Implementing active-learning in an international context:
A study in introductory physics
G. Zavala1 and C.H. Kautz2
1
Tecnologico de Monterrey, Monterrey, N.L. 64849, Mexico, genaro.zavala@itesm.mx
Hamburg University of Technology, D-21071 Hamburg, Germany, kautz@tu-harburg.de
2
Abstract
Active learning has become widely recognized as a desired strategy for teaching in engineering
education. Many of the active-learning instructional materials have been developed in the US.
Instructors in non-English speaking countries wanting to implement these materials therefore face
the choice between (a) using the materials in the original English versions, and consequently
teaching in a language other than their students’ native language; and (b) using translations into the
local language. Two sets of implementations of a particular set of instructional materials for
introductory physics form the context for our investigation, one in Mexico and the other in
Germany. At each institution, we have collected and analyzed data from students in locallanguage courses and courses taught in English. Results from both institutions indicate that, on
average, students using the materials in English perform better than those using a translation. In
our effort to explain this result, we have identified several variables that affect student
performance. These include instructor factors such as commitment to active learning, as well as
student factors such as reasoning skills, English and native language proficiency, mathematical
skills, and prior academic performance. In our report, we analyze and discuss the influence of
each of these factors.
Keywords: Active-learning,
international context.
introductory
physics,
student
difficulties,
misconceptions,
1. INTRODUCTION
While active learning is becoming more widely recognized as a preferred mode of teaching in engineering
education, instructional materials that use this approach effectively are still rare. Many of the materials that are
available have been developed in English-speaking countries, most often the US. For institutions elsewhere, this
situation raises the question if and how these resources could be used either (a) for instruction delivered in
English to predominantly non-native speakers, or (b) for instruction delivered in the local language if the
materials are used in translation. There has been little research, however, on whether such materials can
successfully be implemented outside of English-speaking countries, and whether a translation may have any
adverse effect. This question is of particular importance due to the more intensive use of verbal reasoning in
active-learning conceptual teaching materials compared to traditional (formula-based) science and engineering
instruction.
2. OUTLINE OF THE PAPER
In the present paper we report on two sets of implementations of a particular set of instructional materials for
introductory physics at a large private university in Mexico and a small public university in Germany. We first
present the way we implemented the educational strategy at the two sites both in the original language and in
translation. Then, we discuss the ongoing assessment of the materials in these implementations through
multiple-choice tests and other instruments, including some of the analysis tools we are using to gain information
about the students’ level of understanding after working through the materials. Finally, we present some results
we have obtained in recent years, discuss them in terms of the different variables that are likely to affect the
learning outcomes, and present some conclusions based on the data gathered.
3. IMPLEMENTATION
Among the several active learning methodologies that have been developed in the last decade as a practical result
of Physics Education Research, PER, Tutorials in Introductory Physics [1] shows three distinct advantages: a) it
can easily be adapted to almost any kind of course structure since it covers the usual curriculum of introductory
physics; b) it places little demands on classroom time, materials, human and financial resources; and c) literature
reports [2] indicate that Tutorials represent one of the most effective teaching strategies for introductory physics.
Tutorials in Introductory Physics are a set of paper and pencil activities, helped in a few cases with very simple
laboratory equipment. The tutorial cycle (for each of the topics covered) consists of a pre-test, the Tutorial
worksheet, and a set of homework problems. The first and the last are activities carried out by the students
individually (and generally outside of the classroom) while the Tutorial is worked out in groups of 3 or 4
students during class time with the help of an instructor guiding them with a Socratic-style dialog.
The teaching strategy can be summarized in three basic steps: eliciting the student’s ideas about the specific
concepts involved, confronting these ideas with evidence provided by the Tutorial, and finally resolving the
inconsistencies. The pre-tests serve mainly the first step, while the Tutorial worksheets cover the remaining two
objectives [3]. The homework assignments are intended to help students strengthen and extend their
understanding of the concepts considered in the Tutorials.
The Tutorials were designed to be used as a complement to lectures, especially in large-enrolment courses that
are common at many research universities in the US. (In this setting, the tutorial workshops often replace more
traditional small-group “recitation” sessions in which problem solving is demonstrated to students by teaching
assistants.) Adopting the Tutorials at institutions that do not follow this pattern of instruction often requires that
an existing teaching format is found in which the Tutorials can be implemented. Moreover, implementations in
other countries can pose additional challenges. These may include the question of the language of instruction,
i.e., whether a translation to the local language is used or instruction in English is given to non-native speakers.
Other issues pertain to how student performance is monitored and assessment is carried out.
At Tecnologico de Monterrey (ITESM), introductory physics is taught in three separate semester-long courses,
that cover mechanics in the first; hydrostatics and hydrodynamics, mechanical waves, and thermal physics in the
second; and electricity and magnetism, as well as optics in the third course. All three courses are offered each
semester, and at any time throughout the academic year, more than 1800 students are enrolled in total. The
students are divided into lecture (and laboratory) sections of about 36 (and 18) students each. Every semester,
two of the lecture sections of each course are taught in English for students who are enrolled in an International
Program (IP) while for the others in a regular program (RP) the instruction is in Spanish. These sections have
the same curriculum and the same strategies as the Spanish sections. Tutorial worksheets are used in the lecture
and in the laboratory format, using English and Spanish, respectively, for the IP, and only Spanish for the RP
students. A Spanish translation of the Tutorials [4] was published by a commercial publisher and has now been
available for several years.
At Hamburg University of Technology (TUHH), the Tutorials have been adopted for the physics instruction of
students in General Engineering Science (GES) and in Electrical Engineering (ET = “Elektrotechnik”). The
former take a one-semester physics course that covers mechanics as well as a brief introduction to thermal
physics, oscillations and waves, and optics. As in most other first-year courses in the GES program, instruction is
carried out in English. Students in Electrical Engineering take a two-semester physics course that covers
mechanics and thermal physics in the first semester, and optics and an introduction to modern physics in the
second semester. Instruction for the ET students, as in almost all courses that are part of this program, is in
German. Since a German translation of the Tutorials is not yet commercially available, one of the authors (CK)
has translated the worksheets that were included in the two-semester course. The existence of both courses at
TUHH provides us with the opportunity to implement the Tutorials in both languages, mirroring the situation at
ITESM. In a two-year pilot run, Tutorials in the German course were first done on a bi-weekly basis before
adopting a weekly schedule as in the English course.
3.1 Pretests
At ITESM, in a previous semester pretests were implemented as voluntary on-line but only 40% of both IP and
RP students took the pre-tests. Currently pre-tests are mandatory and about 80% are taking them. At TUHH,
pretests had been implemented as voluntary on-line supplements in the ET course for two years and in the GES
course for one year. Averaged over the entire semester, student participation was relatively low in both courses:
less than 40% in the English (GES) course and less than 20% in the German (ET) course. In the current
academic year, different approaches were taken. In the ET course, pretests were no longer offered to the
students. In the GES course, they were made an integral part of the course by awarding a small amount of credit
(about 3% of the total credit points) for participation, regardless of the correctness of the students’ answers. As a
result, average student participation in the on-line pretests rose to about 75%, which is comparable to pretest
participation rates in Tutorial implementations at US universities.
3.2 Preparation of Tutorial instructors
Due to the non-traditional teaching style that is being used in the Tutorials, any implementation of these
materials requires a substantial amount of instructor training. In “standard” implementations at many US
institutions (where the Tutorial sections are facilitated by undergraduate or graduate teaching assistants [TAs]),
weekly preparation meetings are held for this purpose. During these meetings, first-time TAs are taking on the
role of a student while more experienced TAs or other instructors may model the behavior of a Tutorial
instructor. Ideally, seminars on student learning and results from physics education research complement these
TA preparation meetings.
At ITESM, some of the Tutorials are implemented during times that are scheduled as lectures, and are therefore
facilitated by the lecture instructors. These instructors are full- or part-time employees of the university and are
largely independent in their choice of teaching styles. There are three instructors’ meetings per semester, during
which preparation for two Tutorials worksheets occurs each time. These meetings are conducted as described
above, with the course coordinator acting as an experienced instructor. While it is not uncommon for instructors
to miss some of these sessions, most of the instructors have attended at least one preparation meeting for each
Tutorial that is currently being used in their course.
At ITESM, undergraduate teaching assistants (uTAs) are hired to teach laboratory session and assist with
instruction in lectures. Most uTAs are physics or engineering majors beyond their fifth semester with aboveaverage grades. All uTAs attend regular preparation meetings with the course coordinator. These meetings
follow the model described above and occur in an environment that resembles the classroom where they will
help instructors to implement the Tutorial.
The remaining half of the Tutorials are implemented during laboratory sessions. Here, a single uTA serves as an
instructor for 18 students. Undergraduate teaching assistants for the laboratory go through a similar preparation
as those assisting the lecture instructors.
At TUHH, Tutorials are implemented in small sections of less than 25 students in both the German (ET) and the
English (GES) course. In the ET course, these sections are taught by one or two undergraduate teaching
assistants (uTAs). As is the case at ITESM, the uTAs are physics or engineering students in their third or fourth
year of studies. In most cases, they have not gone through Tutorial instruction themselves and are therefore
required to attend a weekly preparation meeting similar to the ones described above. In the GES course, there is
only one lecture section of about 25 students that is taught by one instructor. Tutorials are implemented in a
workshop setting that is facilitated jointly by the instructor and an additional uTA. Largely due to the language
requirement, uTAs for this section have always been students in the GES program and (apart from the first
individual in this position) have therefore experienced Tutorial instruction in their own physics course.
4. ASSESSMENT OF MATERIALS AND DATA ANALYSIS
Our assessment of the effectiveness of the materials and their implementation relies to a large extent on
standardized multiple-choice (MC) tests. Such tests allow easy evaluation of large populations of students and
comparison with results reported in the literature. However, to allow the instructor some insight into student
thinking, the tests need to be constructed on the basis of prior research. If the distracters for each question form a
complete taxonomy of alternate conceptions and learning difficulties, they can be used to obtain a picture of the
students’ learning state, i.e. an inventory of alternate conceptions and their prevalence in a student population.
When administered both as pre- and post-test, such questions can be used to study the progress of student
learning and thereby assess the effectiveness of instruction in a particular course. Among the tests that fulfill
these criteria, we chose the Force Concept Inventory (FCI) [5] and the Conceptual Survey of Electricity and
Magnetism (CSEM) [6]. In some instances, we complemented these tests with free-response questions.
Both the FCI and the CSEM contain questions from several concept areas or dimensions. The FCI is a 30-item
test that is based on results of educational research about student alternative conceptions concerning force and
motion. It is composed of six dimensions that are related to Newtonian mechanics: kinematics, Newton’s 1st,
2nd and 3rd law, the superposition principle, and types of forces.
The CSEM is based on similar research on student understanding of electricity and magnetism. It is a 32-item
test that covers 11 concept areas of electricity and magnetism ranging from Coulomb’s Law to Faraday’s Law
with two to six items in each area. Since the CSEM does not include questions on electric circuits (which are part
of the course content) a modified version of the CSEM (hereafter referred to as modCSEM) was administered. It
consists of the entire CSEM plus 12 questions on electric circuits that were taken from the Electric Circuits
Concept Evaluation [7] but modified to fit the format of the CSEM (i.e. five answer choices for each question).
These questions on circuits add four concept areas: current, potential difference, equivalent resistance and RC
circuits.
For either test, a learning gain can be computed from pre- and post-instruction scores to assess the result of
instruction. A formula for the relative gain [8] is given by Equation (1).
g=
χ post − χ pre
1 − χ pre
(1)
Here, χpost and χpre are the fraction of correct answers for an individual student or for the class average in the
post-test and pre-test respectively. This parameter is widely used and is interpreted as a measure of what a
student or group of students learned relative to what they could have learned. Gains can be calculated for a
whole test or, if more detailed analysis is required, for a specific conceptual area of a test.
5. RESULTS
At Hamburg University of Technology (TUHH), the assessment of Tutorial instruction has so far largely
concentrated on administering the FCI. Pre- and post-test scores were used to calculate a relative learning gain.
The resulting value (g = 0.50) in the course taught in English (GES course), is comparable to values found for
research-based instruction at US institutions (g above 0.40). However, the outcome in the ET course using a
translation of the Tutorials into German was substantially lower (g = 0.28).
As mentioned above, the FCI is a standardized test that assesses students in six different areas or dimensions.
Table 1 presents the relative learning gains corresponding to the entire FCI, its individual dimensions, and two
specific questions, both for the course taught in English (GES) and the one in German (ET). Since the general
gain for GES students is substantially higher than that of ET students, it is not surprising that in every dimension
GES students have higher gains than ET students. However, the differences are not the same for all dimensions.
The greatest difference is in superposition. GES students have a gain of 0.56 while ET students have a gain of
only 0.08.
Item/Course
FCI
Kinematics
First Law
Second Law
Third Law
Superposition
Forces
Question 4
Question 17
GES
0.50
0.34
0.56
0.38
0.53
0.56
0.48
0.91
0.68
ET
0.28
0.22
0.23
0.20
0.24
0.08
0.20
0.44
0.29
TABLE 1. Learning gain of GES students compared to ET students
for the entire FCI test, the six dimensions and questions 4 and 17 of
the test.
In table 1 we also present results of questions 4 and 17 of the FCI to show examples of specific students’
conceptions and the differences on those conceptions between the two courses. Question 4 is related to Newton’s
third law. The question asks students to compare the force that a large truck exerts on a compact car in a head-on
collision to the force that the compact car exerts on the truck in the same collision. Students in the GES course
perform somewhat better in the pre-test than students in the ET course. Only 22% of ET students chose the
correct answer, i.e. that the forces are equal in magnitude. The remaining 78% of the ET students all chose the
same incorrect answer, indicating that the larger car exerts a larger force. This answer is the most common
misconception among college-level students, as reported in the literature. On the other hand, 35% of the GES
students chose the correct answer. About 85% of the students answering incorrectly stated that the larger car
exerts the larger force. After instruction there is a large difference in performance. While only 5% of the students
in the GES course chose an incorrect answer, 54% of the ET students still answered incorrectly (with all of them
choosing the most common misconception). It has been shown [9] that this alternative conception is very
persistent also in other student populations. While the Tutorials seem to have helped most of the GES students to
overcome the alternative misconception, they were not nearly as successful with the ET students.
Question 17 is related to Newton’s second law. The question asks students to compare the magnitude of two
opposite forces exerted on an object when it is moving at a constant velocity. The most common alternative
conception is that for an object to be moving, a force has to be applied [10]. 20% of GES students chose the
correct answer, i.e. that the forces are equal in magnitude in the pre-test. 75% of students with a wrong answer,
chose an answer related to the most common misconception, the force in the direction of the motion has to be
greater. The result of the post-test shows a very good improvement: 65% picked the correct answer. Among the
ones choosing an incorrect answer, 71% chose the most common incorrect reasoning. On the other hand, ET
students performed similar in the pre-test, 16% with the right answer and 74% of students with a wrong answer,
thought that the force in the direction of the motion is greater. However, the post-test shows different results.
About half of students were right and half were wrong. 74% of students who picked a wrong answer, chose the
answer related to the most common misconception. The difference between GES and ET students in
performance responding this question is not as significant as the previous, however, it shows that, in general,
GES students (those who take the course in English) overcome students alternative conceptions better than ET
students using the same instructional materials which are designed precisely with the objective of resolving
students difficulties.
At Tecnologico de Monterrey (ITESM), both the FCI and CSEM have been administered to students as a pretest
before and posttest after instruction. Students taking physics at ITESM are divided into groups of 15 to 36
students. The groups are taught by individual instructors who are either faculty members or part-time lecturers.
Although there are about 700 students each semester taking Mechanics and 500 students taking Electricity and
Magnetism (E&M), results will be presented for only those students who are enrolled with instructors who use
Tutorials.
Figure 1 shows typical results of learning gain at ITESM for the CSEM in the Fall 2005 and Fall 2006 semesters
as well as for the FCI in the Spring semester 2007. Learning gains are in general greater for the IP (those who
take the course in English) students than for the RP (those who take the course in Spanish) students. The
differences vary from semester to semester. A greater difference occurred in the Fall 2006 semester than in the
Fall 2005 semester. In general the gains and the difference between the two groups are smaller in the FCI than in
the CSEM as is evident from the figure.
Figure 1. Results of different semesters of the CSEM and FCI at ITESM. The figure presents
the learning gain of all students, IP (international program, in English) students, RP (regular
program, in Spanish) students and some groups with instructors who taught at the same
semester groups in English and groups in Spanish.
In figure 1 some results of students from individual instructors are included. During the Fall 2005 semester,
instructor B was teaching a group in the IP (in English) and another in the RP (in Spanish). The result for that
instructor was that IP students performed slightly better than RP students. During the Fall 2006 semester, there
were two instructors teaching E&M to groups in both programs. In both cases the difference between the IP
students and RP students is significant. However, the FCI results of Spring 2007 semester show that 1) gains are
significantly lower in the FCI than those in the CSEM for both programs, 2) IP students learning gains are
greater but almost the same as those of RP students, and 3) for an instructor who taught mechanics in both
programs, RP students performed better than IP students.
A summary of results in the last four years at ITESM is presented in table 2.
Summary of gains of FCI and CSEM
combined in entire participant student
population (8 semesters):
• In
four
semesters
IP-gain
is
substantially better than RP-gain
• In two semesters IP-gain is slightly
better than RP-gain
• In two 2 semesters IP-gain is the same
as RP-gain
Summary of gains from instructors teaching
both IP and RP groups (7 semesters):
•
•
•
•
In
three
semesters
IP-gain
is
substantially better than RP-gain
In one semester IP-gain is slightly better
than RP-gain
In two semesters IP-gain is the same as
RP-gain
In one semester IP-gain is lower than
RP-gain
TABLE 2. This is the summary of learning gains for eight semesters. The left part shows the
results for the entire populations of students both in the IP and RP. The right part shows the
results for students in the IP and RP with instructors who taught the course in both programs.
In general, there is a better performance of students in the IP program. In six out of eight semesters the learning
gain of students taking the course (mechanics or electricity and magnetism) in English is greater than that of
students taking the course in Spanish. In the other two semesters the gain is the same. Analyzing students of
individual instructors who taught the course in both English and Spanish during a semester the result is similar.
We presented results of the two institutions and found similar results. Students taking physics in English had
better learning gains measured with the FCI and CSEM than students taking physics in the local language
(German in TUHH and Spanish in ITESM). In the following section, we will discuss the possible reasons for
these results.
6. DISCUSSION
As indicated by the results from the FCI in both institutions and the CSEM at ITESM, students who are enrolled
in courses in English performed better (in our study) than those in courses in the local language. There are
several factors that may have contributed to this result.
We believe that a large part of the observed variation is due to differences between individual instructors. It has
been our experience in the past that a committed instructor with a well-chosen and clearly defined instructional
strategy can have a considerable positive impact on student learning whereas a more traditional instructor is
more likely to strengthen unwanted alternative conceptions in physics. We believe that this effect may account
for some of the differences in student learning gains.
To try to see how instructor affects learning gains, a report from uTAs (undergraduate teaching assistants who
help instructors implement Tutorials in the classroom) at ITESM was introduced during the Spring semester
2007. In the report four items were assessed: 1) percentage of Tutorials implemented (how many of them were
actually implemented), 2) percentage of worked Tutorials (an average of how far the students went working with
Tutorials worksheets), 3) student work (an assessment of how students worked from a very collaborative way
focus on the subject to a very individualistic approach or not focus at all), and 4) instructor interaction (the way
the instructor implemented the Tutorial, from establishing a Socratic style instruction all the time to
explaining/lecturing students all the time). With these four factors a grade was assigned to each instructor on a
scale from 0 to 100 and a “level of implementation” between 1 (best) and 3 (least) was constructed. Results are
presented in Table 3.
Instructor
Tutorials
Extend
Students (3)
Instructor (3)
Grade (100)
Level
1
36%
40%
2
2.5
13
3
2
81%
45%
2
2.3
35
3
3
100%
67%
1.2
1.2
83
1
4
95%
93%
1
1
93
1
5
83%
68%
2
2.2
43
3
6
92%
66%
1.1
1.8
66
2
7
100%
92%
1.5
2.5
60
2
8
17%
80%
1
2
12
3
9
100%
89%
1
1.2
93
1
TABLE 3. Average results from the survey for the different instructors of E&M at ITESM. The
grade is a factor that represents how well the implementation is done with that particular group of
students who had that instructor.
As Table 3 indicates, there are great differences among instructors. Implementation grades range from 12 to 93
(out of 100). The greatest influence to calculate the grade is the percentage of Tutorials implemented since the
results of the other three factors is multiplied by this factor. This is done because no matter how well the
instructor implements the Tutorial, if he or she implements two out of six, his or her students will not benefit at
all from the other four.
Instructor effect is related to implementation grade. The correlation factor between the average gain of students
of each instructor and the implementation grade of each instructor is 0.81. This is a high correlation factor and
means that instructors who are more committed to the instructional strategy had better results. An instructor who
implements all six Tutorials, interacts socratically with students, guides them to work as far as possible with the
worksheets and promotes collaborative work among the students, will obtain better results that instructors who
do not follow this strategy.
This is probably one of the most important factors of the difference in students’ learning gain. For instance,
during the semester the report was implemented, instructor 4 was an instructor who continuously taught the
English courses (International Program) and whose students have high learning gains. In both semesters Fall
2005 and Fall 2006, students of instructor 4 (course in English) performed better than the IP groups of instructors
B and C in figure 1.
However, there is still another factor since implementation does not explain everything. If we look at instructors
B and C (instructors with a level of implementation of 2) in figure 1, we notice that even though the results of
their students are above average in both programs (supporting the importance of instructor commitment), their IP
students perform better than their RP students. There should be another factor.
To see how important other factors are, a multi-variable analysis was performed. In the Fall semester 2007 we
gathered information of students taking electricity and magnetism. We obtained their grade point average in high
school (GPA), the TOEFL score at admission, the Lawson test [11] result (a test of scientific reasoning skills,
from now on LAW), and the pre-test result of the CSEM (preCSEM).
A simple correlation analysis of the CSEM gain against the mentioned variables shows that the Lawson test
correlates most strongly (0.39), followed by the high school GPA (0.38), then TOEFL (0.27) and lastly
preCSEM (0.17). Another interesting result is that TOEFL and Lawson correlate more strongly to each other
(0.42) than any of them to the CSEM gain. These results indicate that statistically there is a relationship between
the learning gain and the level of reasoning ability of the student and that the level of reasoning ability is related
to the level of English proficiency. Therefore, the better results obtained by IP students compared to RP students
at ITESM could be due to a better cognitive preparation of students since the level of scientific reasoning is
better.
A cluster analysis was done with results in the Fall semester 2007. The objective of that analysis was to find
clusters of class groups that are statistically similar in their performance according to learning gain. With a level
of similarity of 78%, it was found that there were five clusters given in table 4.
Cluster
1
2
3
4
5
Groups
1, 2, 6, 7, 9
3, 5, 8, 10, 11, 12, 13, 16
4, 14
15
17,18
TABLE 4. Clusters of statistically similar sections
measured by learning gain.
Cluster 1 in table 4 is formed by groups with instructors with implementation level of 1 and 2. Cluster 2 is
formed by groups with instructors with implementation level of 2 and 3. Cluster 3 is formed with groups with
instructors with implementation level of 3. Cluster 4 is formed by one group, an instructor with implementation
level of 1 who had only that group. Finally, cluster 5 is formed by two groups with the same instructor of
implementation level of 1 who had only those two groups that semester. As can be seen, there is a very good
relation between the level of implementation and how the clusters are formed. This result corroborates that
instructor is an important factor for learning gain.
7. CONCLUSION
In this paper, we have presented assessments instruments and data analysis for an investigation of student
learning in an international context. The FCI and the modCSEM have been administered and results have been
analyzed. Results from both institutions indicate that under the given circumstances students taking a course in
English perform better than students taking a course in the local language. We have discussed possible causes
and concluded that instructor qualification and commitment plays an important role, student reasoning skills as
indicated by the Lawson test have a large influence, and students’ English proficiency is an important factor.
These last two factors at ITESM are related to each other making difficult to generalize for other institutions. We
are currently gathering more data in both institutions to better understand the phenomena. Also, we are analyzing
the effect of the translation on student learning which it is possibly another important factor.
Acknowledgements
The authors acknowledge the support of the European Consortium of Innovative Universities (ECIU) project
funds. One of the authors (GZ) acknowledges the additional support received from Tecnologico de Monterrey
through grant number CAT050.
References
[1]
L. C. McDermott and P. S. Shaffer, “Tutorials in Introductory Physics”, Prentice Hall, first edition (2002).
[2]
E. Redish and R. Steinberg, “Teaching Physics: Figuring Out What Works”. Physics Today 52, 24-30
(1999).
[3]
L. C. McDermott, P. S. Shaffer and M. D. Somers, “Research as a guide for teaching introductory
mechanics: An illustration en the context of the Atwood's machine”. Am. J. of Phys. 62, 46-55 (1994).
[4]
L. C. McDermott and P. S. Shaffer, “Tutoriales en Física Introductoria”, Prentice Hall, pre-edición,
Buenos Aires, (2001).
[5]
D. Hesteness, et al., “Force Concept Inventory”. Phys. Teach., 30, 141-58, (1992).
[6]
D. P. Maloney, et al., “Surveying Students' conceptual knowledge of electricity and magnetism”. Am. J.
Phys., 69, S12-S23 (2001).
[7]
R Thornton and D. Sokoloff. “The Electric Circuits Concept Evaluation (ECCE)”, unpublished.
[8]
R. Hake, “Interactive engagement vs. traditional methods: a six-thousand student survey of mechanics test
data for introductory physics”, Am. J. Phys. 66, 64-74, (1998).
[9]
R. K. Boyle and D. P. Maloney. ‘‘Effect of written text on usage of Newton’s third law,’’, J. Res. Sci.
Teach. 28, 123–140, (1991).
[10] J. Clement. “Students’ preconceptions in introductory mechanics,” Am. J. Phys. 50, 66–71, (1982).
[11] Lawson,
E.
Classroom
Test
of
Scientific
Reasoning,
revised
ed.
http://lsweb.la.asu.edu/alawson/LawsonAssessments.htm