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Students reinventing the general law of energy conservation
Logman, P.S.W.M.
Publication date
2014
Link to publication
Citation for published version (APA):
Logman, P. S. W. M. (2014). Students reinventing the general law of energy conservation.
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Conclusion
Introduction
In the Netherlands the curriculum innovation committees for the exact sciences have advised a context-based approach (Boersma et al., 2007; Commissie Vernieuwing Natuurkunde onderwijs havo/vwo, 2006; Driessen & Meinema, 2003). Two unsolved problems in context-based education are the difficulty to achieve transfer (Parchmann et al., 2006; Schwartz, 2006; Goedhart et al., 2001) and the difficulty to develop abstract concepts in contexts (Parchmann et al., 2006; Pilot & Bulte, 2006; Schwartz, 2006). The concept of energy conservation is an abstract concept which is difficult for students to apply to various situations (Borsboom et al., 2008; Liu et al., 2002) and to adjust when necessary (Kaper, 1997).
The main question for our research has therefore been stated in Section 1.1 as: “How do context and concept interact in context-based education that is suitable to develop a versatile concept of energy?”
To answer this research question we have developed a context-based teaching-learning sequence in which a versatile conception of energy conservation may be developed. To improve the versatility of students’ conceptions we have chosen a guided reinvention approach (Freudenthal, 1991). We have chosen to embed the teaching-learning sequence in authentic practices (Boersma et al., 2007).
To research the development of the intended teaching-learning sequence and analyze its results and the learning process within it, we have divided the main question for our research into four researchable questions in Section 1.3. Based on the results given in Chapters 2 through 6 we will answer each of these four questions.
7.1 Research question 1 - Developing a versatile concept of
energy conservation
The first question as posed in Section 1.3 is:
“How can we organize the development of a versatile concept of energy conservation by students while making use of a teaching-learning sequence set in authentic practices?”
In Chapter 4 we have described our final educational design partly based on the results of Chapters 2 and 3. The results of the evaluation of the learning process of the final educational design have been presented in Chapter 5. A quantitative analysis of how many students successfully improved the versatility of their
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conception of energy conservation in the teaching-learning strategy is given in Chapter 6.
Description of final educational design
In our final educational design we have chosen to make use of guided reinvention to increase the versatility of resulting conceptions and to substantiate the general law of energy conservation with evidence. We have embedded our teaching-learning strategy in contexts to motivate students. Authentic practices have been used to let them experience the relevance of what is learned and to get students to understand how this knowledge functions in society. We have combined this with the problem posing approach to give students a reason to perform every step in the learning process (see Section 4.1 for a more elaborate background of the choices we made).
The learning process is subdivided into three consecutive learning steps: reinventing partial laws from measurements, combining those partial laws into one combined law, and extrapolating that combination process to arrive at the general law of energy conservation (see Section 4.2.1 for a more elaborate description and Sections 6.4.1, 6.4.2, and 6.4.3 for expected students’ results). We have embedded these learning steps in three technological design assignments (conceptual learning step I) followed by three consecutive scientific assignments (conceptual learning steps II and III) (see Section 4.2.2). These assignments have been shaped into work phases which are characteristic for the authentic practices so they can show how the resulting concepts function in these practices (see Section 4.4).
We will now discuss the three conceptual learning steps in more detail.
Conceptual learning step I
The results on deriving a partial law from measurements improved from the first to the last assignment (see Section 5.5).
Because in the scientific assignments the conceptual goal and contextual goal are almost the same the need for a physical law is more clear in such assignments than in the technological design assignments where the contextual goal contains many other aspects (e.g. special safety features) than the conceptual goal (a partial law of energy conservation) we aimed for. To assure that the relevance of the partial law that we aimed for in the technological design assignments was clarified to more students than only those that applied the law in their advice reports we used classroom discussions based on students’ reports and aimed at finding the optimal solution accepted by all students. In these discussions it was observed that the students chose the solutions in which the intended partial law was applied as the best (see Section 5.4.1). Therefore we conclude that embedding the teaching-learning sequence in technological design assignments enables students to see the relevance of the reinvented partial conservation laws.
147 the transition from merely testing a laboratory scale model of their solution
to investigating a quantitative relationship, and
the derivation of a relationship from measurements.
To improve the results on these two issues a few extra hints for the teacher and the addition of certain questions to the educational material are suggested in Section 5.4.1.
Conceptual learning step II
Students learn how to include a new variable into the conservation law during conceptual learning step II. This includes combining a new partial conservation law with the one established earlier. As a preparation for performing such a combination by themselves during the final scientific assignment the teacher showed the students how the combination procedure is performed during the first two scientific assignments.
The steps from studying the new variable up to performing an experiment to find a new partial law did not cause major problems (see Section 5.4.2), except for describing a suitable experiment to find a new partial law, and describing the procedural steps to perform a combination of such laws. Other steps that are needed before both laws can be combined and that went well are: describing phenomena that can connect the new variable with a variable that is already included in the conservation law, naming the preconditions and domains of earlier established partial laws, and describing the procedural steps for the derivation of a new partial law from measurements.
After the teacher had given the results of an appropriate experiment to the students about two thirds of them derived the partial law of energy conservation that describes the results of the experiment (see Section 6.5.2) Most of those students started combining the new partial law with the earlier established law but only about half the students that derived the new partial law finished this procedure successfully and met our strict requirements (see Sections 5.5 and 6.5.2).
The two main issues left are that students had difficulty in applying preconditions to their proposed experiments and in identifying which procedural steps were necessary to successfully combine partial laws of energy conservation (see Section 5.5).
The analysis for conceptual learning step II has shown that it is possible, in principle, for students to take every substep of conceptual learning step II (see Section 5.4.2). We have also observed that a classroom discussion can be used to guide students through the process of combining partial laws (twice) to enable at least a part of the students to do it themselves a third time (see Section 5.5). However because only about a third of the students (see Section 6.5.2) were capable of reaching the goal of this conceptual learning step improvements are needed.
Specific recommendations on expanding the role of preconditions in all assignments and on making students see the need for each step in the combination procedure in the scientific assignments are given in Section 5.4.2.
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Conceptual learning step III
Having chosen a guided reinvention approach we want the students to substantiate the general validity of the law of energy conservation with evidence. To do so the students are expected to discuss each step of the combination procedure to determine whether expanding the conservation law is always possible when necessary. The procedural reflections in the first two scientific assignments serve as a preparation for this step but the step itself can only be taken by the students themselves in the third and final scientific assignment.
During the preparation for conceptual learning step III about a fifth of the students described the combination procedure completely.
In answering the question on the general validity of the conservation law about a third of the students discussed at least one of the seven necessary procedural steps (see Section 6.5.3). Each of the seven procedural steps was discussed by at least one of the students but there was no student discussing all procedural steps (see Section 5.5). A few students discussed six out of the seven procedural steps. In the end almost two third of the students were explicitly convinced that it would always be possible to expand the law. None of the students explicitly stated that this would not be the case (see Section 6.6).
The main issues left concern the recollection and critical understanding of the procedural steps by the students.
By adding a scientific debate after the students have formulated their evidence for the general validity of the conservation law the results may improve. The teacher can make sure that each of the seven procedural steps are discussed at the end of the first two scientific assignments so the students may see the need of discussing all the steps to form a substantiated opinion on the general validity of the law. The discussion will also help them expressing their opinion on the general validity of the law better (see Section 5.5).
The learning process as a whole
For a new teaching approach a first step is to try out whether the various substeps in the intended learning process are feasible (Plomp, 2007; Gravemeijer & Cobb, 2006; Nieveen, 1999). We took on such a challenge by developing a teaching-learning sequence in which students are to reinvent the general law of energy conservation and we have shown that it is possible for each step in the learning path to be taken by at least part of the students. The interaction between context and concept in the teaching-learning sequence may be described as follows:
1. the need for a concept stems from a characteristic (the built-in need for an extrapolation) of a specific problem within a context (see Chapter 2), 2. the concept is subsequently generalized by comparing various situations
within the same context (conceptual learning step I), and
3. the concept is then applied to the original problem within that context to come up with a specific solution to it.
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There are more aspects to the concept such as its domain, its preconditions, and the procedure by which it is derived. As for the concept itself also for these aspects a need must be created for them and these aspects subsequently may be applied in new assignments. However, the need for these aspects becomes apparent at different stages in the context than the stages where the need for the concept shows itself. The same holds for the stage in which they are applied (see Section 5.5).
For example the need to generalize the domain of the concept shows itself in describing as many future problems as possible. This is used to guide the students in the classroom discussion at the end of each technological design assignment. The application of the domain does not occur until an experiment is to be proposed to solve a subsequent technological design or scientific problem.
7.2 Research question 2 - Characteristics of authentic
practices
The second question as posed in Section 1.3 is:
“Which characteristics does an authentic practice have that is suitable for developing a versatile concept of energy conservation?”
The discussion in Section 7.1 shows that it appears possible to develop an abstract concept such as energy conservation while embedding the learning process in authentic practices.
Based on the results from various chapters we can now identify characteristics of authentic practices that contribute to the learning process. In Chapter 2 we discussed the first design and try-out of our material and as a result identified a characteristic of technological design practices in which students can reinvent partial laws of energy conservation. Chapter 3 discussed the second design and try-out which added a characteristic to that first result and made us choose to use scientific practices for the learning step of combining partial laws and extrapolating the combination procedure to reinvent the general law of energy conservation. In Chapter 4 we have mentioned these characteristics and explained how they are applied in our final educational design. In Chapter 5 the try-out of this final design is described from which one more characteristic was drawn for a scientific practice in which combining partial laws and the extrapolation of that procedure is encouraged.
The identified characteristics are summarized in the following paragraphs. In Chapter 3 we noticed that some students did not see the need for experimenting when a ready-made solution was available to the context (e.g. electric lifting apparatus).
A characteristic for technological design practices that makes students see the need for an experiment turned out to be the following:
1. the problem needs to be set in a time or place in which a ready-made solution is not available (see Section 3.4).
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In our educational design we experienced that we could use the same characteristic for scientific practices to prevent students from coming up with combined laws from other sources without knowing how to combine partial laws themselves.
In Chapter 2 we noticed that in descriptions for technological design problems in which the solution could be tested on a realistic scale students logically did not see the need for a physical law to translate their laboratory scale results to the real solution. The following characteristic has been tried out to solve this: 2. the problem needs a solution that cannot be tested on a realistic scale but
can be tested only on laboratory scale to make students see the need for a physical law to extrapolate the laboratory-scale solution to the real solution (see Section 2.6).
Dierdorp (2011) found a similar characteristic for using authentic practices in mathematics.
To prepare students for combining partial laws by themselves we needed students to find specific preconditions of the partial laws of energy conservation. In the second try-out of the assignment of designing a rollercoaster we noticed that for students the absence of friction was more essential to the problem in designing an uphill rollercoaster than in designing a downhill rollercoaster (see Section 4.3). The precondition of having no friction is necessary to derive the specific partial laws we aimed at but also later on in the learning process for taking conceptual learning step II in which students are to combine partial laws with specific preconditions.
Thus, for technological design practices in which students are to combine partial laws of energy conservation we identified the following characteristic:
3. the technological problem should be such that any solution to it requires an insulated system, e.g. friction is undesirable for an uphill rollercoaster (see Section 4.3).
In trying to take the final conceptual learning step III we wanted students to discuss all seven procedural steps for combining partial laws (see Table 5.12) in order to form a substantiated opinion on the general validity of the law of energy conservation. More than half the students did not discuss any procedural step and only a few discussed six out of seven (see Section 6.6). We propose to organize a scientific debate among the students to improve these results. Therefore we formulate the following characteristic for a scientific practice: 4. the practice needs to lead to a scientific debate on the validity of the
generalization of a procedure in a natural way to make students see the need of discussing procedural steps before validating a generalization of a procedure like combining partial laws (see substep 22 in Section 5.4.2).
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7.3 Research question 3 - Resulting versatility of students’
conceptions
The third question as posed in Section 1.3 is:
“To which extent can students develop a versatile conception of energy conservation in context-based education making use of authentic practices?”
In Chapter 6 we presented the results of our summative evaluation. These will be discussed together with the recommendations we formulated in Chapter 5. In Chapter 1 we subdivided versatility into applicability and revisability. The first is described by the domain in which the students are able to apply their conception of energy conservation, the second describes students’ capability of revising their conception of energy conservation. For the latter we have described various levels (see Section 1.2.3):
Revisability level 1.1: students are able to generalize a partial law from specific situations.
Revisability level 1.2: students are able to combine various partial laws into one combined law.
Revisability level 1.3: students are able to extrapolate the combination procedure for partial laws to establish the general law of energy conservation.
These levels coincide with the expected results of learning steps I, II, and III so quantitative results for these levels are reported in Chapter 6 and summarized in Section 7.1. For all types of versatility (applicability and revisability) except revisability level 1.3 we have shown that part of the students are capable of attaining them (see Section 6.6). For improving the results for revisability level 1.3 we have given recommendations to also make this revisability level attainable for students.
The applicability results for sixteen- or seventeen-year-olds answering the Energy Concept Inventory (Swackhamer & Hestenes, 2005)(see Section 6.5.4) were comparable to the results for eighteen-year-olds given in preliminary research by Borsboom (Borsboom et al., 2008). We have divided the various situations in which students were to apply their conception of energy into very near transfer, near transfer, and far transfer. Very near transfer meant that students were to apply their conception in the situation from which they had derived a partial law of energy conservation. Near transfer meant that students were to apply their conception of energy conservation to other situations from the same domain but not the one they derived the law from. Far transfer meant that students had to apply their conception to uninvestigated domain parts of a combined law. Dividing the Energy Concept Inventory questions according to these categories again showed similar results for sixteen- or seventeen-year-olds that had followed our teaching-learning sequence as those for eighteen-year-olds in preliminary research (see Section 6.5.4). Furthermore about three quarters of the students were capable of answering questions comparable to
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those of the Dutch exam without making conceptual mistakes (see Section 6.5.4). Overall the applicability results are comparable to traditional approaches. Of our student couples 64.7% (n=34) were able to reinvent a partial law from measurements and thereby showed that they attained revisability level 1.1 (see Section 6.5.1). By combining partial laws of energy conservation correctly 32.4% of our student couples showed that they attained the accompanying revisability level 1.2 (see Section 6.5.2). Most of our recommendations concern this revisability level. Generalizing the combination procedure in order to end up with the general law of energy conservation was only tried out once. None of our students showed a complete discussion of the combination procedure but 38.2% discussed at least one of the procedural steps to substantiate their opinion that the law of energy conservation is generally valid (see Section 6.5.3). About two thirds of all the couples concluded by themselves in assignment 6 that it is always possible to expand the conservation law when necessary and none of the couples stated that this would not be possible. The procedural reflection functioned for only just over a third of the students. The question whether such a procedural reflection is attainable for students at this level is difficult to answer.
The recommendations we have for future try-outs include giving more attention to the development of the domains during the combination procedure to clarify each step in it and to expand the role of preconditions in selecting experiments suitable for the research at hand (see Section 5.5).
7.4 Research question 4 - Achieved competencies as a
physicist
The fourth question as posed in Section 1.3 is:
“Can a teaching-learning sequence that is aiming at the general law of energy conservation also enhance the competencies of a student as a physicist?”
This question is seen as a part of our evaluation of the learning process given in Chapter 5. It is also discussed together with the given recommendations in that chapter.
For the technological design skills we were able to analyze possible improvement by tracking students’ skills from the first assignment to either the second or the third which were done in parallel.
Students clearly showed progress in skills such as formulating uncertainties containing the essence of a technological design problem, proposing experiments that fit the research at hand, performing measurements, and deriving physical laws from them (see Section 5.5).
It was harder to analyze students’ progress on the scientific skills because in the first two scientific assignments the teacher was allowed to show the students in a classroom discussion how to apply the most important of the scientific skills: combining partial laws. For that skill we therefore only had one measurement
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during the final scientific assignment. Several of the scientific skills for which we could track progress already showed 60% to 80% of the students capable of it from the start. The scientific skills for which we were able to identify improvement were describing the procedure to derive laws from measurements and actually deriving such laws (see Section 5.4.2).
In traditional teaching the concept of energy conservation, technological designing and the scientific method are normally treated separately. We have shown that a separate treatment is not necessary.
By embedding the learning process in authentic practices, besides making progress towards the conceptual goal of our teaching-learning sequence, it also proved possible to improve students’ skills as a physicist in technological design practices and scientific practices.
7.5 Reflection
To conclude, all our answers and recommendations are discussed in the light of future teaching of the subject of energy, possible variations of our educational design, social acceptability of our approach, the relation between our research and the current Dutch curriculum innovation, and the contributions to educational research.
Future teaching of the subject of energy
Because the research was performed by a teacher-researcher first of all it is interesting to discuss what it has delivered for future teaching. First, the teachers involved in the second and third try-outs developed new ideas on teaching the subject of energy conservation. These ideas can also be applied to teach other subjects in contexts (e.g. crash test engineers reinventing Newton’s second law ). The approach consumes about 30% more contact hours than a traditional introduction to energy conservation but the approach combines this conceptual goal with learning how to solve technological design problems and how to employ the scientific method. By embedding the teaching of energy conservation in authentic practices the students enhance their competencies as a physicist and get to know how physicists function in technological design and scientific practices as well.
Possible variations of our educational design
The six assignments were now given sequentially in one course but the assignments may also be spread over more time and even more school years. The technological design assignments may be given in any order and also earlier or in the same grade as we did (sixteen-year-olds). It may be more suitable to give the scientific assignments a grade later (seventeen-year-olds) because especially combining partial laws seems to be more demanding. A clear connection between the assignments however has to be assured.
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Social acceptability
Compared to traditional approaches our educational design seems to fit the new Dutch exam requirements better. The educational design addresses many exam requirements in one coherent course that results in similar conceptual results as for traditional approaches.
Deriving physical laws from measurements embedded in technological design practice (conceptual learning step I) has proven to be effective. This approach can be applied for other concepts as well. It is too early to make similar claims for conceptual learning steps II and III. Further research on these two steps is necessary in which the given recommendations can be tested on their effectiveness. For many concepts in physics and other exact sciences these conceptual learning steps however are not necessary. They are only necessary for the more abstract concepts in which several generalizations succeed one another (e.g. conceptual learning step II appears necessary in a guided reinvention of the ideal gas law ).
Relation between our research and the current Dutch curriculum innovation
At the start of this research project we decided not to test our ideas using the new materials that were created at that time in preparation for the new Dutch exam program. Even though those materials are based on contexts they are still traditional in handing the students the general law of energy conservation as an indisputable fact. At that stage of the research we did not have strong enough arguments to convince the authors responsible for those materials to try a different approach. At the end of the research we think we now have stronger arguments to make the writers consider a different approach. This implies that even though the innovation committees took ample time to try out new materials to test the new exam program it is advisable to have educational research on a new approach precede the development of new material.
Contributions to educational research
First of all we have expanded the theory on versatility (Dekker, 1993; Van Parreren, 1974) by subdividing it into applicability and revisability. We have subdivided the latter further into several revisability levels using the ideas of assimilation and accommodation.
We have given evidence that it is possible to develop abstract concepts in contexts and have given characteristics for authentic practices suitable to develop such abstract concepts.
Last but not least we have shown that a new phenomenological approach to teaching the concept of energy conservation is feasible. Because of the lack of data from other approaches it is difficult to compare this approach to other approaches. More data and more research on the various approaches to teach the concept of energy are needed to be able to decide in the future which approach is most suitable for which aspect of energy and for which type of students.
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Teacher and researcher in one
Being both a teacher and a researcher has had advantages and disadvantages. At the beginning of the research I first had to develop all sorts of educational research skills. Having come from a technical background this broadened my view on scientific research. It also made me respect social research more because of the tough analysis phase it contains. Now, at the end of this research, I think this has made me what I set out for: a broader developed person.
My limited knowledge of the physics educational research knowledge database was a disadvantage. As a teacher it is difficult to obtain access to educational research articles. If one wants to bridge the gap between teachers and educational research it would be my first advice to give interested teachers free access to the most important educational research material.
Being an experienced teacher it made me dare to take more chances in developing the teaching-learning sequence than educational researchers might have done. This has made the teaching-learning sequence more suitable to research our ideas on versatility and context-based education.
It has also given me an intermediary role between teachers and researchers which helps to bridge the gap between them. Besides that I got to see some excellent teachers and laboratory assistants at work in their own environment sparking a great exchange of ideas between us.
In the end this research made me a better teacher in many ways although I have to admit that at busy stages in the research I had to reduce my attention to my school tasks to a minimum. It has been a trying period of my life but in the end it was worth it. “There are no shortcuts to any place worth going.” 1
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