Students reinventing the general law of energy conservation - Chapter 2: Energy: an experiment-based route from context to concept

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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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Energy: an experiment-based route from

context to concept

Abstract

In order for students to develop a quantitative conception of energy we propose an experiment-based context to concept learning trajectory.

Design engineering contexts provide opportunities to have students discover quantitative physical laws using laboratory-scale experiments. In our teaching experiment we have met two major problems to such an approach. Initially students don’t see a contextual need for doing experiments nor for extracting a law from these experiments. The design engineering context offers the opportunity to ask students context-based questions to clarify these needs. To help teachers do so we have created a list of context-based responses to such problems. We have also set up a classification scheme to keep track of students’ progress along our proposed learning trajectory as they overcome the major problems. Using this classification scheme we analyzed the learning process and tested three different design engineering contexts.

In this paper we only focus on partial laws of energy conservation. This teaching experiment is part of a larger project in which we plan to propose a fully context-based trajectory aiming at the general law of conservation of energy.

2.1 Introduction

Curriculum innovation committees for the exact sciences in the Netherlands have advised a context-based approach to education. A number of criteria for

1 _{This chapter has been presented in 2010 as a paper at the GIREP-ICPE & MPTL} Conference and has been published after peer-review as Logman, P. S. W. M., Kaper, W. H., & Ellermeijer, A. L. (2010b). Energy: an experiment-based route from context to concept. In GIREP-ICPE-MPTL 2010 International Conference, Teaching and Learning Physics today: Challenges? Benefits? Reims, France.

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the use of contexts have been described by Gilbert (Gilbert, 2006) which we will be using as precisely as possible.

Goedhart (Goedhart, 2004) says contexts could obscure the concept yet Gilbert (Gilbert, 2006) says concepts seem to be taught as effectively as in more traditional approaches. Choosing energy as our subject, being a difficult and abstract concept, should provide us with a proper test case for these findings. Besides that, students’ ideas in current secondary education on energy are diagnosed as inflexible in formal examination tasks (Borsboom et al., 2008). The same problem has earlier been observed with students attending university chemistry courses on thermodynamics (Kaper, 1997).

As the scientific method has historically proven to produce flexible concepts we try to stay as close to the practice of science as possible. For these reasons we chose an experiment- and context-based approach from which students should grasp the concept of energy.

With this in mind we posed the following main research question for our project: Which characteristics and what educational approach does a successful experiment- and context-based teaching-learning sequence have which develops a versatile conception of the general law of energy conservation in secondary school students?

In this paper we focus on reaching partial laws of energy conservation only.

2.2 Theory and design principles

2.2.1 Development of a conception of energy

Students enter secondary education with a preconception of energy that connects to the world in which they live (Watts, 1983). In a couple of years students’ understanding of energy should develop towards the scientific view. Opinions on the way in which this development should be organized vary widely. Several representatives say we should stay true to the scientific view of energy from the very introduction of the concept (Peters, 1981; Warren, 1983; Swackhamer, 2005) which makes it necessary to introduce highly abstract concepts like energy densities or fields at an early stage. Swackhamer adds that the traditional educational concept of energy forms contradicts this scientific view and should therefore not be used. Staying close to the scientific view Falk (Falk et al., 1983) introduces energy carriers to describe energy transport and Lawrence (Lawrence, 2007) introduces energy stores for energy storage. In Lawrence’s approach it becomes clear that energy transport is very different to energy storage as it needs to be described by transfer of energy from one store to another.

We, like Warren, think the scientific view of energy may be too abstract a concept for secondary school students to attain in one go. So instead of staying perfectly true to the modern scientific view of energy we suggest to stay as close

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to the scientific method as possible by having students develop a conception of energy from experiments. For example within a set of similar experiments (e.g. the mixing of liquids of different temperatures) students observe a regularity. Students can then state the governing law and are able to find a pre-form of the general law of conservation of energy (e.g. ) (see Figure 2.1). Kaper (Kaper et al., 2002a, b) has shown that energy forms are consistent and valid within limited domains and we assume that the same holds for these pre-forms of the energy conservation law. And by limiting ourselves to energy storage we, like Lawrence, make a clear distinction between energy transfer and energy storage.

Figure 2.1 Generalization towards a pre-form of the law of conservation of energy.

As soon as some of these pre-forms of the energy law are known to students, two additional steps are necessary to attain the concept of energy.

First we show students that in some experiments one can exchange a portion of “ ” for a portion of “ ” according to a certain exchange ratio. This makes it possible for students to combine the two separate pre-forms into a bigger law like in which g and c together make up the exchange ratio between the two phenomena. This bigger law now predicts additional phenomena and covers a larger domain which can be checked by the students to build up trust in this new law.

After combining a couple of pre-forms of the energy law in this manner a pattern becomes evident. Students may now give names to the elements of the pattern: each phenomenon has a characteristic variable which together with some constants determine its portion, or, we might say, its “energy”. These terms might then be called “forms of energy” and the sum itself “total energy” so students can reach the conclusion that “the sum of all forms of energy is constant” for a certain system.

2.2.2 On the use of contexts

Curriculum innovation committees for the exact sciences have advised a context-based approach to education as it connects better to students’ interests,

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it enhances their motivation and it shows the relevance of newly learned concepts better (Commissie Vernieuwing Natuurkunde onderwijs havo/vwo, 2006).

Gilbert (Gilbert, 2006) describes a number of criteria for the use of contexts: - Contexts must arise from the students themselves, from actual social issues

or industrial settings and must address the zone of nearest development in students.

- The assignments need to clarify a certain way of operating and must consist of clear examples of major concepts.

- The context needs to give rise to a coherent jargon for students to use. The context decides which concepts are useful to achieve this.

- Every important subject needs to be related to background knowledge. Students need to be able to recontextualize.

The practice of either technological designers or scientists contains in certain instances the need for construction of an empirical law. Staying as close to real life experiences as possible we have chosen to start with design engineer practices. In the Netherlands the Techniek15+ approach has been in use for several years now (Techniek15+, 2002). It has been developed by a project group involving five Dutch universities to teach students the principles of designing so we decided to adopt this approach.

With our choice for design engineering we think we can satisfy Gilbert’s conditions because such contexts arise from an industrial setting and we can choose our specific contexts to contain clear examples of pre-forms of the energy conservation law. It is our aim that students construct some of the pre-forms of the energy law, purely driven by needs that arise from the technological context. Through this the usefulness of these laws to the context will become clear. The Techniek15+ approach has a problem orientation phase in which the context is connected to the background knowledge of the students. By introducing contexts to grasp a concept we have to realize that we now have two different goals to reach by the students: a contextual and a conceptual goal. The contextual goal is to solve the context-based problem. The conceptual goal is to attain a pre-form of the energy conservation law.

The teaching setup explained above serves in this research to answer the following more specific research question:

Does a teaching-learning sequence, using design engineering contexts, structured according to Techniek15+ enable a versatile conception of partial laws of energy conservation in a way that motivates students?

2.3 Design implementation

We wanted contexts with convincing experiments and chose the following: moving a very heavy optical table, designing a thermostatic mixer tap, and

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designing a rollercoaster. The student’s situation (an engineering bureau), their client, and this client’s problem were sketched by the teacher. Groups of students were then to start work on solving the client’s problem (contextual goal). The whole learning process should be led only by reasons stemming from these contexts.

We structured the design process according to the six phases from the Techniek15+ program (Techniek15+, 2002; Ellermeijer et al., 2004). We used laboratory-scale experiments to test unknown factors in the design. In our choice for the context-based problems, we took care that in this phase students would need a law (e.g. to scale their conclusions from a laboratory experiment to a real-sized problem solution) so we added a phase in which a generalization is to be made. Furthermore the contexts were chosen such that the needed law to our best estimate would be one of the pre-forms of the energy conservation law (conceptual goal). In their reports to their clients we expect students to show the relevance of the found law to their chosen solution.

Using this approach we expect students to move subsequently through the phases as mentioned in Table 2.1.

Table 2.1 Overview of the various learning phases Phase Activity

I Problem orientation (teacher acts as client) II Demands analysis

III Idea matrix IV Design proposal

V Laboratory-scale experiments

VI Generalization to a first law (needed e.g. for scaling) VII Final reports to clients after discussion

The generalizations we assume students will come up with from their experiments are shown in Table 2.2 (any equivalent formulation will be acceptable in the students’ advice reports as well).

Table 2.2 Contextual goals versus conceptual goals per context Contextual goal Conceptual goal

Moving an optical table Thermostatic mixer tap

Rollercoaster

In our first teaching experiment the researcher taught the classes making it easy to respond to smaller and bigger problems students showed in reaching the conceptual goals. Phases I to III and phase VII did not show major issues so we will discuss these phases concisely. During the phases IV to VI in several cases

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the teacher/researcher had to explain why design engineers work the way they do, and we will elaborate on his responses to the students.

Phase I-III: Problem orientation, Demands analysis & Idea matrix

In phases I and II the teacher needs to know the context very well making him able to answer any context-related questions the students may pose. In phase III some explanation on how the idea matrix works was needed for some students. Phase IV-V: Design proposal & Laboratory-scale experiments

After phase III students understand the contextual problem and have imagined various possible solutions. Students however are not always aware of problems left in their solutions so we created a worksheet in which they had to write down all the things they were not sure of. Then these uncertainties were discussed in class to decide which were the major ones to address.

Even after this discussion some groups may address the minor, easier to solve problems first. To focus the students on the major problems the teacher explained that in design engineering practices there is only a limited amount of time available to come to a solution and that in this solution the client needs an answer to the major problems most.

Next we expect the students to test their solutions to the major problems experimentally but students (a) may not be used to this or (b) trust others to have done the testing for them (when using established techniques in their solution). The teacher’s response to (a) was to compare the context to other contexts in which the need for experiments is clear (e.g. the problem with sealing the oil well in the Gulf of Mexico). In the case of trusting ready-made solutions (b) the teacher tried several responses but we have not found a satisfying response yet.

At this point students should design their experiments. Some students have trouble doing so and the teacher helped in this process by suggesting to make drawings and build laboratory-scale models of their solutions as design engineers do.

An overview of the issues for phase IV-V and the respective responses of the teacher can be found in Table 2.3 which shows we do not yet have an effective response to the issue of trusting established techniques.

Table 2.3 Issues and our responses in phase IV-V: scale experiments

Issue Response

Focus on minor problems - Design engineers address major problems first - Add worksheet in which students have to write

down questions and insecurities

- Classroom discussion of encountered problems Not used to testing ideas with

experiments

- Teach to do so by testing ideas with experiments - Compare context to other contexts in which a

solution is as yet unknown Trusting established techniques - no effective response yet Designing experiment - Think of a laboratory-scale version

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Phase VI: Generalization

Untrained students have a hard time generalizing a useful law from experiments. Their problems stem from three successive stages: pinpointing relevant variables, recognizing that a law would be useful and finally constructing such a law.

To pinpoint relevant variables students were helped by being asked which variables would be relevant in the real situation instead of in the experiment (e.g. “what would the movers be interested in?”, students:”of course the weight that can be lifted and how high it can go”).

Some students do not recognize that a law would be useful but instead insist on measuring the real situation in a similar way. To address this the teacher explained that it would not be very practical if things went wrong in the real-size try-out. Designers need to be able to say that there’s a fair chance of things going right after doing laboratory-scale experiments.

Last but not least we expect students to have a hard time constructing a possible relationship between the relevant variables. We noticed however that during the experiments as we asked about the workings of the various apparatus students started to make generalizations by themselves in describing the workings. For instance, it became clear that one could make it very easy to lift a heavy object by some apparatus but then one would have to cover such long distances that it would take very long to hoist it up or down one floor.

In Table 2.4 we have made an overview of all the issues for this phase and our corresponding responses.

Table 2.4 Issues and our responses in phase VI: generalization

Issue Response

Pinpointing relevant variables - Compare experiment to real situation - Help measuring difficult variables No need for generalization - A real-size tryout could be disastrous

- There’s a need for a fair chance in succeeding in one go

Find relationships between relevant variables

- Ask about the workings of the chosen apparatus

Phase VII: Final reports

In Phase VII we did not find major issues. Help by the teacher was only needed in structuring the advice report.

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2.4 Research method

The teaching-learning sequence has been tested in a first experiment with a class of seventeen 16-year-olds from the researcher’s school. It replaces the regular quantitative introduction of the concept of energy.

In this phase of our research we want to find out whether our learning process is possible for students to follow so we want to identify which are the most difficult phases in this process and what are the laws students come up with during the learning process. To identify these difficulties and laws we recorded the lessons on video and made audio recordings of both the teacher helping the students through this process and one group of average students in particular. To stimulate discussion and thereby enhancing our measurements students worked in groups. Based on our findings we created a classification scheme which we subsequently used to analyze the groups’ progress with. To find evidence that the groups saw their construction of a pre-form of the law of energy conservation as relevant to the various contexts their advice reports were used.

The classification scheme we came up with shows the student’s progress along the most problematic phases (see Table 2.5). Phases I-III are combined into level 1, phases IV-V in level 2, phase VI can be compared to level 3, and level 4 shows the relevant use of the new found law in an advice report (phase VII).

Table 2.5 Classification scheme for a context-concept learning process Learning process

level

Description

0 Student is not interested in the assignment or does not know what to do.

1 Student shows signs of interest or knowing what to do. 2 Student uses the word scaling and starts experimenting. 3 Student uses a law to describe results or in their advice report. 4 Student uses a law derived consistently from their experiment to

explain choices in their solution to the context-based problem.

Once we have established evidence that a student has attained a certain level we assume that this student also has command of every lower level or has overcome any earlier problems in attaining those levels.

2.5 Results

In the end all groups came up with laboratory-scale experiments (level 2) even though some were still trusting established techniques. Because trusting ready-made solutions is a logical thing to do when they are available in the context this shows such contexts need redesigning.

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We were able to classify our groups into the various levels of our scheme according to statements they made. Examples of student’s statements are shown in Table 2.6.

Table 2.6 Examples of student’s statements showing levels 1 to 3 Learning process

level

Student’s statement

1 “I’m not sure whether such a hydraulic lift can cope with that.” 2 “So in theory it’s this and then in practice you are not sure. Yes, we

can test whether that is strong enough.” 3 “So 150 grams, 80 grams. That’s half !”

In Table 2.7 we give examples of consistent laws students came up with in their advice reports and which we used as showing evidence of attaining level 4.

Table 2.7 Examples of consistent laws per context Context Relationship between variables

Moving an optical table and to describe a hydraulic elevator Thermostatic mixer tap ( ) ( )

Rollercoaster ( )

Because of our open design students came up with more diverse experiments than expected. Where beforehand the researchers had come up with two possible experiments the students came up with four, only one of which was thought of by the researchers. However the new experiments did not pose a problem as through the context they quite naturally led to the same law as intended.

Using our classification scheme it’s not difficult to find positive evidence for attaining a certain level. Negative evidence could only be found for level 4 if students used a non-relevant law or a law that was not consistent with their experimental data in their advice report.

Analyzing the advice reports and the video and audio recordings to ascribe the various levels to the various groups we attained the following results for the first context of moving a heavy optical table (see Table 2.8).

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Table 2.8 Attained levels for the first context

(- indicates evidence of not achieving corresponding level; + indicates positive evidence of achieving corresponding level; in between brackets the lesson in which the evidence

was found) Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Level 0 Level 1 + (1) + (1) + (1) + (1) + (1) + (1) + (1) + (2) Level 2 + (4) + (4) + (6) + (4) + (4) + (6) + (5) Level 3 + (6) + (6) - + (5) + (6) - Level 4 + (6) - + (6) + (6) -

All groups at least showed evidence of attaining level 1 and 2 for this context (group 1 did their experiment at unrecorded hours). From the recordings we gathered that 6 out of the 8 groups did generate a useful law from their experiment (groups 3 and 6 used it in their advice report). We cannot be sure about the groups that did not use this law consistently in their advice report whether they saw the relevance of the law to their solution or not. Only 3 groups did use their new found law in their advice report to explain their solution of the context-based problem (level 4). All groups seem to follow our planned phasing of the learning process.

For all contexts we analyzed the advice reports to determine whether groups reached level 4 (see Table 2.9).

Table 2.9 Attainment of level 4 for the various groups in the various contexts Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 context I + - + + - context II + + + + + context III + + + +

In the audio recordings of the first context (moving a very heavy optical table) students of groups 1, 2, and 7 talked about possibly useful laws and so may have achieved level 4 as well but they did not show the relevance of the law in their advice reports. Groups 4 and 8 used non-relevant laws in their advice report to the first context. In the second and third context we didn’t find any use of a non-relevant law in the advice reports anymore. We did find however that while

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groups 4 and 8 had used a non-relevant law in the first context they now used a relevant law in the new contexts and therefore may have attained level 4 during the series of lessons. A further analysis of the audio and video recordings should bring more conclusive results on the groups for which we had to remain undecided.

2.6 Conclusion

Design engineer contexts which have the need for simulations on laboratory-scale seem to be able to provide motives for students to generalize their experiments into a relationship between variables. The contextual need for this may be revealed by asking the right context-based questions. By choosing the context appropriately the generalization constructed by the students can be a pre-form of the energy conservation law.

Using contexts like these in a first try-out we have found that designing an experiment and extracting a law from such an experiment is difficult for students but not impossible. The two main difficulties were that initially students don’t see a contextual need for doing experiments nor for extracting a law from these experiments. Most students can be motivated to overcome these difficulties by asking the right context-based questions. Students can be motivated to formulate a law by pointing out the need for upsizing the results of their laboratory-scale experiments. In this way they become versatile in using the law (they predict a situation that was different from the one in the experiment), as well as they appreciate the need for such versatility. The issue of students trusting established techniques could not be resolved within the context, at least for the context of moving the heavy optical table. Our current estimate is that we should redesign this context.

Based on the above mentioned critical phases we have created a classification scheme for such a context to concept learning process. By using this scheme on our first try-out we can conclude that 3 out of the 8 groups monitored have realized the trajectory as planned. On the other groups no conclusive evidence can be given without further analysis. Our analysis of the students’ progress on the first 4 levels shows that every group has attained level 4 for at least one of the design engineer contexts chosen which makes us confident that these contexts are suitable to achieve an experiment-based route from context to concept for energy and possibly for other concepts as well.

2.7 Discussion

Limiting ourselves to advice reports of all groups and video recordings and audio recordings of the teacher and only one group there will always be groups of students we have not monitored at essential phases and we therefore have to

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be undecided on whether they made a certain step in the learning process or not. Our use of groups of students of course diminishes our view on what individual students are capable of. In future cycles we will be testing students individually in the end and give them an individual questionnaire as well.

There are many routes to lead students to understand the concept of energy besides the traditional teaching (Herrmann, 1989; Swackhamer, 2005; Lawrence, 2007). We think our proposed strategy may be an interesting addition to these strategies as it may be both convincing, motivating and showing the usefulness of the concept of energy by means of its empirical and contextual base.

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