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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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An innovative educational approach
aiming at a versatile concept of energy
combining context-based education with
guided reinvention
1Abstract
In the Netherlands curriculum innovation committees for the exact sciences have advised a context-based approach. A promising interpretation of context-based education is to have students develop concepts while solving problems stemming from authentic practices. Two well-known issues in context-based education are the lack of transfer and a difficulty to develop abstract concepts from contexts. The lack of transfer causes developed conceptions to be little versatile.
In traditional education students may develop non-versatile conceptions as well. An example of that is the general law of energy conservation. To develop a teaching-learning sequence that may improve the versatility of abstract conceptions developed in a context-based approach we therefore have chosen the law of energy conservation as our target concept. To have students develop their conception of energy conservation within authentic practices we have chosen guided reinvention as our conceptual approach. Thinking critically throughout its reinvention we expect students to construct a more versatile conception of energy conservation than in traditional education.
Choosing a combination of guided reinvention and a context-based approach that makes use of authentic practices led us in three rounds of try-outs to develop an innovative teaching-learning sequence that may guide students to a more versatile conception of energy conservation. In developing our teaching-learning sequence we have found that a gradual shift from technological design contexts towards scientific contexts may be deployed to guide students to reinvent abstract quantitative physical concepts.
1 This chapter has been submitted for publication as Logman, P. S. W. M., Kaper, W. H.,
& Ellermeijer, A. L. (2014). An innovative educational approach aiming at a versatile concept of energy combining context-based education with guided reinvention.
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4.1 Educational design problem
Students’ conceptions of energy at the end of Dutch secondary education have been assessed as inflexible in formal examination tasks (Borsboom et al., 2008). University engineering students have also been observed not being able to apply their conception of energy to specific problems (Liu et al., 2002). A comparable flexibility problem with university students following chemistry courses on thermodynamics has been identified by Kaper (1997). The general law of energy conservation is mostly taught as an unsubstantiated fact and as such has lost the connection to its practical scientific origin. This may cause students not to see the general applicability of the law while they also tend to believe it is not true because the concept contradicts their life-world experiences (Borsboom et al., 2008; Doménech et al., 2007; Liu et al., 2002; De Vos et al., 2002; Kaper, 1997; Driver & Warrington, 1985).
To substantiate the general law of energy conservation with proof a very different approach is needed. Knowledge and ability, when acquired by one’s own activity, stick better and are more readily available than when imposed by others (Freudenthal, 1991). Therefore we have chosen guided reinvention as our conceptual approach for a new teaching-learning strategy that aims at contributing to a solution to the afore-mentioned problem.
Guided reinvention does not mean the students need to follow history’s path exactly. History teaches us how concepts in physics have evolved including the blind alleys and numerous circuitous paths. In hindsight we can guide the students along a more efficient route: “children should repeat the learning
process of mankind, not as it factually took place but rather as it would have done if people in the past had known a bit more of what we know now”
(Freudenthal, 1991).
Historically the energy concept has grown from establishing partial laws of energy conservation each with their specific applicability (e.g. Huygens’ discovery of the conservation of vis viva for elastic collisions (Hugenii, 1728)), and connect those when a situation calls for it. Joule described many experiments connecting caloric, living force, and other variables (e.g. the heat evolved by a revolving bar of iron is proportional to the square of the magnetic influence to which it is exposed (Joule et al., 1884a)). Because he knew about all these possible combinations Joule was already convinced there should be a fixed relation between mechanical energy and heat before he did his famous experiment (Joule, 1850). His famous experiment only confirmed this conviction (Joule et al., 1884b):
“The general rule, then, is, that wherever living force is apparently destroyed, whether by percussion, friction, or any similar means, an exact equivalent of heat is restored. The converse of this proposition is also true, namely, that heat cannot be lessened or absorbed without the production of living force, or its equivalent attraction through space.
Thus, for instance, in the steam-engine it will be found that the power gained is at the expense of the heat of the fire,—that is, that the heat occasioned by the combustion of the coal would have been greater had a part of it not been absorbed in producing and maintaining the living force of the machinery. It is right, however, to observe that this has not as yet been demonstrated by experiment. But there is no room to doubt that experiment would prove the correctness of what I have said.”
We have chosen to try bringing our students to a similar point as Joule, by letting them discover several partial laws of energy conservation first. The next thing we will ask the students to do is to combine the discovered laws to expand the applicability of the law. The partial laws involved do not necessarily have to be the ones that were discovered first historically nor does the order in which they are combined need to follow history. The procedure of ever further combining partial energy conservation laws could suggest to students, like it did to Joule, that conservation of energy is applicable at all times and under all circumstances. We hope this will make the usefulness and validity of the general law of energy conservation clearer to our students and in that sense will increase the versatility of the law. In situations where energy appears to be missing such students will look for a missing term in the law conform Feynman’s Dennis the Menace story in his introduction to energy conservation (Feynman et al., 1963).
We think that the process of reinvention is needed to convince students of the general validity of the law (cf. Feynman et al., 1963; Joule et al., 1884b). In this approach, the law will, as we prefer, become debatable and will no longer be an unsubstantiated fact. Students that take a risk in stating that the law is generally valid (like Joule) and students that criticize that idea (like Thomson initially did (Smith & Wise, 1989)) are both necessary (Popper, 1963). Through scientific discourse between the two science progresses.
Knowing the way in which the law is constructed and critically thinking throughout its reinvention may cause the students’ conception of energy conservation to be more susceptible to later necessary adjustments and in that sense also make it more versatile.
Versatility of a student’s conception thus shows two sides:
1. Applicability: are the students able to use their conception in many diverse situations?
2. Revisability: can the students extend/adapt their conception when new situations call for it?
We want to design our approach in such a way that it can guide our students towards reinventing a versatile concept of energy conservation in both senses of versatility.
To motivate students and to make them appreciate the relevance and usefulness of science in general, innovation committees for the exact sciences in the Netherlands have advised a context-based approach (Commissie
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Vernieuwing Natuurkunde onderwijs havo/vwo, 2006). In context-based education two major issues are found: a difficulty to achieve transfer from one context to another (Parchmann et al., 2006; Schwartz, 2006; Goedhart et al., 2001) and a difficulty to develop abstract concepts in contexts (Parchmann et al., 2006; Pilot & Bulte, 2006; Schwartz, 2006). More research is needed on these two issues, which are relevant for education on energy conservation. Energy conservation is an abstract concept and lack of transfer may obstruct the applicability of a student’s conception of it. Because our research is focused on both of these aspects this strengthens our choice for energy conservation as the target concept of our teaching-learning sequence.
We follow Gilbert in his choice for ‘context as the social circumstances’ as the most promising category of contexts (Gilbert, 2006). As a member of the innovation committees for the exact sciences Boersma (2007) specifies this choice for biology more precisely by choosing authentic practices as contexts for education. Bulte (2006) states that such practices are a means to learn concepts that are valued by our society, and to learn how this knowledge functions in society. We adhere to this more precise interpretation of contexts as well. In his analysis of contexts as the social circumstances Gilbert (2006) states that the context determines which concepts are useful to it. The problem posing approach (Lijnse & Klaassen, 2004) concurs with this in requiring that learning should be driven by problems that students can identify with. Every step in the learning process should be useful in solving such a problem, in the eyes of the student. During this process the teacher has to be careful not to use guidance stemming from the intended conceptual goal.
In light of the above we can summarize the criteria we imposed on our educational design as follows:
1. To be able to increase both types of versatility of the students’ conception
of energy we will make use of the guided reinvention approach consisting of taking learning steps in the way described earlier: starting by extracting several partial laws of energy conservation from experiments followed by combining those laws and ending in extrapolating that combination procedure.
2. To motivate students to appreciate the relevance and usefulness of the
energy concept and to teach them to some extent how physicists work we will embed our approach in contexts, further specified as authentic practices.
3. To guide the students through the learning process we will make use of the
problem posing approach by making sure that for taking every learning step only reasons are used that stem from assignments within a certain authentic practice.
In the following section we will describe our educational design rationale by drawing inferences from the above criteria, using research results from others as well as from our first two rounds of try-outs (Logman et al., 2010, 2011). Subsequently the implementation of that rationale will be illustrated in our educational design.
4.2 Educational design rationale
The teaching-learning sequence aims at students reinventing the general law of energy conservation in a way that should make their conception versatile. First we will describe the main conceptual learning steps. Subsequently we will describe suitable authentic practices to embed the learning trajectory.
4.2.1 Design of conceptual development
With our teaching-learning sequence we aim at sixteen- or seventeen-year-old pre-university students who have little or no quantitative knowledge about the concept of energy. Our goal is to have the students construct a versatile conception of energy. Only after one of its main characteristics, namely that it is conserved, has become clear, we introduce the term ‘energy’ to describe the student’s conception. We think that in this way we can avoid a necessary conceptual change at the beginning of our teaching-learning sequence. Instead the students construct a conception of energy clearly demarcated from, and next to, the students’ preconception of energy (Genseberger & Lijnse, 2007; cf. Warren, 1982). We think that if the students get time to construct a conception of energy that is strong enough it is possible to replace the very persistent preconceptions of energy they may have (Kaper, 1997; Solomon, 1983). This way the necessary conceptual change is facilitated by placing it at the end of the learning process. Even though we do not build upon their preconceptions, we do intend to build upon the students’ general technological and scientific knowledge (like performing experiments, measuring variables, extracting laws, etc.) by embedding the assignments in suitable contexts.
We assume that for most students it is not possible to reinvent the general law of energy conservation in one go. Therefore, to make sure that the students can reinvent the general law of energy conservation from their assignments, we need to divide the learning process into smaller steps that are manageable for our students to take. As a first learning step (I), following history, we hope students to reinvent what we call partial laws of energy conservation each with its own applicability domain (for examples see Table 4.1).
Table 4.1 Examples of partial laws of energy conservation
Example situation from applicability domain Examples of partial laws of energy conservation2
Lifting and lowering objects in balance. ∑ Insulated mixing of hot and cold substances
(Lavoisier).
∑
2 The constants in these partial laws of energy conservation are only constant under
specific preconditions and may thus depend on other variables and vary over different experiments.
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Elastic collisions (Leibniz/Huygens). ∑
Frictionless object on a spring in a horizontal plane.
∑ ∑
Frictionless object on a spring. ∑ ∑ ∑
In a second learning step (II) the students are asked to combine these partial laws into more and more general laws of energy conservation (e.g. combining
∑ with ∑ to form ∑ ∑ ). Because it remains possible that new terms will show up, this combination procedure does not lead to a point where one can be sure that the law is complete: the result may still be only a partial law of energy conservation.
Therefore the students need to take a third learning step (III) in which they are to extrapolate the steps needed in the procedure of every combination of laws and check whether those procedural steps are always possible. If the student arrives at the conclusion that combining a new term into the law is always possible when needed, in the student’s mind the law must now have become applicable to any situation and can therefore truly be called general (as opposed to partial): the general law of energy conservation has been reinvented. If however the student is not convinced of the general applicability, at this point he can be asked to come up with arguments why.
Either way, at this point the students should be able to apply this law to many different situations. Even in situations in which the students do not know all the relevant terms we expect them to look for and reinvent the missing term(s) to make the law complete for that specific situation (cf. Feynman et al., 1963). An increase in the two aspects of versatility has been built into the learning trajectory. Every time that in the course of steps I, II, and III the students revise their conception successfully, the applicability of the physical law increases from a specific situation via an expanded domain to finally incorporating any possible situation.
An overview of the three intended learning steps and their conceptual goals is given in Table 4.2.
Table 4.2 Learning trajectory
Conceptual learning step Conceptual goal
I: Reinvent partial law of energy conservation. e.g. ∑
II: Combine partial laws of energy conservation. e.g. ∑ ∑
III: Extrapolate the combination procedure through reflection.
∑ ∑ ∑ 3
Conceptual learning step I
Reinventing a partial law of energy conservation comprises more than only summarizing the data from an experiment: the students need to establish the
3 Meant to describe the general law of energy conservation including any terms as yet
scientific boundaries of the domain of the partial law as well and hypothesize that the partial law applies to all the situations within that domain. Every time after a partial law of energy conservation is supposed to be reinvented we use a worksheet to guide a discussion between the students and the teacher to reflect on the domain of the newly reinvented law and its preconditions.
During learning step I it is difficult to reinvent partial laws involving more than two characteristic variables. Therefore we have chosen to limit step I to reinventions of partial laws involving no more than two characteristic variables.
Conceptual learning step II
In this learning step the students are asked to combine several partial laws aiming at a more generally applicable law of energy conservation. Because a new term containing a new characteristic variable may always be added the result is still only a partial law of energy conservation. To be able to add a new term, a partial law needs to be available that involves both the new characteristic variable and an already incorporated characteristic variable. If we were to add more than one term at a time this would involve a partial law containing at least three characteristic variables which again would be difficult to reinvent. Therefore in our teaching-learning sequence we have chosen to expand the original partial law of energy conservation by only one term, containing one characteristic variable, at a time.
In this combination procedure the applicability domain of the law expands from the two separate original domains in which only the original variables vary. After a successful combination the new domain includes extra domain parts in which not only the original variables may vary but all variables are allowed to vary at the same time as well (see Table 4.3).
Table 4.3 Domain overview INCREASES Height Temperature D EC R EA SE S Height ∑ ∑ ∑ Temperature ∑ ∑ ∑
Combining two terms results in four domain parts, adding a third term expands the domain to a 3 × 3 matrix containing nine domain parts, etc. Even without counting possibilities for more than two variables to vary at the same time, the combined domain shows a larger than linear growth in domain parts per added term4. During the learning process we use a matrix similar to Table 4.3 to
4 Each cell in the matrix stands for a domain part in which one variable increases and
another decreases. If the variable that increases is the same as the one that decreases that domain part involves two objects. If two different characteristic variables
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convince the students of the usefulness of combining partial laws of energy conservation.
Every time after a combination is planned a similar reflection as in step I is used to initiate a discussion of the domain of the newly combined law and its preconditions.
For the students to be able to take learning step II at least two partial laws need to be reinvented. If a partial law involving both an old and a new term is not yet available, step II necessitates the reinvention of such a partial law as well.
Conceptual learning step III
During the last learning step the students are asked to extrapolate the combining of partial laws to see how far the procedure may extend. During this part of the learning process again we use a matrix similar to Table 4.3, this time in a worksheet to guide the students in identifying a new term (and its characteristic variable) to be added to the already established law. The procedure of combining this new term into the law can now be investigated to see how the combination procedure actually takes place and whether the steps in that procedure are always possible.
If students have become convinced that this is the case they can be introduced to the term energy because at this point one of its main characteristics, namely that it is conserved, has become clear. If they have not become convinced they are still expected to be able to discuss the validity of the general law of conservation of energy.
We think that to be able to take this final learning step, the students need to have performed at least two combinations (to see what they have in common) and therefore at least three partial laws need to be reinvented. The final learning step however incorporates a new combination (an extra step II) which in its turn again may necessitate the reinvention of a certain partial law (an extra step I), as explained in step II above.
Bearing in mind the above we can now design a complete learning path of assignments up towards our intended conceptual goal. We have chosen to have the students reinvent five partial laws of energy conservation in total (five times learning step I: see left column in Figure 4.1) and combine them into an ever more general law in three separate steps adding one term at a time (three times learning step II: middle column in Figure 4.1). During the last of these three combinations the students are to reflect upon the combination procedure and check whether the steps needed in that procedure can always be performed (one time learning step III: the right in Figure 4.1).
increase or decrease its domain part can be seen as a combination of the constituting cells.
Figure 4.1 Overview of the conceptual learning trajectory.
In situations where energy appears to be missing the students need to become able to add a missing term which means they need to reinvent a new partial law (step I) directly followed by combining it into the already established law (step II). To prepare the students for this some of the steps I may be taken together with a subsequent step II. This is especially the case for the final step II. Two examples of such a step I are indicated in the left column of Figure 4.1 by the different greyscale of their edges. The other examples of step I can be taken separately from step II. For similar reasons the final step II may be taken together with step III to guide the students in reinventing the general law of energy conservation (again indicated by a different greyscale of its edge).
4.2.2 Design of contexts
Having established a conceptual route to reinvent the general law of energy conservation we now need to embed that route in contexts. For his model ‘context as the social circumstances’ Gilbert (2006) describes a number of criteria for the use of contexts in education:
i. Contexts must arise from the students themselves, from actual social issues or from industrial settings and must address the zone of nearest development in students.
ii. The assignments need to clarify a certain way of operating and must consist of clear examples of major concepts.
iii. The context needs to give rise to a coherent jargon for students to use. The context determines which concepts are useful to achieve this.
iv. Every important subject needs to be related to background knowledge. Students need to be able to recontextualize.
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In Gilbert’s criteria the word context may be interpreted as the actual problem within an authentic practice. In order to avoid this ambiguity we will consistently use the word context to mean authentic practice and not the specific problem within such a practice. In each authentic practice (or context) many, very different problems are solved. By designing our authentic practices well we intend to meet as many of Gilbert’s criteria as possible. Whenever in the following subsections we show how we intend to meet a certain criterion, we will refer to it using brackets.
Concurring with Bulte and others (Dierdorp et al., 2011; Westra, 2008; Bulte et al., 2006; Westbroek, 2005) we combine the use of authentic practices with the problem posing approach. In her research Bulte (2006) found that in the use of authentic practices it is recommended to create a need for making the procedural steps explicit when applying knowledge to the situation at hand, and to contextualize the reflection phase by focusing on other typical problems within the same practice. She did however encounter problems fitting the reflection phase within the coherent flow of activities in the authentic practices that she used.
To guide us in the choices for the implementation of contexts in our educational design we have used Bulte’s results together with Gilbert’s criteria.
Choice of contexts
There are many authentic practices in which the general law of energy conservation can be applied and we want students to experience this vast domain of applicability. However, applicability alone does not meet our requirements. We require practices in which there is a need to reinvent the general law of energy conservation or parts of it. This limits the number of suitable practices considerably because the practices in which the general law of energy conservation can only be applied are not suitable to our needs. In our conceptual learning trajectory physical laws need to be reinvented or combined and such work is mostly done by either technological designers or scientists (ii). Both technological design and scientific practices can be considered authentic practices as defined by Bulte (2004) because their practitioners:
- consist of a homogeneous group of people in society (in our case design engineers or scientists),
- are working on respectively technological design or scientifically relevant problems and have a common motive for solving these problems (i), - are working according to either a technological design or a scientific type of
process (ii)
- leading to an outcome and using knowledge about energy conservation and other aspects of the sciences in doing so (iii).
In authentic practices both student and teacher need to take on an authentic role. In engineering companies (groups of) engineers led by their group leader try to solve problems that their clients have encountered. In our instructional version of this practice the students take on the role of engineers while the teacher is their group leader. In some cases the teacher needs to take on the
role of client as well, when the student-engineers are unclear about certain aspects of the problem. In scientific institutes the roles are very similar except that the students are not engineers but scientists and the problem and its solution need to be tuned with the scientific community of fellow scientists instead of with a client. Using such authentic practices offers students not only the possibility to reinvent the general law of energy conservation but also the possibility to get to know to some extent how design engineers and scientists work.
Table 4.4 Overview of the various roles in technological design and scientific research practices
Technological design Scientific research
Role of students Engineers Scientists
Problem origin Client Scientific community
Role of teacher Group leader/Client Group leader/Fellow scientist
Choice of contexts per learning step
Deriving a physical law from experiments is done by both technological designers and scientists. For technological designers a resulting law normally would be of direct practical use to their solution whereas for scientists the use of the resulting law does not need to be apparent immediately. Combining laws in trying to construct more generally applicable concepts is a more common task for scientists.
Having direct practical use makes it easier for technological design practices than for scientific practices to connect to life-world experiences of our students (i). By using technological design practices for conceptual learning step I, the scientific practices can now easily be connected to students’ experiences gained during the technological design practices (i) because conceptual learning steps II and III (scientific practices) build upon the knowledge gained by the students during conceptual learning step I (technological design practices).
Therefore we have chosen to use technological design assignments to embed learning step I (the reinvention of partial laws of energy conservation) and to use scientific assignments to embed learning steps II and III (combining partial laws and the reflection thereupon)(see Table 4.5).
After having reinvented several partial laws of energy conservation set in technological design practices the focus shifts to combining partial laws set in scientific practices. In cases where for such a further combination of partial laws the reinvention of a new partial law is needed both steps I and II are embedded in one scientific assignment.
Table 4.5 An overview of which contexts were used in which learning step
Learning step Context
I: Reinvent partial law of energy conservation. Technological design II: Combine partial laws of energy conservation. Scientific
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Implementation of technological design and scientific contexts
In comparing the technological design process to the scientific process Ellermeijer and De Beurs (2004) identified the work phases for technological design and scientific research shown in Table 4.6. These phases are comparable to the phases in the problem posing approach (Lijnse & Klaassen, 2004).
Table 4.6 Work phases in technological design and scientific research Technological design process Scientific research process Analyzing the problem Analyzing the phenomenon Defining the problem Defining the problem Cognitive modeling Cognitive modeling
Design proposal Experiment proposal
Constructing a prototype Carrying out an experiment
Evaluation Evaluation
For every phase in authentic practices there is a reason and by handing these reasons to the students we can give them a need-to-know for every step in each assignment and guide them through the learning process of each assignment (ii). By using this setup we aim at students developing not only their conceptual knowledge but also their contextual knowledge about what technological designers and scientists do and why they do so.
We do not expect the students themselves to come up with suitable assignments so we need to make sure that the assignments we give them are assignments as real to the design engineering industry or scientific community as possible, and, more importantly, we need to make sure that students can be convinced that the assignments are realistic assignments in the specific practice. To convince the students further, during the problem definition phase in the scientific assignments we ask the students to state the reason why the research is of interest to them or the scientific community (i).
To connect the problem to the background knowledge of the students during the problem analysis phase in the technological design assignments the students were asked to orient themselves on what they already knew about the problem (iv). For the scientific assignments the results of the technological design assignments in the form of partial laws of energy conservation form the background knowledge students have to build upon (iv). The procedural knowledge for each authentic practice is naturally recontextualized during each new assignment.
Both procedures end in an evaluation and, if any physical law has been reinvented during the particular learning step, the reflection on that law’s domain and preconditions can take place here. This reflection is focused by the group leader to the law’s domain and preconditions in order to find as many problems that are covered by the law as possible. This way we aim to solve Bulte’s problem of embedding this reflection, and at the same time aim to reveal to the students the full domain of the reinvented law and its preconditions. By
focusing the reflection on the domain and preconditions of the reinvented laws we do not simply focus on similar problems as suggested by Bulte, but we try to formulate the complete domain of similar problems (infinitely many) that are covered by the law.
By handing the students one or more worksheets per phase we make the procedural steps of the authentic practice explicit to the students as suggested by Bulte. For the need of extrapolating the combination procedure, during learning steps II and III the students are asked to make the procedural steps for both reinventing and combining partial laws of energy conservation explicit as well. In this way both the procedural steps of the practice and the procedural steps of the learning process are to be made explicit.
An overview on how we intend to meet most of Gilbert’s criteria is given in Table 4.7.
Table 4.7 Overview of our implementation of Gilbert's criteria in technological design and scientific assignments
Gilbert’s criterion
Implementation in
technological design practice
Implementation in scientific practice i Assignment as real to technological
design practice as possible.
Assignment as real to scientific practice as possible.
Use problem definition phase to state reason for research.
ii Use authentic practice. Use specific assignment.
Use authentic practice. Use specific assignment. iii Use authentic practice.
No ready-made solution available. Extrapolation necessary.
Use authentic practice.
No ready-made solution available. iv Analyzing the problem.
More than one assignment. Exercises.
Assignment builds on earlier assignments.
More than one assignment. Exercises.
Our teaching-learning sequence has been designed in such a way that the intended concept gave us criteria for choosing contexts to start with while making certain that a learning path back towards the intended concept remained possible. If we put the context at the bottom and the concept at the top (see Figure 4.2) this involves a learning path for the students that starts from the bottom (the contexts), yet was designed starting from the top (the intended concept). To find suitable authentic practices we have formulated criteria that stem from the intended conceptual learning step (top-down) while making sure that these authentic practices function as a start to the learning process (bottom-up). This top-down/bottom-up design approach can also be found in the criteria we used in choosing our experiments. The experiments need to be suitable for deriving the intended partial laws of energy conservation (top-down). By making sure that no ready-made solutions are available to the
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students we facilitate the process from context to experiment (bottom-up)(Logman et al., 2011). Ensuring that an extrapolation is necessary facilitates the process from experiment to a partial law of energy conservation (bottom-up)(Logman et al., 2010).
Figure 4.2 A top-down/bottom-up approach to educational design.
The top-down design may be connected to the bottom-up learning path by analyzing students’ interpretations of each stage of the learning process and comparing them to the intended setup for that stage. For example, the experiments students come up with should resemble the experiments we had in mind and from those, the students should be able to derive the intended partial law of energy conservation.
4.3 Summary of empirical design results from the first two
try-outs
Some of the criteria stated in our educational design rationale were established during our first two outs (e.g. Logman et al., 2010, 2011). During these try-outs we have been able to strengthen the similarities between the intended learning activities and actual students’ activities by developing responses to situations in which students did not do what we expected them to do. These responses were of two kinds: either we changed the worksheets as given to the students, or we changed the teacher’s manual, including specific instructions about what to do if the issue occurs.
Conceptual learning step I was tested during both the first and second try-out. From these try-outs we found that it was possible to guide sixteen-year-old students to reinvent the intended partial laws of energy conservation while
working on technological design problems. Issues and responses for this conceptual learning step are given in Table 4.8.
Table 4.8 Issues in taking conceptual learning step I including responses developed during the first and second try-out
Issue Response
Students were not used to solving problems without a unique solution (physics exercise questions generally do have a unique solution).
The teacher clarifies that in technological design problems any solution contributes to deciding which solution works best.
Students focused on minor sub-problems that they were capable of solving.
We have inserted a worksheet in which students are asked to write down their major questions and uncertainties (this did not solve the issue completely).
The teacher discusses the student’s questions and asks whether answering those questions can solve the given problem.
Students were not used to testing their ideas with experiments.
The teacher compares the context to other contemporary design contexts in which a solution is as yet unknown (like the oil spill in the Gulf of Mexico or the problems after the tsunami at the Fukushima nuclear reactor). Students relied on the use of
established techniques like engines, lifting jacks, etc., thereby evading the need to test their solution.
We have set the problems in a time or place in which a ready-made solution is not available.5
Students did not see the need for a generalization.
In describing the assignments we have made sure that the students need an extrapolation to translate the (laboratory-scale) prototype solution to a real solution in solving the given problem.6
Students could not pinpoint the relevant variables.
The teacher clarifies which variables are relevant by comparing the students’ experiment to the real situation (this did not solve the issue completely).
We have inserted a worksheet in which we ask the students to brainstorm on which variables play any role at all in the problem and then ask them to pinpoint the relevant ones.
Students had trouble measuring the relevant variables.
The teacher helps the students in measuring the relevant variable but only after the students had specified which they were. Students proposed experiments in
which the system is not insulated (energy either entered or exited the system: for example through friction).
We have designed the problems in such a way that any possible solution should only involve insulated systems (e.g. friction is undesired in an uphill rollercoaster).
5 See (Logman et al., 2011).
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During the second try-out conceptual learning step II was tested for the first time. For this part of the try-out we used worksheets that had not yet been set in an authentic practice because at that time we were not certain we would be able to identify a suitable practice. Besides the worksheets we used a classroom discussion to see whether it would be possible for students to take conceptual learning step II. This try-out convinced us that a scientific practice would be suitable to facilitate this learning step. It also showed us how the various worksheets would fit into such a practice and where in the learning process new worksheets were needed. An overview of the issues and responses we encountered in this part of the second try-out is given in Table 4.9.
Table 4.9 Issues in taking conceptual learning step II including responses developed during the second try-out
Issue Response
Students did not notice the precondition common to earlier found partial laws to exclude outside influences. Therefore, to combine a new characteristic quantity into the law, they proposed experiments that did not involve an insulated system.
The teacher shows or reminds the students that the earlier found partial conservation laws only apply when outside influences must be minimized.
Students suggested multiplying or dividing partial laws to combine them into one law (e.g. ∑ ∑ or ∑ ∑ ) instead of adding the terms (in mathematics students are taught that multiplying and/or dividing is allowed when dealing with equations).
The teacher shows the students during a classroom discussion what this would mean if one of the characteristic variables happened to be zero.
Students suggested adding the terms together without making the terms containing the same characteristic variable identical (e.g. ∑ ∑ ∑ ∑ ).
The teacher shows the students during a classroom discussion what would happen if the two terms containing the same characteristic quantity in the suggested combined law changed into one another (e.g.
: this contradicts one of the earlier found partial laws).
Students personally told the researcher that they would not have been able to combine the partial laws of energy conservation themselves.
For the first two combinations the teacher shows the students during a classroom discussion how to combine partial laws. To prepare for this we added a question to the reflection on the technological design assignments that asks how the law can be rewritten in order to describe as many future problems as possible.
4.4 Educational design
We embedded the final conceptual learning trajectory in six assignments (see Table 4.10). In order to avoid role changes as much as possible we changed practice from technological designer to scientist only once. To clarify the start of new assignments within such a role, we used separate modules for each assignment in our teaching-learning sequence. After assignment 3 the focus shifts from reinventing partial laws to combining partial laws. Therefore during assignments 4 and 6 the extra step I that is necessary at that stage is bundled with step II into one scientific assignment. During the final assignment the extrapolation of the combination procedure is added to it as well.
Table 4.10 The intended conceptual learning trajectory embedded in authentic practice assignments
Assignment Authentic practice Conceptual learning step
1 Technological design I: Reinvent partial law for domain A. 2 Technological design I: Reinvent partial law for domain B. 3 Technological design I: Reinvent partial law for domain AC.
4 Scientific I: Reinvent partial law for domain AB.
II: Combine partial laws for domains A, B & AB. 5 Scientific II: Combine partial laws for domains A, B, AB &
AC.
6 Scientific I: Reinvent partial law for domain BD.
II: Combine partial laws for domains A, B, AB, AC & BD.
III: Extrapolate the combination procedure.
Choice of partial laws of energy conservation for learning step I
To choose with which partial laws to start our teaching-learning sequence, we created a 9 × 9 matrix for the following energy storage forms: kinetic, chemical, electrical potential, magnetic, rotational, radiation, thermal, elastic, and gravitational energy. We filled this matrix with student experiments, demonstrations or thought experiments and came up with 177 experiments (Logman, 2009). These experiments can be categorized into two kinds of experiments, namely experiments in which two objects exchange energy of the same form and experiments in which one form of energy is transformed into another. The first are governed by partial laws of energy conservation containing only one characteristic variable (e.g. height in ∑ ) and the second are governed by partial laws of energy conservation containing two characteristic variables (e.g. height and temperature in ∑ ∑ ).
In this matrix we subsequently identified student experiments that would best suit our needs for taking learning step I. To this end we developed the following criteria:
1. Convincingness regarding one of the possible partial laws of energy conservation which means the experiments need to be of a quantitative
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nature and need an efficiency of nearly 100 %. Is it possible to extract the intended concept from the experiment we wish to use?
2. Possibility for a motivating technological design context and corresponding situations for the experiment connecting to students’ everyday life experiences. Is it possible for such a context to give rise to the experiment we wish to use?
These conditions resulted in experiments involving either gravitational, kinetic, or thermal energy separately or a combination of gravitational and kinetic energy. We chose to start off with experiments involving gravitational energy only, followed by experiments involving thermal energy only, and end with experiments involving both gravitational and kinetic energy to take learning step I.
Designing technological design assignments for learning step I
In order to reinvent the three partial laws of energy conservation we gave the students three technological design assignments (see Table 4.11):
Table 4.11 Examples of technological design assignments Technological design assignment Intended partial law Learning step
Design a lifting apparatus. ∑ I
Design a thermostatic mixer tap. ∑ I
Design a rollercoaster. ∑ ∑ I
In our teaching-learning sequence we implemented the work phases as follows. First the students received the assignment in writing, set in a technological design context (e.g. Figure 4.3). Our goal was to make sure that the students are convinced as much as possible that the assignments are realistic assignments to the technological design industry. Therefore the reasons for the students’ activities should only stem from the problem at hand or the way technological designers normally operate. Besides that, we wanted students to reinvent the intended partial laws. In case of an extrapolation well beyond the measured data, a law would clearly be useful. From earlier try-outs we had found that to make an extrapolation of the measured data necessary we had to make sure that solutions to the assignment could not be tested in real size but had to be tested on laboratory scale (Logman et al., 2010).
Figure 4.3 Example of a technological design assignment in writing (i.e. the 3rd assignment).
After the problem description the students are given a general explanation on how to write an advice report.
In the problem analysis phase students receive a worksheet in which they are asked to find out as much as possible about the circumstances in which the technological design needs to work and about any other designs available in solving similar problems. This worksheet is intended to connect the problem to the students’ background knowledge. The worksheet ends in asking the students to create a list of tasks and requirements that their design needs to fulfill. In the problem definition phase a second worksheet is given to the students in which they are asked to define the problem as precisely as possible. In their definition we expect the students to name the preconditions under which the problem needs to be solved. The students can check their problem definition with the teacher who now takes on the role of client.
The cognitive modeling phase consists of two worksheets. In the first the students are asked to split the main assignment into as many partial tasks as possible and select from those tasks the four most important ones to address. In
An amusement park wants to construct a new rollercoaster but not an ordinary one (see Figure […]).
[…] Top Thrill Dragster […]
They want to shoot the cars from below with a maximum speed of 180 km/h. Along a track the cars will move upwards towards the top only to come down along the other side of it. Of course the amusement park wants to build a rollercoaster as high as possible in which the cars do not get stuck at the top by accident. The amusement park asks an engineering company for advice concerning which height can be reached and how. You work for that engineering company and have to come up with at least one feasible solution. Of your solution as many details as possible should be clear, so the amusement park can estimate how much effort (and money) the construction will cost.
1. Design, in groups of two, the rollercoaster in such a way that you can tell the amusement park which is the maximum height possible according to your design. Discuss your solutions well and work as structured as possible. […]
2. Subsequently you will have to test your plan on scale to see whether it will work and to resolve uncertainties. […]
3. Write a report on your laboratory test and draw conclusions from it for the amusement park. […]
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the second worksheet the students are asked to creatively think up as many partial solutions to those four tasks as possible and choose the best combination of those partial solutions to solve the main problem.
For the next phase (design proposal) only one worksheet is used in which the students are asked to write down their uncertainties about their design and propose a test experiment which they can perform to resolve those uncertainties. Because no ready-made solutions are available we assume that the students cannot be certain that their solution will work and thus have to come up with an experiment to test their solution (Logman et al., 2011).
Next the students construct a prototype during the course of a couple of lessons to answer their uncertainties after which they write an advice report to the client. Because we think a test experiment is inevitable no specific worksheet was created for this phase. During this experiment we expect students to perform measurements and derive a partial law of energy conservation from them. This involves a procedure as shown in Table 4.12. We expect to find the results of this procedure in the students’ advice reports.
Table 4.12 Example of procedural steps necessary to derive a law from measurements Procedural step to derive a partial law
1 Perform measurements.
2 Draw a graph from these measurements. 3 Linearize that graph when necessary. 4 Calculate the slope of the graph. 5 = the slope of the graph.7
Once the reports have been delivered they are extensively compared and evaluated. The assignment now changes from the actual problem at hand to future similar problems and whether the students’ solutions can be applied to such problems as well, as suggested by Bulte. In this phase the students receive four worksheets.
The first asks which of the students’ solutions would be the best solution to the original assignment and similar future problems and why. In the second worksheet the students are asked to rewrite the law into as many notations as possible and choose the most widely applicable, yet easiest one to use. In the third worksheet the students are asked about whether zero points for the variables involved can be freely chosen or not, and whether one should take care in using other than standard units (Logman et al., 2014). In the last worksheet the students are asked whether the law can be expanded to more objects than two, followed by the question to which situations the law is not applicable. After answering all these questions in a classroom discussion with the teacher in his role of group leader, the students again are asked to choose the notation of the reinvented law that is most widely applicable to future
7 In general the slope delivers a negative number because one quantity decreases as
problems, yet is also the easiest to use. During the full discussion the teacher has to be aware not to use guidance stemming from the intended conceptual goal. After all, the reasons for every step in the learning process need to stem from either the problem at hand or the way technological designers work. These four worksheets are intended to have the students establish the intended partial law of energy conservation including its full domain.
In order for the students to establish their understanding of the domain, at the end of each assignment the students were given several descriptions of situations asking whether the law is applicable to these situations or not. To check whether they are able to use the law like we intended this was followed by some more exercises in which the law needs to be applied. These exercises were meant for the students to train themselves so they were given the answers to these exercises after answering them.
The process described above is summarized in Table 4.13.
Table 4.13 Implementation of a technological design practice Work phase Worksheet Expected student activity
A Read introduction to the assignment. B Read description of the report structure.
Problem analysis C Find circumstances.
Find solutions to similar problems. List tasks and requirements. Problem definition D Define problem accurately.
Use preconditions in problem definition. Cognitive modeling E
F
List partial tasks.
Choose the four most important ones.
Find partial solutions to the most important tasks. Combine partial solutions into a preliminary complete design.
Design proposal G Formulate uncertainties.
Propose experiment to test uncertainties. Constructing a
prototype
(none) Construct prototype. Answer uncertainties. Perform measurements.
Derive partial law from measurements. Write advice report.
Name partial law in advice report. Apply partial law in advice report.
Name preconditions on partial law in advice report.
Evaluation H
K
Describe best solution to assignment and future similar problems.
Rewrite law.
Check zero points and units for involved variables. Expand to more objects than two.
Describe situations outside the domain of the law. Choose most widely applicable, yet easiest usable notation.
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X Y Z
Exercises on applicability. Exercises on using the law. Answers to exercises.
Designing scientific assignments for learning steps II and III
To combine our first two partial laws of energy conservation we needed an experiment that connects gravitational energy to thermal energy. We decided to go for the obvious choice of Joule’s famous experiment. Having students setup such an experiment would take too much time so we decided to use a demonstration of it. After combining gravitational energy with thermal energy the rollercoaster assignment provided a connecting experiment between gravitational and kinetic energy making a further expansion of the combined law possible.
To have the students take learning steps II and III we handed them three subsequent scientific assignments (see Table 4.14).
Table 4.14 Examples of scientific assignments
Scientific research questions Intended law Learning
steps Do experiments exist in which h
increases while T decreases or the other way around?
If so, can a new law describing such an experiment describe all experiments so far?
∑ ∑ I, II
Can the law for the rollercoaster be
incorporated in the same manner? ∑ ∑ ∑ II How many more terms can be added
to the law? ∑ ∑ ∑
8
I, II, III
In our teaching-learning sequence we implemented the work phases as follows. First the students received the assignment in writing, set in a scientific context (e.g. Figure 4.4). Our goal was to make sure that the students are convinced as much as possible that these are realistic scientific assignments. Therefore the reasons for the students’ activities should only stem from the problem at hand or the way scientists operate. During an earlier try-out we found reasons to set the technological design assignments in a time in which a ready-made solution was not available (Logman et al., 2011) so we did the same for these scientific assignments. To do so we set the scientific assignments in a time in which the intended combined law had not yet been discovered whereas the relevant partial laws of energy conservation had been.
8Meant to describe the general law of energy conservation including any terms as yet
Figure 4.4 Example of a scientific assignment (i.e. the 4th assignment).
After the problem description the students were given a general explanation on how to write a scientific report. We combined the phenomenon analysis phase with the problem definition phase. First students receive a worksheet containing a matrix similar to Table 4.3. Aiming to connect the knowledge gained during the technological design contexts to the problem at hand the students were asked to place the already investigated phenomena into this matrix. Subsequently they were asked to state the reason for performing the research to show that they realize why a solution to the problem is useful. To understand the problem better and to distinguish suitable phenomena from unsuitable ones the students were asked to find and describe phenomena that meet the research problem requirements. These new situations could now be investigated to see whether a combination of the original partial laws is possible.
To connect their procedural background knowledge to the problem at hand, in the following two worksheets the students were asked to compare what they already knew about the preconditions and domains of the involved partial laws, about the assignments themselves and about the experiments they were extracted from.
In the technological design assignments the problems we gave the students still needed to be defined more precisely in physical terms. In the scientific practices, however, we handed the students assignments which had already been clearly defined in physical terms (see Table 4.14). Therefore a special worksheet for stating the problem more precisely was not necessary. We realize that this perhaps makes our scientific practices less authentic but several other aspects of this problem definition phase had already been incorporated in the earlier worksheets.
Suppose you are a wealthy scientist living in the time that the two laws concerning height and temperature have just been discovered. You are glad that with those two laws you can describe experiments in which objects move up because of other objects are moving down and experiments in which the temperature of objects rises because other objects cool down. At this point a fellow scientist comes and visits you and during the course of your conversation on the experiments you ask yourselves the following questions:
1) Are there experiments in which the temperature of an object rises as a result of another object moving down (or the other way around: an object that moves up as a result of another object cooling down)? 2) If such experiments exist, can they be described by a similar law as
derived previously?
3) Does that new law describe both the new experiment(s) and the previously performed experiments?
You decide to investigate these questions and keep each other updated through letters, as was usual at that time. Can we make progress on these questions? To organize our research we will form groups, as is usual nowadays, which get the task to formulate a substantiated answer to the three questions so we can convincingly inform our colleague on our progress. […]
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During the cognitive modeling phase the students were asked to identify which variables need to be varied (and which to be kept constant), how to measure them and which steps are to be taken afterwards to come to an answer. The cognitive modeling phase culminated in proposals by the students for experiments that are suitable to connect the new variable to an already incorporated variable. We expected the description of the necessary steps to become more and more precise after each assignment both in the derivation of a partial law and in its combination with the earlier reinvented partial laws. For deriving a law these steps should be similar to the ones described in Table 4.12 in the previous section on technological design assignments. We expected the students to describe the procedural steps aiming at combining partial laws in a similar way as shown in Table 4.15.
Table 4.15 Example of procedural steps necessary to combine partial laws Procedural step to combine partial laws
1 Remove fractions by multiplying both of the equation sides with denominator. 2 Expand Δ-notation.
3 Expand brackets.
4 Remove minus signs by adding negative terms to both sides of the equation.9 5 Identify terms with the same characteristic quantity in both laws.
6 Make terms containing the same characteristic quantity identical by multiplying with constants.
7 Add all different terms into one new law.10 8 Combine constants where possible.
9 Add summation signs to the new law to be able to apply it to multiple objects.11
In the first scientific assignment the experiments were illustrated in a demonstration of a connecting experiment prepared by the teacher (Joule’s experiment).
After the demonstration a worksheet asked the students to derive a new law from the measurements which was to be used again later in their scientific reports. To see whether the students could actually combine the various partial laws into one, in a second worksheet we asked them to now try out their suggested combination steps. In a classroom discussion during the first two combinations (assignments 4 and 5) the teacher was asked to show the students how to combine the partial laws, because it was new to the students and we
9 At this point two clear partial laws of energy conservation are found: e.g.
, and
.
10 This is the procedural step in which the partial laws are actually combined:
.
11 This finally results in the following law (or its more common notation dividing all
terms by 2):
expected it to be a difficult step for them. In the final assignment (assignment 6) the students had to perform the combination on their own.
After the combination, the students were asked to write a scientific report on their findings to answer the posed problem. We expected the students to apply the combined law in their scientific report. To answer the problem completely we also expected the students to mention the preconditions on the combined law together with its domain in their scientific report. In the final assignment adding to the previous we expected the students to discuss the substeps in the combination procedure (Table 4.15) to answer whether adding a new term to the law would always be possible when necessary.
This was followed by a summary and questions about the newly included domain parts that were not investigated before. This in its turn was followed by a reflection guided by the teacher on which steps were taken to establish the expanded law and the reasons behind those steps. This reflection was asked from the students as a preparation for similar (scientific) problems just like at the end of the technological design assignments. This conforms to Bulte’s recommendation to make the procedural steps explicit.
This process which the students went through three times, is summarized in Table 4.16.
Table 4.16 Implementation of scientific practices
Work phase Worksheet Expected student activity
A Read introduction to the assignment. B Read description for the report structure. Phenomenon analysis C
D & E
State reason for performing the research. Describe phenomenon that connects two partial laws.
Compare earlier assignments, experiments, and laws.
Name preconditions of the partial laws. Name domain of the partial laws.
Problem definition - Not applicable
Cognitive modeling F Describe experiment that combines the two laws.
Roughly describe steps to be taken.
Experiment proposal G Describe steps to derive a new partial law from measurements as precisely as possible.
Describe steps to combine partial laws of energy conservation as precisely as possible.
Describe reasons behind every step.12
Carrying out
experiment
- H I
Watch demonstration, use earlier data, or read description.
Describe measurements. Derive partial law from data. Start combining partial laws.
