting to do something on
their own while you help them is, I think, the key. It’s labor
intensive though.”
2. Student Expectations: Students might react negatively to
requirements such as providing a reasoned approach to the
solution.
“If I had given this a low score and the student came back
and said ‘but I got it right’ I would tell them that they didn’t
show that they were using the right principles. I usually give
them the benefit of the doubt when grading.”
3. Assessment considerations: Instructors recognize that
reflective practice is not assessed.
“There’s nothing specifically that we test for that really brings
these things [reflective problem-solving skills] out.”
11
How do Instructors Resolve the Conflict?
Have Limited Expectations of
What Students Will Learn
“The types of things in this stack [reflective problem
solving skills] are not built up over one course … I
hope they learn some of it in the course, but it's not,
these are things that aren't in the syllabus and that
you hope over 4 years of a university education, that
they cultivate.”
Instructors don’t expect students to
develop reflective skills during the course.
Yet, they believe that students without
these skills will not succeed.
12
Limited Expectations of What Students Will Learn
Appropriate
knowledge
[Fig. 3]
consists of
consists of
Knowledge & Skills
Related to Problem
Solving
(1,2,3,4,5,6)
Affective
Characteristics
(2)
Expert Problem Solving
Skills Are Not Learned
solving novel
problems (4)
demonstrated
by
consists of
consists of
consists of
consisst of
consists of
consists of
PHYSICS
CONCEPTS
(1,2,3,4,5,6)
APPROACH TO
SOLVING A
PROBLEM
(1,2,3,4,5,6)
SPECIFIC
TECHNIQUES
(1,2,5,6)
SELF
EVALUATION
(1,2,3,4,6)
Physicists beliefs
about problem
solving (1,3,6)
Physicists
style (5)
which
to
students
as used within
can depend on
learn well (4) which
(2,3,4,6)
which
can be
can be
can be
students
don't learn
(1)
students learn
somewhat
(1,3,5)
context of a
particular problem
(1,2,3,4,5,6)
which
which
students learn
somewhat (5)
get a solution after
deciding on
approach (1,2,5,6)
which
which
students
learn well (2)
General approach
not tied to a
particular problem
(3,4,5)
students learn
somewhat (5)
Evaluating if
headed in right
direction (1,3,4,6)
which
which
students
learn well
(2,4)
which
students
don't learn
(1,3,6)
which
students
don't learn (1)
e.g.
e.g.
e.g.
Working in an
organized way (3,4)
be aware of a
difficulty
(1,3,6)
knowing what
needs to be done
(4)
students learn
somewhat (5)
e.g.
students
don't learn
(6)
helps with (3,4)
students
learn
somewhat
(1,5,6)
which
Evaluating the
answer
(1,2,3,6)
it is "macho" to
put numbers in
only at the end (5)
e.g. that
by considering
reasonability
(2,3,6)
by checking
units (1)
Play around to see
what approaches
might be valuable
(6)
problem solving
involves
exploration (1,6)
most problems
cannot be solved in
a single step (1)
solving a problem
is not always a
linear process (1)
solving problems
is not a plug-andchug process (6)
problems can be
solved by logically
applying the laws of
physics (3)
13
Discussion
Instructors highly value reflective practice. They
perceive it as necessary for success in the
course. Yet, they do not impose it on students.
A possible explanation for this apparent conflict:
It is a norm in introductory physics courses that
reflective practice is not assessed. Thus it is a
lower priority and instructors are not committed
to invest time (their own and in class) to
constrain students to achieve it.
“If I had given this a low score and the student came back and said ‘but
I got it right’ I would tell them that they didn’t show that they were using
the right principles. I usually give them the benefit of the doubt when
grading.”
14
Implications
1. We don’t have to invest effort to convince
instructors of the need to develop
reflective learning skills
2. A possible key for change – renewed
assessment goals
•
Develop and suggest accessible assessment tools
that assess reflective practice
15