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The effect of computer science on physics learning in a computationalscience environment

Rivka Taub * , Michal Armoni, Esther Bagno, Mordechai (Moti) Ben-AriScience Teaching Department, Weizmann Institute of Science, 234 Herzl St., Rehovot 7610001, Israel

a r t i c l e i n f o

Article history:Received 30 June 2014Received in revised form4 March 2015Accepted 5 March 2015Available online 9 April 2015

Keywords:Interdisciplinary projectsProgramming and programming languagesSecondary educationSimulationsTeaching/learning strategies

a b s t r a c t

College and high-school students face many dif culties when dealing with physics formulas, such as alack of understanding of their components or of the physical relationships between the two sides of aformula. To overcome these dif culties some instructors suggest combining simulations' design whilelearning physics, claiming that the programming process forces the students to understand the physicalmechanism activating the simulation. This study took place in a computational-science course wherehigh-school students programmed simulations of physical systems, thus combining computer science(CS) and mathematics with physics learning. The study explored the ways in which CS affected thestudents' conceptual understanding of the physics behind formulas. The major part of the analysisprocess was qualitative, although some quantitative analysis was applied as well. Findings revealed that agreat amount of the time was invested by the students on representing their physics knowledge in termsof computer science. Three knowledge domains were found to be applied: structural, procedural andsystemic. A fourth domain which enabled re ection on the knowledge was found as well, the domain of execution. Each of the domains was found to promote the emergence of knowledge integration processes(Linn & Eylon, 2006, 2011), thus promoting students ’ physics conceptual understanding. Based on these

ndings, some instructional implications are discussed.© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Computational science is a eld that deals with the construction of mathematical models of scienti c phenomena. The models requireextensive computational resources to explore large amount of data or non-linear systems. It is an interdisciplinary eld that combinescomputer science (CS) and applied mathematics, in order to understand and solve complex scienti c problems. Developing computationalmodels combines science (e.g., physics, biology), mathematics, programming, simulation design, modeling and more ( Shi et & Shi et,2006; Yasar & Landau, 2003 ). Computational science is a continuously changing and growing eld, re-de ning its boundaries and para-digms ( Post & Votta, 2005 ). It has reached predictive capabilities similar to those of the traditional experimentation and theory ( Sloot, n.d. ).The success of this approach has led to the proposal that computational science should be taught in secondary schools so that students willbe exposed to this scienti c method, and will acquire knowledge and strategies to solve complex problems. Another goal addressed in

computational science courses is the enhancement of students' understanding of scienti c issues while developing computational modelsfor them.Modern approaches of teaching science and mathematics make use of computer systems ( Skryabin, Zhang, Liu, & Zhang, 2015; Taka ci,

Stankov, & Milanovic, 2015 ). Studies show that science courses enriched with computational environments foster students' scienti c un-derstanding ( Chabay & Sherwood, 2008 ; Louca, Druin, Hammer, & Dreher, 2003 ; Redish & Wilson, 1993 ). The study reported in this paperaimed to explore whether and how, among other reasons, the elements of the computational environment foster understanding of thephysics expressed in formulas. Speci cally, it investigated the way the discipline of computer science affected the conceptual understandingof physics formulas achieved by computational-science students. Observations revealed that computational-science students achieved

* Corresponding author. Tel.: þ 972 89344203.E-mail address: [email protected] (R. Taub).

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Computers & Education

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Computers & Education 87 (2015) 10 e 23

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conceptual understanding of physics formulas. 1 Toexplore what affected this learning, episodes of students learning were explored by usingthe knowledge integration (KI) perspective ( Linn & Eylon, 2006, 2011 ). This perspective describes four processes that are essential inachieving conceptual understanding. We used the KI perspective to carefully identify the changes in students' conceptual knowledge andtheir causes and focused on changes that were triggered mainly by CS. Three major steps were applied in the analysis process: (a) detectionof the KI processes emerged in the learning episodes; (b) qualitative identi cation of the ways that CS triggered the emergence of theseprocesses; (c) quantitative examination of the most frequently used KI process and the role of CS in it.

This paper opens with the theoretical background relevant to the research(Section 2). It continues with the methodology (Section 3). Thendings are then presented (Section 4), concluded and discussed (Section 5).

2. Theoretical background

This section starts with some background on dif culties that students face when dealing with physics formulas. It continues with studiesthat show the positive outcomes of learning physics in a computational environment. It ends with a description of the knowledge inte-gration perspective that was used to assess the students' learning.

2.1. Dif culties related to learning physics formulas

Years of research have outlined the dif culties students face while trying to understand the physics behind the formulas they learn(Halloun & Hestenes, 1985; McCloskey, 1983; McDermott, Rosenquist, & Van Zee, 1987 ). Bagno, Berger, and Eylon (2008) found that high-school physics students provide a vague description of the components of a formula. For instance, they related only to the force F denoted inthe formula P F ¼ m a! and ignored the net force. As another example, the students explained the meaning of the variable t in a formula as‘ time ’ , while an accurate explanation should have been ‘ the time elapsed since t ¼ 0 ’ . Another dif culty Bagno et al. (2008) described is thatmany students were unable to explain the conditions under which a formula can be applied. For instance, in the formula x ¼ x0 þ v0t þ ½ at 2,80% of the students did not mention the fact that the formula applies only for objects moving with constant acceleration. Another studyreportedby Shaffer and McDermott (2005) , examinedwhether 20,000 college anduniversity students were able to associate the direction of the acceleration and the net force denoted in the formula P F ¼ m a! . They found that when asked about the direction and magnitude of theacceleration of a ball moving on a ramp, only 20% of the students answered correctly. The others thought that the direction of the accel-eration is toward the bottom because 'gravity causes the motion'. The authors' explanation for this is that some of the students did notassociate the direction of the acceleration with that of the net force.

Some studies explored epistemological aspects regarding students' use of physics formulas. Domert, Airey, Linder, and Kung (2012) askedphysics students to scale the importance of statements related to learning physics formulas. They discovered that the students believed thatknowing what physics quantities are involved, understanding the underlying physics, establishing a link to everyday life and knowing howand when touse the formula are important in using equations. Still, students tend to deal with formulas in a rote manner. When they solve aphysics problem in a textbook, they many times look for a formula that consists of variables that are compatible with those appearing in theproblem being solved ( Sherin, 2001b ), a “ plug-and-chug ” strategy. Redish, Saul, and Steinberg (1998) explain that physics students usephysics formulas as an arithmetic way to calculate numbers, and fail to understand the deeper relationships they represent.

2.2. Using computational environments to overcome dif culties of understanding physics formulas

In order to improve the physics learning, some instructors suggest combining computational-science programs into ordinary physicsintroductory courses (e.g., Chabay & Sherwood, 2008 ). The rationale behind this suggestion is that such a combination requires that physicsknowledge will be organized and represented as computational models of physical systems, i.e., computer programs. Abelson, Sussman, andSussman (1996) explain that computerprograms aremore than just sets of instructionsfor the computer in orderto perform tasks. They alsoserve as frameworks for organizing ideas about processes. They deal with data that represent objects in a given system, and procedures thatrepresent the rules for manipulating the data. These attributes of computer programs enable computational-science students to organizetheir ideas about physical objects and processes.

Research on combining computational-science elements in physics introductory courses shows positive effects. Redish and Wilson(1993) developed an Introduction to physics course that was based on the computerized M.U.P.P.E.T environment. The authors intro-duced programming at the beginning of the traditional calculus-based introductory physics course at the University of Maryland. Theyfound several bene ts of teaching physics in a computer-based environment, among them are: using the environment to overcome lack of

intensive mathematical knowledge, exposing students to research methods that professional physicists use, and being able to discuss real-world problems such as projectile motion with air resistance.

Chabay and Sherwood (2008) list pros and cons of learning physics while programming it. One bene t is that when programming thephysics, there are no “ black boxes ” of the physics knowledge at the basis of the simulation. Another bene t is the link generated betweendifferent representations of the same physics idea, an algebraic equation and programming code. Among the negative aspects of usingprogramming for learning physics they mention the fact that a large portion of the students have no background in programming andtherefore teaching programming spends a lot of time needed for physics learning.

Sherin (2001a) compared between what he termed algebraic-physics and programming-physics . Two groups of his students solvedphysics problems. One group solved ordinary textbooks problems (algebraic-physics) and the other was asked to develop simulations onphenomena similar to the algebraic ones (programming-physics). He concluded that the algebraic notation of the physics formulas does notnaturally imply on causal relationships between parameters, therefore students tend to infer the existence of equilibrium between the twosides of an equation, instead of on causal relationships. In contrast, programming-physics leads more naturally to understanding processes

1

These results are in preparation to be described elsewhere, but examples in the current paper were chosen to demonstrate the new understandings the students gained.

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and causality, stemming from the importance of the order of the lines in the program. In Sherin's words: “ algebra-physics instruction leavessome undiscovered intuitive cobwebs in this territory, and … the act of programming tends to expose these cobwebs ” (p.49). Sherin addsthat getting dynamical feedback is easier in programming since learners can simply run the simulation.

Our research aims to expand these ndings in that it aims to understand how programming leads to physics understanding, as reportedin the above described studies. For this purpose we used the knowledge integration perspective which enables the examination of studentslearning processes while achieving conceptual understanding.

2.3. Knowledge integration

Conceptual understanding includes understanding of new concepts and of the interrelationships among them ( Rittle-Johnson, Siegler, &Alibali, 2001 ). To evaluate conceptual understanding, it is important both to compare between the learner's knowledge before and after alearning session and to examine the learning processes leading to the knowledge gain. This paper examines the learning processes of computational-science students in order to understand how they achieved conceptual understanding of physics formulas. To do so we usedthe knowledge integration perspective ( Linn & Eylon, 2006, 2011 ) that emphasizes the importance of relating new knowledge to priorknowledge, and, furthermore, it provides terminology to describe the mechanism underlying the establishment of this relationship: theevaluation of the new knowledge in light of different criteria.

The KI perspective was developed on the basis of research into science learning and instruction. It brings together recent trends indevelopmental, constructivist, socio-cultural and cognitive perspectives on learning. According to KI, learners build knowledge by goingthrough four processes:

Eliciting ideas. Learners become aware of their pre-existing knowledge. Adding newideas. Learners are introduced to ideas that are new to them. These ideas maycome from various sources such as a teacher,a textbook, a peer, or the Internet.

Developing criteria to evaluate ideas. Questions and tests that the learner use to evaluate whether he/she considers the ideas asacceptable or not. Examples of such criteria are: whether the origin of the new ideas is reliable (i.e. based on scienti c principles), andwhether there are contradictions within the ideas acquired, or between them and the ideas that are already known to the learner.

Sorting out and re ecting. The learners re ect and differentiate between their pre-existing ideas and the newly acquired ones basedon criteria.

The four processes do not necessarily appear oneafter another, and not always in the described above order. Instead they mayappear in adifferent order and be intertwined so that the same learning incident includes two or more processes altogether.

The KI framework has been used, tested and revised over the past two decades. It has been used for several purposes: (a) as a guide forthe design of instructional activities. Forexample, WISE (Web-based Inquiry Science Environment) is based upon the four KI processes( Linn,Clark, & Slotta, 2003 ); (b) as an assessment tool to evaluate learners' scienti c knowledge ( Liu, Lee, Hofstetter, & Linn, 2008 ). For example,Lee and Liu (2010) used the KI framework to assess middle-school students' knowledge of energy concepts acrossthe physical, life and earthsciences by conducting multiple-choice questionnaires; (c) as a tool to analyze learning processes using a micro level analysis. Yerushalmi,

Puterkovsky, and Bagno (2012) used the framework to characterize the learning processes of two pairs of high-school physics students whoparticipated in an on-line troubleshooting instructional activity. One pair of students reached a high level of physics understanding, whilethe other, although gained knowledge in the described experience, reached a lower level one. The authors showed that the KI perspectivewas sensitive enough to characterize the differences between the two learning experiences. For instance, one of the differences was thestudents' application of different types of criterion. The current research used KI in a similar way and aimed to characterize the learningprocesses in terms of the KI perspective. Most of the research done in the context of KI dealt with knowledge within a single discipline, suchas learning concepts of physical sciences or life sciences, sometimes in the presence of technological tools ( Kali, Orion, & Eylon, 2003 ). Someresearch has been done in interdisciplinary contexts: Chiu and Linn (2011) used “ design principles ” that were intended to promote the KIprocesses to develop an interdisciplinary curriculum in engineering and science. Their curriculum supported the learning of engineeringskills and concepts (such as systems thinking and collaboration) while learning science, and assessed the students' acquisition of theseconcepts. It did not assess, however, howthe learning of one discipline affected the learning of another. In fact, we could not at all ndsuch aKI-related study. This research aims to use the KI perspective to explore the effect of CS on the understanding of physics formulas by adetailed analysis of students' learning.

3. Methodology

The research was conducted in a computational-science course that has been activated for eight years. The research goal was to observethe learning taking place during the course. The research question investigated is: what is the effect of CS on the students' understanding of physics formulas in a computational-science course?

3.1. The context

This research took place in a course on Computational Science intended for talented high-school students who come from different high-schools. The course was developed and taught by physics teachers, neither of whom were a part of the research staff. The three-year course(tenth through twelfth grades) was interdisciplinary: students learned how to program computational models of physics phenomena,which required that they learn physics, mathematics and computer science. Most of the material was learned independently by the stu-dents, while the teacher served as a mentor. The instruction was directed by a textbook during most of the school year. The students wererequired to develop interim and nal projects of their own, working in pairs. All the classes took place once a week in the afternoon for 3 h,

after regular school hours.

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This research was carried out with tenth and eleventh grade students. During the course these students learned programming concepts,the Java language, kinematics, dynamics and optics. The software the students used in these classes was Easy Java Simulations 2 (10t e 11thgrades) and Maxima 3 (11th grade).

The authors of this paper were neither developers nor teachers of the course.

3.1.1. Easy java simulationEJS is a software package, created by Francisco Esquembre ( Christian & Esquembre, 2007; Esquembre, 2004 ). It enables the construction

of computational models by providing a user-friendly environment for Java. The audience towards which EJS is directed is science students,teachers and researchers who want to avoid putting too much effort in programming and more emphasis on the scienti c content. This isdone by the fact that the user interface can be created without any programming knowledge of the simulation's designer. Therefore she/hemay focus on the algorithm to design the scienti c model.

This software breaks the modeling process into three activities which are selected by pushing radio buttons: (a) documentation (b)modeling (c) interface design. In the modeling activity the designer implements the physics into Java code.

3.1.2. MaximaMaxima is a Computer Algebraic System (CAS). It is a system for the manipulation of symbolic and numerical expressions, including

differentiation, integration, ordinary differential equations, systems of linear equations, polynomials, and more. In the computational-science course being explored here, eleventh grade students studied random models in a CAS environment, differential equations, usingMaxima to nd analytic and numeric solutions of differential equations, writing a program to solve linear equations, and more.

3.2. Projects for analysis

We observed and recorded the work on six nal projects. Four of them were done by tenth grade students and two by eleventh graders.One of the pairs was recorded both in tenth and eleventh grades. The students volunteered to participate in the research. Out of the vol-unteers we chose all the girls (two), since we wanted to have both genders in the research population. The students worked on the projectsin pairs, each work lasted approximately 10 h (four lessons).

In this paper three examples are provided, in order to demonstrate the ndings of the analysis of all the projects. The rst exampledemonstrates howtenth grade students managed to characterize the kind of mathematical model they neededto describe a circular motion.The secondexample demonstrates howtenth grade students who used optics formulas without understanding their parameters reached anunderstanding of one of the parameters. The third example demonstrateshow programming promotedthe understanding of eleventh gradestudents of the relationship between the net force and acceleration.

3.3. Research tools

A documentation of the work of pairs of students on six nal projects took place. Debut screen-capture 4software was used for thispurpose. It recorded their screens, including the work on the programming les; actions done by the mouse, such as scroll and click; and thestudents' voices while talking to each other during their work. In addition, one of the researchers randomly observed sessions of thestudents' work and took eld notes.

3.4. Analysis framework

As explained above, we used the KI perspective to analyze the students' discourses. At this context, the operational de nitions we usedfor the four KI processes are:

Eliciting ideas. Exhibiting memory of pre-existing knowledge by recalling facts, terms, basic concepts and answers. Adding new ideas. Acquiring knowledge from external source to the learner, such as the Internet, a friend or a teacher. Developing criteria to evaluate ideas. Asking questions and making judgments about information, validity of ideas or quality of work,comparing between some ideas.

Sorting out and re ecting. Demonstrating understanding of facts and ideas by organizing, translating, interpreting, giving descriptions,stating the main ideas, and re ecting on the process of acquiring the new ideas.

The process of sorting out and re ecting is referred to by Linn and Eylon (2006, 2011) as a continuous process of re ecting and developingcriteria, thus gradually sorting out scienti cally from non-scienti cally accepted ideas. Here we wanted to capture all the details in thisprocess; hence we categorized every single statement that demonstrated physics understanding as expressing the process of sorting out andre ecting . Statements that demonstrated re ection on the process of acquiring new knowledge were categorized to this process as well.

3.5. Analysis procedure

The procedure of analyzing the students' discourse was mainly qualitative but involved a quantitative method as well. The analysisprocess was as follows:

2 http://fem.um.es/Ejs/ .3 http://maxima.sourceforge.net/ .4

www.nchsoftware.com .


http://fem.um.es/Ejs/http://maxima.sourceforge.net/http://maxima.sourceforge.net/http://www.nchsoftware.com/http://www.nchsoftware.com/http://maxima.sourceforge.net/http://fem.um.es/Ejs/

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a. Sampling the data. Since the protocols of the transcription of students' discourse arevery long, we sampled them, as Chi (1997) suggests,based on a “ noncontent ” criterion: we analyzed the second and third lessons of the work of each pair. This choice was based on theassumption that in the rst lesson the students were busy with deciding on which phenomena to simulate, and not on learning theintensive related physics or on programming. The analysis was done on a sequence of two lessons to be able to capture the continuity of the learning processes.

b. Searching for statements in the students' discourses that expressed KI processes and categorizing them as one of the KI processes.c. Categorizing each KI statement as related to CS or to physics. For example, statements of students who evaluated the correctness of a

physical idea based on a given equationwere categorized as the process of developing criteria related to physics. A CS related criterion , onthe other hand, could be a decision not to use some physics procedure since it requires the computer to activate too much processingpower.

d. Searching for CS activities that were involved in the KI processes and appeared to trigger them.e. Counting the KI processes that appeared in the students' discourses.

Actions b e d of the analysis procedure were applied twice by the rst author who is a CS education researcher. The third author, a physicseducation researcher, independently analyzed 10% of the data and the two analyzes were compared to check inter-related reliability.Cohen's Kappa was calculated, k ¼ 0.8969.

4. Findings

This section is divided to twoparts. It startswith presenting the frequencies of the students' application of the KI statements, and the roleCS playedin triggering the most frequently used process:developing criteria. It continues with an explanation of the effect of CS on students'physics learning and how it triggered all KI processes. The rst part is based on quantitatively counting the appearances of the KI processesand comparing between the numbers of physics-related to CS-related processes. The second part is based on a qualitative analysis of thedata.

4.1. The most frequently used KI process and the role of CS in triggering it

In order to nd the relative portion of each KI statement in the students' work, we counted the number of the statements related to KIfrom all the projects. Out of 5209 statements that were analyzed, 2820 statements were KI-related. Fig. 1 shows the distribution of the KIprocesses appeared in the students' statements, in terms of percentages. Goodness of t Chi-square test showed that this distribution issigni cantly different than the null hypothesis of an equal distribution of 25% per each KI process ( p < .05). Cramer's V ¼ 0.2362.

The pie chart presented in Fig. 1 also shows that the most frequently used process was developing criteria . Goodness of t Chi-square testshowed that the difference between this process and the second most frequently used- sorting out and re ecting -is signi cant ( p < .05).Cramer's V ¼ 0.0419.

Since there was diversity in the distributions of the KI-statements within the different projects, Table 1 brings the percentages of the KIprocesses applied by each pair of students (named Project1-Project 6). It can be seen that for some of the projects the process of developing criteria was the most frequent one, while for the others it was the process of sorting out and re ecting . Note that the later process is based oncriteria developed by the students, as well (see Section 2.3 for further explanation).

Our next examination concerned the portion of CS KI-related statements versus physics ones. Fig. 2 shows that overall, the portions arevery similar.

Since the most frequent KI process appliedby the students was developing criteria (Fig.1 ), we checked the portion of CS versusphysics KI-related statements. Results show that when taking all the projects together, more statements were related to CS than to physics ( Fig. 3). Agoodness of t chi square test revealed that these differences were signi cant ( p < 0.05 ). Cramer's V ¼ 0.2695.

Since there wasdiversity in the distributions of the KI-statements regarding CS or physics within the different projects, Table 2 brings thepercentages of the KI processes applied by each pair of students in relation to CS or to physics (named Project1-Project 6). Note that the CSKI-related statements' percentage was large in all projects, although de nitely not always the largest.

Fig. 1. Percentages of KI processes in use in all the projects.


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Tosum up the quantitative ndings, we saw that during their learning processes, the KI process most frequently used by the students wasdeveloping criteria . In addition, we found that more developing criteria statements were related to CS than to physics. We believe that these

ndings may indicate on the important role CS played in the students' physics learning.

4.2. The effect of CS on physics learning

One of the basic aspects of CS is knowledge representation for solving problems ( Wing, 2006 ). In the computational-science courseexamined in this research, a great amount of the time was invested by the students on representing their physics knowledge. Three CSknowledge domains were used for the representation of physics knowledge: structural knowledge, procedural knowledge, and systemicknowledge. The structural knowledge domain involved dealing with the structure of programming entities that represent the materialcomponents of the simulated system. The procedural knowledge domain involved representations of the mechanism underlying thesimulated system as programming procedures. The systemic knowledge domain involved representing the main characteristics of thephysics system as, for instance, programming objects, and their inter-relations. Working in this domain is done on a higher level of abstraction.

In the context of software development (programming), another domain was found to be applied by the students, the execution domain.While the rst three domains serve as representations of the physics knowledge, the fourth enables re ection on this knowledge, as will be

Table 1Percentages of KI processes applied by each pair of students.

Project#/Percentage of KI statements Eliciting Adding Developing criteria Sorting out and re ecting

Project 1 9.95 9.84 39.71 40.50Project 2 13.36 18.87 44.08 23.69Project 3 2.91 18.02 52.62 26.45Project 4 10.60 23.04 40.09 26.27Project 5 25.25 14.22 28.19 32.35

Project 6 4.56 21.16 21.99 52.28

Fig. 2. CS versus physics KI-related statements.

Fig. 3. Developing criteria statements related to physics and to CS.


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elaborated later on. Our analysis of all the episodes revealed that each of these domains contributed to the emergence of the KI processes,thus promoting students ’ physics conceptual understanding.

Before we describe the four CS domains, we present some examples that illustrate the analysis. The rst example is very detailed anddemonstrates how KI processes were triggered by the two disciplines of physics and CS. The other two examples are shorter anddemonstrate how CS promoted the emergence of KI processes that led to physics conceptual understanding.

The examples are followed by a discussion of how the four CS domains promotedthe emergence of the KI processes in all the six projectsanalyzed.

4.2.1. Examples4.2.1.1. Example1 5: characterizing a mathematical model of a circular motion. S1 and S2 (tenth grade) developed a simulation of a car drivingon a circular road ( Fig. 4). The program randomly sets the radius of the circle, the angle of the road's slope, and the coef cient of friction. Theuser chooses the velocity of the car so that it completes one round under a pre-set time limit (the velocity should be high enough) without

ying out of the road (the velocity should not be too high).Here we bring the analysis of the rst 66 min of the second lesson. By reading it the reader will get a sense of how the KI processes

(emphasized in Italics ) emerged and whether they were triggered by physics or by CS.At the time of the previous lesson, S2 was familiar with some of the laws and formulas related to uniform circular motion, while S1 was

not familiar with them at all. Towards the end of this lesson, they succeeded in de ning the forces acting on the car as correspondingprogramming variables, and wrote the programming code relevant to the physics' formulas.

The session was opened with S1 eliciting their existing knowledge on circular motion, understanding that they have to look for the relatedformulas. After reading about them in Wikipedia ( adding ), he described them and explained why, in his opinion, they were useless for them;this led to the understanding that they need to seek additional new ideas:

S1: We saw now formulas of circular motion, but they do not help us because this motion is not uniform, its direction is all the timechanging. I need a formula toexpress x, the distance fromthe beginning of the circle; that's myproblem. I don'tknow how to doit. I want

Fig. 4. Screenshot of a simulation of a car driving around the road developed by students S1 and S2.

Table 2Percentages of the KI processes applied by each pair of students in relation to CS or to physics.

Project# CS KI-related statements' percentage Physics KI-related statements' percentage

Project 1 54 46Project 2 45.18 54.82Project 3 62.39 37.61Project 4 42.4 57.6Project 5 36.05 63.95

Project 6 59.34 40.66

5

An extended example appears at Taub, Armoni, and Ben-Ari (2013) .


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to know its location each second on the circle. It's not as simple as it looks. We must consult with someone who knows physics well, F [afriend]!

S1 thought that their current knowledge is lacking both in physics ( “ I need a formula to express x; that's my problem ” ) and in computerscience, since he did not know how to express the car's location in the simulation ( “ I want to know its location each second on the circle ” ).Their friend F added information in physics. However, the formula he wrote down was x ¼ vt which deals with linear motion (instead of circular motion). S1 realized that he had to examine the new information based on some criterion and asked F whether there is a corre-

spondence between the formula and the requested circular motion:S1: That's interesting, but this formula is for linear motion and I want circular motion. Is it the same?

F: Yes. Your x is the circumference of the circle. It's 2 p R. Your x is recursive [he means iterative]; every time the car gets to the beginning,x becomes 0 again.

F explained that the formula x ¼ v t may describe circular motion since the x that is described in linear motion appears in circular motionas well ( criterion) . To reinforce his explanation, he exempli ed the behavior of x by describing the algorithm to be used to present the car'smotion around the circle ( “ your x is recursive, every time the car gets to the beginning, x becomes 0 again ” ). By using this algorithmiclanguage, F connected the formula to the concrete motion of the car. He explained to S1 that the circle may be treated as a straight line andbe used with linear motion formulas; with the extension that circular motion is an iterative linear one, i.e., the car returns every time tox ¼ 0.

Afterwards, it seemed that S1 could not accept the argument about the location of x on the circle expressed as a CS criterion : whether thesoftware can “ understand ” that the linear motion formula now refers to circular one, or not.

S1: But I want to nd its distance from the beginning of the circle. Your formula will make the computer present the motion along astraight line instead of a circle.

F: No, it can't be a simple straight line formula because we have radial acceleration, as well [ adding ]. You do x ¼ 2 p R. Let's say thatx ¼ 100 m, therefore it's easy to calculate the radius. Now, the formula of radial acceleration says that a radial ¼ v2/R. You have the velocityof the car, because the user sets it, and you calculate R, therefore you can calculate a radial of the circular motion.

S1: But we still don't know how to calculate the location of the car on the circle.

The above discussion between F and S1 exposed another difference between linear and circular motion: circular motion relates to radialacceleration.

Accordingly, S1 evaluated the correctness of using the straight line formula for their project and decided to reject F's suggestion ( sorting out) :

S1: No, I have a problem with how the computer will present it, we should nd another way.

F suggested a new idea ( adding ) stemming from a CS point of view, to refer the circle as a series of small straight lines. The software cantreat each one of them sequentially by using the straight line formula x ¼ v t :

F: A circle may be viewed as a set of very small vectors.

S2: OK, but won't it require a lot of processing power? It is a huge for-loop.

S1: You're right, it's too much.

The criterion that caused S2 and S1 to drop this suggestion stemmed, again, from the CS perspective, an ef ciency criterion. They realizedthat F's way of viewing circular motion from a linear motion point of view will not promote their project. As S1 stated:

S1: I'm quite sure there is a simpler way to calculate it … x equals something, something, something. That's what I'm looking for.

In the above episode, F came up with two suggestions stemming from a straight line point of view, i.e., using the straight line formulawith the addition of radial acceleration and referring to the circleas a set of small straight vectors. The students rejected this point of view byusing CS criteria. Therefore they were looking for a formula that referred both to the location on the circumference of the circle and to theradial acceleration.

At this point, the students turned back to Wikipedia, to the circular motion formulas they studied at the beginning of the lesson(adding ). This time, interestingly, they noticed that circular motion involves an angle corresponding to the location of the car on thecircle.

After several failures to express the angle q , S2 and S1 understood that they still lack physics understanding; therefore they went back tothe formulas. They started by discussing the variable t (time) in the formula q ¼ u t :

S2: t is the time. We should nd its value.

S1: We have its value, the simulation runs 100 times per second. It's being added to the value of t [S2 wrote the code: t ¼ t þ 0.01; ].


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S2 explained that t is 'the time', an explanation physics students usually tend to give, without referring to the cumulative nature of thisparameter. The fact that the simulation runs 100 times per second emphasized that t is more than a particular value of time; it is the timeaccumulated since the beginning of the simulation's execution.

Next, the students wrote the equations for calculating the angle q and the angular velocity as programming code. They then calculatedthe coordinates of the location of the car on the circle, by de ning graphical segments creating the angle q and the related equations ( x ¼ Rcosq ; y ¼ R sinq). At this point they ran the simulation ( criterion ), but errors occurred.

S2 re ected on the process of writing the code, a process that led S1 to understand their mistake (sorting out) :

S2: Let's see, we started by de ning two segments that create q and the coordinates x and y. It seems correct. Now, the equations arecorrect, as well. Where is the problem, then?

S1: Let me see … I know! We wrote the equations for calculating the angle q after the calculation of the coordinates of each point on thecircle. This way wecalculate x and y using q , beforewe calculated q . Weshould reverse the order, put the equations rst and only then thecalculation of the coordinates.

They changed the order, ran the simulation and checked it for different and extreme values of velocity (criteria) :

S2: Let's check it for both, very high and very low velocities.

The car was moving as expected, causing them to understand that their calculations were correct ( sorting out ).To summarize, we saw that at the beginning of the lesson, despite of their checking of circular motion formulas, S1 and S2 had no idea

how to express the location of the car on the circle and consulted a friend ( adding ). The need to program the circular motion made them try

to apply the linear motion formula to their simulation. This triggered an examination of the difference between linear and circular motions,which was resolved due to various criteria stemming from CS aspects. The students explored the physics formulas ( adding ) and used theneed to program them to clarify the meaning of some of the parameters, such as the time t . This was done by the students continuouslyrelating the formulas they were discussing to a concrete situation, a car driving around the road. Finally they found the way to calculate thecar's location based on the formulas. It is important to emphasize the difference between the rst time the students checked the formulas,and the second one. At rst, they checked the formulas in a rote manner and could notconnect them to their question of howto calculate thelocation of the car. Later, after working with several criteria that clari ed the characteristics of such a calculation, they were able to un-derstand the very same formulas and nd the answer they were looking for. At the end of a session that took about 1 h long, they had amore-or-less correct simulation of a car moving around the circle. Note that the entire development process was carried out independentlywith no intervention by a teacher.

In terms of the KI perspective, this learning episode demonstrates the emergence of all the KI processes. The students ’ initial elicitation of their physics knowledge led to the adding of new ideas, coming from Wikipedia and a friend. They examined the new ideas by developingcriteria, stemming from physics and CS aspects. Based on these criteria the students sorted out the various ideas and decided which of themshould be used for their simulation and which should be rejected.

4.2.1.2. Example 2: understanding the meaning of a variable in a formula. Students S3 and S4 had to simulate an object positioned in front of alens (concave or convex), where the lens is positioned in front of a mirror (plane, concave or convex). The simulation should present theimage of the object created by the lens and the image of the image that the mirror creates (see Fig. 5 for a screenshot of the simulation). Thestudents recalled (elicited) a formula they had previously studied, 1/ v þ 1/ u ¼ 1/ f , appropriate for both lenses and concave and convexmirrors. In addition, they recalled that for plane mirror, the distance between the image and the mirror is equal to the distance between theobject and the mirror. See Fig. 6 for a sketch that illustrates the variables in the simulation.

They tried to develop an algorithm that calculates the position of the image created by the mirror, in order to locate it in the simulation.They wrote the following code:

Unintentionally, for the case of the plane mirror they calculated the distance between the image and the origin as de ned by the EJSenvironment; but for the concave and convex mirrors they calculated the distance between the image and the mirror(and not the origin), asit appears in the formula they studied. After writing the code, they re-read it and noticed the inconsistency:

S3: What's that? For concave and convex mirrors, we calculated v1 to be the distance between the nal image and the mirror. However,forthe plane mirror we calculated v1 to be the distance between the nal image and the origin. We have to determine where to locate theimage in the simulation.

The need to represent the knowledge of howto calculate the location of any nal image in the simulation (relativeto the origin) servedas

a criterion to examine whether the formula can be used for this calculation, a criterion that is rarely used in ordinary physics tasks ( Sherin,


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2001b ). This is in contrast to manually locating a speci c image on a paper, where the learner may avoid generalizing the calculation. Thispromoted the students' understanding (sorting out) of the meaning of the variable v1 in the formula.

4.2.1.3. Example 3: understanding the relationship between the two sides of a formula. S1 and S2, the students from the rst example, wererecorded again in eleventh grade. They simulated launching a rocket and intercepting an enemy rocket. See Fig. 7 for a screenshot of thesimulation. Before the students started programming they studied the relevant physics formulas from scienti c papers and the Internet.They started programming by declaring the programming variables corresponding to a list of the physics variables that they had previously

listed. One of the variables was ae (acceleration of the enemy rocket) and S2 was wondering whether the name of the variable truly re ectedits physical meaning:

S2: What is ae ? Acceleration, right? What is the direction of the acceleration of the rocket?

S1: Toward the bottom, because of gravitation.S1 referred only to the gravitational force causing the direction of the acceleration.

S2: So let's name it aey [y refers to the y axis].

S1: [changing his mind] No, the product won't be toward the bottom. The direction needs to be calculated every time.

S2: Why?

Fig. 6. A sketch illustrating the variables in the simulation of students S3 and S4.

Fig. 5. Screenshot of an execution of the simulation of S3 and S4.


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S1: Because not only gravitation is acting on the rocket.

S2: Right! There is also air resistance. OK.

We see that even though the students studied the formulas and physics variables prior to programming them, this discussion clari edtwosigni cant issues. First, the criterion of looking for a meaningful name forthe variable, clari ed the causal relationship between the forceand the acceleration. Second, S1 raised the criterion of the requirement to calculate the direction of the acceleration every time. This led tothe understanding that the acceleration is determined by all the forces acting on the rocket, not only by the gravitational force.

4.2.2. The four CS domainsProgramming a simulation of a physics system involves representing physics knowledge and re ecting on it. This is done by four do-

mains, of which the rst three refer to knowledge representation (in this case, knowledge of physics), and the fourth refers to the re ectionon this knowledge: structural knowledge, procedural knowledge, systemic knowledge, and execution. Our analysis of all the episodesrevealed that each of these domains contributed to the emergence of the KI processes, and promoted students ’ physics conceptualunderstanding.

4.2.2.1. The structural knowledge domain. The structural knowledge domain involves dealing with the structure of programming entities

that represent the material parts of the simulated system. Processes in programming that participate in this domain include identifying therequired programming variables and determining the appropriate programming objects the declaration of programming variables and thecreation of programming objects.

Identifying the required variables, choosing meaningful names for them and designing their initialization them elicit the students' priorknowledge in physics and make them discuss its meaning. We observed that even this preliminary programming stage enabled the studentsto clarify relationships between concepts that the literature reports to be dif cult (e.g., Bagno et al., 2008 ). Example 3, dealing with therockets, demonstrates how the criterion of choosing a meaningful name for the acceleration variable led to an understanding of the rela-tionship between the acceleration and all the forces acting on the rocket.

Determining objects is another action related to structural knowledge. When using programming objects corresponding to the physicalobjects of the system, the learners use criteria to distinguish among different structures of physical objects; to decide which properties orprogramming variables should be attributed to each object. Finally, the learners sort out the structure of each physical object.

4.2.2.2. The procedural knowledge domain. The procedural knowledge domain refers to the code activating the programming variables andobjects. It represents the mechanism underlying the simulated system. Procedures include statements of input, output, control structures

(e.g., conditional execution, repeated execution) and assignment. Additionally, they include functions. Examples of such procedures areinstructions to physical objects to move in some direction under certain conditions (e.g., force orthogonal to the direction of the velocityof an object would cause it to move in a circle); and instructions for molecules to get higher values of temperature when being close to a

re.All the four KI processes are triggered when developing procedures. First, the learners elicit their physics knowledge that is related to the

simulated phenomenon. They expose the formulas and laws that they already know. Subsequently, the process of criterion usage isemployed. The learners evaluate whether and how the physics formulas and laws explain the mechanisms they wish to describe. Therelevance of each formula and law to howthe phenomenon occurs should be examined. At this stage learners many times discover that theylack additional knowledge. Learners then try to sort out how the physics formulas and laws can be integrated to a coherent procedure. Finallythey translate the procedure to programming code and apply it.

Example 2, dealing with the simulation of lens and mirror that create images, demonstrates how the students ’ effort to calculate theposition of the nal image led to their examination of the meaning of a parameter in the formula.

In example 1, students S1 and S2 found a better procedure to express the car's location on the circular road by relying on the criterion of ef ciency. A friend F suggested thinking of the circle as a set of very small lines. Although S1 thought that this suggestion was correct in

terms of physics, he rejected it because it was not ef cient.

Fig. 7. Screenshot of an execution of the simulation (students S1 and S2). A rocket intercepting the enemy's rocket.


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4.2.2.3. The systemic knowledge domain. The systemic knowledge domain refers to characteristics of the system being simulated and anunderstanding of the relationships among objects in it. At this manner, it is less important to understand the exact details of how one objectmanipulates another. It is more important to understand the qualitative nature of the effect of one object on the other. Object-orientedprogramming, as in the projects done by the students in the EJS environment, promotes an understanding of relationships among objects. One of the reasons to the emergence of this understanding is that EJS forces the programmers to de ne graphical objects and toconnect them with variables and procedures.

For example, students S1 and S2 from example 1 who simulated the car, de nedin the previous lesson the twoprogramming objects ‘ car ’

and ‘ road ’ . They de ned corresponding programming variables and tried to determine to which of the objects each variables is related(criterion ). Theyexamined allthe forces acting on the objects ( elicitation and adding ) and decided on the origin of each force. This made themrealize that some forces (the normal force and the friction force) stemmed from the meeting of the two objects, leading to an understanding(sorting out ) of the nature of the relationship between the car and the road.

4.2.2.4. The execution domain. The execution domain involves re ecting on the knowledge represented in the simulation. Every time thestudents push the Run button in order to execute their simulation, all KI processes may take place:

Eliciting students existing knowledge: The simulation was created by the students coding their own physics knowledge. Executing thesimulation presents a reality-like phenomenon, which is a re ection of the students' knowledge on it.

Adding new information: The simulation's execution does not only enable the students to re ect on what they know, but it may alsosupply them with new information. As a computational model, the simulation is designed to provide new knowledge. The models areexpected to give additional information that the developers do not have and to simulate experiments that are harder to perform in reallife.

For example, S1 and S2 wanted to learn how the angle of the rocket affects its chances to hit the enemy rocket. They added dynamicgraphs that expressed the velocities of both rockets as functions of the time elapsed since the launching of the hitting rocket ( Fig. 8).

Criteria for evaluating the students' physics knowledge: Running the simulation provides feedback regarding the students' knowledge;if errors occur the students must look for gaps in their knowledge. The students examine their knowledge in several ways:- Students use the simulation's execution as a criterion by comparing its behavior and their predictions regarding it. S1 and S2 in

example 1 used the execution of the simulation to examine whether the equations they wrote as code were correct.- Students use the simulation's execution as a criterion by checking the behavior of the simulated system in different and extreme

physics cases. In example 1 the students executed the simulation both for high and low values of velocity to check its behavior. Re ecting and sorting out: Following the execution of the simulation, the students went through the process of debugging. They re-

ected on how they programmed the simulation, and if necessary examined their physics knowledge, which led to decisions (sorting out) what in their knowledge was correct, false or should be revised.

To summarize, CS provided a language to represent the students' physics knowledge and tools to check and correct this knowledge. This

was done by triggering the emergence of the KI processes, which in turn led to conceptual understanding.

5. Discussion

Understanding the physics behind the formulas is not an easy task. High-school and college students tend to use such formulas in a rotemanner, and do not understand the meaning of each variable in them. Moreover, the algebraic notation of the physics formulas does notnaturally imply on causal relationships between variables, therefore students sometimes infer the existence of equilibrium between the twosides of an equation instead of causality ( Sherin, 2001a ). Programming simulations may assist in overcoming these dif culties. Research has

Fig. 8. Screenshot of a graph of the velocities of the enemy's rocket and the hitting one (students S1 and S2).


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shown that computational contexts are ef cient in physics learning (e.g., Redish & Wilson, 1993 ), and have some advantages over usingalgebra to express the physics ( Sherin, 2001a ).

Our research expanded previous studies by exploring how the computational context improved physics learning. It examined thethinking processes, as described by the KI perspective that were stimulated by the programming. Our ndings indicate that CS played animportant role in the students' physics learning. Four different domains that exist in CS and triggered all KI thinking processes weredetected: the structural knowledge, procedural knowledge and systemic knowledge domains that deal with knowledge representation; andthe execution domain that enables re ection on the represented knowledge. In the work of Sherin (2001a) , for instance, mainly proceduralknowledge was represented.

These four CS domains differ not only in the physical content knowledge they represent, but also in their levels of abstraction. Theexecution domain is at the most concrete level, since it includes the implementation of the programming code with speci c inputs, a visualrepresentation of the physical system. The structural knowledge domain that represents the physical entities in the system is at a higherlevel of abstraction, since the representation is done as an algorithmic design which is more abstract than the graphics. Still, this domainfocuses each time on a single physical entity, therefore at a lower level of abstraction than the procedural one. The procedural knowledgedomain represents a mechanism that connects between more than one physical entity, thus is related both to the system's structure and toits underlying procedures. The systemic knowledge domain is at the highest level of abstraction since it represents physical entities andrelationships among them, without getting into the speci c details of the structure of each entity and the procedures activating them.

The CS domains promoted all the KI thinking processes. Nevertheless, a closer examination revealed that the students mainly applied theKI process of developing criteria . Moreover, a large portion of these criteria were related to CS. These ndings point to the importance of thecriteria learners use in order to evaluate the knowledge they acquire and on the contribution of CS to such a dominant thinking process (cf.Taub et al., 2013 ).

This paper provided evidence that CS was effective in promoting different learning processes than ordinary physics tasks (e.g., Sherin,2001b ). It did not claim, in any way, that solving physics problems in a computational environment is the only instructional method thatpromotes such KI processes and enhances physics learning. Research should be conducted to compare between the computational methodand other methods, such as computerized tutors, in terms of the KI processes they encourage.

Based on the above ndings, instructional implications should be considered. Analysis of all the projects revealed that programmingphysics phenomena is a complex situation. On the one hand, it mayconfuse the students and prevent them from focusing on physics aspects.On the other hand, CS was shown here to be much more than a technical tool. In particular, it forced the students to unfold the physicsmeanings and relationships expressed in the formulas. Moreover, programming simulations provided context-rich problems, similar to real-life.

Physics and computational-science instructors are facing this dilemma when considering the inclusion of programming sessions inphysics classes. Several suggestions for instructions are brought here, based on: the KI framework, the theory on cognitive load ( Chandler &Sweller,1991 ) and the ndings of this work. The theory of cognitive load seems as a natural choice to lead instructional recommendationsfor an interdisciplinary course, in particular where each of the disciplines is considered to be dif cult on its own.

In light of the KI perspective used in this work and of other related studies ( Kali et al., 2003 ), activities that encourage the emergence of the KI processes should be included in the course's materials. Speci cally, the KI process of developing criteria was found in this research tobe the most dominant one. Instructional activities may explicitly demand that the students develop criteria by comparing between the new

knowledge they learn and their prior one, explaining the differences or similarities between them.In light of the cognitive load theory, three types of cognitive load are described in the literature: intrinsic, extraneous ( Chandler &

Sweller, 1991 ), and germane ( Sweller, Van Merri€

enboer, & Paas, 1998 ). Cognitive architecture and instructional design. Educational Psy-chology Review, 10 (3), 251 e 296. Intrinsic is the level of dif culty inherent to the learning task; extraneous is generated by the manner inwhich the information is presented to the learner; and germane is the load devoted to the processing, construction and automation of schemata. In that manner, intrinsic and extraneous are the “ bad ” loads and germane is the “ good ” one, since instructional effort should beput to creating schemata of information to make the learning ef cient.

Learning the disciplines of CS, physics and mathematics may cause intrinsic load, since each discipline is dif cult by itself. Moreover, itmay cause extraneous load as well, due to the instruction of three different disciplines at the same time.

One of the possible ways to reduce the extraneous load would be to provide the students with more intensive physics training. Some of the training may take place apart from the programming, so that students would understand the physics before they mix it with theprogramming. Similarly, the students should be instructed with CS strategies apart and maybe after learning some of the physics content.

In order to strengthen the desired, germane load, it is recommended that instructors explicate the connections between CS and physics.For example, they can demonstrate how each CS knowledge domain represents a different aspect of the physical phenomenon, as was

described above. This would engage the students into an interdisciplinary way of thinking, which has strong roots in the disciplines of CSand physics.

In light of the ndings of this work, we suggest that the instruction of the computational-science course explicitly focus on some issuesthat this paper suggested evidence for. First, the four CS domains of structural knowledge, procedural knowledge, systemic knowledge, andexecution shed light on different aspects in the physical system. For instance, the structural knowledge domain includes identifyingappropriate variables and objects and therefore illuminates on the physical entities that compound the simulated system. The proceduralknowledge domain, on the other hand, illuminates on the mechanism underlying the same system. Instruction that emphasizes theseunique relationships between the physics knowledge and the CS representations may enhance a more complete and coherent under-standing of the physical system. Second, instruction may emphasize the different levels of abstraction being expressed in the CS domains.The students then consciously move between levels of abstraction, thus strengthening their abstraction ability, a highly desired instruc-tional outcome ( NRC, 2010, 2011; Wing, 2006 ). Third, since the development of criteria was found to be central in the students' physicslearning, instruction may strengthen the role of CS in developing such criteria.

The current research explored the effect of CS on physics formulas learning. It did not refer to other factors that may have affected thelearning as well. The students investigated were considered gifted but we did not compare their learning to that of non-gifted students.

Further research is needed in order to explore the possible effect of such interventions on such students. Another factor that was not


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examined concerns the high motivation demonstrated by the students for developing a working and correct simulation. Once they startedthe programming process, they were committed to complete it. We believe that this motivation was one of the reasons that promoted thestudents' conceptual understanding in physics, exploring each parameter in the formulas and the underlying mechanisms.

Computational science is an important interdisciplinary scienti c eld which should appear more often in science education. It includesnot only the three different disciplines of physics, CS and mathematics but it also combines an intensive use of technology. Further researchis needed in order to investigate whether the described above contribution stemmed mainly from the activities related to computer scienceor also from the technological ones, and whether these contributions can be distinguished.

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