Teaching Measurement in the Introductory Physics LaboratorySaalih Allie, Andy Buffler, Bob Campbell, Fred Lubben, Dimitris Evangelinos et al. Citation: Phys. Teach. 41, 394 (2003); doi: 10.1119/1.1616479 View online: http://dx.doi.org/10.1119/1.1616479 View Table of Contents: http://tpt.aapt.org/resource/1/PHTEAH/v41/i7 Published by the American Association of Physics Teachers Related ArticlesMeet your new editor by Karl Mamola Phys. Teach. 51, 326 (2013) Resistivity in Play-Doh: Time and Color Variations Phys. Teach. 51, 351 (2013) This Is Rocket Science! Phys. Teach. 51, 362 (2013) Combining two reform curricula: An example from a course with well-prepared students Am. J. Phys. 81, 545 (2013) A Closer Look at Teachers' Assessment of Math Preparation Phys. Teach. 51, 297 (2013) Additional information on Phys. Teach.Journal Homepage: http://tpt.aapt.org/ Journal Information: http://tpt.aapt.org/about/about_the_journal Top downloads: http://tpt.aapt.org/most_downloaded Information for Authors: http://www.aapt.org/publications/tptauthors.cfm

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Teaching Measurement inthe Introductory PhysicsLaboratorySaalih Allie and Andy Buffler, University of Cape Town, South Africa

Bob Campbell and Fred Lubben, University of York, UK

Dimitris Evangelinos, Dimitris Psillos, Odysseas Valassiades, Univ. of Thessaloniki, Greece

Traditionally physics laboratory courses at thefreshman level have aimed to demonstratevarious principles of physics introduced in

lectures. Experiments tend to be quantitative in nature with experimental and data analysis techniquesinterwoven as distinct strands of the laboratorycourse.1 It is often assumed that, in this way, students will end up with an understanding of the na-ture of measurement and experimentation. Recent research studies have, however, questioned this as-sumption.2,3 They have pointed to the fact that fresh-men who have completed physics laboratory coursesare often able to demonstrate mastery of the mecha-nistic techniques (e.g., calculating means and standarddeviations, fitting straight lines, etc.) but lack an appreciation of the nature of scientific evidence, inparticular the central role of uncertainty in experi-mental measurement. We believe that the probabilis-tic approach to data analysis, as advocated by the In-ternational Organization for Standardization (ISO),will result in a more coherent framework for teachingmeasurement and measurement uncertainty in the in-troductory physics laboratory course.

Over the past few years we have researched4–7 fresh-man physics students’ understanding of the nature ofmeasurement. The group at Thessaloniki has probedstudents’ views of a single measurement. They con-cluded that, after completing a traditional laboratorycourse, the majority have ideas about measurement

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that are inconsistent with the generally accepted scien-tific model.4 For example, a large fraction of studentsview the ideal outcome of a single measurement as an“exact” or “point-like” value. A sizeable minority feelthat since the ideal is not attainable, only an unquantified “approximate” value can be obtained inpractice. Only if a measurement is considered really“bad” would it then be reported in terms of an interval.5

The studies carried out by the Cape Town-Yorkgroup have focused on aspects of dispersion in datasets. A model of student thinking has been developedthat has been termed “point” and “set” paradigms.6

In brief, in the “set” paradigm the ensemble of data ismodeled by theoretical constructs from which a “bestestimate” and the degree of dispersion (an interval) arereported. However, the majority of students who arrive at university operate within the “point paradigm.”6 They subscribe to the notion that a “cor-rect” measurement is one that has no uncertainty asso-ciated with it. For many students, therefore, the idealis to perform a single perfect measurement with theutmost care. When presented with data that are dis-persed, they often attempt to choose the “correct” val-ue (for example, the recurring value) from amongstthe values in the ensemble. It was found7 that even af-ter a carefully structured laboratory course,8,9 moststudents had not shifted completely to “set” paradigmthinking.

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What Is Wrong with TraditionalTeaching About Measurement?

Although one of the most important aspects ofputting together a teaching sequence is bringing to-gether the philosophy, logic, and modes of thinkingthat underlie a particular knowledge area, introducto-ry measurement is usually taught as a combination ofapparently rigorous mathematical computations andvague rules of thumb. We believe that this is a conse-quence of the logical inconsistencies in traditional data analysis, which is based on analyzing the frequen-cy distribution of the data. This approach, oftencalled “frequentist,” is the one used or implied in mostintroductory laboratory courses.

In the frequentist approach, “errors” are usually introduced as a product of the limited capability ofmeasuring instruments, or in the case of repeatedmeasurements, as a consequence of the inherent ran-domness of the measurement process and the limitedpredictive power of statistical methods. These twodifferent sources of “error” cannot be easily recon-ciled, thus creating a gap between the treatments of asingle reading and ensembles of dispersed data. Forexample, the theory applicable to calculating a meanand a standard deviation is premised on the assump-tion of large data sets (20 or 30). Yet, when studentsperform an experiment in the laboratory, they oftentake five or fewer readings. Furthermore, there is nological way to model statistically a single measurementwithin this approach.

Traditional instruction usually emphasizes randomerror for which there is a rigorous mathematical mod-el, while systematic errors are reduced to the technicallevel of “unknown constants” that have to be deter-mined by examining the experimental setup. Theconcept of a “scale reading error,” usually taught at thebeginning of the course, cannot be related to eitherrandom or systematic errors that are taught during thetreatment of repeated measurements. Moreover, theterm “error” misleads students by suggesting the exis-tence of true and false experimental results, possiblyendorsing the naive view that an experiment has onepredetermined “correct” result known by the instruc-tor, while students’ measurements are often “in error.”Readers will be all too familiar with the phrase “due tohuman error” often used by students in order to ex-plain unexpected results!

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In short, we consider that the logical inconsisten-cies in the traditional approach to data treatment, together with the form of instruction that ignores stu-dents’ prior views about measurement, further culti-vate students’ misconceptions about measurement inthe scientific context.

What Should be Done?The need for a consistent international language

for evaluating and communicating measurement re-sults prompted (in 1993) the ISO (International Organization for Standardization) to publish recom-mendations for reporting measurements and uncer-tainties10 based on the probabilistic interpretation ofmeasurement. All standards bodies including the U.S.National Institute of Standards and Technology(NIST) have adopted these recommendations for re-porting scientific measurements. A number of docu-ments currently serve as international standards. Themost widely known are the so-called VIM (Interna-tional Vocabulary of Basic and General Terms in Metrol-ogy)10 and the GUM (Guide to the Expression of Uncertainty in Measurement),11 with a U.S. version12

distributed by NIST. A shorter version of the latter ispublicly available as NIST Technical Note 1297.13

We believe that the probabilistic approach advocat-ed by the ISO will help in setting up a systematicteaching framework at the freshman level and beyond,and promote a better understanding of the nature ofmeasurement and uncertainty. In addition, the coher-ence of the approach will foreground the central roleof experiment in physics and highlight the interplaybetween scientific inferences based on data and theory.

A Probabilistic and MetrologicalApproach to Measurement

The recommended approach10,11 to metrology isbased on probability theory for the analysis and inter-pretation of data. A key element of the ISO Guide ishow it views the measurement process. In paragraph2.1 of TN1297 it is stated that, “In general, the resultof a measurement is only an approximation or esti-mate of the value of the specific quantity subject tomeasurement, that is, the measurand, and thus the re-sult is complete only when accompanied by a quanti-tative statement of its uncertainty.”13 Uncertainty

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itself is defined as “a parameter associated with a mea-surement result, that characterizes the dispersion ofthe values that could reasonably be attributed to themeasurand.”11,12

The measurement process involves combining newdata with all previous information about the measur-and to form an updated state of knowledge (see Fig.1). The formal mathematics used are probability den-sity functions (pdfs) with the (true) value of the mea-surand as the independent variable. (We note thatthere is no difference between the terms “the value ofthe measurand” and “the true value of the measur-and.”)11,12 Thus, the measurement process produces apdf that best represents all available knowledge aboutthe measurand. The last step in the measurementprocess involves making inferences about the measur-and based on the final pdf. We emphasize that boththe case of the single reading and the case of a set ofrepeated observations with dispersion involve seekingthe final pdf for the measurand.

Although the ISO recommendations11,12 do not refer explicitly to the underlying philosophy, the formalism relies on the Bayesian approach to dataanalysis (see for example Ref. 14 and its references).Readers familiar with Bayesian terminology will see inFig. 1 that the process can be described as the priorpdf convoluted with the likelihood (or sample func-tion) to form the posterior pdf, which contains all theinformation about the measurand. The final pdf isusually characterized in terms of its location, an inter-

Fig. 1. A model for determining the result of a mea-surement.

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val along which the (true) value of the measurand maylie, and the probability that the value of the measur-and lies on that interval. In metrological terms theseare, respectively, the best estimate of the measurandand its uncertainty, and the coverage probability, orlevel of confidence (the percentage area under the pdfdefined by the uncertainty interval). A measurementresult includes these three quantities and ideallyshould include an explicit statement about the pdfused.

The ISO Guide11,12 suggests the use of three pdfsfor most situations (a uniform or rectangular pdf, atriangular pdf, and a Gaussian pdf ). If the pdf is sym-metrical (as is the case with these three), then the bestestimate (the expectation or mean value) will coincidewith the center of the distribution, while the standarduncertainty is given by the square root of the variance(the second moment of the distribution). Typicalstatements describing a measurement result are of theform “the best estimate of the value of the physicalquantity is X with a standard uncertainty U and theprobability that the measurand lies on the interval X� U is Z %.” (The coverage probability associatedwith a standard uncertainty for the Gaussian pdf isabout 68% while those for the triangular and rectan-gular pdfs are about 65% and 58%, respectively.) Inthis approach, instrument readings are considered asconstants, while the concept of probability is appliedto any claims made about the value of the measurand,which is considered a random variable. Neither themeasurand itself nor the data “possess” either uncer-tainty or probability, but these concepts are applicableto the inferences that are made. This contrasts withthe traditional approach, where expressions are usedsuch as “the error of the measurement” or “the uncer-tainty of the instrument scale.”

The ISO Guide11,12 classifies uncertainty into twotypes based on the method of evaluation. A Type Aevaluation of uncertainty is based on the dispersion ofa set of data using statistical methods, while a Type Bevaluation is estimated using all available nonstatisti-cal information such as instrument specifications, previous measurements, the observer’s personal judg-ment, etc. It should be stressed that uncertainties resulting from Type A and B evaluations do not corre-spond to “random” and “systematic” errors. For in-stance, the ISO Guide states that “Type B standard

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uncertainty is obtained from an assumed probabilitydensity function based on the degree of belief that anevent will occur,”11,12 implying that systematic errorsshould acquire a probabilistic description, since theyare never precisely and accurately known. This is notthe case in the traditional scheme. Type A evaluationsare applicable to situations involving repeated obser-vations with dispersion, while Type B evaluations areapplicable in all measurements.11,12 The general pro-cedure for evaluating the overall uncertainty associat-ed with a measurand is to list all the possible sourcesof uncertainty and evaluate each individual contribu-tion (using an appropriate pdf ). This is referred to asan uncertainty budget. The overall or combined un-certainty uc is then calculated using the usual uncer-tainty propagation formula.11,12 A key point is thatany number of uncertainty components can be com-bined in this way, whether they result from a Type Aor a Type B evaluation.

Examples We present two examples below in which the quan-

tity of interest is directly determined from the measurement.

(a) A single digital readingThe case of having only a single reading often oc-

curs in introductory laboratory courses. The tradi-tional approach offers no coherent framework, andvarious ad hoc prescriptions are usually presented.However, it is easily dealt with in a logically consistentway in the probabilistic approach using the Type Bevaluation based on assigning rectangular, triangular,or Gaussian probability density functions. Thus, thedichotomy between the so-called “classical” estima-tion of uncertainty (½ least-scale division) for singlemeasurements and the formal “statistical” estimation(standard deviation) for dispersed measurements doesnot surface.

Suppose a digital voltmeter with a rated accuracy of�1% is used to measure the voltage across the termi-nals of a battery [see Fig. 2(a)]. The best estimate ofthe voltage is clearly 2.47 V. In order to calculate theoverall uncertainty, we need to identify all the possiblesources of uncertainty, for example, the resolution ofthe scale of the instrument, the rated accuracy, contactresistance, environmental factors such as the tempera-

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ture, etc. For illustrative purposes we will assume thatthe uncertainties due to the scale resolution us and therated accuracy ur are the dominant contributors to thecombined uncertainty uc, and proceed to evaluateeach of them.

In the traditional teaching practice, it is oftenwrongly assumed that the rated accuracy is smallenough to be ignored. Therefore, usually only a so-called “least- count error” is attached to the reading,so that the experimental result becomes “2.470 �0.005 V.” However, this expression does not have aprobabilistic meaning within the frequentist approachbecause there is only a single recorded value. In orderto describe the same experimental datum within theprobabilistic approach, use a suitable distribution,such as a rectangular (uniform) pdf [see Fig. 2(b)],with the best estimate at the center of the distributionand the limits defined by the range of the last digit ofthe digital scale. Note that the area under the pdf isalways normalized to unity. The standard uncertaintyus is then given by the square root of the variance (thesecond moment of the distribution)11,12 or

Fig. 2. (a) A single digital reading. (b) The uniform pdf usedto model the uncertainty due to reading the scale of theinstrument, expressing that the measurand could lie withequal probability at any position within the interval. Thevalue of 0.0029 V is the standard uncertainty us associatedwith the scale reading only. A similar uniform pdf modelsthe uncertainty due to rated accuracy ur = 0.0143 V, as wellas the combined uncertainty uc = 0.0146 V. The measurementresult is expressed as Vresult = 2.470 ± 0.015 V (see text).

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us = = �0�.0

30�5

�

= 0.0029 V.

We now have to convert the rated accuracy of thevoltmeter, given as � 1%, to a standard uncertaintyur. This can be achieved by assuming a uniform pdf(as suggested in the GUM11,12), in which case thehalf-width of the distribution will be

(0.01) (2.47) = 0.0247 V.

The standard uncertainty ur is then given by

ur = �0.

�02

3�47� = 0.0143 V.

The combined uncertainty uc is therefore

uc = �u2�s +� u�2r� = �(0�.0�0�2�9�)2� +� (�0�.0�1�4�3�)2� = 0.0146 V.

In practice this uncertainty estimate would be largerif some of the other sources of uncertainty, neglectedhere, are included in the uncertainty budget. Wealso note here the practice used in the GUM ofquoting two significant figures for all final uncertain-ty estimates. Therefore, the measurement result isexpressed as Vresult = 2.470 � 0.015 V.

Should one wish to emphasize the aspect of priorinformation during teaching, one can proceed as follows. Students are presented with a 3-V batteryand a voltmeter, and asked to describe (model) the in-formation available about the measurand (V) beforemeasuring it. Reasoning about the measurand beforeobtaining data is an essential feature of the Bayesianapproach. This stage aims at demonstrating that anyconclusion about the measurand has the form of aninterval, in this case from 0 V (depleted battery) tonominal 3 V (full battery). Students are then asked todraw a graph of the probability of the statement “thevalue of the voltage is x,” where x is in the interval [0,3]. We have found that most students have little diffi-culty in drawing a rectangular probability distribution(similar to Fig. 2), an intuitive conclusion compatiblewith the Bayesian principle of insufficient reason. Asubsequent single measurement, as illustrated above,serves to demonstrate how new information modifies

half of the width of the rectangle����

�3�

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the existing knowledge of the measurand, reduces un-certainty, and narrows the probability of the posteriordistribution. Finally, successive measurements withanalogue or digital meters demonstrate that despitethe gradual reduction of uncertainty, absolute knowl-edge of the measurand is not possible. There are someindications that such a teaching approach may befruitful when dealing with students’ initial tendencyto view single measurement results as “exact” or“point-like.”4,7

The treatment outlined for dealing with direct sin-gle measurements is of course applicable irrespectiveof the type of instrument used. As an extension to theprevious example, we can consider the case if the samevoltage were measured by an analog voltmeter. Thenthe scale uncertainty would again be modeled by a pdf(e.g., uniform or triangular). In this case, the limits ofthe pdf depend on both the least-count division of theinstrument being used and the judgment of the exper-imenter in reading the scale. As before, this scale un-certainty would be combined with the uncertaintyarising from the accuracy rating of the instrument.

(b) An ensemble of repeated readings that are dispersed

Consider an experiment where we make 20 repeat-ed observations of a time t under the same conditions,for example, in measuring the period of a pendulumwith a stopwatch having a resolution of 1 ms and rated accuracy of 0.1 ms. The 20 readings are summa-rized and represented as a histogram of relative fre-quencies [Fig. 3(a)]. According to the traditional approach, the measured values ti are modeled as valuesof a random variable tmeasured. The 20 values are con-sidered to be sampled from an idealized Gaussian dis-tribution, which would occur if the data were infiniteand the histogram bins were reduced to zero width.From our sample we can estimate the parameters ofthis idealized Gaussian through the familiar quantitiesof the arithmetic mean t– of the N = 20 observations as

t– = �N1

� �N

i = 1ti ,

and the experimental standard deviation s(t) of theobservations,

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.

The calculations for the data in question yield thatt– =1.015 s and s(t) = 0.146 s.

Based on the result from the central limit theoremthat the sample means are distributed normally, theexperimental standard deviation of the mean s(t– )11,12 is given by

s( t– ) = ��s(t

N�)

�,

which yields s( t– ) = 0.033 s in the present example.In the traditional approach s( t– ) is often termed the“standard error of the mean” and is denoted by �m.

The interpretation of this result according to math-ematical statistics is that “we are 68% confident thatthe mean (of any future sample taken) will lie within� 0.033 s of the measured mean of 1.015 s” (Conclu-sion I).

Physicists tend to interpret Conclusion I in accor-dance with their needs for making an inference aboutthe true value as follows: “we are 68% confident thatthe ‘true value’ (of the measurand) lies in the interval1.015 � 0.033 s” (Conclusion II).

However, Conclusion II cannot easily be justifiedin the traditional approach since t– and s( t– ) are cal-culated from observed values, and can only summa-rize what we know about the data since there is no for-mal link between knowledge of the measurand (Con-clusion II) and knowledge of the data (Conclusion I).Thus, the measurement result cannot be representeddirectly on Fig. 3(a) because the relative frequency his-togram and the predicted Gaussian of infinite mea-surements [Fig. 3(a)] are plotted against tmeasured.

In the probabilistic approach, however, all infer-ences about the measurand are expressed via the pdf ofFig. 3(b), which is plotted against ttrue. Using the con-cepts of prior information and data at hand, we areable to conclude in a straightforward and logicallyconsistent way the final result as follows: “The best es-timate of the value of the time is 1.015 s with a standard uncertainty of 0.033 s, and there is a 68%probability that the best estimate of the time lies with-in the interval 1.015 � 0.033 s, assuming that the dis-tribution of measured times is Gaussian.” In practice,of course, the uncertainty budget for this measure-

2

1

1( ) ( )1

N

ii

s t t tN =

= −− ∑

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ment of t would include a number of additionalsources of uncertainty, each of which would be esti-mated using a Type B evaluation, so that the com-bined uncertainty would be larger than 0.033 s.

When teaching the case of repeated measurements,the most important objective is to bring studentsaround to the notion that an ensemble of dispersedvalues obtained by repeated observations must bemodeled by theoretical constructs that represent theensemble as a whole.2,7 Regarding the shape of theGaussian, this can be made plausible by constructinghistograms of relative frequencies of simulated or ac-tual data and showing how the distribution tends to-ward a bell-like shape as the number of readings in-creases and the bin width decreases. Making the con-ceptually correct link between relative frequencies,based on past experience, and probabilities, for infer-ence, is an important step at this stage.15

ConclusionThe ISO approach solves one of the key problems

associated with the traditional frequentist approach tomeasurement, namely that the statistical formulaelead logically only to statements about the data them-

Fig. 3. (a) Distribution of relative frequencies for the timereadings tmeasured. The dotted line represents the predictedGaussian distribution of the population from which the 20readings were sampled. (b) A Gaussian pdf used to modelthe measurement result. The final result tresult indicatedassumes that all other sources of uncertainty are negligible(see text).

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selves. Therefore, it is not valid to make the logicaljump that is usually made in laboratory manuals to in-terpret a standard error as a standard uncertainty. Stu-dents (and others) have difficulties understanding thisdiscontinuity in logic. The probabilistic approach, asoutlined, leads directly to inferences about the mea-surand in a natural way, in both cases of single and repeated measurements. In addition, representing thestates of knowledge graphically as pdfs, and not asnumbers or intervals, provides a persuasive and consistent explanatory framework for all cases of mea-surement.

Experimentation and measurement lie at the heartof physics, and it is important that students developan understanding of these concepts. However, theway in which these have been dealt with does not ap-pear to have been effective. Two possible reasons are,first, that students’ prior knowledge about the natureof measurement has not been taken into account and,second, that there has been no logically consistentframework that could be used to teach the basic con-cepts. By adopting the probabilistic approach, the lat-ter can be effectively addressed (apart from the factthat this is what research scientists have to adhere to!).In addition, the guidelines suggested by the ISO, suchas the concept of an uncertainty budget and the levelof calculational detail to be reported, should also assistpedagogy. It should be noted that there now existsoftware packages16 that can be used to perform thesometimes tedious calculations required for a givenuncertainty budget.

We argue that by adopting the view that the intro-ductory laboratory course should be focused on exper-imentation and intelligent data analysis based onprobability theory, the experimental aspects of physicscan be placed at the center of the course rather thanrelegated to an “add on” to the theoretical aspects.The concepts of probability and uncertainty shouldbe addressed as early as possible in the teaching as fun-damental to physics, highlighting the uncertain andtentative, yet quantifiable, nature of scientific knowl-edge. The groups involved in the present paper aredeveloping and refining various laboratory teachingmaterials based on this approach.

Finally, the language of probabilistic metrology of-fers access to other areas of physics such as quantummechanics and statistical mechanics, as well as to cur-

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rent technologies such as image processing. From abroader perspective, an understanding of the interpre-tation of data, and hence of evaluating “scientific evi-dence” is an essential life skill in the present informa-tion age.

AcknowledgmentsOur work has been partially funded by theUniversities of Cape Town, Thessaloniki, and York,and by the National Research Foundation (SouthAfrica), the British Council, and the EuropeanUnion (LSE project PL 95-2005). We wish to thankprofessors Joe Redish, Craig Comrie, Roger Fearick,and Sandy Perez for useful discussions.

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ward Arnold, London, 1988).

2. M-G. Séré, R. Journeaux, and C. Larcher, “Learningthe statistical analysis of measurement error,” Int. J. Sci.Educ. 15 (4), 427–438 (1993).

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4. D. Evangelinos, O. Valassiades, and D. Psillos, “Under-graduate students’ views about the approximate natureof measurement results,” in Research in Science Educa-tion: Past, Present and Future, edited by M. Komorek,H. Behrendt, H. Dahncke, R. Duit, W. Gräber, and A.Cross (IPN Press, Kiel, 1999), pp. 208–210.

5. D. Evangelinos, D. Psillos, and O. Valassiades, “An in-vestigation of teaching and learning about measure-ment data and their treatment in the introductoryphysics laboratory,” in Teaching and Learning in the Sci-ence Laboratory, edited by D. Psillos and H. Niederrer(Kluwer Academics, Dordrecht, 2002).

6. F. Lubben, B. Campbell, A. Buffler, and S. Allie, “Pointand set reasoning in practical science measurement byentering university freshmen,” Sci. Educ. 85 (4),311–327 (2001).

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8. S. Allie and A. Buffler, “A course in tools and proce-dures for Physics I,” Am. J. Phys. 66 (7), 613–624(1998).

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9. S. Allie, A. Buffler, L. Kaunda, and M. Inglis, “Writ-ing-intensive physics laboratory reports: Tasks and as-sessment,” Phys. Teach. 35, 399–405 (Oct. 1997).

10. International Organization for Standardization, Inter-national Vocabulary of Basic and General Terms inMetrology (VIM) (ISO, Geneva, 1993).

11. International Organization for Standardization, Guideto the expression of uncertainty in measurement (GUM)(ISO, Geneva, 1995).

12. American National Standards Institute, U.S. Guide tothe Expression of Uncertainty in Measurement (1997),ANSI / NCSL Z540-2-1997.

13. B.N. Taylor and C.E. Kuyatt, Guidelines for Evaluatingand Expressing the Uncertainty of NIST Measurement Re-sults (NIST Technical Note 1297, 1994). Available inelectronic form at http://physics.nist.gov/Pubs/ guidelines/contents.html .

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15. G. Shafer, “What is probability?” in Perspectives in Con-temporary Statistics, edited by D.C. Hoaglin and D.S.Moore (Mathematical Association of America, 1992),pp. 19–39.

16. The best we know of is the GUM Workbench athttp://www.metrodata.de.

PACS codes: 01.40Gb, 01.50Q, 06.20Dk

Saalih Allie, coordinator, Academic DevelopmentProgramme in Science, University of Cape Town, SouthAfrica; saalih@science.uct.ac.za

Andy Buffler, professor, Physics Department, Universityof Cape Town, South Africa; abuffler@science.uct.ac.za

Bob Campbell, head, Department of Educational Studies,University of York, UK; rmc1@york.ac.uk

Dimitris Evangelinos, Ph.D. candidate, PhysicsDepartment, University of Thessaloniki, Greece;evangelinos@physics.auth.gr

Fred Lubben, senior research fellow, Department ofEducational Studies, University of York, UK; fel1@york.ac.uk

Dimitris Psillos, professor of science education, Schoolof Education, University of Thessaloniki, Greece;psillos@skiathos.physics.auth.gr

Odysseas Valassiades, professor, Physics Department,University of Thessaloniki, Greece; valassiades@physics.auth.gr

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