LEARNING AND EVALUATION OF TERMINAL VELOCITY IN A COLLEGE PHYSICS COURSE

C.P. Suarez Rodríguez 1,2, Cesar Mora Ley 3 M.H. Ramírez Diaz3 E. Arribas Garde4

1 Universidad Autónoma de San Luis Potosí (MÉXICO) 2 Escuela Normal de Estudios Superiores del Magisterio Potosino, Plantel 5 (MÉXICO)

3 Instituto Politécnico Nacional (MÉXICO) 4 Universidad de Castilla La Mancha (SPAIN)

Abstract

In Newtonian physics, free fall is any motion of a body where its weight is the only force acting upon it. Most students, even when they have a good understanding about free fall, are not able to understand what happens with an object’s velocity when it falls under the influence of other forces like the air resistance. When an object is falling under the influence of gravity or some other constant driving force, it is subject to a resistance or a drag force, which increases with velocity and the objet, will ultimately reach a maximum velocity where the drag force will equal the driving force. This final constant velocity of motion is called a terminal velocity. When this matter is discussed in the classroom in an introductory college physics course, the students very often have difficulties in learning this concept. Reason why we designed a didactic sequence with the objective to guide the students to understand, identify and change their misconceptions. This didactic sequence includes a 20 question multiple-choice test and an assessment tool to determine the level of conceptualization of students. The questions were initially selected to assess student’s qualitative conceptions about the causes of terminal velocity. In this paper we discuss the instrument design, the application and implementation of the didactic sequence in a group of 17 engineering freshmen. The didactic sequence used as the main core is a journalistic note based on the fall of a parachutist who tries to break the record in free fall, which brings the student to a real-life problem. Didactic sequence promotes active learning through collaborative student learning and promotes metacognition skills.

Keywords: terminal velocity, didactic sequence, assessment learning.

1 BACKGROUND

To enable students to take an active role in their learning process and develop the cognitive-metacognitive necessary abilities to acquire, procedural, conceptual knowledge, values and attitudes towards science, specifically in the subject of Physics, it is an essential process in academic development and requires a substantial transformation in their teaching, learning and assessment [1], along with teaching strategies that enable students to acquire skills to solve low complex problems under this perspective.

To make an instructional design, it is very important to consider a planning of didactic units [2], which takes in consideration the mental representations of the process and change of constructing that students have to learn. In order to be able to understand a scientific theory, students should be able to build models, emphasizing that to understand the mathematical structure of a theory, to build a physical model of the theory is not a necessary condition [3]. If it is certain that it should be encouraged to develop procedural skills, the instructional process must not nail down only to this but to develop skills that contribute to their scientific training.

Learning outcomes do not depend solely on how the teacher presents information, but also the way in which the student processes, internalizes, stores [4] and applies that information. It has been seen that students are able to build physical models, give explanations, propose alternative solutions and evaluate them and review the actions that lead them to those approaches and procedures that took them there, which implies an understanding the meaning of concepts and its application [5].

Precisely, these characteristics are called cognitive abilities, defined as mental operations and procedures that the student can use to appropriate contents and the process used for this, in other words acquire, process, retain and retrieve different types of knowledge and implementation. Rigney classifies such characteristics in representing capabilities (reading, images, speech, writing and drawing), selection capabilities (attention and intention) and auto directive capabilities (Auto Program and self) [6]. Although, they are also classified as general cognitive abilities and cognitive skills related to the mastery of content, and vary according to the discipline [7]. Herrera Clavero (2001) classifies them as cognitive (knowledge facilitators, allow to analyze, understand, process and store) and metacognitive skills (facilitators of the quantity and quality of knowledge you have, the products that demonstrate learning, control, address their application to problem solving tasks, processes) [8].

These characteristics are considered in Biggs’ instructional design, where from the Dunkin and Biddle’s proposal (1974), student’s perspective was integrated in the teaching-learning process [9]. The integral education that students of this decade require, should encourage teachers of all disciplines to develop teaching sequences that promote higher-order thinking involving science, technology and society harmoniously and interdependently, as we see it in unschooled life. To improve teaching, Biggs proposes to consider the approach to learning. He considers two main approaches: the deep and superficial, which describe the ways in which students interact with a teaching and learning environment; the factors that are relevant to the student are not independent of education, since the teacher can do a lot to encourage deep learning, desired in students [10].

The 3P model (Prognosis, Process and Product) proposed by Biggs states that learning occurs in three stages: Prognosis (before training), process (during) and the product (learning outcomes), at each moment certain factors related to learning are identified, in the prognosis step two factors are considered: the dependent student and dependents of the teaching context. Within the dependants of the student we can find the prior knowledge relevant to the topic, interest, ability, beliefs toward discipline, etc. In the teaching context, some factors are included, such as what and how it is taught among others, hence if the teacher considers, within the teaching-learning activities, relevant factors for the student. This factor of prognosis can be influential to favor deep learning which requires high levels of cognitive skills, which are necessary for science learning, like theorizing and scenario development, besides the application of knowledge to other contexts. This is where the challenge of the science specialist lies, how to include these aspects in a supportive learning environment that integrates the above mentioned aspects? Biggs model considers what, but not how to. For this, the proposed development of didactic sequences is made, based on the science teaching recursive model REC, for science education at the University.

In this sense, REC guides to planning activities in order to ensure the alignment proposed by Biggs it also enhances the contextualization of academic content so that students can go linking science, technology and society as a synergistic whole, starting from the design of didactic sequences that are inserted into the current interests of students to build and rebuild its learning and the appreciation about physics contents. The design of this didactic sequence provides an academic content linked to the environment but requires a complex understanding of scientific and technological aspects with which it interacts. This sequence was used in a group (n = 17) students in the first semester of physics at a public university in the state of San Luis Potosi, Mexico. The design procedure of the teaching sequence and its application is described next.

2 JUSTIFICATION

Planning is vital to ensure the quality of the educational process [11], In Mexico didactic planning is frequently used at the basic level of education, but it is not at the university level, where teachers are specialists in discipline but have little pedagogical training. It has been seen that strong disciplinary training does not assure a successful teaching. Scientific knowledge must be transformed for its teaching, on this basis, the strategies should help to represent and formulate the content in a way that is understandable to others, that can evidence organization of information according to the teaching objectives and the competences to develop in students. This requires time, design and pre-selection of the activities to develop both the student and the teacher [12]. The design of these sequences is aimed to student-centered learning as well as the processes of acquisition and construction of knowledge. Some authors have designed models of planning of sequences and teaching units, a comparative table is shown in Table 1.

Table 1. Comparison of different models for developing teaching sequences.

Autor Sánchez Blanco y Valcárcel, [13]

Magnusson, [14] Tobón [15] Driver y Scott [16]

Educative Level Basic Basic Basic and High School

Basic

Model Model for the design of Didactic Units

- Model GesFOC (Systemic management of skills training)

Constructivist Teaching Sequence

Oriented to: Develop pedagogical content knowledge of the teacher who designs i [17]

Consider the beliefs and knowledge of teachers and students

Assure the quality in the learning processes from competences.

Foster conceptual change based primarily on cognitive conflict.

Components Scientific and didactic analysis. Selection: objectives, teaching strategies and evaluation.

Knowledge and beliefs about: Science curriculum. Student understanding of specific topics of science. Orientations toward science teaching. Instructional strategies for teaching science. Assessment in science.

Problem situation in context. Skills training. Learning activities and assessment Means. Metacognitive process.

Explicit the students' ideas on the subject Restructure ideas Review and consider changes resulting from their conceptions (García, 2006)

Considers Scientific analysis Training analysis Targeting Selection of teaching strategies Selecting assessment strategies.

Beliefs

The context. Metacognition. Affective teacher mediation. Integration of other disciplinary fields.

Explanation of students Experimental work. Construction of explanations Confrontation of ideas of students Consolidation application of the constructed models.

Approach Nature of Science and nature of teaching and learning

Constructivism Socio formative Constructivism

Discipline Experimental Sciences.

Sciences Different disciplines. Sciences

Source: Own Elaboration

The teaching profile of higher education requires to consider a solid disciplined formation, be provided with sufficient knowledge to understand how the process of student learning occurs, that their teaching activities are grounded in constructivist current which departs from the previous experiences of students, encouraging cognitive conflict that triggers a search for solutions through discovery, generalizations or reasoning placing its application in daily life situations, and determined by the environment and especially in a social historic environment [18]. It requires a university professor who is conscious of the educational reality and the social role and contributes to the building of students as socially situated subjects, with the ability to respond to the challenges that the economic and cultural development imposes and also requires to promote sensitivity to the needs of their peers. It is then necessary that teachers design educational situations for students to play a more active role in class that constitute an alternative to simply memorizing [19].

On the other hand, educational models should close as much as possible to the specific needs of college students, and take into account their characteristics according to the environment in which they live, as background for instructional design. The question, is then, promote learning that is meaningful to the students and their belief towards science and learning it is positively transformed. How to achieve that Physics become a subject of reflection, and not only a solution of exercises without being interesting to the student? This brings us that the experience and constant reflection of teachers toward their educational practice should be active, planned and intentional, and promote steady and consciously student motivation to learn and develop skills in research, analysis, synthesis, critical judgment and decision-making as well as the ability to socialize their learning. In the words of Mastache, it is considered that a person is technically capable and works properly according to their own standards

thereof. A competent person is someone who not only has the knowledge and technical skills, but also the practical and psychosocial skills required by the situation [...] and is able to clearly communicate their ideas to others, to coordinate their work with other professionals, understand the views of others involved ... The world never presents technical situations; the world is, by definition, socio-technical. A science teacher should then consider how to include such aspects in instructional design. [20]

This implies the union between academic contents, independent student’s living and learning and teaching strategies designed by the teacher, as stated by Villalobos Every educational action takes place in an educational space formed by these three structures, [Educational content-teacher-student] and although each one follows its own development process and also there is an interaction with the other two structures, they are all characterized by their mutual independence through a process of permanent displacement. Only from this combination, the professional in education can effectively fulfill its educational activities and offer comprehensive education [21].

That is why a REC model is proposed for the development of didactic sequences for a university level, considering aspects of the models presented in Table 1, but unlike them, a development of nonlinear teaching sequence is proposed, that is, from the results of activities, misconceptions and/or procedural student, to design activities that can add up to the initial proposal. In this proposal, besides considering beliefs, prior student’s knowledge and metacognition activities, the mental model is also considered. The proposed activities of the model are shown in Figure 2.

Fig. 2. Descriptive diagram of Recursive Model of science education (REC). Source: Own Elaboration

3 DESIGN AND IMPLEMENTATION

To identify points that are relevant in learning about the concept of terminal velocity, and develop learning strategies to include in the teaching sequence, the previous ideas that the students had were identified. So its function was trifold: 1) know the preconceptions of students 2) develop a teaching sequence and 3) understand the evolution of concepts due to the instruction with the teaching sequence.

For this, an instrument with an objective test of 18. The topics test aims to identify what is relevant to the student, according to academics contents that are wished to evaluate and stimulate interactions between their ideas. According to Adkins (1990) this type of testing can assess the mental processes of high level deduce principles and relationships, form combinations of ideas, to extend these principles to new situations, etc. Although for them it is necessary that the student has expertise related to academic content to value. The author recommends that the answers are hierarchically ordered in some form of scale, therefore it has been considered to use the proposed levels by the SOLO taxonomy (Structure of Observed Learning Outcomes) by John Biggs (2006). In addition, it is wanted to contribute to align learning.

Recalling that the subjects are enrolled in an introductory course in general physics, where contents of kinematics and dynamics are reviewed and is wanted to know the effectiveness of the teaching sequence based on the REC model, the validity of the test is of content [22], it is therefore to make the design, first the academic contents to be evaluated were identified, afterwards the sequence and the way to structure it, to classify the level of complexity of the items it was considered the proposed levels of the SOLO Taxonomy as it can be used to evaluate the quality of learning and to establish the

objectives of the curriculum [10]. To reduce the unreliability of content test a conceptual map, which is shown in Figure 3, was prepared.

Fig. 3. Conceptual map about content associated physical terminal velocity. Source: Own Elaboration

In Table 2 it can be observed the classification of reactive according to their level of complexity, where the action to be performed by the student and the evaluation thereof is described. In the classification of reactive pre structural level was not considered because according to the curricular there is already a precedent of the concepts of physics since they are college students. The number shows the reactive number in the test relate to the specific situation.

Recalling that the reliability of a test refers to the degree to which the test serves the purpose for which it was created, to minimize the unreliability derived qualifier, as to the influence of irrelevant factors such as the order in answers specific suggestions were given to students to narrow the range of expected responses. To reduce the vagueness or lack of key grade categories of possible responses, some categories were considered, both to ensure correct and incorrect assessment standards validity of the instrument. To avoid restricting the range of the assigned grade a key grade was prepared which noted the scores according to the responses. Instructions and directions were integrated to guide the student in the expected response even though they didn’t know what it was being explored about their knowledge in terminal velocity. They were assigned the space for the response to ensure that the student did not extend the argument beyond what I expected.

Table 2. Identification of the degree of difficulty of the test according to the SOLO taxonomy.

Biggs’ Levels

Contents

Unistructural Multistructural Relational Amplified Abstract

Free Fall Identifies that the free fall is an accelerated motion. (13)

Classifies the differences in the distance in the same time, related to how quickly. (3) Identifies that free fall is an accelerated motion. (13)

Explains the difference in the speed change by the effect of the acceleration due to gravity. (4)

Vectors Recognizes that the magnitude of a vector is associated with the size of the arrow (18) Identifies the vector sum by the graphical method (19)

Force Recognizes that an accelerated movement has changes in speed (17) Recognizes that the net force is the result

Analyzes the effects of the net force on the acceleration (16)

of the vector sum of all forces (19)

Drag Force Identifies the definition of air resistance. (15)

Reports that the decay time can vary in different fluids (6) Repa the fall time can vary due to the shape of the object. (9)

Explain the effects of the frictional force experienced by the body during its movement in terms of the density of the medium. (7) Predicts the effects of the frictional force on the speed (8, 11) Explain the effects of the contact area on the frictional force (10)

Thinks about the effects of the falling speed of the friction force (12) Predicts that the frictional forces cause a variable acceleration (14, 20)

1st. Newton Law Recognizes the first Newton Law(21)

2nd. Newton Law

Applies the 2nd Newton Law object mass m subjected to the action of gravity. (1.2)

Theorizes about the effects of the medium in motion of objects subjected to the action of gravity. (5)

Source: Own Elaboration.

The test results helped to identify areas where students need to reaffirm their knowledge. These academic contents were selected for consideration in the teaching sequence. Resources and learning objects were selected from free materials available on the web, magazines, etc. which facilitates the teacher's work, experiments and educational prototype was designed by the teacher.

One aspect was to consider activities that facilitate students to transit between different mental models. Mental models are representations of a system and are essential for modeling physical phenomena and the conceptualization of the world around us. Its operation is given when decisions and/or explanations of a phenomenon are made without performing mathematical calculations, but only based on past experiences and using analogies [23]. Latkin and Chabay (1989) conclude that expert students, when trying to solve problems, qualitatively describe concepts, that is to say without using equations, imagine and propose the solution [24]. To facilitate the construction of an adequate mental model that favors the appropriation of the concept of terminal velocity have been introduced in the teaching sequence elements that foster student-observation, description, explanation and argumentation of the facts, scilicet to promote their scientific reasoning around this problem, passing from the idealized physical model, the formulation of explicit model up to the construction of appropriate mathematical model and the description and interpretation of a physical law [23].

In the case of falling bodies, building activities were conducted to provide students with tools that allow them to navigate between different mental models, which are shown in Table 3. In order to promote higher order cognitive skills and communication skills, in addition to the skills required to perform scientific work.

Table 3. Proposed activities within the teaching sequence for the construction of an appropriate mental

model based on Kofman.

Mental Model

(Kofman, 2000). Academic Content Characteristics Description

Idealized Idealized representation of the system.

Free falling bodies The system is described from the selection of certain parameters and discarding those that are deemed necessary.

The effects of frictional forces with the environment, the shape and size of the object are discarded

Explicit Operative representation of the physical world

Objects subjected to frictional forces.

The physical model material is selected.

Even if all the real conditions are neglected, the effects of frictional force on the falling

bodies are introduced.

Mathematical Model Mathematical representation of a system through Mathematical equations or statistical distributions of random values.

Model of motion in the presence of resistive forces.

Obtaining a mathematical model through video analysis using Tracker free software and conference presentation given by the teacher

Obtaining the model through an experiment and solution of a differential equation.

Source: Own Elaboration.

The experiment aims to enable the student to analyze the relationship between the frictional force and the velocity of a falling object in different ways, for them a strategy is implemented using shareware. It is proposed to make a video to determine the landing position of an object in function of time. The experiment involves videotaping the fall of the object and later, using a software to analyze the video and its position, velocity and acceleration using the tools provided by the software, it has been seen that this technological tool facilitates experimental work at low cost [25], [26]. Measuring the position of the object is possible because the images are constructed by pixels that provide insight labeled variation as they advance on the photograms [27]. It has been considered an experiment based on the use of free software called Tracker. The integration of the aforementioned aspects allowed structuring the teaching sequence shown in Table 4. During the development of the lesson plan some aspects were identified that require attention therefore during the process some activities were integrated which are also shown in Table 4. This was due to doubt or errors that students had during the development of activities that must have been solved.

During the teaching process, we found necessary to help the students to understand the movement under a drag force that is why we proposed two extra experiments who help the students to build the concept. After those experiments, they were able to explain, calculate and apply the mathematical model in different contexts situations.

Table 4. Description of a lesson plan, the results of the teaching sequence made from the REC Model.

Activity

Propose Activity Source Evidence Academic content

Introductory focal Activity Activation of prior knowledge 30 min

Favoring a cognitive conflict. To introduce the student to the subject. Calculation of speeds using the mathematical model of free fall

Presentation of reading one day in advance. Basic questions: From the reading: Identify if the case is a real situation. What is the social importance of the experiment: from the perspective of: Government, society, science and scientists. In a plenary make recovery of prior knowledge. The student will make an individual description of the problem. With individual contributions the students going to build a group conclusion

Newspaper article Guided discussion sheet.

Open and expectant attitude. Answers to questions guide. Single conclusion. Group Conclusion.

Identification of the problem. Contextualization of the teaching situation. Freefall.

Reflecting on the variables involved in a movement in freefall. Contrasting results 30 min

Reflecting on the variables involved in a movement in freefall. Contrasting results

Video presentation, ask one day in advance. Basic questions: What similarities are between the jump Kittinger with Baumgartner? What disciplines of science were required to make this leap? Calculate the speed at different points. Compare your results. Calculate the velocity

Felix Baumgartner Jump http://www.youtube.com/watch?v=7QFbC1jMres

Report to calculations Answers to questions guide. Single conclusion. Conclusion group.

Fall in a real context.

Problem solving

Take the student to

Show the video to students Power Point presentation to

Notes. Textbook.

Friction force.

20 min the conclusion that there is a problem of free fall, but in the presence of resistive forces.

Set and solve the problem using freefall using problem-based learning. The student will attend counseling with the teacher open for solving doubts. The teacher opens a discussion around these issues identified by students in solving the problem and conclude that the problem is not in freefall but resistive forces are present

explain the solution. Textbook, chapter motion with constant acceleration, free fall. Guided discussion.

Guided discussion. Metacognition activity.

Experiment different fluids 20 min

Qualitatively identify the presence of the frictional force in liquids with different densities.

The student will enter an object of mass m in containers with different liquids such as air, water, cooking oil, motor oil. They will report the movement characteristics in different liquids. Report its findings in groups. The teacher will open a plenary discussion about the conclusions drawn by the students, and the theoretical justification for the proposed solution.

Student Notes. Textbook. Guided discussion.

Experiment report.

Relation between related variables

Mathematical model presentation 60 min

Analytical solution

Professor conduct the presentation of the mathematical model, with a focus on questioning (by inquiry)

Professor conduct the presentation of the mathematical model, with a focus problem by questioning l

Student report Analytical solution of the problem through a differential equation approach and the application of Newton's laws.

Felix Blumgartner. case 60 min.

The mathematical model applied to the solution of real problems

Students work in collaborative teams following the ABP in solving the problem by applying the mathematical model. Present their results in plenary.

Student Notes. Textbook. Guided discussion.

Student Notes. Textbook. Guided discussion.

Application of the analytical solution to a real life problem.

Model application 30 min.

The mathematical model applied to the solution of problems

Students will solve individually with teacher's guidance three exercises selected by the teacher. Students will present the Solutions.

Student Notes. Textbook. Guided discussion.

Evidence for troubleshooting.

Application of the analytical solution to several problems.

Close activity 15 min.

landing concepts

Develop a list of keywords and points that were considered important in solving the problem. It will draw a single conclusion from the report of metacognition. landing concepts

A graphic organizer of their choice. It may be a concept map.

Retrieve information about basic aspects of terminal velocity.

Synthesis of terminal velocity concept.

Suggested activities due to the identification of needs for the implementation of the teaching sequence

Experiment falling objects in different medium. 120 min

Measure the effects on the speed of the friction force in liquids with different densities.

Provide guidance for the development of the experiment. The student will enter an object of mass m in containers with different liquids such as air, water, cooking oil, motor oil. They will report the movement characteristics measured with the video analysis help. Report its findings by computer. The teacher will open a plenary discussion about the conclusions drawn by the students, and the theoretical justification for the proposed solution.

Experiment guide guided discussion Tracker software for video analysis and measurement of physical parameters associated with the problem

Report experiment Personal conclusion. Group conclusion Metacognition report.

Measurement of friction forces in each medium. Experimental measurement of the terminal velocity.

Experiment Slow descent 60 min

Identify the effects of the frictional force decreasing in speed.

Students work in collaborative teams following the ABP in solving the following problem: Design and create an artifact, using a sheet of A4 paper 80 g / m2 to take as long as possible to fall to the ground through a

Student Notes. Textbook. Guided discussion.

Oral presentation. Personal conclusion. Group Conclusion. Report Metacognition Report.

Identifying parameters related to the friction of a falling object.

vertical distance of 2.5m. A small amount of glue can be used. Investigate the influence of relevant parameters. Present results in plenary

Source: Own Elaboration.

4 CONCLUSIONS

This work shows an example of the construction of didactic sequences to promote the learning of science at university level, considering not only the context, the beliefs, the previous knowledge and interests of students, considering the misconceptions identified during the process which allows to satisfy the learning needs, since the activities of metacognition and socialization of learning have allowed to exchange experiences that promote knowledge construction. Currently it is being worked on the evaluation of the use of didactic sequences in the construction of complex thought attending the dimension of problem solving elements: problem formulation, analysis and causality approach options for problem solving and decision-making. The recursive model for Science learning differs from other models, in which the construction of didactic sequences is that normally during the proposed activities initially are maintained until the end and does not consider the inclusion of other activities even when the need is evident of building an intermediate concept, as well as not all activities are set to the whole group but they are proposed to address the particular needs of a group of students or even for one student. This allows continuous assessment through a feedback process rather than one feedback. This model suggests the importance of using free materials like articles or news from newspapers, television commercials, and/or any free resource to facilitate teachers’ work design. It is noteworthy that in Mexican universities especially in public universities, it is not common for teachers to develop teaching sequences and even less for them to build based on a model, this proposal demonstrates the usefulness of developing didactic units beyond the particular considerations teachers.

REFERENCES

[1] Pozo J. I. Gómez-Crespo (1998). Aprender y enseñar ciencia. Morata. Madrid España.

[2] Campanario, J. M. y Moya A. (1999). ¿Cómo enseñar ciencias? Principales tendencias y propuestas. Investigación didáctica. Enseñanza de las ciencias, 1999, 17 (2), 179-192

[3] Greca, I.M., Moreira, M.A. (1998). Modelos Mentales y Aprendizaje de Física en Electricidad y Magnetismo. Enseñanza de las Ciencias, 16 (2), 289-303.

[4] Weinstein C.E. Mayer R.F. (1986). The teaching of learning strategies: Handbook of research teaching New York McMillan 315:327

[5] Chi, M.T.H., Bassok, M., Lewis, M., Reimann, P., y Glaser, R. (1989). Self-explanations: how students study and use examples in learning to solve problems. Cognitive Science, 15, 145-182

[6] Rigney, J.W. (1978). Learning strategies: a theoretical perspective. En O'Neil, H.F. (Ed.): Learning strategies. Academic Press, New York, 165

[7] Corbi R. G. (2003). Adquisición de habilidades cognitivas. Factores en el desarrollo inicial de la competencia experta. Tesis Doctoral. Universidad de Alicante. 1: pp 10-38

[8] Herrera C. F. (2001). Habilidades Cognitivas. Notas del departamento de Psicología Evolutiva y de la educación. (Universidad de Granada. España) Disponible en: http://www.cprceuta.es/Asesorias/FP/Archivos/FP%20Didactica/HABILIDADES%20COGNITIVAS.pdf consultado 15 de noviembre del 2013.

[9] Dunking M. Biddle B. (1974), The study of teaching. Ney York, New York. NY: Holt, Rinehart & Wiston.

[10] Biggs, John (2006). Calidad del aprendizaje universitario. Narcea, S.A. De ediciones. España

[11] Tobon S. (2006). Competencias, calidad y educación superior. Coop. Edición Magisterio.

[12] Kind, V. (2009) 'Pedagogical content knowledge in science education: potential and perspectives for progress, Studies in science education. 45 (2). pp. 169-204

[13] Sánchez Blanco, G. y Valcárcel Pérez, M.V. (1993). Diseño de unidades didácticas en el área de ciencias experimentales. Enseñanza de las ciencias, 11 (l), 33-44.

[14] Magnusson, S., Krajcik, J. y Borko, H. (1999). Nature, Sources and Development of Pedagogical Content Knowledge for Science Teaching, en Gess-Newsome, J. y Lederman, N.G. (eds.). Examining Pedagogical Content Knowledge , pp. 95-132. Dordrecht: Kluwer Academic Publishers

[15] Tobon S. (2010). Tobon Tobon S, Pimiento Prieto J. H. Garcia Fraile J. A. (2010). Didácticas: Aprendizaje y evaluación de competencias. Mexico D.F: Pearson.

[16] Driver R. Asoko H. Lean J. Scott P. Mortimer E. (1994) Constructing knowledge in the classroom. Educational researcher. 23; 5.

[17] García Franco, A. y Garritz Ruiz, A. (2006). Desarrollo de una unidad didáctica: el estudio del enlace químico en el bachillerato. Investigación didáctica. Enseñanza de las ciencias, 24(1), 111–124

[18] Hernández, Hernández, P. (2005). Psicología de la Educación [5a reimpresión]. México: Trillas.

[19] Campanario, J. M. Y Otero, J. C. (2000). Más allá de las ideas previas como dificultades de aprendizaje: Las pautas de pensamiento, Las concepciones epistemológicas y las estrategias metacognitivas de los alumnos de ciencias. Enseñanza de las ciencias, 2000, 18 (2), 155-169.

[20] Mastache, A. (2007). Formar personas competentes. Desarrollo de competencias tecnológicas y psicosociales. Argentina: Noveduc.

[21] Villalobos Pérez-Cortés, E. M. (2007). Didáctica integrativa y el proceso de aprendizaje. México: Trillas.

[22] Adkins Wood, Dorothy. (1990) Elaboración de test: Desarrollo e interpretación de test de aprovechamiento. 2ª. Edición. México. Editorial Trillas. 2ª edición 2008.

[23] Kofman, S del Estero (2000). Modelos y simulaciones computacionales en la enseñanza de la Física. Revista Educación en Física. 6: 13. Disponible en: fiq.unl.edu.ar Consultado el 15 enero 2014.

[24] Larkin, H., Chabay R. (1989). La investigación sobre la enseñanza del pensamiento científico: implicaciones para la enseñanza basada en computadoras. Recopilación de Resnick, Lauren B. y Klopfer Leopold E. “Curriculum y cognición”. Editorial Aique.

[25] Gil, S, Reisin, H. y Rodríguez, E. (2006) Using a digital camera as a measuring device. Am. J. Phys. 74 (9), pp 768 –775.

[26] Calderón E. S., López-González S. y Gil. S. (2007) Determinación de la fuerza de roce con el aire usando nuevas tecnologías. Revista de Enseñanza de la Física Vol. 20 (1) 55-6.

[27] Laws y Pfister, H. (1998) Using Digital Video Analysis in Introductory Mechanics Projects, Phys. Teach. 36,282-287.