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Advances in Social Sciences Research Journal – Vol. 10, No. 12
Publication Date: December 25, 2023
DOI:10.14738/assrj.1012.16112
Georgaki, M. & Stefanidou, C. (2023). Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot
Research. Advances in Social Sciences Research Journal, 10(12). 253-261.
Services for Science and Education – United Kingdom
Primary Student Teachers’ Views on Scientific Measurement and
Uncertainty: A Pilot Research
Maria Georgaki
Department of Primary Education,
National and Kapodistrian University of Athens
Constantina Stefanidou
Department of Primary Education,
National and Kapodistrian University of Athens
ABSTRACT
The paper presents primary student teachers’ views on the basic concepts related
to scientific measurement and uncertainty. A pilot study was conducted, and a
qualitative content analysis method was used, by distributing an open-ended
questionnaire in a convenient sample including 24 primary student teachers. The
first findings revealed that student teachers have some general idea about the
importance of scientific measurement, they recognize uncertainty as human error
or instrument failure, but they lack the deepest conceptualization of uncertainty as
an aspect of the nature of scientific measurement. The above-mentioned views are
discussed in the context of their influence in teaching practices of science and
mathematics in primary education and their epistemological perspectives.
Keywords: measurement, uncertainty, science curriculum, primary student teachers
INTRODUCTION - LITERATURE REVIEW
Measurement is applied in a range of fields, from quantum physics to daily commercial
transactions, because of its special epistemic role: its results are rightly assumed to be more
reliable than, say, opinions and guesses [1]. Measurement is a core concept of primary and
secondary school curriculum documents around the world [2]. The concept of measurement
uncertainty incorporates several concepts and skills, such as random and systematic error,
calibration, replication, hypothesis testing, populations and samples, experimental design,
modeling, approximation, etc., that are key elements of the scientific method. The concept of
uncertainty of measurement, in the context of education can be considered as one of the science
teaching’s "threshold concepts", as it fulfills the five necessary characteristics: (1)
transformative, (2) comprehensive, (3) possibly irreversible, (4) delimiting, and (5) potentially
"disruptive" to learning [3]. A key reason for highlighting measurement uncertainty as a
'threshold concept' is the importance of understanding measurement uncertainty concepts. It
is important for students to understand how to identify different sources of uncertainty,
quantify results, and take these results into account when planning experiments, analyzing data
and drawing logical conclusions from that data. Assessing the consequences of uncertainty is
an essential characteristic and ability of an effective scientist. Moreover, a lot of experiments
aim to make precise quantitative measurements and a lot of theoretical predictions are
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expressed as numbers. However, traditional science curricula underestimate the concept of
measurement uncertainty and keep it in the narrow context of the laboratory. As a result, for
many students, the process for identifying, quantifying, and propagating the uncertainties of a
measurement seems tiring, and often it distracts them from the goal of obtaining a result [4].
The degree to which students understand the basic concepts related to measurement and
uncertainty varies according to their level of education and how much they have been exposed
to these concepts in the context of teaching science and mathematics.
Primary School Students' Views on Measurement Uncertainty
Uncertainty of measurements is a concept that often gives students difficulty. The idea of
quantifying a quantity that, by definition, they are uncertain about and cannot directly measure
be challenging. The realization that data-on which theories depend-is inherently uncertain and
that the measurement process is imperfect leads students to question the basis of physical
knowledge, which confuses them as they desire clarity and certainty. In the measurement of
natural quantities, various ideas of students that are not scientifically correct prevail. Students
believe in the existence of a "unique right answer" to any experimental observation. Therefore,
when they notice the variation in repeated measurements or get an answer different from the
expected result, they believe they have made a "mistake". They consider that there is no
uncertainty in scientific results, and a scientifically correct measurement is the one that is not
accompanied by any uncertainty. The ideal for them is to carefully perform a single perfect
measurement [5]. One measurement with a scientific instrument is enough, as they consider
scientific instruments to be highly accurate. In addition, for students, there is no separation of
the concepts of error-uncertainty, and they do not recognize errors as systematic or random.
The term "error" proves misleading to students as they categorize experimental results into
true and false, believing that each experiment has a predetermined correct result, and their
measurements may be wrong. Thus, unexpected results are commonly accompanied by the
phrase "due to human error" [5].
Secondary Students' Views on Measurement Uncertainty
Several studies have focused on students' conceptual understanding of key features of the
experimental process. These are concepts related to the need for repeated measurements, the
importance of estimating data, as well as the validity and reliability of statistical data processing
[6],[7]. These studies mainly focus on students' perceptions of measurement sets and how a
measurement could be made as accurate as possible.
For many middle and high school students, the process for identifying, quantifying, and
propagating uncertainty in a measurement is a tedious task and distracts them from the goal of
obtaining a result. More specifically, preliminary research conducted by Coelho and Sere [8] on
French secondary school students, aged 14-17, regarding the characteristics that students
attribute to the readings of laboratory instruments showed that students consider the
laboratory instruments to show "high precision", which in turn implies reliability, i.e., they have
the belief that a given measurement does not need to be repeated.
Undergraduate Students' Views on Measurement Uncertainty
Most of the studies that have been done on understanding measurement uncertainty focus on
undergraduate science students. According to a related study by Buffer, Allie & Lubben [9],
students seem to be able to handle the tools for processing measurements and analyzing data
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Georgaki, M. & Stefanidou, C. (2023). Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot Research. Advances in
Social Sciences Research Journal, 10(12). 253-261.
URL: http://dx.doi.org/10.14738/assrj.1012.16112
but at the same time, they struggle to understand the deeper reasons for these processes. Sere,
Journaux, and Larcher [6] reported a study conducted on French first-year university students.
After completing the study, it was observed that most students did not have a full
understanding of the statistical procedures required. More specifically, the students considered
the first readings as "prominent" while they used the following ones only to confirm the
previous ones. Furthermore, they could not make a distinction between the concepts of
accuracy and reliability. These findings are in accordance with Garrett, Horn, and Tomlinson
[10] who conducted research on first-year chemistry students in the UK. Regarding primary
student teachers and primary teachers, very limited research is available. For example, O’Keefe
& Bobis [11] investigated teachers’ perceptions of their content knowledge and how they
perceive this knowledge impacts on their teaching. The study revealed teachers’ inability to
clearly articulate their knowledge of important concepts and processes relating to
measurement.
Taking related studies into account, it seems that primary student teachers' views have not
been investigated sufficiently. Especially in Greece, it seems that there is a necessity for such
research. According to Greek educational legislation, primary education includes K1-K6 grades
(6-12 years old students). Primary teachers are assigned to teach all subjects, from language
and history to mathematics and science. There is evidence in the literature that teachers’
content knowledge affects student learning and is improved by professional development [12].
The present study aims to investigate primary student teachers' views on basic concepts and
processes of measurement of physical quantities and the core ideas of uncertainty and error
which are related to it.
METHODOLOGY
Research Questions
Research questions of the present study are as follows:
• To what extent do students recognize the value of measurements in scientific research?
• What is students' ability to pursue for less or more precision, depending on the
measurement situation?
• To what extent do students understand the concept of uncertainty as an integral part of
measurement?
• To what extent are students able to distinguish error from relative error?
• To what extent are students able to distinguish random from systematic errors?
Sample-Place-Time
The research took place during the academic year 2022-2023 in the Department of Primary
Education of the National and Kapodistrian University of Athens. The research sample is
convenient and consists of 24 primary student teachers.
Data Collection
Students’ views research tool was a questionnaire consisting of ten open-ended questions (see
Appendix). The questionnaire was based on the manual for the teaching of measurement in the
introductory physics laboratory of the Department of Physics, of the Cape Town University
[13], which is a GUM-compliant Laboratory Manual (ISO, 1995). The questionnaire was
structured in five (5) categories, in accordance with the above-mentioned research questions.
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Regarding the validity of the questionnaire, it is provided by the fact that all questions are
related to five research questions under consideration (content validity) and vice versa, the
questionnaires include all research practices. Moreover, the questionnaires are thoroughly
tested by two experts, experienced schoolteachers. They both agreed on the content validity of
all items [14]. Questionnaires were created and distributed in google form format.
Data Analysis
Qualitative inductive content analysis method was used to analyze the data [15]. Students’
answers were divided in categories according to their content. Categories depicted the extent
to which each concept of measurement was conceptualized by students.
Limitations
There are numerous limitations to our research which don’t allow the generalization of findings
and conclusions. The sample is very limited and convenient. Even if questions of the
questionnaires were open-ended, interviews would be very helpful to refine students’ answers.
RESULTS AND DISCUSSION
Regarding the 1st Research Question
Students’ Answers in Question 2:
Most students recognized the process of measurement as an important scientific practice. Ten
out of the twenty-four students expressed the opinion that measurements make scientific
processes more objective and testable by other scientists. These findings are in accordance with
related literature that revealed students’ high expectations of scientific instruments’ precision
[7]. Seven out of the twenty-four students emphasized on measurement as a process of laws
and theories confirmation but also as a resource of deriving new patterns. The remaining seven
out of twenty-four students expressed their acceptance of measurements’ value in other, more
general ways, such as for example that without measurement no research can be done.
Regarding the 2nd Research Question
Students’ Answers in Question 3:
Most students had difficulties in realizing that precision in measurements is required according
to the context. Specifically, more than half of the students did not realize that measuring sugar
at the cooking level does not require very high precision, and ten out of twenty-four answered
that they would have to subtract 2 grams of sugar to make the measurement "correct", while
four out of twenty-four answered that they need to reweigh to confirm the original
measurement of 52 grams. Ten out of twenty-four students seemed to realize that the
difference of 2 grams in the context of cooking is not significant, and therefore answered that
they would add all the sugar.
Students’ Answers in Question 4:
Regarding measurements in scientific context, specifically in a chemistry experiment, all
students agreed that precision is needed. Fourteen out of the twenty-four students suggested
removing 2 of the 52 grams of the chemical substance, considering that this difference could
make a bigger difference in the result. Ten out of the twenty-four students answered that we
should do the measurement again and again to make sure that the mass of the substance is
indeed 52 and not 50 grams, as this difference could be due to some measurement error.
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Georgaki, M. & Stefanidou, C. (2023). Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot Research. Advances in
Social Sciences Research Journal, 10(12). 253-261.
URL: http://dx.doi.org/10.14738/assrj.1012.16112
Students’ Answers in Question 5:
Regarding the comparison between the previous contexts, a little more than half of the students
(fourteen out of twenty-four) realized that in the chemistry experiment greater accuracy is
sought in the measurement than in the process of a cooking recipe. Eleven out of the fourteen
argued that the chemistry experiment is a scientific one, so precision is a characteristic of the
scientific method, while three out of fourteen argued that we should be precise with the
chemistry measurements for security reasons. However, eight out of fourteen students
answered that in both measurements we must have the same accuracy, that is, they do not
distinguish the context of the measurement in the kitchen and in the laboratory. These findings
are in accordance with related research [9] that revealed undergraduate students’ difficulty in
conceptualizing the deeper nature of scientific measurement.
Regarding the 3rd Research Question
Students’ Answers in Question 6:
Almost all students admitted that uncertainty is always present in scientific experiments, even
though scientists struggle with it. Specifically, twenty three out of twenty-four students
answered that "Scientists can measure the value of a physical quantity with great precision, but
uncertainty exists" and only one out of twenty-four students answered that "Scientists with
careful handling and with the modern instruments at their disposal, they are able to perform
measurements with 100% accuracy". In their explanations, fifteen out of the twenty-four
students answered that the uncertainty is due to various errors including instruments as well
as human errors, five out of twenty-four students did not explain their reasoning but repeated
that there is uncertainty, two out of twenty-four answered that science is uncertain because it
evolves, that is, they confuse the uncertain nature of science with uncertainty in measurement.
Finally, two out of twenty-four students answered off-topic. These findings are in line with
related literature that shows us that students’ attribute uncertainty mainly in “human error”
and they do not accept random errors as significant [5].
Students’ Answers in Question 7:
In this question students were asked whether it is possible to eliminate measurement errors.
Twenty three out of the twenty-four students answered that such a thing is not possible.
Specifically, twelve of them answered that we cannot eliminate errors, but we can reduce them,
and they even mentioned various types of systematic and random errors. Eleven out of twenty- four students responded that we cannot eliminate errors, but they did not explain further.
Regarding the 4th Research Question
Students’ Answers in Question 8:
Regarding students’ conceptualizing of relative error, only six out of twenty-four correctly
answered that the first measurement is more accurate than the second and reasoned that this
is because the same error corresponds to a larger value. Eighteen out of twenty-four students
did not seem to realize that accuracy is related not only to the error but also to the mean value
to which the error refers. Specifically, eight out of twenty-four students answered that the two
measurements are equally accurate, two out of twenty-four that the error of the second
measurement (the one with the smallest value) is greater, seven students gave off-topic
answers and one student answered that he did not know. These findings confirm previous
studies that revealed difficulty in deeper understanding of error and uncertainty in science [9].
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Regarding the 5th Research Question
Students’ Answers in Question 9:
Ten out of the twenty-four students gave completely acceptable answers on the examples they
were given to distinguish between systematic and random errors. Fourteen out of the twenty- four students answered incorrectly for at least one of the three error examples. Specifically,
four out of the twenty-four students estimated the error of the ruler scale as random and not
systematic, while six out of the twenty-four students considered the experimental error in
measuring the time of a mobile between two points to be systematic and not random.
Students’ Answers in Question 10:
However, students’ proposals for dealing with these errors are interesting. Nine out of twenty- four students suggested calibrating the measuring instruments or replacing them if necessary.
In the case of measuring the time between two points, they strongly suggested increasing the
number of measurements, to limit the effect of random error. Five out of twenty-four students
suggested that the experimenter should be more careful in measuring time, while for the
measurement of mass and length they also suggested calibrating the instruments. Four out of
the twenty-four students suggested the use of a more technologically developed way of
measuring time, so that the measurement does not depend on the user and his reflexes. Finally,
six out of twenty-four students made other types of suggestions to mitigate errors.
CONCLUSIONS AND IMPLICATIONS
Some of the literature on the role of the uncertainty in scientific measurement in science
education has referred to primary and secondary students’ difficulties. Some researchers have
also focused on science teachers’ views, but very limited research has been done on primary
teachers’ views and difficulties on measurement and its uncertainty. Our research belongs to
this last category and refers to primary student teachers of the Department of Primary
Education of the National and Kapodistrian University of Athens. According to students’
answers, it seems that most students recognise scientific measuring as an important part of the
scientific process, but they presented several difficulties regarding the concept of uncertainty.
Half of them could not distinguish between uncertainty in the kitchen and uncertainty in the
laboratory, and most of them could attribute uncertainty in systematic errors but they could
not conceptualize random errors as part of the measurement precision.
Limitations of our research do not allow us to generalize. These limitations give suggestions for
further research, such as to conduct some interviews to better depict primary student teachers'
views on uncertainty and connect it to uncertainty as an aspect of Nature of Science. Moreover,
the uncertainty in measurement could be an adequate context for introducing primary teachers
in epistemological issues such as objectivity of the process of measurement and
intersubjectivity of the results, which are already studied in different contexts [1],[16].
References
[1]. Mari, L., Carbone, P., Giordani, A., & Petri, D. A structural interpretation of measurement and some related
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ISSN 0039-3681, https://doi.org/10.1016/j.shpsa.2017.08.001
[2]. National Council of Teachers of Mathematics. Principles and standards for school mathematics. National
Council of Teachers of Mathematics, 2000.
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Georgaki, M. & Stefanidou, C. (2023). Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot Research. Advances in
Social Sciences Research Journal, 10(12). 253-261.
URL: http://dx.doi.org/10.14738/assrj.1012.16112
[3]. Meyer, J.H.F. and Land, R. Overcoming barriers to student understanding: Threshold concepts and
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[4]. Wilson, A., Akerlind, G., Francisa, P., Kirkup, L., McKenzie, J., Pearce, D., Sharmad, M-D. Measurement
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[5]. Allie, S., Buffler, Α., Campbell, Β., Lubben, F., Evangelinos, D., Psillos, D., & Valassiades, O. Teaching
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[6]. Sere, M-G., Journaux, R. and Larcher, C. Learning the statistical analysis of measurement error. International
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[11]. O’Keefe, M., Bobis, J. Primary Teachers’ Perceptions of Their Knowledge and Understanding of Measurement.
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[12]. Hill, H.C., & Ball, D. Learning mathematics for teaching: Results from California’s mathematics professional
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[13]. Buffer, A., Allie, S., Lubben, F., & Campbell, B. Introduction to Measurement in the Physics Laboratory: A
Probabilistic Approach, 2009.
https://science.uct.ac.za/sites/default/files/content_migration/science_uct_ac_za/2535/files/Introductio
n%2520to%2520Measurement%2520manual%2520%2528UCT%2520Physics%2529.pdf
[14]. Polit DF, Beck CT. The content validity index: are you sure you know what's being reported? Critique and
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[15]. Mayring, P. Qualitative Inhaltsanalyse: Grundlagen und Techniken. Weinheim: Beltz, 2015.
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[16]. Stefanidou, C. and Skordoulis, C. Subjectivity and Objectivity in Science: An Educational Approach. Advances
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Appendix
The distribution of this questionnaire is done in the context of an educational research on students' views on
measurement and its uncertainty. The completion is optional, completely anonymous, and not related to the
evaluation of the course.
Name/Surname: ................................................
Questions
1. What is an experiment according to your opinion?
2. Scientific processes include measurements. Give some reasons, according to your opinion, why measurements
are so important for scientific research.
3. Imagine that a recipe says “add 50 grams of sugar”. You put some sugar on your kitchen scale and the display
reads 52.0 g. Choose the answer that you agree most with:
A. I think that it is OK.
B. I think that it is not OK. We have to measure it again.
C. I think that it is not OK. We have to take out 2 grams of sugar.
4. Imagine you are in the chemistry lab and an experiment requires 50.0 grams of a chemical. Weigh a quantity
of the material on a laboratory scale and the reading on the screen is 52.0 gr. Which of the following sentences
do you agree with?
A. It is OK. We can add to the experiment the whole amount of chemicals we weighed
B. I think we should weigh in again.
C. I think we should remove 2 grams of chemical.
Explain your choice.
5. Now, compare the answers you gave to the two above questions. Explain why they are the same or why they
are different.
6. The students at a high school class attended a scientific lecture. The other day physics’ teacher wrote on the
board two proposals that refer to the results of the measurements which scientists do in the most modern
laboratories, to ascertain the opinion formed by the students after the lecture. Which of the following
statements do you agree with?
A. Scientists with careful manipulations and with modern instruments that they use, can perform
measurements with 100% accuracy.
B. Scientists can measure the value of a physical quantity with great precision, but always with some
uncertainty.
Explain your answer.
7. Do you think that in a laboratory measurement we can have zero errors? State your opinion.
8. You are given the result of measuring the length of a book (23.4±0.2cm) and a notebook (17.3±0.2cm). Which
of the two measurements do you think is more accurate? Justify your reply.
9. In a school laboratory guide, we read the following text:
Errors in measurements can be divided into two categories:
A. Those that remain unchanged in successive measurements. They are mainly due to imperfection of the
measuring instruments, or the method used, but they may also be due to the experimenter himself and
are called systematic errors.
B. Those due to various unforeseen factors which vary randomly with time can be negative or positive, and
called random errors.
Now, you are given the following error cases:
A. The pointer of an analog scale is slightly shifted. When it doesn't have a body placed on the scale the
pointer is not exactly at zero.
B. We measure lengths with a sub decameter with a scale of 0 to 20cm, but due to some manufacturing
problems, this is about 2mm smaller.
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Georgaki, M. & Stefanidou, C. (2023). Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot Research. Advances in
Social Sciences Research Journal, 10(12). 253-261.
URL: http://dx.doi.org/10.14738/assrj.1012.16112
C. We measure the movement time of a small electric motor with a stopwatch car between two seats on the
school hall floor. Repeating the measurement, we do not find the same value, because its operator timer
can "press" the start and end of the count shortly before or after the car passes the original or the final
position.
In what categories would you place the error listed in one of the above three cases, and why? Explain yourself.
10. Now think what you could do in the above cases’ errors to reduce them. Briefly report below.