students' beliefs about the role of atoms in radioactive decay … · 2013-11-21 ·...

ABSTRACT

Contemporary science education research emphasizesthe importance of considering students pre-instructionalbeliefs when designing effective, learner-centeredinstructional strategies. When scientists teach aboutdating geological events, most often the concepts ofradioactive decay and half-life are presented. However,the research base on student understanding of radiationand radioactivity is currently quite limited. The principalresearch question used to focus this investigation asked:What are the common difficulties that studentsexperience when trying to learn about radiation andradioactivity? Our research illustrates that studentsbring to the classroom many inaccurate ideas andreasoning difficulties on the topics of ionizing radiation,radioactivity, and radioactive decay that are well-poisedto interfere with students' understanding of how half-lifeis used to determine geologic time. To uncover the rangeand frequency of the dominant student beliefs, weperformed individual demonstration interviews andadministered open-response and multiple-choiceconceptual tests to students from a wide-range of sciencebackgrounds. Our results show that students are oftenunable to differentiate between the ideas of irradiationand contamination, and that many of these students'reasoning difficulties about radioactive decay andhalf-life stem from their inaccurate mental modelsregarding the atom.

INTRODUCTION

The topics of radioactivity, radioactive decay, andhalf-life are foundational concepts in geology,astrobiology, chemistry, physics, biology, paleontology,astronomy, mathematics and planetary science classes.Many laboratory activities (Mak, 1999; Hoeling et al.,1999; Peplow 1999; Russo, 1999; Lumb, 1989; Austen andBrouwer 1997), analogy-based teaching strategies(Wunderlich, 1978; Evans, 1974, Celnikier, 1980;Kowalski, 1981; Priest and Poth, 1983; McGeachy,1988),and calculation or computer-based exercises (Weinberg,1997; Caon, 1995; Ruddick, 1995; Shea, 2001; Huestis,2002), are offered in the literature to help students betterunderstand radioactive decay and half-life. However,the fundamental naive beliefs and reasoning difficultiesheld by many students are poised to interfere with themajority of these novel instruction methods. Theunderlying problem is that the majority of thesematerials and teaching strategies are not informed byrecent research into student learning and reasoningdifficulties on these topics and thus fail to effectivelyelicit or help students resolve the naive ideas that theyhold prior to instruction. In fact, of the greatest potentialconcern is that many of the activities listed above arelikely to enhance or reinforce the student difficultiesdescribed here.

The principal research question used to focus thisinvestigation asked: What are the common difficultiesthat students experience when trying to learn aboutradiation and radioactivity? Prior research (see Part I)

suggests that one student learning difficulty with thesetopics stems from their inability to correctly differentiatebetween irradiation and contamination, believing that anobject exposed to ionizing radiation will becomeradioactive. In addition our research suggests that half ofcollege students enrolled in introductory physics coursesbelieve that orbital electrons are causally related to theradioactive state of atoms and to the decay process.Making matters worse, an equal percent of thesestudents believe that the mass and volume of aradioactive substance will decrease in the period of ahalf-life.

We assert that the students' naive beliefs andreasoning difficulties related to a particular topic whichare identified from an investigation conducted in onesubject area (such as physics) are certainly also poised tointerfere with instruction on the same topic while beingcovered in a different subject area (geology, chemistry,astronomy etc.) Furthermore the overall population ofstudents who enroll in the introductory non-sciencemajor course through the introductory majors course inone subject area (such as geology) may well provide arepresentative sample of the general population ofstudents that enroll in the same range of courses withinany of the other subject areas (listed above) that teachabout radiation and radioactivity. We argue that theresearch herein serves to both identify students' ideasand inform the development of innovative instructionalstrategies centered on helping students overcome theirnaive beliefs and reasoning difficulties when beingtaught in any of these subject areas (Prather, 2000).

PART I - PRIOR RESEARCH FINDINGS

Studies conducted in Europe, with students of middleschool and high school age, found that many studentshave a weak understanding of the transport andabsorption properties of radiation and radioactivity(Eijkelhof and Millar, 1988; Lijnse et al., 1990; Millar,1993; Millar and Gill, 1993; Millar, 1994). This researchidentified that these students have an inability toproperly differentiate between the concepts ofirradiation and contamination. The initial stages of ourresearch confirmed that the students' beliefs andreasoning difficulties identified by these Europeanstudies were also held by college students enrolled inintroductory physics classes here in the United States(Prather and Harrington, 2002). When asked to reasonabout situations that involved the exposure to, orabsorption of, radiation we found that many studentsinappropriately involve the concept of radioactivity.These students often stated that objects exposed toradiation would either become sources of radiation orhave radioactive properties. Some of these studentsdescribe ionizing radiation as having the same propertiesas radioactive materials. Furthermore, we identified thatit is indeed possible for students to provide the correctanswer to questions involving irradiation andcontamination while employing faulty reasoning.Additional studies conducted in the United States and inEurope focused on elementary aged students' andpre-service teachers' ideas about the nature of geological

Prather - Students’ Beliefs About the Role of Atoms 345

Students' Beliefs About the Role of Atoms in Radioactive Decayand Half-life

Edward Prather Department of Astronomy, University of Arizona, 933 N Cherry Ave., Tucson, AZ85721 [email protected]

time (Ault Jr., 1982; DeLaughter et al., 1998; Trend, 1998;Trend 2000). The later stages of our research, detailed inPart III, suggest that students' ability to reason aboutgeological time is potentially limited by their naïvebeliefs about the concept of half-life.

To properly account for radioactive phenomena, one must have a fundamental understanding of how theatom (or atomic nucleus) behaves during the decayprocess. Either students do not have a clearunderstanding of the role of atomic nuclei in radioactiveprocesses or they fail to access this knowledge whenasked questions about radioactivity. To move beyondstudents' ideas about irradiation and contamination ourinvestigation next targeted students' understanding ofthe role the atom plays in the radioactive decay process.Results from this phase of the investigation will bedescribed in the following sections of this manuscript.

We will describe this research in an atypical formatin that we will report our methodologies, researchpopulations and results in a somewhat interwovenmanner and sequence. This is done because the researchwas conducted iteratively with each result influencingthe next methodological step. The research tools usedand corresponding results provided do not easily lendthemselves to conventional quantitative measures ofreliability. Rather they are created from a theoreticalframework of grounded inquiry and, as such, are basedon student' responses from sequential steps of theresearch.

It is worth noting that the results from all phases ofthis investigation were used to continually guide thedevelopment of instructional strategies and materialsincluding interactive lectures, hands-on laboratory-based activities, and tutorial worksheets. Thesestrategies and instructional materials were structuredaround a directed inquiry approach and have beenshown to substantially increase the understanding ofstudents over conventional lecture and lab methods forteaching about irradiation, contamination, radioactivedecay and half-life and are described in detail elsewhere(Prather, 2000).

Part II - STUDENTS' BELIEFS ABOUT THEROLE OF THE ATOM IN RADIOACTIVEDECAY

Materials that are commonly referred to as "radioactive"contain both stable and unstable atoms. Unstable atomsare also referred to as "radioactive." These atoms containan unstable nucleus and have a non-zero probability ofundergoing a transformation and emitting ionizingradiation. Therefore, a thorough understanding ofstudent beliefs related to radioactive phenomenarequires that we investigate their understanding of bothstable and unstable atoms. Our research question guidedour investigation to focus on the extent to which wecould develop a deeper understanding of how students'ideas about radioactive atoms differ from their ideasabout stable atoms. Our investigation was designed toelicit whether or not students have a model, or mentalpicture, that they use to describe the atom in general andin particular how they use their model to account for theradioactive decay process at the atomic level. Allstudents participating in the investigations described insections A-D below were enrolled in undergraduatephysics courses taught at a medium-sized researchlevel-one university located in the Northwestern UnitedStates. Specific information on student populationnumbers and courses will be provided to accompany thespecific phase of the research being reported.

Results from Open-response Conceptual Questionson the Stable Atom - In an open-response conceptualquestion used during a preliminary phase of thisresearch, 180 non-science major physics students wereasked to sketch a picture of an atom and label each part ofthe atom. In addition, students were asked to indicate thelocation of any particles having a net positive or negativecharge and to describe, in words, the location of theparticles. In particular we were very interested to seewhat representations students would choose whentrying to describe or draw an atom.

The majority of these 180 non-science major physicsstudents who responded to this preliminary questionprovided what we considered to be a reasonablycomplete drawing of the atom involving electrons and anucleus. Of these students, more than half (56%) drew aBohr-like representation. These drawings showed acentral nucleus composed of protons and neutrons, aswell as electrons surrounding or orbiting the nucleus.Approximately one-quarter of these students (23%) drewpictures of the atom that involved two or three differentparticles in orbit about a central sphere. The orbitingparticles provided in these representations included allcombinations of electrons, protons, and neutrons.Overall, only about half (51%) of the students correctlystated that electrons have a negative charge, protonshave a positive charge, and that neutrons have no netcharge. As the results from our further investigations(detailed below) illustrate, students' ability to properlyidentify the location and state of charge for these atomicparticles rests at the core of many of the naive ideasstudents have about the nature of radioactivity.

Results from Interviews on the Radioactive Atom -Informed by the results described in part A, we shiftedthe emphasis of this investigation to examine students'ideas about the role that the atom plays in connectionwith the concept of radioactivity, including the processof decay. As a first step, we conducted a series of sixindividual demonstration interviews in which studentswere asked to perform specific tasks, and answerconceptual questions, designed to provide insight intotheir beliefs about concepts related to radioactivity. Acombination of both open-ended and pre-determinedprotocols was used with each of these interviews, whichaveraged 1/2 - 3/4 hour in length. Each interview wasvideotaped for later analysis of students' responses andactions. These interviews were conducted with twostudents that were enrolled in the introductorycalculus-based physics course, two students enrolled inthe introductory algebra-based physics course and twoundergraduate physics majors who had completed theyear long introductory calculus-based physics series anda sophomore level modern physics class in which theyhad specific instruction on radiation and radioactivity.The information obtained from these interviews wasthen used to guide the design of open-response andmultiple-choice questions administered on pre- andpost-instruction questionnaires.

Each interview began by providing the studentswith three sets of different colored clay balls, whichcould be used during the interviews at any time. The useof clay balls during interviews was implemented inresponse to students' initial difficulties with using adrawing to represent their ideas about an atom during aset of pilot interviews. The clay balls could be easilypaired together or reshaped and thus provided a way forstudents to create a three-dimensional physical model torepresent their mental picture of an atom (Wefelmeier,1937). We hoped that students would find the clay ballshelpful when trying to describe what makes an atom

346 Journal of Geoscience Education, v. 53, n. 4, September, 2005, p. 345-354

radioactive and to illustrate more subtle details of thedecay process at the atomic level.

When asked to construct their model for the nucleusof an atom we found that students used the clay balls in avariety of ways. While some students used the clay ballsto represent the simplest case of the hydrogen nucleusothers used several clay balls to represent an atomcomposed of multiple protons, neutrons and electrons.After students created their clay model atom, they wereasked if the arrangement of balls had any significance.The interviewer then asked different questions about theproperties and behavior of radioactive atoms during thedecay process. The specifics of these questions dependedon the type of response provided by students earlier intheir interview. Overall we were interested in probingwhat students thought happens to an atom duringradioactive decay, whether or not the atom wouldchange (and if so how) during the decay process, andwhat might cause the decay process to occur.

From analyzing the interview transcripts we foundthat overall these students' used a select set of key ideasto describe the role the atom plays in the radioactivedecay process. Overall their ideas appear to be connectedto fundamental physics concepts or properties of matter(such as force, energy, charge and mass) that they havedeveloped or heard about during prior instruction (bothon the topic of radioactivity and on other topics).Students appear to be drawing from ideas that they feltmore comfortable or confident with when they wereasked to reason about the less familiar topic ofradioactivity and the process of decay.

When asked to explain what makes an atomradioactive, students would often reason that the atomwas in some way out of balance or unstable. These statesof instability in the radioactive atom were typicallyconnected to the arrangement or number of charges (orcharged particles) present in the atom. In other cases thestate of instability was attributed to an interaction orforce between the particles making up the atom. Theexcerpts from interviews provided below illustratestudents beliefs about how protons, neutrons, electrons,and, in particular, the concept of charge and force, are allconnected to the idea of radioactivity. Again it isimportant to attend to how students seem to apply theirideas about one topic (for example electrostatics) toaccount for the less familiar phenomena of radioactivity.

• The electro-negativities are unstable• This is unstable because there are two protons

and only one neutron.• The atomic weight, you add up all the masses of

the protons and neutrons and if you're above acertain number it's [the nucleus is] radioactive. Itwould have to have more protons than neutronsto make it [the nucleus] heavier.

• You need the neutrons to shield the protons fromeach other and if there is not enough of theneutrons, and there are too many protons, andthey are all close together, then they start beingrepelled.

• In like a stable atom you are supposed to haveequal numbers of protons and electrons so thatit's a neutral atom. Then if you have a lot ofelectrons and not enough protons then it's gonnabe like a negatively charged particle. The excessof negative charge is gonna interact with these[the protons in the nucleus] and make this [thenucleus] unstable in the fact that protons aredealing with each other but also the fact thatoutside [electrons] is sort of attracted to it.

When asked to describe what would occur duringthe decay process, students’ responses often providedexplanations that illustrated a connection to their initialthoughts about what they felt made the atom unstable.Some responses were centered on a change in the atom tobring about a state of balance or change in force or energyto a more stable configuration of protons, electrons andneutrons. In other cases students suggest that the word"decay" may promote a set of colloquial ideas about theprocess of radioactive decay. The excerpts below areprovided to illustrate the variety of ideas used bystudents to describe how atoms change during theprocess of radioactive decay.

• It's losing pieces, electrons until itdisintegrates…I guess it would just get smaller.

• It means that one of the neutrons would beejected from the nucleus [student removes a clayball neutron from their clay ball nucleus] andwith that there would be some release of energyneutron away. Because the neutron doesn't haveany charge they are more easily ejected.

• The electrons in one state will jump up to anotherstate and obviously can't stay there 'cause it'sunstable, and then when they drop back downthey give off a photon of a certain frequency.

• Well, if you get rid of a proton, and this [thenucleus] isn't too heavy, and there are not toomany protons, and there are just enoughneutrons, and it [the nucleus] can stick togetherthen it's done. But if you get rid of a proton, andthere's still too many protons, and they are stillbeing repulsed you've got to get rid of some more until it gets down to the point where it's relativelystable in terms of the forces inside of the nucleus.

• They are differently charged particles that getejected, so they change the balance of the chargeand everything.

As these excerpts illustrate, overall these studentshave a weak or incomplete understanding of theradioactive decay process and that they reason about therole the atom plays in radioactive decay in a variety ofdifferent ways. The use of the terms "unstable," and to alesser degree "disintegrate" (perhaps in place of "decay"),indicate that students may have been simply recallingwords they have previously heard and associated thosewords with radioactive phenomena. For some students,the ideas of radioactive instability and decay appear to beconnected to the state of charge of the atom and theinteraction (energy, motion and forces) of electrons,protons and neutrons. These ideas are characterized bystudent responses describing radioactivity as having anelectron that is in an excited state, and go on to state thatradioactive decay is the emission of a photon resultingfrom the change in energy state of the excited electron.What is particularly interesting about the reasoning usedby these students is their inappropriate application ofelectron-states and the Bohr model of the atom to explainradioactivity. In addition we identified the followingthree features that appeared to characterize the mostcommon ideas students had about the radioactivenucleus: (1) instability is the result of repulsion betweenprotons, (2) neutrons are able to shield the repulsionbetween protons and thus limit the instability of thenucleus, and (3) through the emission of protons nuclearinstability is decreased. Furthermore it appears thatsome students' understanding of radioactivityincorrectly involves an interaction between the nucleus



Figures 1, 2, and 3. Student drawings and explanations.

and orbital or valence electrons (referred to as valenceelectrons from this point forward). For studentsreasoning this way, an electron-proton interactionappears to exist due to an excess amount of one type ofcharge, positive or negative (or from an imbalancebetween the number of protons or electrons). Balance isachieved for this situation through the emission(radioactive decay) of the particle carrying the excesscharge, thus restoring stability to the atom. To extendthis investigation, we created conceptual questions toidentify whether or not the ideas we identified fromstudents' statements during the interviews wereprevalent among the much larger population ofintroductory physics students.

Results from Open-response Conceptual Questionson the Radioactive Atom - Guided by the results of ourprevious research we designed and administered anopen-response conceptual question to students enrolledin the calculus-based course, the algebra-based course,and the course for non-science majors. These questionswere administered prior to instruction on radioactivityin each of the courses. In the first part of the question,students were asked to sketch a radioactive atom.Students were also asked to show explicitly how theprotons, neutrons and electrons are arranged and toexplain why the atom they drew was radioactive.

Approximately 60% of the drawings provided bystudents from each population correctly identified thelocation of the electrons, protons, and neutrons (a resultsimilar to the drawings/results given by students whenasked to draw and identify the parts of a stable ornon-radioactive atom as reported from the preliminaryphase of this research.) The ideas expressed in theexplanations accompanying these drawings were overallvery similar to the responses provided by studentsduring interviews. Figures 1 - 3 illustrate the range of thedrawings and explanations provided by students whenresponding to this question.

By carefully analyzing the drawings andexplanations given by students from each population,we were able to organize student responses intocategories that were common to students from all threepopulations (see Table 1).

Student responses involving valence electrons wereprovided by 54% of the students in the calculus-basedcourse, 48% of the students in the algebra-based course,and 61% of the students in the non-science major course.Again we found that many of the explanations providedwere similar to statements made by students duringinterviews. The majority of these responses described animbalance or interaction between valence electrons andthe particles of the nucleus. While other explanationsdescribed the emission of valence electrons.

Approximately 20% of the students from eachpopulation attributed radioactivity to the particles in, orstructure of, the nucleus. The explanations

accompanying these responses typically focused on theabundance of either protons or neutrons. However, theseresponses were not always given for the correct reasons.As we found during the interviews, some students mayrefer to the nucleus in reference to radioactivity, eventhough they may claim that the instability of the nucleusis due to Coulomb forces between protons or neutrons.

While these results provide a good first step towardidentifying students' beliefs about the structure of theradioactive atom, the information provided in thedrawings and written responses was not alwayssufficient to infer a clear picture of the students' beliefsabout the underlying cause of radioactivity.

Results from Combined Multiple-choice andOpen-response Conceptual Question on RadioactiveDecay Processes - To obtain a better understanding ofwhat students think about the behavior of an atomduring the radioactive decay process, we created acombined multiple-choice and open-responseconceptual question shown below. This question wasadministered prior to instruction to students in thecalculus-based course, the algebra-based course, thecourse for non-science majors, and in addition tostudents in a high school science course. It is important tonote that the language used in choices A-E was designedto best reflect the natural language used by studentsduring interviews and on open response questions.Choices B, C, and E were provided to represent theradioactive decay processes associated with alpha, beta,and gamma radiation respectively. For those studentswho think valence electrons play an important role in theradioactive decay process, we included choices A and D.It is worthwhile to note that although the eventsdescribed in these choices (A and D) do not accuratelyreflect what happens during radioactive decay, theseevents do occur during other types of atomic processessuch as ionization. From a instrument design standpoint,we were careful to couple the phrases "valence electron"and "from an atom" to best match the natural languageused by students to describe the emission of electronsfrom their orbit about the nucleus when accounting forwhat happens to an atom during decay. By contrast, thephrase "from the nucleus" is provided to allow studentsaware of beta emission a choice that does not allow forthe ambiguity that arises when the language "from theatom" is offered. There was an additional choice Fprovided for students that did not feel that the choicesA-E correctly characterized what happens during theradioactive decay process. Students selecting choice Fwere asked to provide their own description of what theythink happens during the radioactive decay process.

Circle the statement(s) which characterize(s) whathappens during radioactive decay.


Calculus-Based(N=41)

Algebra-Based(N=53)

Non-Science(N=34)

Responses involving only the nucleus 24% 25% 18%

Responses involving valence electrons 54% 48% 61%

Responses involving the emission of an unidentifiedparticle 7% 6% 0%

General statement about isotopes or instability 10% 11% 9%

Other 5% 11% 12%

Table 1. Summary of student respones.

If you do not like any of the statements, use the spaceat letter F to specify what would better characterizeradioactive decay.

A. A valence electron is emitted from an atom.B. Some combination of protons and neutrons are

emitted from the nucleus.C. An electron is emitted from the nucleus.D. A valence electron drops to a lower energy level,

releasing energy (emits a photon).E. A proton or neutron drops to a lower energy level,

releasing energy (emits a photon).F. Other (specify):Explain your reasoning for each

statement you circled.

With each choice, students were asked to explaintheir reasoning. In their explanations, we hoped that theywould describe their thoughts about the underlyingreasons or mechanisms that cause radioactive atoms toundergo decay. The following examples illustrate thewide range of reasoning used by students. The threeletter acronyms CBS (calculus-based students), ABS(algebra-based students), NSS (non-science majorstudents), and HSS (high school students) will be used toidentify the student population associated with eachexample response. At the end of each example response,located in brackets, are the letters of the choice made bythe student.

CBS: When a radioactive atom "decays," one of itsvalance electrons drops to a lower energy level. Aradioactive atom is "unstable", one of its electronshas been moved to a higher electron orbit due toadded energy. [A and D]

ABS: I know that valence electrons can drop to lowerenergy levels resulting in energy. I don't think anelectron would be emitted because this wouldresult in a different charge on the molecule, which Idon't think happens. Protons and neutrons don'tusually move around and they don't have energylevels. [D]

NSS: I would say D due to the release of energy. I'mthinking it can't be C or E because electrons aren't inthe nucleus and protons or neutrons aren't inenergy levels. [D]

ABS: Radioactive decay involves the disintegrationof an unstable nucleus because there is a mismatchof protons and neutrons. So the nucleus ends upgiving up one or the other to balance itself out. Indoing this, it also gives up energy. [B and E]

NSS: I chose B because huge atoms can be unstable sothey split. I chose C because a neutron loses itsnegative charge and becomes a proton in thenucleus. [B and C]

ABS: Protons and neutrons are emitted as both alphaand beta particles and electrons are emitted asenergy. Electrons also give energy when they dropto lower energy levels. [A, B and D]

ABS: There is a decrease in mass during half-life andmass of an atom is in the nucleus, so you wouldneed to release protons and neutrons. There also isa loss of radioactivity, so there must be an attemptat stabilizing the atom, whether it is emitting anelectron or dropping it down a field to try tostabilize it. [A, B and D]

NSS: First the electron is lost. Then after enoughelectrons are lost there isn't enough negative chargeso some number of protons and neutrons is releasedto get the atom back into balance. [A and B]

HSS: I chose A, B and D because protons, neutronsand electrons need to be emitted during radioactivedecay since the system must get smaller. [A, B, andD]

CBS: The protons breaks down into a neutron and apositron, which is emitted from the nucleus. [F]

ABS: A combination of electrons, protons andneutrons is emitted. The reason is that radioactiveelements are the highest number on the periodictable they decay because the electrons are so farfrom the neutrons that they can't be held in.Neutrons and protons must be emitted if thesubstance is to lose mass because the majority of themass of a substance is in the neutrons and protons. [F]

For one analysis of this data, student responses weregrouped together using a sorting schema based on fourseparate categories. The first category (1) reflects choicesthat involve only valence electrons and includesresponses involving only letters A and D. The secondcategory (2) reflects choices that involve protons,neutrons, and the nucleus and includes responsesinvolving only letters B, C and E. The third category (3)reflects choices that include valence electrons as well asprotons, neutrons and the nucleus. This categoryincludes responses involving letters A and or D alongwith any combination of letters B, C and E. The fourthcategory (4) contains responses created by those studentswho chose only letter F. For the small number ofresponses (< 5% for each population) that included letterF along with another choice from letters A-E, the studentresponse was categorized based on the student's choicefrom letters A-E. A summary of student responses to thisquestion using this four-category sorting schema isprovided in the Table 2.

To gain a better understanding of how manystudents included the idea of valence electrons in theirresponses we grouped together all answers that includedthe lettered choices A and D. This grouping includesresponses from both categories (1) and (3). Responsesinvolving valence electrons were provided by 68% of thestudents in the calculus-based course, 61% of thestudents in the algebra-based course, 67% of the studentsin the non-science major course and 74% of the studentsin the high school course. Perhaps most interesting is thelow percentage (approximately 30%) of students fromeach population that correctly provided responses in


Response TypeCalculusCourse(N=43)

AlgebraCourse(N=139)

Non-Science(N=76)

HighSchool(N=19)

(1) Responses involving only valence electrons. 56% 39% 46% 37%

(2) Responses involving only neutrons, protons, and the nucleus. 33% 34% 32% 26%

(3) Mixed responses involving both valence electrons and the nucleus. 12% 23% 21% 37%

(4) Other 0% 4% 1% 0%

Table 2. Student responses by type.

which the process of decay was limited to only thenucleus.

We found that many students' understanding ofradioactivity inappropriately involves the idea of thevalence electron. Student beliefs regarding the role of theelectron in connection with radioactivity typicallyinvolve reasoning about:

1. The electric charge of the electron or net charge of theatom due to the number of electrons.

2. The energy associated with the electron, includingthe emission of radiation due to electron statetransition.

3. The interaction of electrons with protons orneutrons.

4. The activity or motion of electrons, including theejection of electrons from the atom.

Responses that involved only the nucleus were againtypically centered on limiting the abundance of, orimbalance between, protons and neutrons. In some ofthese cases, students used language such as "too heavy,""too many," and "above a certain number" in theirresponses. Other explanations emphasized changes inthe mass of the nucleus or atom. Some students indicatedthat they were aware of alpha, beta, and gammaradiation; however, these students were typically unableto explain correctly the relationship between nucleonsand the radiation emitted.

A small number of students provided responsesconsistent with the belief that radioactivity could be


Figures 4, 5, 6, and 7. Student explanations of radioactive half-life.

induced in a stable atom. These unexpected, but veryinteresting, student responses typically attributed thisinduced radioactivity to either the absorption oremission of energy or particles. In these cases it is worthnoting that there were not any students who correctlydepicted neutron bombardment and gamma emission intheir responses.

Up to this point, we have described how interviews,along with, open-response and multiple-choicequestions, were employed in this investigation totriangulate students' understanding of the role the atomplays in the radioactive decay process. Guided by theinsights gained from the research results reported thusfar we next focused our investigation on students'understanding of radioactive half-life.

STUDENTS' BELIEFS ABOUTRADIOACTIVE DECAY AND HALF-LIFE

The concept of radioactive half-life is one of the mostcommon topics covered during traditional instruction onradioactivity. For this reason, we felt that it wasimportant to find out what students believe happens to aradioactive object as it decays over the period of ahalf-life. We were also interested in identifying to whatextent students' ideas about irradiation andcontamination, and the behavior of radioactive atomsduring the decay process, would influence or beconnected to their ideas about the concept of radioactivehalf-life. Again note that all students participating in theinvestigations described in sections A and B below wereenrolled in undergraduate physics courses taught at amedium-sized research level-one university located inthe Northwestern United States. Specific information onstudent population numbers and correspondingenrolled courses will be provided to accompany thespecific phase of the research being reported.

A. Results from interviews on radioactive decay andhalf-life - As part of the interviews described in aprevious section of this manuscript, we asked each of thestudents interviewed to provide their definition ofhalf-life and to reason about the resulting changes that aradioactive object would undergo during the period of ahalf-life. The example responses provided belowillustrate the very subtle ways students use the term halfwhen describing what happens to an object undergoingradioactive decay for the period of a half-life.

• The time it takes for an object to become half ofwhat it was before.

• Half-life is the amount of time it takes for thenucleus or a radioactive material to breakdowninto half of its original form.

• We have some radioactive substance, after onehalf-life, only half of it will be radioactive.

• The half-life of an element is the time that it takesfor half of that quantity to decay. This isessentially based on probability. You can say thatwith pretty decent certainty that given thisamount of time, that half of this [the radioactiveclay block] will be gone

As these examples show, students correctly attemptto incorporate the idea of time into their definition ofhalf-life. Based on the statements: "half of what it wasbefore," "breakdown into half of its original form," and"half of this [the radioactive clay block] will be gone," it istempting to infer that these students believe that half of aradioactive object disappears after a half-life. We cannotbe certain, however, that this interpretation is correct. Itis also possible to infer that these students think that halfthe radioactive material has simply changed intosomething else.

To gain a better understanding of whichinterpretation is correct, and to focus this portion of theinterviews, students were also provided with a 3 cm x 3cm x10 cm rectangular block of clay. They were told toimagine that the clay was made of a radioactivesubstance that was undergoing radioactive decay. Theywere told that the block had a volume of 100ml and amass of 100g. We then asked students to describe howmuch of the block would be left after the substanceunderwent radioactive decay for a half-life. Each studentresponded that either the mass and/or volume of aradioactive material would decrease by half in the periodof a half-life. The responses provided by students duringinterviews illustrate how students' incorrect beliefsabout radioactive decay can lead to inappropriatepredictions about the physical properties of radioactivematerials during a half-life.

Next, we will describe our investigation to find outwhich of the reasoning difficulties demonstrated bystudents during interviews are common among thegeneral populations of students enrolled in introductoryphysics courses.


Response Type Calculus Course (N=39) Algebra Course (N=65) Non-Science (N=39)

Correct 39% 29% 23%

Little or no decrease in theobject’s mass and volume 26% 14% 15%

Half the atoms havedecayed, transformed orchanged. Only half the

atoms are now readioactive.

13% 15% 8%

Incorrect 61% 63% 49%

Mass will be .50 g andvolume will be 75 cm3. 51% 51% 23%

The object will now havehalf the original mass or

volume. Half of the originalobject will be left or lost.

10% 12% 26%

Other 0% 8% 28%

Table 3. Student response to radioactive decay half-life question.

B. Results from Open-response ConceptualQuestion on Radioactive Decay and Half-life - Wedesigned an open-response conceptual question that wasmodeled after the mass and volume questions usedduring interviews. The question was administered tostudents in the calculus-based course, the algebra-basedcourse, and the course for non-science majors. Studentswere asked to describe how a substance composed ofradioactive atoms, with a mass of 100 g and a volume of150 cm3, would change after one half-life. To help usinterpret the student responses, we also asked studentsto explain their reasoning and draw a diagram to supporttheir answer. Students were not explicitly asked toreason about the mass or volume of the radioactiveobject, nor were they instructed to perform anycalculations. Figures 4-7 illustrate the types of drawingsand explanations provided by students in response tothis question.

A summary of student responses to theopen-response conceptual question about half-life areprovided in Table 3.

On average, half the total number of radioactiveatoms in a radioactive object will decay in the period of ahalf-life. However, the total number of atoms in theobject will remain constant. Furthermore, the mass of theemitted ionizing radiation is negligible in comparison tothe total mass of the decaying atom. We would thenexpect the size, mass and volume of a radioactive objectto remain nearly constant during radioactive decay.Responses consistent with this line of reasoning wereprovided by 39% of the students in the calculus-basedcourse, 29% of the students in the algebra-based course,and 23% of the students in the non-science majors course.Students responding in this way typically ignored theinformation provided in the problem statement aboutthe radioactive object's mass and volume.

Students also provided responses consistent with thebelief that an object's mass and or volume will decrease

by a factor of two during a half-life. Responses of thistype were provided by 61% of the students in thecalculus-based course, 63% of the students in thealgebra-based course, and 49% of the students in thenon-science major course. Note that 28% of the studentsin the course for non-science majors provided responsesthat were categorized as other. These responses weredominated by statements describing a decrease in the"life time" or "radioactive life" for the object.

Many students provided responses consistent withthe belief that radioactive objects disappear ordisintegrate during radioactive decay. These studentsoften predict that the mass, volume, and number ofatoms for radioactive objects decrease by half during ahalf-life. For many students it appears that the word halfacts like a mental trigger that leads the student to divideby two. These students appear to perform this divisionwithout any further thought about the radioactive decayprocess. These reasoning difficulties likely stem fromstudents' inability to properly reason about theradioactive decay process at the atomic (or nuclear) level.Unfortunately, even for those students who do have anunderstanding of radioactivity that involves the atom,they often also predict that half of the radioactive objectwill disappear after a half-life.

Students' incorrect beliefs may be reinforced by theinformation provided in the textbooks used in theirphysics courses. For an example of this see Figure 8. Thedrawing and description shown come from the textbookused in the introductory algebra-based physics courseand were intended to illustrate the idea of radioactivehalf-life (Cutnell and Johnson, 1998). The descriptionprovided is particularly problematic, as it states thatradioactive half-life is "the time in which one-half of theradioactive nuclei disintegrate." Also, note the strikingsimilarities between this textbook's drawing and thedrawings of students shown in Figures 6.

Potentially misleading statements about radioactivehalf-life can also be found in textbooks used in otherdisciplines. As an example, consider the following quotetaken from an introductory general chemistry textbook(Kroschwitz and Winokur, 1990).

• Because radioactive elements disappear as theyemit radiation and are transmuted into otherelements they are said to disintegrate or decay

CONCLUSION

As the re sults pre sented here strongly sug gest, many in -tro duc tory sci ence stu dents en ter the class room withmany be liefs about the na ture of ra di a tion and ra dio ac-tiv ity that dif fer from the sci en tif i cally ac cepted be liefs ofthe dis ci pline. As con cerned in struc tors and re search ers,we would like to better un der stand how these stu dentbe liefs af fect the learn ing and teach ing of ra dio ac tiv ity.One in sight we can of fer co mes from a post-instructionas sess ment of stu dents en rolled in an al ge bra-based in -tro duc tory phys ics course. These stu dents re ceived ap-prox i mately 3-hours of tra di tional lec ture, 2-hours ofrec i ta tion (fo cused on prob lem-solving) and 2-hours oflab o ra tory in ves ti ga tion on ra dio ac tiv ity. We found that59% of these stu dents con tinue to be lieve that the massand/or vol ume of a ra dio ac tive ob ject would de crease byhalf in the pe riod of a half-life. Fur ther more, the rea son-ing and draw ings pro vided with these re sponses in di-cate that these stu dents still be lieve that a ra dio ac tiveob ject dis ap pears as it de cays. Note that prior to in struc-tion ap prox i mately the same per cent age of stu dents(63%) from the al ge bra-based course had re sponded thatthe mass and/or vol ume would change by half (Prather,2000). These re sults il lus trate how tra di tional lec tures,


Figure 8. Graphical representation of radioactivedecay.

lab o ra tory ex per i ments and home work prob lems canhave lit tle im pact on the na ive be liefs of these stu dents.Not sur pris ingly, these stu dents were able to carry outthe nec es sary ex per i ments, per form the re quired cal cu la-tions, reach the an tic i pated con clu sions, and yet emergefrom this quite typ i cal and tra di tional class room in ter-ven tion with out be com ing in tel lec tu ally en gaged at alevel suf fi cient to ob tain a fun da men tal un der stand ing ofthe phe nom ena un der in ves ti ga tion. This re sult is notunique to the topic of ra dio ac tiv ity. To the con trary,phys ics ed u ca tion re search ers have shown that manystu dents emerge from in tro duc tory level phys ics courseslack ing a ba sic con cep tual un der stand ing of the coursetop ics (McDermott and Redish, 1999).

The research base on student understanding ofradiation and radioactivity is currently quite limited.There have been a number of studies conducted inEurope into the beliefs of middle and high school agedstudents on the topic of radiation and radioactivity. Theresults described here extend the research base to includethe beliefs and reasoning difficulties of college levelstudents in the United States. Furthermore, while ourfindings complement the findings of others, they alsoextend the research base to include: (1) students'understanding of the radioactive decay process at theatomic and nuclear level, and (2) students'understanding of the concept of radioactive half-life.And yet the most current articles published on teachingradioactivity not only fail to address these findings butcontinue to precisely model, if not promote, the naivebeliefs students' hold about radioactivity and half-life(Fairman et al., 2003; Jesse, 2003).

If we want our students to develop a powerfulunderstanding of science topics, it is necessary to treatthe teaching and learning of science as a complex andinterconnected system rather than a one-way transactionbetween the curriculum and the student. In particular,we must work to create a more effective instructionalenvironment by taking into account student needsincluding their pre-instruction beliefs. It is, therefore,essential that we better understand and incorporate howstudents construct their knowledge and how this processis related to their current beliefs about the topics underinvestigation. Only then can a learning environment beestablished that appropriately challenges students andmotivates deep intellectual engagement.

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