Investigating how students collaborate to generate physics problems through structured tasks
IInvestigating how students collaborate to generate physics problems through structured tasks
Javier Pulgar ∗ Departamento de Física, Universidad del Bío Bío, Concepción, Chile.
Alexis Spina † Gevirtz Graduate School of Education, UC Santa Barbara, CA, USA.
Carlos Ríos ‡ Departamento de Enseñanza de las Ciencias Básicas, Universidad Católica del Norte, Coquimbo, Chile. (Dated: March 31, 2020)Traditionally, scholars in physics education research pay attention to students solving well-structured learningactivities, which provide restricted room for collaboration and idea-generation due to their close-ended nature.In order to encourage the socialization of information among group members, we utilized a real-world problemwhere students were asked to generate a well-structured physics task, and investigated how student groups col-laborated to create physics problems for younger students at an introductory physics course at a university innorthern Chile. Data collection consists of audio recording the group discussions while they were collaboratingto develop their physics problems as well as the solutions they created to their problems. Through interviews,we accessed students’ perceptions on the task and its challenges. Results suggest that generating problemsis an opportunity for students to propose ideas and make decisions regarding the goals of the problem, con-cepts and procedures, contextual details and magnitudes and units to introduce in their generated problems. Inaddition, we found evidence that groups tested the validity of their creations by engaging in strategies oftenobserved with algebra-based physics problems, such as mathematical procedures and qualitative descriptions ofthe physics embedded in the problem, yet groups invested more time with algebra-based strategies comparedto more qualitative descriptions. Students valued the open-ended nature of the task and recognized its benefitsin utilizing physics ideas into context, which in turn enabled collaboration in a way not experienced with tradi-tional algebra-based problems. These findings support the use of generative activities as a pathway for studentsto engage in real-world physics problems that allow for a range and variety of collective processes and ideas.
I. INTRODUCTION
There is a strong tradition among physics education re-search (PER) scholars to focus on students engaging in well-structured learning activities, such as algebraic problems.However, research has shown the limitations of such activ-ities in fostering conceptual development [1, 2], and for ef-fective collaboration [3, 4]. Such learning problems tend tobenefit from individualized performance [5, 6] rather thancollaboration, because of their embedded low levels of pos-itive inter-dependency [7, 8]. This motivated us to reflecton alternative tasks that would encourage the socializationof information for collective learning, and would enable pro-cesses associated with idea-generation. For such purposes,this work is grounded in the use of a real-world activity con-sisting of students generating physics problems for youngerstudents. Real-world problems are defined as open-ended ac- ∗ Departamento de Física, Universidad del Bío Bío„ Avda Collao 1202,Concepción, [email protected] † Gevirtz Graduate School of Education, UC Santa Barbara, 93106-9490,CA, [email protected] ‡ Departamento de Enseñanza de las Ciencias Básicas, Universidad Católicadel Norte, Larrondo 1281, Coquimbo, [email protected] tivities that demand higher levels of creative thinking com-pared to algebra-based tasks [3, 9]. Designing physics cur-riculum with more creative tasks responds directly to the needof developing appropriate skills for collaboration and innova-tion for contemporary life and work [10–12]. In this paper,we explore this collaborative work, and physics related ideasand processes students groups engaged in when generating aphysics learning activity for high-school students (i.e., real-world problem). We showed the challenges and benefits forusing this type of task in physics courses as a way of fosteringidea-generation and problem solving strategies often associ-ated with both novice and expert problem solvers [4, 13–15].In addition, we explored how students perceived the benefitsand difficulties linked to building up ideas with their team-mates, and their forms of collaboration with classmates whenfacing this creative task.
II. ALGEBRA-BASED PHYSICS PROBLEMS VERSUSGENERATING PHYSICS PROBLEMS
Algebra-based physics problems mirror well-defined sys-tems of equations that lead solvers towards unique solu-tions, [8], and are often labeled as textbook physics prob-lems [1, 2, 16]. Such problems tend to present simplifiedversions of reality, and are primarily appropriate for the im-plementation of mathematical representations of physics con-cepts and principles. Their well-defined nature and purpose a r X i v : . [ phy s i c s . e d - ph ] M a r makes most of these problems appropriate for the analysisof physics ideas, while an exemption of them might demandstudents knowledge utilization, the highest level of cognitivedemand according to the taxonomy of introductory physicsproblems [17]. Differently, qualitative physics problems, alsowell-defined, have shown richer opportunities for learning[13, 18, 19] as well as collaboration [20, 21].Studies have found that solving algebra-based problemsdoes not necessarily add to adequate conceptual develop-ment [1, 2]. According to Byun and Lee [1, 2], the bestpredictor of conceptual development depends on the strate-gies used for solving the problems rather than the number ofproblems. Experts problem solvers tend to tackle problemsthrough knowledge-development ; that is, they begin by build-ing an extensive conceptual understanding before attemptingto solve problems [2]. Alternatively, Means-End Strategy consists of focusing on the problem’s goals before attempt-ing to build conceptual meanings, where students work back-wards and overlook the meanings associated to solving theactivity [3, 22]. Consequently, algebra-based problems tendto push students towards Means-End Strategy, or ‘plug-and-chug’, known as the practice of finding the formulae that bestfit the problem, a behavior typically associated with novicestudents [1, 2, 14]. The equation-driven approach enacted bynovices has also been labeled as bottom-up logic [18, 23],whereas experts are more likely to engage with top-downstrategies, where they begin from general principles and thenmove down to mathematical representations and equationsthat would enable access to the solution [14, 22].Generating physics problems is associated with real-worldtasks [9, 24], which are open-ended and lack constrainingconditions (e.g., initial conditions) [8, 25]. A real-world prob-lem requires solvers to have the ability to generate subjectiveassumptions over issues relevant to the problem context, inorder to transform and constrain the open-ended scenario intoa well-defined one [9, 26]. Consequently, real-world prob-lems are designed for the highest level of cognitive demand,known as Knowledge Utilization [17, 27], which includescompetencies associated with idea-generation and decisionmaking, a set of processes that benefit from collaboration[28, 29]. For instance, when generating a real-world physicsproblem, solvers are encouraged to transfer knowledge andmake decisions over multiple domains [24]. In physics educa-tion, algebra-based problems might be rather familiar for stu-dents, whom could support their work by recalling past expe-riences. Nonetheless, generating physics problems as a real-world task, is unfamiliar for students in traditional physicscourses. Having been exposed to such cognitive demand iswhat separates novices and experts from successfully solvingreal-world problems [9]. According to Fortus [9], when solv-ing real-world physics problems, the hardest assumptions tomake are associated with the absolute or relative magnitudesof the variables involved, a practice rarely found in introduc-tory courses and related tasks. In contrast, easier assumptionsrelate to physics variables and principles involved in the prob-lems [9]. The uniqueness of generating physics problems as a real-world activity is found in both the lack of constraining con-ditions and the great number of features that solvers mustdecide on (e.g., context, variables, questions, etc.). For in-stance, Hardy and colleagues [30] designed a course wherestudents periodically were asked to create their own multiple-choice questions, resulting in positive learning outcomes, es-pecially for low and middle performance students. Accordingto Mestre [24], generating questions is a cognitively demand-ing task that might shed light on the development of students’expertise and knowledge transfer.
III. COLLABORATION AND PROBLEM SOLVING
In the context of problem solving as a group activity,algebra-based physics problems might be associated with dis-junctive activities [5], as these do not necessarily demandcollective efforts for finding the right solution. Contrary, theactivity of generating physics problems might be associatedwith additive tasks [5], because a good performance wouldlikely emerge as the sum of all members’ contributions andrelevant abilities. This creative problem would enjoy higherlevels of positive inter-dependency [7] compared to algebra-based tasks, as its solution would benefit from collective con-tributions [31–35].For the mentioned reasons, it might not be surprising thatboth algebra-based problems and the activity of generating aphysics problem would respond differently to collaboration.For instance, when facing context-rich problems in mechan-ics, groups provided better problem solutions than individu-als working alone [3, 4]. Recent evidence has shown perfor-mance on algebra-based problems is negatively affected byhaving more social connections in the classroom, particularlyif these social ties were used for accessing information [6],however beneficial for generating physics problems. Yet, thiseffect would strongly depend on whether the learning envi-ronment fosters collaboration, as well as motivates studentsto engage in the processes of idea-generation and decision-making [36].The literature on social networks highlights the importanceof social interactions for solving problems [37–41]. Fromhere, it is possible to identify two distinctive collaborativemechanisms that would enable group performance: (a) cre-ative combinations, where good solutions emerge when con-ventional knowledge is combined in original and appropri-ates ways [42]; or alternatively, (b) interrogation logic, thatis, through a a deep examination of the local knowledge (i.e.,physics content) related to the problem [43]. Creative combi-nations is likely to occur when individuals access novel infor-mation outside their groups, whereas interrogation logic tendsto be observed in cohesive groups with reduced outside inter-actions, and whose members invest most of their time and en-ergy in addressing the information managed by their workingunite [6, 43]. Creating physics problems in groups may facil-itate either of the latter processes, as team members may feelthe need to search for ideas on other groups, in order to ac-cess new information to recombine with their unique knowl-edge [44, 45]. Conversely, because each group must come upwith a unique solution, students may feel like it is wastefulto seek out new ideas from other groups, and therefore, col-laboration may be observed only within the group. Knowingwhether students perceived either of the aforementioned pro-cesses as useful for generating problems would shed light onpedagogical mechanism to encourage effective collaborationin physics classrooms and through non-traditional tasks.
IV. METHODS
In this study, we explore how student groups work to gen-erate a physics problems for younger students. In doing so,we attempted to answer the following research questions: • a. What are the physics and task related ideas that stu-dent groups addressed when generating a physics prob-lem for high school students? • b. What are the perceived the benefits and challenges ofgenerating a physics problem for high school students? • c. How do student groups collaborate when generatinga physics problem for high school students?For this study we observed four student groups from twodifferent sections of an undergraduate physics courses in aUniversity in Northern Chile. The course content consistedof Newtonian Mechanics, which addressed content such asVector Algebra, Kinematics, Newton’s Laws, Rotational Dy-namics and Newton’s Law of Universal Gravitation, and par-ticipants were engineering majors in their first or second yearof higher education. Groups 1 and 2 belonged to section 1,while groups 2 and 3 were observed in section 2. During aproblem solving session on the seventh week of the semester,we tasked students with the activity depicted on Fig. 1. A. Data Collection and Analysis
We gathered audio on four student groups during the prob-lem solving session (1.5. hours) on the seventh week of thesemester, while they solved the task assigned (Fig. 1). Atotal of 295 minutes of audio were transcribed by identify-ing first turns of speech (e.g.,
Student 1 : How did you obtainthe number of revolutions? Did you multiply the number bysomething?;
Student 2 : There is one revolution and two rev-olutions). Later, we revisited the data to separate these turnsof speech by message units (
Student 1 : [“How did you obtainthe number of revolutions?] [Did you multiply the number bysomething?];
Student 2 : [There is one revolution and two rev-olutions]), as the former may include more than one messageunit, and consequently, a variety of ideas may be expressedduring the same turn of speech. After the session, we in-terviewed 4 students (one from each group) and asked them about their experience on creating a physics problem, bene-fits, challenges and the way they collaborate with their team-mates and others. Interviews lasted between 15-20 minutes,were latter transcribed.Coding was conducted in NVivo 12 plus software and wasintended to elicit the different set of ideas and processes stu-dents groups engaged with for generating a physics problemusing the concepts and principles of circular motion. First,we reviewed 25% of the data, and identified emergent issuesand ideas students discussed for solving the problem by at-tending to the dimensions that require decision making, andstrategies for solving physics problems (i.e., algebra, concep-tual understanding). This analysis led to a first draft of cod-ing definitions for themes. We met with a trained graduatestudents in qualitative research whose first language is Span-ish (research subjects are Spanish native speakers) to reviewand re-define the codebook for the analysis of the data, withexamples taken from the 25% of data utilized initially, untilagreement was reached. Later, we coded 15 (6.25%) min-utes of the transcribed data while negotiating the selectionof codes. Finally, the trained graduate students coded inde-pendently 45 min (18.25%) of the data, obtaining a Cohen’sKappa of 0.94 for inter-rater reliability. Finally, we analyzedstudents’ interviews by paying attention on two key ideas: 1.Perceived benefits and challenges of generating a problem;and 2. Nature of the collaboration among students for gener-ating a physics problem.
V. RESULTS
The analysis produced to main themes that emerged duringthe generation of a physics problem. Table I shows these cate-gories labeled Decision Making and Problem Solving Strate-gies, and the different themes corresponding to each category.These categories and themes responded to the different sets ofideas, arguments and processes groups engaged in during theactivity, which enabled their decision-making and the trans-fer of physics content into real-world scenarios. First, wedescribe the nature of these categories and themes, utilizingdirect examples taken from the data. Further, we exploredstudents’ perceptions regarding the benefits and challengesof the task, as well as the ways in which they collaborate fordoing so.
A. Decision Making
The first category (Decision Making) refers to processesrelated to making decisions and generating ideas in order tocreate the physics problem. During these processes, teamsdiscussed and decided on issues, such as the learning goals ofthe activity, the concepts and procedures, and the contextualdetails of how these elements would be presented in writtenform. They also decided on the data to be included to makethe problem well-defined and the questions that would be ap-
FIG. 1. Ill-structured problems administered to course participants.TABLE I. Codebook of emergent categories and themes addressed by 4 student groups during the task of generating a physics problem.Code Description Example
Decision Making
Learning Goals Team discusses and makes decisions regarding the learn-ing goals for the generated problem, and the expectation ofwhat the targeted students should learn from it, which me-diates the degree of difficulty taking in consideration theschool level of the targeted students.
What is the goal of this (activity)? I mean, ofteaching this? ; It would be like explaining them(high school students) how these (movements)work.
Physics Concepts &Procedures Team identifies, poses and decides on the physics conceptsto use into the problem, as well as the ways in whichthese concepts align with the generated problem to be well-structured, and consistent with the task requirements.
I supposed we need to include the equations.That way they only need to replace ; So the prob-lem must be in order. First you calculate one(value), which then allow you to find other.
Problem Context &Wording Team poses and decides on the contextualization of theproblem (i.e., place, subjects, actions etc.), and the word-ing of the problem.
Let us do something cool, like a wooden spin-ning top. ; If I want to say that the car wants tomove from A to B, is that displacement?
Discussing Magnitudes& Units Team discusses and decides the magnitudes scores and val-ues, as well as measurement units for the physics concepts(e.g., 10 km/h, 20 s, 2.5 km) to be introduced into the prob-lem’s description.
How much do we say the acceleration will be? ; Do you want the car to get to its destination fastor slow?Prob. Solving Strategies
Algebraic Procedures Team describes algebraic steps to obtain physical quantitiesas a way of solving the problem, normally mentioned tojustify the appropriateness of the designed problem.
Because you have the angular speed at 3s,which is 10 π , so 10 π is equal to (angu-lar)acceleration plus the initial angular speed.So then you clear and get the (angular) accel-eration. Physics of Circular Mo-tion in Context Team engages in a qualitative description of the physics re-garding the circular motion in the context under considera-tion for the problem.
There is also velocity, this velocity that goes tothe middle. This is the one that enables... Thiswas related to forces if I remember. The topic ofthe two forces pointing out to one side. propriate to ask, while also taking into consideration the de-cided data. From Table II, readers might notice that groupsspent most of their time addressing themes related to DecisionMaking, which included approximately 75% of the messageunits analyzed.
1. Learning Goals
Student groups discussed and made decisions regarding thelearning goals for their problem, and expectations of whatthe targeted students should learn. The learning goals of the
TABLE II. Frequencies and percentage of categories and themes ad-dressed by 4 student groups during the task of generating a physicsproblem for high school students.Categories and Themes Frequency (%)
Decision Making
Learning Goals 25 (4.18%)Physics Concepts & Procedures 209 (34.95%)Problem Context & Wording 128 (21.4%)Discussing Magnitudes and Units 90 (15.05%)
Problem Solving Strategies
Algebraic Procedures 98 (16.39%)Physics of Circular motion in Context 48 (8.03%)Total 598 (100%) problem consisted of enabling secondary school students toutilize their physics knowledge (e.g., “The idea is that theywould exercise with the problem we give them”). The schoollevel of the targeted secondary students emerged in multipleopportunities in favor (e.g., “If we think on the students’ age,they should know how to do such operations.”) or against(e.g., “Maybe that is too much for a kid in 10th grade. Be-cause that is something they would do in 11th grade.”) thedifficulty of the problem in terms of mathematics representa-tions and concepts. In Group 2, this discussion concentratedon the reasons for using circular motion as the key concept,its importance for them (university students) and the targetedsecondary students. From the example below, it is possibleto perceive the intention of making sense of the activity andthe overall objective of learning concepts and principles ofcircular motion:Student A: What is the goal of this (activity)? wemean, of teaching this?Student B: What thing?Student A: All this equations and concepts.Student B: For us or for students who would besolving this?Student A: Well, for both.Student B: It is assumed that almost every move-ment is circular, as there is rare to find trulystraight movements. These do not exist. You willsee that this (movement) has no angles, but in re-ality it has.Student A: It would be like explaining to them(high school students) how these (movements)work.The discussion about the learning goal emerged from theexplicit objective of the task, yet was not necessarily sup-ported by the argument made by student B in regards to theever-present circular motion, which attempted to highlight itsimportance by transferring and extending the real nature ofmotion upon a combination of circular displacements. The latter argument is interesting, as students explicitly attemptedto make sense of the content to be learned for the targetedstudents, yet this idea received no follow up from other teammembers.Group 2 linked the goal of the task to what science teach-ers would do in the face of a similar task. The following seg-ment shows this brief moment of reflection, where the groupattempted to convey the appropriateness of their problem incoherence with the learning objectives:Student C: We have to be clear with the goal,which consists of teaching and learning kinemat-ics of circular motion to 12th grade students. So,it is like a teacher preparing to teach circular mo-tion. That way, each element of circular motioncould be linked to different contexts from dailylife, or just one. It has to be didactic for them(high school students) to understand.Student D: Let us do problems similar to the onesour instructor has used.Student C: That is it, didactic.This segment provided evidence that, in finding the learn-ing goal, students mirrored what experts [secondary schoolteachers] would do in contextualizing the content, and pro-jected their own expectations into what a physics problemshould look like. Finally, in Group 3, we observed a deeperreflection of the learning goal, where a student highlightedthe importance of the real-life context for learning:So, if you include a difficult exercise, but theydo not know how to solve it through equations,they would remember that they tackle a probleminvolving a laundry machine where there was acircular motion and were able to calculate thespeed. Consequently, and lastly, they would un-derstand and know how to calculate angular andtangential speed for a laundry machine, and theywould imagine the same type of motion but ondifferent problems.According to this quote, the context would mediate the dif-ficulty of the problem in the case that the targeted studentswere incapable of using the needed equations, as they wouldultimately associate the context of the laundry machine withcircular motion. Through this link, the student argued thatlearners would draw similarities in the use of equations forthe purpose of calculating quantities across different scenar-ios. This, in essence, is the notion of transferring knowledge,or in other words, the use of information from a well-knownto an unknown situation.
2. Physics Concepts and Procedures
During this process, teams identified, posed, and decidedon the physics concepts to use in the problem. In addition,they looked at how these concepts aligned for the generatedproblem to be well-structured, and consistent with task re-quirements. Defining procedures was in direct connectionwith the learning goal, as teams engaged in the former processto meet the expectations previously defined. When address-ing this theme, groups attended to and emphasized differentsets of elements, such as the algebraic steps through manipu-lation of equations, concepts and the combination of quanti-ties for an appropriate problem structure. Figure 2 would al-low readers to identify the set of concepts used by each groupon their respective problems. For instance, Groups 1 and 2from section 1 decided to use the angular version of speed,distance, acceleration as data to determine the magnitudes de-fined as questions. In contrast, Groups 3 and 4 from section 2selected the linear version of speed, distance and accelerationas initial conditions that would allow solvers to determine thenumber of revolutions completed at the end of motion, thefinal distance covered, speed, and other questions.We observed two different sets of strategies for address-ing the early stages of this process and making decisions:Equation-driven and Concept-driven. The first approach(Equation-driven) was observed in teams that primarily fo-cused on the mathematical dimension of the problem for de-cision making, whereas concept-driven strategies emphasizedthe conceptual dimension of the situation to then reflect onmathematical representations. Group 1 mostly utilized theEquation-driven approach when defining concepts and proce-dures. In doing this, they proposed to include the equationsin the problem so that students could easily ‘plug and chug’and find the solution (e.g., “I supposed we need to include theequations. That way they only need to replace what’s there.”).Consequently, this process was guided by the (implicit) ideathat a problem is constructed in the same way that one maysolve it, which refers to following very structured set of steps(e.g., “So the problem must be in order. First you calculateone (value), which then allows you to find other.”). The exam-ple illustrates the algorithmic nature of developing a problemfor Group 1. Similarly, Group 4 engaged in such a strategy fordefining concepts and procedures, yet transitioned towards aConcept-driven description of the phenomena after establish-ing the situation to be used:It will start from rest, and that way we couldcalculate the movement of the barrel. So then,we would tell them that the barrel is accelerat-ing constantly and that it needs certain time inseconds to hit the target. Because after someseconds the barrel will be there, at its final po-sition. That is, it will impact the target, so thenthey could begin their calculations for differentthings, like angle and everything.This quote from a member of Group 4 showed a simplephysics analysis of the situation used (i.e., a barrel is thrownto a person), as the student analyzed the position and evolu-tion of the object through time, and enabled further under-standing of the procedures the targeted students are expected to go through for solving the problem.Even though deciding on concepts and procedures utiliz-ing Concept-driven approach is not absent from the atten-tion to equations for decision making, the subtle differenceis that the equations emerged after deciding on the conceptsfirst. For instance, a student in Group 2 stated: “So let’s cre-ate a situation where we combine angular speed, accelerationand everything else, like a situation that involves circular dis-tance.” This approach helped the group to create a problembased on the relationship between concepts rather than on theexclusive use of equations. In Group 3, this was insinuatedby a member arguing against the equation-driven approach inthe description of the physics regarding the situation selected:More than the equations, it would be better tosay the there is a force acting over there, whereasthere is another force but in that direction. . . Weneed to be more specific. For instance, say thatthere is a force acting to the inside, and anotherto the outside.Even though the use of forces is beyond what is expectedfor the target students to know, this qualitative descriptionprovided a conceptual framework for the group to decide onthe physics for the problem.
3. Physics Context and Wording
Groups posed ideas and decided on the contextualization(i.e., place, subjects, actions etc.) and wording of the prob-lem. This process required groups to invest considerableamount of time (21,4% of the data, see Table II), which isnot surprising taking into account the need to select a dailysituation where circular motion is observed. Groups experi-enced some conflict to find the right contextual elements touse. For instance, Group 1 started by only focusing on ob-jects with wheels, yet members attempted to achieve somedegree of novelty by pushing the conversation towards situ-ations beyond wheels (i.e., “Is there one without wheels? Icannot think of anything.”). Group 4 wanted to create some-thing fun for students to be motivated with (e.g., “Let us dosomething cool, like a wooden spinning top.”). Other par-ticipants suggested ideas like a fisherman moving his fishingrod and describing a circular motion, or an ant walking onthe inner wall of a bottle. Here, originality was controlled bytheir level of confidence in exploring such situations throughtheir physics knowledge, (e.g., “We do not need to compli-cate ourselves with that.“) and ended up using more familiarsituations.As seeing in Figure 2, Group 1 selected the wheels of a carmoving and covering a trip between places; Group 2 decidedon the use of a person trapped in a barrel in motion; Group 3decided on the motion of a bicycle; and Group 4 utilized ref-erences from a problem created by their instructor to design asituation where Donkey Kong moves a barrel.
FIG. 2. Problems generated by groups 1, 2, 3 and 4.
The wording of the problems illustrated the use of tech-nical language, and became an opportunity for participantsto challenge their own conceptual understandings. A simpleexample emerged from Group 1, where a student asked thefollowing when deciding on the right wording of the prob-lem: “If I want to say that the car wants to move from A toB, is that displacement? “ Because displacement is definedas a vector, then to properly use it, the group needs to in-corporate a direction. There is no evidence in the data whenthis correction was made, but the problem is worded usingscalars rather than vectors, and framed the phenomena as “acar wants to move”.Another example of negotiating the wording with a cor-rect use of physics concepts was observed in group 4, whenstudents discussed the conditions under which Donkey Kongwould make the barrels move:Student P: For this, he tosses the barrel fromrest?Student O: You cannot toss a barrel from rest. Itreleases the barrel then. He let the barrel go.Student P: Ah, okay.Student O: Or better, he tosses it with an initialspeed, is that okay?This segment showed students’ understandings of motionin connection with an appropriate use of language to conveythe idea that releasing and tossing the barrel implies differ-ent physical conditions. Here, a body that begins its motionfrom rest must be release to accelerate due to the presenceof an external force (e.g., gravity), and will therefore gainspeed. Differently, tossing implies an interaction (i.e., force) that boosted energy and therefore speed to the object that wasmoving. Both ideas showed comprehension of motion and theimplications of forces for the motion defined in the problem.
4. Discussing Magnitudes and Units
During this process, groups engaged in discussions and de-cision making regarding relative values and magnitudes, aswell as measurement units for the physics concepts (e.g., 10km/h, 20 s, 2.5 km) to be introduced into the problem’s de-scription. This process is important as it brings a sense of‘reality’ to the physics of the phenomena and situation underdesign. This process enabled groups to identify and selectappropriate values to link with the physics concepts used asdata. The validity of these magnitudes was tested through thecalculation of their unique responses. For instance, Group 2discussed the appropriateness of a high angular accelerationfor the barrel that yield to 1,400 rpm (revolutions per minute),and decided to ‘Lower the values’. Similarly, in Group 1, weobserved the following interaction for deciding on the accel-eration of the car:Student A: What do we say the acceleration is?Student B: 20.Student A: 20 what?Student B: Meters by square second.Student A: Is that too much?Student B: I know it is a lot. Do you want the carto get to its destination fast or slow?Student A: I want it to get there at a normalspeed.This dialogue reflects the intention to utilize magnitudesthat resemble real life situations. Later on in this process, thesame group tested the problem with an acceleration of 10 m/s,and obtained a final speed of 200 m/s, an unrealistic result fora common car moving in the city.
B. Problem Solving Strategies
The following set of themes emerged from students en-gaging in processes often associated with solving algebra-based problems, where students are likely to utilize physicsconcepts, their mathematical representations, and enact onphysics descriptions connected to the context of the activity.The literature on novice and experts physics problem solverssuggest that the former group tends to utilize algebra-basedstrategies (e.g., ‘plug-and-chug’) rather than qualitative de-scriptions, a strategy associated with expert behavior [13, 18].
1. Algebraic Procedures
This process relates to algebraic steps that the group wentthrough to obtain physical quantities needed to solve and testthe appropriateness of their designed problems. This includedsuggesting strategies to determine a physics quantity (e.g.,“Here we will use a proportionality rule. If one revolutionis 2 π , then x revolutions will be. . . ”); and/or requesting ad-vice on how to proceed in order to get the right value (e.g.,“How do we transform this to radians? Does someone knowhow to?”). Most of the evidence found here emerged whenstudents wanted to achieve either of the latter two goals.To contextualize the use of algebra in this context, it is im-portant to remember that kinematics problems rely on threefundamental physical quantities: position [ (cid:126)r ( t ) ], velocity[ (cid:126)v ( t ) ] and acceleration [ (cid:126)a ( t ) ], all functions of time t . Eventhough these concepts are defined as vectors, in this contextstudents utilized these mathematical representations to deter-mine scalar quantities, or the magnitudes of the vectors at anygiven time. In circular motion, these concepts are written inan angular form: angular position [ θ ( t ) ], angular speed [ ω ( t ) ]and angular acceleration [ α ( t ) ]. The link between these lin-ear and angular magnitudes comes from s = θR (i.e., arc), v = ωR and a = αR . Consequently, in order to test theirproblems, students manipulated some or all of the latter math-ematical relations. For instance, students in Group 4 had thefollowing argument to determine the angular position of dis-tance covered by the barrel:Student L: And how would I get the angle?Student M: With the (angular) acceleration thatis obtained from the equation. With the angularspeed. Because you have the angular speed at 3 s, which is 10 π , so 10 π is equal to (angular)acceleration plus the initial angular speed. Sothen you clear and get the (angular) acceleration.Here, student M suggested the use of angular speed [ ω ( t ) ]at time 3 s, to determine the value of angular accelerationby isolating this value from the equation, because all otherelements were given. Once this was done, the argument, al-though not explicitly mentioned, oriented to the use of thisvalue of angular acceleration into the equation for angular po-sition, and calculate θ at 3 s. Once again, this was possiblebecause all other elements in the equation are defined.Another interesting example was observed in Group 1,as they used the equations (cid:126)r ( t ) = (cid:126)r + (cid:126)v t + 1 / (cid:126)at and (cid:126)v ( t ) = (cid:126)v + (cid:126)at to determine the time that it will take the carto reach its destination. The following interaction depicts theset of algebraic steps suggested for one member to achievethis goal:Student A: So we have that the initial position iszero, and the initial speed is zero. And we havethat (in the equation), only the acceleration forthe square time will remain.Student B: And then?Student A: That will give you 10 m/s (magnitudeof the acceleration) times the square time, andwith that you can obtain the time. So, it will bethe square root of something, and then we willuse only the positive root.This interaction shows an appropriate use of the equation (cid:126)r ( t ) = (cid:126)r + (cid:126)v t + 1 / (cid:126)at to obtain the time, given that allthe elements but the time are known (final distance is givenin the heading of the problem and is equal to 2 km). Becausemathematical manipulation may be perceived as a rather in-dividual exercise, it is not surprising that the audio recordingonly captured brief descriptions of the strategies to be imple-mented to find numerical values, and the request for adviceon how to calculate them.
2. Physics of Circular Motion in Context
This theme consisted on groups addressing the qualita-tive description of the physics regarding the circular motionin the context under consideration for the problem. Thisprocess enabled access to students’ conceptualization of thephysics phenomena in question and the ways in which theywould explain such situations. The sample size of examplesthat illustrate this process is rather small and does not pro-vide evidence on the most difficult concepts. Consequently,the observed frequency (see Table II) reflects the disparitybetween algebraic-versus-qualitative strategies students dis-played. Moreover, qualitative descriptions emerged from thedata when students tried to make sense of the situations andphysical objects considered for the problem.There is evidence that students attempted to explain revo-lutions, tangential velocity, and inertia, the last being used todetermine what would happen if someone were to fall from afast-spinning carousel. The concept of a revolution was con-ceptualized through the perimeter of a wheel: “Suppose thatfirst there is a point that moves along the perimeter until here.That will be one revolution”. This description is very simpleand does not really reflect deep understanding of a physicsconcept that one were to associate with motion.A more interesting example was provided by Group 4 in anattempt to understand the relationship between angular andlinear speed in the context of a wheel moving. First, angu-lar speed is defined as the change of angular position per unitof time (i.e., ω = ∆ θ/ ∆ t ), and may be difficult to under-stand because it does not imply distance units, such as metersor kilometers. Secondly, an object spinning will measure thesame angular speed at any distance from the center of rotation(i.e., radius) at a particular time. However, the linear or tan-gential speed will increase according to the distance from thecenter of rotation as shown by the equation ( v = ωR ). Next,the discussion unfolded as follow:Student E: If this is supposed to be in the samewheel, then why? If you advance five meters,you will complete the same number of revolu-tions.Student G: Yes, you are right. So, how many. . .Student F: The angular speed will change at dif-ferent points of the wheel.As one would notice, the claim made by student F sug-gested a misconception regarding the nature of angular speed,because this quantity remains constant regardless of the dis-tance from the center of rotating object. Consistent with thedefinition of angular speed, the comment made by student Ewould have made more sense if instead of using 5 meters asthe distance covered, he would have used angular measure-ments to highlight the distinction with linear speed.The last example that illustrates the nature of qualitativedescriptions used by students emerged in Group 3 when dis-cussing the nature of acceleration and forces on circular mo-tion: Student S: There is also velocity, this velocitythat goes to the middle. This is the one that en-ables. . . This was related to forces if I remem-ber. The topic of the two forces pointing out toone side. Now I remember, centripetal and cen-trifugal force.Student T: Centrifugal force was like. . .Student U: It is the one that points inside.Student T: No.Student S: Centripetal force points to the inside.Student T: Okay, centripetal force points to theinside. But centrifugal points to the outside. And those two forces would make that. . . “Therewere like equals and. . .Student U: Both forces allow the circular motion.Student T: But this centrifugal force was some-thing like hypothetical, or something that wasnot real. . .According to the interaction, students attempted to makesense of the physical interactions that enable circular motion:in this instance, centripetal force. The ideas related to cen-tripetal force are correct: it is an interaction that is directed tothe center of the circumference described by the motion, andit is responsible for the circular motion. However, centrifugalforce, as corrected by student T at the end of the interaction,is not a force but rather the effect of inertia, defined as resis-tance to change the state of motion and is often referred toas a “fictitious force”. Finally, this interaction provides someinsights on students’ understandings, but again fall short togive substantial evidence to assess whether students are actu-ally understanding the underlying physics of circular motionbeyond the use of equations. VI. STUDENT EXPERIENCE
Students shared their perceptions regarding generating atask while taking into consideration their experience withalgebra-based physics problems in school and universityphysics courses. From here, they recognized the differencesbetween addressing such well-structured activities and that ofcreating a physics problem for younger students. Among thechallenges of these creative tasks, student 1 (from Group 1)posed the lack of familiarity with the process of coming upwith appropriate assumptions and different ideas for uniquesolutions. Such difficulty has been documented in Fortus[9], and identified as a reason why novices and experts per-formed differently on real-world problems. In line with this,the same participant suggested the learning benefits of usingopen-ended problems more often, as a way to get accustomedwith the requirements of tasks where they need ‘to create,search and define the problem’.For student S2 (from Group 2), the creative nature of thetask was perceived as an interesting feature that allowed stu-dents to ‘think in what to do, and to generate the problem thatyou want.’ Student 2 (S2) suggested that even though thisactivity pushed him to reflect more on the content because itis more engaging, he doubted whether this generative activ-ity would foster higher level learning compared to traditionalproblems: ‘I do not know if you learn more compared to agood [well-defined] example with formulae and its applica-tion’. For him, the biggest bit of uncertainty was linked to theopen-ended nature of the tasks and not mastering the content:‘the tendency to include more that what it is actually needed,because you are not sure whether with this or that you aregoing to get the expected results’.0For student S3 (from Group 3), generating problems al-lowed her to use her mind more so than algebra-based prob-lems. According to her, ‘one gets more by doing things inreal-life because that is what you will face at the end [workenvironment]. For me personally, that it is more challenging,but I liked them more because they take me to what I woulddo in few more years’. Additionally, student S1 argued thatgenerating a physics problem pushed him beyond the idealscenario where physics magnitudes are often introduced inthe classroom, but in a real context. Further, he (S1) rec-ognized this as a difficult mental exercise due to the lack ofconstraining conditions, as for a real-world phenomena onemust consider ‘all the variables involved’. Such a challengemay be linked to a lack of familiarity in having the libertyto manipulate and utilize physics magnitudes and other vari-ables, and not knowing whether a magnitude set by his groupwas ‘approximate, more or less to what would be real’.
A. Collaboration
According to students S1,S3 and S4, collaboration for gen-erating a physics problem occurred mostly within the group,where they recognized that their solutions came up after col-lective decision-making, but without the need to reach out tomembers of other groups. This collaborative mechanism isassociated with interrogation logic [43], where team mem-bers pay attention to the knowledge managed by team mem-bers for solving the problem. Interestingly, students claimedthat solving an algebra-based problem is a process that mo-tivates social interactions outside their group (e.g., creativecombinations), whereas addressing a generative task some-how discouraged such socialization beyond their teams, be-cause their solutions (i.e., generated problems) were differ-ent. Further, students agreed that depending on the problem,the nature of the social interaction within and between groupswas different in their purpose.For instance, when addressing algebra-based problems,student S1 suggested that ‘the ones [team members] who nor-mally solve the close-ended [algebra-based] problems are al-ways two people. They are always the same two, becausefor them it is easy to seek out the information to include intothe equations, and then get the result...’ This statement is co-herent with problem solving strategies well documented inPER literature, where students would seek out appropriate in-formation for ‘plugging & chugging’ in order to get the nu-merical results to their problems. Additionally, student S1added: "For close-ended problems, because for everyone itis the same [activity], one search for the method they areusing, and if you get lost then someone else may have theanswer.’ The type of information he claimed to seek out inalgebra-based problems refers to ‘specific knowledge’, withlittle attention on the ‘why you are using this?’, but more on‘finding the results and finishing the exercise’. Similarly, stu-dent S4 suggested that for solving algebra-based problems,the interactions for information seeking often took the form of ‘what equation did you use?’ or ‘what did you get?’ Con-trary, when generating a physics problem, student 4 suggestedthat the nature of the interactions enabled their team to an-notate ideas from the brainstorming process that were laterdiscussed, discarded or agreed upon by all group membersfor further development. Student S2 added that ’in an open-ended [generating a physics problem] problem we four haveto do it, because we all have to pay attention in case some-thing it’s left out, because these [problems] require more in-formation.’ On this context, for student 1 the search for in-formation takes a more complex form, as ’you need to takewhat others [team members] are doing into what you are do-ing’, and for such purpose he highlighted the importance ofunderstanding why others perform in the way they did (e.g.,‘Why you did that?’ And ‘How you did it?’). For student S4,the nature of generating a problem is ‘more subjective’, andtherefore discouraged the interaction with other groups in or-der to check for what they are doing. In the same line, forstudent S2 there is no need to interact with peers outside thegroup ‘because all problems [solutions] are different, and I donot need to compare my response with other person becauseit will be completely different’.
VII. DISCUSSION
Generating real-world physics problems is an authentic ac-tivity for educators to engage in. Creating problems that re-quire students to generate, apply, and select subjective as-sumptions [9, 26] is complex and requires further explorationin education. Our first area of results, Decision Making, con-stituted the different dimensions that required subjective as-sumptions in order to solve the problem. These ideas in-cluded: 1. Learning goals; 2. Physics concepts and pro-cedures; 3. Problem context and wording; 4. Magnitudesand units. The second category of results, Problem SolvingStrategies, involved 1. Algebraic procedures and 2. Physicsof circular motion. According to Fortus, assumptions regard-ing the physics variables and principles, and regarding themagnitudes of these variables, are the two main assumptionsnecessary for solving real-world problems. The first assump-tion (i.e., physics variables and principles) is easier to makefor novices (e.g., undergraduate physicists) and experts (e.g.,graduate physicist), compared to assumptions regarding thenumerical magnitudes of the variables used in the problem[9].Connecting with the themes from Decision Making, weargue that Physics Concepts and Procedures mirror the firsttype of physics assumption that is accessible to both novicesand experts, whereas Magnitudes and Units might be con-sistent with the second type of assumption, which more ex-perts are familiar with. Extending the dichotomy, we pro-pose that assumptions about the Problem Context and Word-ing as an alternative and a more accessible assumption tomake for both novices and experts, as both groups of stu-dents are likely to have experience reading different types of1algebra-based problems, with various contextual details andwording. Therefore, students may be more efficient in usingthat knowledge as a resource for making their own assump-tions. In contrast, and even though all participants have beenexposed to learning activities of diverse nature, discussingand making decisions about the problems’ Learning Goalsmay be more challenging, as this entails knowledge of thetarget students, which will ultimately mediate the problem’slevel of difficulty. In sum, having students generate prob-lems adds two alternative types of assumptions with arguablydifferent levels of complexity for both experienced and non-experienced solvers in Problem Context and Wording, andLearning Goals.In addition, results show that developing problems encour-aged students to engage in both quantitative (Algebraic Pro-cedures) and qualitative (Physics of Circular Motion) strate-gies for testing (solving) their problems. It is important torecognize the differences in time invested in these problemsolving strategies, where students tended to favor algebraicprocedures over qualitative descriptions. Reducing the gapbetween the time invested in algebraic procedures and qual-itative descriptions of the content constitutes an additionalchallenge for physics educators, as shown in the literature[2], and further pedagogical innovation and research needsto be conducted on this matter. For instance, one may thinkabout using characteristics from isomorphic sets of physicsproblems [18, 23] in order to encourage students to gener-ate problems with such characteristics (i.e., quantitative andconceptual problems around the same content). Here, gen-erating both mathematical and conceptual problems from thesame content may increase reflection of the content beyondthe utilization of mathematical representations. In the like-liness that students begin by algebraic procedures, one mayexplore qualitative descriptions.Students’ perceptions of facing generative tasks shedssome light on some of the benefits and challenges. Thiscreative task was recognized for giving students the chanceto utilize their knowledge in a real-world context. Again,the lack of familiarity regarding how to engage in real-worldproblems was highlighted as one dimension where they needmore practice. Consequently, education and physics educa-tion might require more opportunities for students to engagein generating assumptions and making decisions based on in-formation, a key set of practices for 21st Century education[10, 12].Further, the ways in which student groups collaborated forgenerating the problem shed light on the nature of the socialprocesses students tend to engage in, and the importance ofsuch processes in supporting learning. For instance, socialinteractions for solving algebra-based problems responded tothe ‘bottom-up’ logic [18, 23], in that students pursued spe-cific information to utilize for solving the problem, ratherthan enacting on a content-oriented strategy, like ‘top-down’logic [14, 22]. Even though this process might have resem- bled the mechanism of creative combinations defined in thesocial network literature [42, 43, 46], as students claimed toseek out information to other groups, the nature and, ulti-mately the purpose and content of the information requestedsignals a practice that does not aim for creative ideas toemerge, but rather the reproduction of conventional knowl-edge in the face of algebra-based physics problems. In con-trast, generating a physics problem in a traditional physicsclassroom enabled in-depth group discussions, where stu-dents paid attention to the ideas and knowledge managed bytheir team members (i.e., interrogation logic) [43], and wherestudents recognized the value of building upon each others’ideas for coming up with a unique solution. The nature ofsuch collective process is evidence of the additive nature ofthe task [5] and its interdependence [7] that motivated themto understand procedures and knowledge utilized by others.
VIII. CONCLUSIONS
The evidence shown in this study encourages the use ofgenerative physics activities, and more specifically, the taskof creating problems. This would allow student groups tospend more time addressing the multiple dimensions of de-cisions that must be made, and thus prioritizing the processof idea-generation, here engaged through effective forms ofcollaboration within their work groups. Moreover, the ex-tent to which the percentage of engagement leads to betterresults in terms of the quality of the problem would dependon the effectiveness of these processes and overall collectiveperformance. However, evidence that students would dedi-cate significant portions of their time to generate ideas for thecreation of problems, or solutions in general, is likely to boostfamiliarity in the face of idea generation using concepts andprinciples of the curriculum, which may ease transfer and thedevelopment of deep learning. Finally, developing the rightset of skills for facing real-world problems seems to be val-ued not only from the great scheme of education, but also forstudents. Consequently, more efforts and innovations must bemade in order to positively respond to such demands.
ACKNOWLEDGMENTS
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