The issue of didactical suitability in mathematics educational videos: experience of analysis with prospective primary school teachers
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The issue of didactical suitability in mathematics
educational videos: experience of analysis with
prospective primary school teachers
La cuestión de la idoneidad de los vídeos educativos
de matemáticas: una experiencia de análisis con
futuros maestros de educación primaria
María BURGOS, PhD. Associate Lecturer. Universidad de Granada (mariaburgos@ugr.es).
Pablo BELTRÁN-PELLICER, PhD. Associate Lecturer. Universidad de Zaragoza (pbeltran@unizar.es).
Juan D. GODINO, PhD. Professor. Universidad de Granada (jgodino@ugr.es).
Abstract: educational intervention with 93 prospective
The number of educational videos availa- primary school teachers, focussed on develo-
ble on the internet on the most varied topics ping their ability to analyse the educational
is rapidly increasing. These include mathe- suitability of videos about proportionality.
year 78, n. 275, January-April 2020, 27-49
matics videos that cover virtually any type of Preliminary analysis of the video revealed
curriculum content. However, their quality as significant errors and inaccuracies in the de-
a learning resource varies greatly. As a result, finitions, propositions, and procedures, as well
it is necessary to provide teachers with tools as shortcomings and inaccuracies in the argu-
revista española de pedagogía
to enable them to analyse the appropriateness ments, and so its level of epistemic suitability
of using educational videos, considering the is rated as medium. However, the majority of
various aspects involved. This paper describes the prospective teachers rated its degree of
the design, implementation and results of an suitability as high in almost all components.
This work was carried out in the framework of the EDU2016-74848-P (Spanish state research agency, ERDF) research
project and FQM-126 (Regional Government of Andalucia) and S36_17D (Regional Government of Aragón and
European Social Fund) groups, Spain.
Revision accepted: 2019-11-25.
This is the English version of an article originally printed in Spanish in issue 275 of the revista española de
pedagogía. For this reason, the abbreviation EV has been added to the page numbers. Please, cite this article as
follows: Burgos, M., Beltrán-Pellicer, P., & Godino, J. D. (2020). La cuestión de la idoneidad de los vídeos educativos
de matemáticas: una experiencia de análisis con futuros maestros de educación primaria | The issue of didactical
suitability in mathematics educational videos: experience of analysis with prospective primary school teachers. Revista
Española de Pedagogía, 78 (275), 27-49. doi: https://doi.org/10.22550/REP78-1-2020-07
https://revistadepedagogia.org/ ISSN: 0034-9461 (Print), 2174-0909 (Online)
27 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
Students regard studying didactic suitability mentación y resultados de una acción forma-
and implementing it through components and tiva con 93 futuros maestros de educación
indicators as positive, believing that this acti- primaria, orientada al desarrollo de la com-
vity facilitates professional reflection. Howe- petencia de análisis de la idoneidad didáctica
ver, mastering this tool requires analysing a de vídeos sobre proporcionalidad. El análisis
greater number and variety of videos and fur- a priori del vídeo reveló errores e impreci-
ther collective discussion of the results of the siones significativas en las definiciones, pro-
analyses performed by the students. posiciones y procedimientos, así como caren-
cias o inexactitudes en los argumentos, por
Keywords: teachers’ education, onto-semiotic lo que el nivel de idoneidad epistémica se
approach, didactical suitability, educational vi- valora como media. Sin embargo, la mayoría
deos, proportionality. de los futuros docentes valoraron su grado
de idoneidad como alto en casi todos los com-
ponentes. Los estudiantes consideran positi-
Resumen: vo el estudio de la idoneidad didáctica y su
La cantidad de vídeos educativos dispo- implementación a través de componentes e
nibles en Internet sobre los más variados te- indicadores, considerando que esta actividad
mas está aumentando a un ritmo acelerado. facilita la reflexión profesional. No obstan-
Así, nos encontramos vídeos de matemáticas te, el dominio de esta herramienta requiere
que cubren prácticamente cualquier tópico incrementar el número y variedad de vídeos
curricular, aunque su calidad como recurso para analizar y mayor discusión colectiva de
didáctico es muy desigual. En consecuencia, los resultados de los análisis que realizan los
year 78, nº 275, January-April 2020, 27-49
es necesario proporcionar a los profesores estudiantes.
herramientas que les permitan analizar la
pertinencia del uso de estos vídeos, teniendo Descriptores: formación de profesores, enfo-
en cuenta los diversos aspectos implicados. que ontosemiótico, idoneidad didáctica, vídeos
revista española de pedagogía
En este trabajo se describe el diseño, imple- educativos, proporcionalidad.
1. Introduction as flipped learning (Bergmann & Sams,
The use of educational videos from 2012), should be the subject of educatio-
YouTube and other platforms has increa- nal research as it is not clear how possi-
sed dramatically in recent years, offering ble it is to achieve meaningful learning
a promising learning resource for students by watching recorded classes. Indeed,
and the general public (Azer, AlGrain, several researchers discuss the role that
AlKhelaif, & AlEshaiwi, 2013). the use of YouTube and other social
media might play in formal education,
These educational resources and the analysing how online resources are or-
pedagogical models that use them, such ganised and how they can be inserted
28 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
as informal tools in specific educational proportionality that are available on the
settings (Borba et al., 2016; Dabbagh & internet.
Kitsantas, 2012; Duffy, 2008; Portugal,
Arruda, & Passos, 2018; Ramírez, 2010). The work is based around the following
It is widely regarded as necessary for sections. Section 2 outlines the theoretical
the field of educational studies to inves- framework and specific research problem.
tigate the adequacy of online educatio- Section 3 describes the design of the tra-
nal resources to ensure that technology ining process implemented. Section 4 in-
is in accordance with learning objecti- cludes a preliminary analysis of the video
ves (Turney, Robinson, Lee, & Soutar, about proportionality, which is used as
2009). an instrument for evaluating the compe-
tences achieved by the future teachers.
Research in mathematics teaching Section 5 shows in detail the results of
regarding the use of educational videos the experiment, analysing qualitatively
emphasises the importance of the tea- and quantitatively the reports drawn up
chers themselves evaluating and recom- individually by the future teachers. The
mending suitable videos for their pupils final section includes a summary of the re-
(Beltrán-Pellicer, Giacomone, & Burgos, search and discussion of its implications,
2018; Ruiz-Reyes, Contreras, Arteaga, & and limitations.
Oviedo, 2017; Santos, 2018). This is be-
cause some of these videos show forma-
lly incorrect procedures, not all of them 2. Theoretical framework and re-
search problem
year 78, nº 275, January-April 2020, 27-49
indicate the educational level for which
they are intended, and the meanings they In the field of research into training
raise might not be relevant to what is be- mathematics teachers, different theore-
ing covered in class. Accordingly, there tical frameworks are used to categorise
revista española de pedagogía
is a clear need to design and implement and promote different types of professio-
training processes that make it possible nal knowledge and competences (Pino-Fan
to promote teachers’ professional growth & Godino, 2015). We consider that the
and develop their knowledge and compe- didactic–mathematical knowledge and
tences (Chapman, 2014; English, 2008; competences (DMKC) model (Godino,
Mason, 2016; Ponte & Chapman, 2016; Giacomone, Batanero, & Font, 2017; Breda,
Sadler, 2013). Pino-Fan, & Font, 2017), developed wi-
thin the framework of the onto-semiotic
In view of this issue, the aim of this approach to mathematical knowledge and
research is to design, implement, and instruction (OSA) (Godino, Batanero, &
evaluate a training activity for future Font, 2007), provides suitable tools for
primary school teachers, focussing on approaching our research problem. This
developing knowledge and competences, model emphasises the importance of de-
relating to the analysis of the epistemic signing and implementing training resour-
suitability of educational videos about ces that promote teachers’ competence in
29 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
analysing educational suitability. Didacti- interpret, generalise, and justify the solu-
cal suitability is understood as the degree tions. Furthermore, the different partial
to which an instructional process combi- meaning of the mathematical objects that
nes certain characteristics that mean it appear must be connected and defined
can be described as appropriate or adequa- (Godino, Font, Wilhelmi, & Lurduy, 2011).
te, the main criterion being the fit between
the personal meanings students construct Using didactical suitability enables
(learning) and the institutional meanings, teachers to reflect systematically on their
whether these are intended or actually im- own practice (Aroza, Godino, & Beltrán-
plemented (teaching), taking into account Pellicer, 2016; Beltrán-Pellicer, Godino, &
the influence of the environment (Godino, Giacomone, 2018; Posadas & Godino, 2017)
2013). This involves coherently and syste- and it can also be applied to analyse par-
matically articulating six criteria relating tial aspects of the instructional processes,
to the facets that affect a training process such as the use of technological resources.
(Godino et al., 2007): epistemic, ecological, Specifically, Beltrán-Pellicer, Giacomone,
cognitive, emotional, interactive, and tho- and Burgos (2018), using the theoretical–
se relating to media. methodological tools from OSA, analysed
the degree of epistemic suitability of a se-
We consider that a mathematics trai- lection of the educational videos viewed
ning process is more epistemically suita- most frequently by users of YouTube™,
ble the better the institutional meanings relating to problems of proportional sha-
implemented (or intended) represent a re- ring. On the one hand, they found a wide
year 78, nº 275, January-April 2020, 27-49
ference meaning. The reference meaning variety of focuses and methods for solving
will relate to the particular educational this type of problem, which can interfere
level and should be drawn up, taking into with the teaching and learning process in
account the different types of problems the classroom if the teacher does not pre-
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and contexts for use of the content taught, viously select or record these videos. On
as well as the operational and discursive the other hand, the epistemic suitability
practices required (Godino, 2013). Conse- of the sample of videos analysed was very
quently, it will be necessary to take into diverse, with videos that contained errors
account the degree of adequacy of the si- and inaccuracies as well as many of them
tuations–problems and it will also be ne- offering an unrepresentative or poorly de-
cessary to consider the variety and ade- fined treatment of the mathematical con-
quacy of the representations, definitions, tent. Finally, they noted that the videos
procedures, and propositions, as well as with the metrics reflecting the greatest po-
the arguments supporting them. High sui- pularity were not the most suitable ones.
tability from an epistemic perspective re- This work is the main antecedent of the
quires the situations–problems proposed present paper.
to involve a variety of representations, to
offer students a variety of ways of approa- We consider that it would be desirable
ching them, and to require students to for teachers to understand the didactic
30 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
suitability of the tool and acquire the neces- Furthermore, before carrying out this
sary competence to use it to analyse edu- research, and in line with the chosen
cational resources critically, particularly in DMKC model, we carried out training
the use of videos available online. workshops with the group of students fo-
cussing on developing the competence of
Furthermore, various pieces of research analysing global meaning (based on iden-
show that teachers, both in their initial tra- tifying situations-problems and the opera-
ining and in service, show difficulties with tional, discursive, and normative practices
teaching concepts relating to proportionali- involved in solving them), and onto-semio-
ty (Bartell, Webel, Bowen, & Dyson, 2013; tic analysis of the practices (description
Ben-Chaim, Keret, & Ilany, 2012; Berk, of the framework of objects and processes
Taber, Gorowara, & Poetzl, 2009; Hilton & involved in the practices) used in the ma-
Hilton, 2018). Teacher training must take thematical activity of solving problems in-
into account the development of mathema- volving proportionality.
tics teaching knowledge and competences
relating to this topic by designing and im- The first session comprised a two-hour
plementing specific training interventions. workshop where the characteristics of the
This is why the trainee teachers were asked theory of didactical suitability were pre-
to analyse a video on proportionality. sented, as well as how the different epis-
temic, cognitive, affective, interactional,
media related, and ecological dimensions
3. Design of the training process of a given study process relate to each
year 78, nº 275, January-April 2020, 27-49
The training experience was carried other. The aim was to involve future pri-
out during the 2018-2019 academic year mary school teachers in a reflection on the
in the framework of the Curriculum need to have a system of specific indicators
Design and Development in Primary that make it possible to evaluate teaching
revista española de pedagogía
Education module with ninety-third year practice systematically.
students from the Primary Education de-
gree. In the next session, also lasting two
hours, the future teachers worked in
During their degree studies, future teams to analyse the epistemic suitabi-
teachers receive specific training about lity of online educational videos on pro-
epistemic (mathematical content), cogni- portionality. The initial group work ena-
tive (mathematics learning, errors, and bled the students to compare, discuss,
difficulties), instructional, and curricular and improve their proposals for evalua-
aspects, so that when carrying out their ting the epistemic suitability of different
school placements, they should be able to educational videos relating to proportio-
put into practice the knowledge they have nality.
acquired to analyse, design, and support
teaching-learning according to specific In the third phase, the students indi-
content (in our case, proportionality). vidually completed the tasks described in
31 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
the following section as a final evaluation In general, the situations-problems pro-
instrument, the results of which are analy- posed in the video are presented in context
sed in this work. and the mathematical ideas are connected.
Various ways of approaching the problems
are proposed, but we consider that the sam-
4. Preliminary analysis of the ple of the problems is not sufficiently repre-
epistemic suitability of the video sentative or defined. The solution methods
In this section we analyse the epistemic proposed are only applied to problems with
suitability of the video, that is, the mathe- a missing value, in which the condition
matical knowledge brought into play in it. of regularity is assumed in advance, and
This analysis will serve as a benchmark problems involving comparing ratios, for
for interpreting the students’ answers example, are not considered. The video fea-
when they evaluate the suitability of the tures a great variety of linguistic registers
educational video. The researchers perfor- and representations: natural registers (oral
med the analysis and preliminary evalua- and written), symbolic (numerical and alge-
tion independently. They then compared braic), tabular, and graphic ones.
them to decide on a common evaluation.
Furthermore, we have identified some
The educational video analysed1 covers errors and inaccuracies in the presenta-
the topic of direct arithmetic proportio- tion of rules (definitions and propositions)
nality from the perspective of presenting and arguments:
the notions of ratio and proportion (Ben-
year 78, nº 275, January-April 2020, 27-49
Chaim, Keret, & Ilany, 2012). The idea is — Error of expression in the handling of
that the future teachers will watch the simplifications of fractions. To simplify,
video closely and critically assess its de- the numbers that appear in the nume-
gree of suitability, in line with the episte- rator and denominator are crossed out,
revista española de pedagogía
mic suitability components and indicators leaving as superscript the factors that
(Godino et al., 2007; Godino, 2013). remain when canceling terms.
Graph 1. Screenshot from minute 7.
Image text: Quotient Equality Method. M1: shirts (units) M2: fabric (m2)
Source: Clasemáticas, 2012.
32 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
— Error in the definition of ratio and pro- relationship that doubling one magni-
portion. tude corresponds to doubling the other.
(1:00) «Ratio, mathematically spea- (4:30) Next, the narrator tells the stu-
king, means quotient. The proportion, the dents the question they should ask after
ratio, the quotient between these two mag- finding the magnitudes: «Will twice as
nitudes is always the same.» many shirts need twice as much cloth?»
Here we see incorrect use of the con- (4:43) «If the answer is yes, and in this
cepts of ratio and proportion. A ratio is not video it obviously will be, because if not,
always a quotient and a ratio is not the we would be looking at another type of
same as a proportion, a confusion found proportionality … then we are looking at a
with some frequency in teaching practice. problem of direct proportion.»
— The doubling rule does not necessarily This is incorrect. The answer to a ques-
denote a relationship of direct propor- tion like the one he asks might be no and
tionality. it might be that no other situation of pro-
portionality is involved.
(3:20) The narrator presents a «trick»
to find out whether two magnitudes are
— Neither the operations in a proportion
directly proportionate: «To find out if two
magnitudes are directly proportionate, all nor the reason for using cross multipli-
you have to do is check that doubling one cation are explained.
is the same as doubling the other, tripling
year 78, nº 275, January-April 2020, 27-49
is the same as tripling.» We consider that the degree of suitabi-
lity regarding relationships between ob-
This is a necessary but not sufficient jects, on a low-medium-high ordinal scale,
condition for two magnitudes to be direct- is medium, as not all of the propositions
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ly proportionate. The proportionality of and procedures have an associated argu-
magnitudes is a linear function established ment. Furthermore, the various meanings
between the values of the magnitudes. of the objects that appear in the exercises
are sometimes but not always identified,
— When the relation of direct proportio- and so the degree of suitability is medium
nality is justified, this is based on the in this aspect.
Graph 2. Screenshot from minute 8:15. General method.
Image text: General Method of Proportionality. M1: shirts (units) M2: fabric (m2)
Source: Clasemáticas, 2012.
33 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
(8:15) «In other words, the quotients term proportion instead of ratio to refer
are equal between the magnitudes, within to the fractions that appear on screen.
them, or comparing one with the other
magnitude, so this quotient is also co-
rrect.» The final procedure for solving propor-
tionality problems that the author of the
In the first method he presents, the video presents is the rule of three:
«equal quotients» one, he uses external
(11:35) Put the magnitudes in a co-
ratios. Here, in what the author calls the
lumn; «we put x is to 72 as 4 shirts is to 32.»
«general proportionality method», he uses
internal ratios, without appropriately ex-
plaining the relationship between the two
proportions. Furthermore, he uses the
Graph 3. Screenshot from minute 11:47. Rule of three method.
year 78, nº 275, January-April 2020, 27-49
Image text: Rule of three method. M1: shirts (units) M2: fabric (m2)
Source: Clasemáticas, 2012.
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(11:47) «And this, in reality, if you the diagram (using arrows), accompa-
rewind the video, is the general method. nied by cross multiplication, which is
The thing is I don’t know why you love pu- not justified in the video.
tting arrows on it. The general method has
a mathematical explanation and this one
doesn’t really.» Based on these analyses, the re-
searchers quantitatively evaluated the
He relates the rule of three method, video’s degree of epistemic suitability
which he solves by cross multiplication, in each of the six components, scoring
to the general method. Thus, he is re- each indicator according to whether its
ferring to to a «debased rule of three», contribution to the suitability is low,
that is to say, he does not present the medium, or high (0, 1, or 2 points, res-
proportional equation, which he distin- pectively). The total maximum score
guishes as another method. Therefore, will, therefore, be 12. Table 1 shows the
what he calls «the rule of three» is, in marks given by the research team.
34 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
Table 1. Evaluation of epistemic suitability by components.
Component Score given to the video
Situations-problems 1
Language 2
Rules 1
Arguments 1
Relationships between objects 1
Articulation of meanings 1
Final score 7
Source: Own elaboration.
5. Results As a result of this session, we saw
For the second working session, we that the future teachers overlooked the
asked the students firstly to watch errors in definitions, propositions or pro-
at home three videos 2 about directly cedures present in the videos and that in
proportional distributions which had the idea-sharing in the working group,
different degrees of suitability. Indivi- they found it hard to agree on the degree
dually, they had to decide on the grea- of suitability of the different videos. Dis-
year 78, nº 275, January-April 2020, 27-49
ter or lesser degree of suitability of the cussing the individual positions in many
videos as well as their level of use of cases led them to modify their prelimi-
algebra, taking into account the type nary analyses, identifying new elements
of solution developed. Afterwards, in of analysis that had gone unnoticed.
revista española de pedagogía
class, they were asked to discuss their
evaluations with the work group and In this section, we analyse the answers
then prepare a group opinion about the the students gave in the final evaluation
degree of suitability of the different task (third working session), which conse-
videos. The instructions given to the quently reflect what these students have
students for analysing the videos are learnt. We then analyse the answers given
the same as the ones proposed in the to the quantitative evaluation instruction
final task. That is to say, should con- for each of the six components of suitabi-
sider: a) the variety of situations-pro- lity, as well as the overall adequacy of the
blems presented; b) the presence of video.
different registers of representation;
c) the clarity and correctness of the Table 2 shows the frequencies and per-
definitions, propositions, and procedu- centages of the answers given regarding
res; and d) the argumentation of the the characteristics of the situations-pro-
propositions and procedures. blems presented in the video.
35 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
Table 2. Variety of situations-problems proposed (n = 93).
Characteristics of the situations Frequency (%)
A representative and defined sample of problems is presented 83 (89.25)
The situations appear in context 83 (89.25)
The mathematical ideas are connected 87 (93.55)
Various ways of tackling the problems are suggested 89 (95.70)
Source: Own elaboration.
We can see that the majority of the In relation to the presence of different
students adequately recognised that the representations and language registers,
situations are presented in context in the students have no difficulty in iden-
the educational video being analysed, the tifying the natural register and the sym-
ideas are connected, and various ways of bolic register. However, they identify the
approaching the problems are provided. tabular and graphic registers to a lesser
The majority of them (89.25%) also accep- extent. Other students, to a lesser extent,
ted that the videos show a representative identify animation and other different
and defined sample of problems. types (Table 3).
Table 3. Identification of linguistic representations (n = 93).
year 78, nº 275, January-April 2020, 27-49
Type of language Frequency (%)
Natural (oral) 92 (98.9)
Natural (written) 93 (100.0)
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Symbolic (numerical) 89 (95.7)
Symbolic (algebraic) 83 (89.2)
Tabular 74 (79.6)
Graphic 28 (30.1)
Animation 49 (52.7)
Others (iconic, multimedia, diagrammatic, etc.) 10 (10.8)
Source: Own elaboration.
The majority of the future teachers guments given for the transformations,
have difficulties locating the errors or or when the relationship of direct pro-
inaccuracies in the definitions, proposi- portionality in the situations presented
tions or procedures, as well as in the ar- is justified (Table 4).
36 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
Table 4. Clarity and correction of definitions, propositions, procedures,
and arguments.
Frequency (%)
Errors and inaccuracies in the Yes but
Explicitly Yes and
rules and arguments Not does not
states there describes
stated specify
are none it
what
Errors in
arithmetic-algebraic 63 (67.7) 21 (22.6) 2 (2.2) 7 (7.5)
treatment
Rules
Errors in definitions 51 (54.8) 22 (23.7) 2 (2.2) 18 (19.4)
Errors in proposi-
51 (54.8) 21 (22.6) 5 (5.4) 16 (17.2)
tions or procedures
Error or inaccuracy
when justifying a
45 (48.4) 20 (21.5) 6 (6.5) 22 (23.7)
relationship
of proportionality
Arguments Error or inaccuracy
when justifying an
54 (58.1) 20 (21.5) 4 (4.3) 15 (16.1)
arithmetic-algebraic
transformation
Other errors or
52 (55.9) 20 (21.5) 2 (2.2) 19 (20.4)
year 78, nº 275, January-April 2020, 27-49
inaccuracies
Source: Own elaboration.
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When the future teachers identify For example, E50 said: «Ratio: the vi-
errors of arithmetic or algebraic processes, deo defines this as the proportion of the
some mention that the author of the video quotient between both magnitudes. This
does not explain some of the symbols used, could cause confusion; one alternative
including subscripts, or that simplifying would be "link between two magnitudes
the results of the operations might confuse that can be compared to each other."»
the students.
— Inaccuracy in the definition of direct
With regards to errors or inaccuracies proportionality.
the students recognise in definitions, we
find the following categories of answers: — Confusing definitions or ones that are
inappropriate for primary school.
— Error in the definition of ratio. This is
the category with most answers that — As well as these categories, some stu-
identify conflicts in the definitions. dents include as errors in the defini-
37 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
tions descriptions that are not relevant numerator, it is easier for the student to
in relation to procedures or modes of place it in denominator of the left fraction
expression. For example, E84 notes (E26).»
that: «The names used for the methods
for calculating the proportion could Or they feel that the explanations that
cause confusion as in different places accompany the procedures are complex or
different names might be used for the- insufficient.
se methods.»
Only one student (E83) refers to the
The future teachers show difficulties error in the proposition: «To find out we-
assigning errors to the appropriate catego- ther two magnitudes are directly proportio-
ries and providing relevant descriptions. nate or not, all you have to do is check that
They refer to «confusing explanations» in doubling one is the same as doubling the
«Errors relating to definitions». For exam- other, tripling is the same as tripling …»
ple, E54 identifies as an error in defini-
tions: No student mentions as an inaccura-
cy the fact that the argumentation of the
In the explanation of the proportionali-
relationship of direct proportionality is
ty method (in the exercise with the shirts)
only based on the proposition that «dou-
he isolates «x» as if it were an equation. He
should have found the proportion between bling one magnitude corresponds to dou-
the shirts and the metres of cloth (how bling the other». Most of the students
many times bigger the metres of cloth are who place an error in this category do so
year 78, nº 275, January-April 2020, 27-49
than the number of shirts) and then divi- incorrectly, either because they indicate
ded the metres of cloth to get «x». «confusing explanation» or «limited ar-
gumentations» or because they refer to
Then adds regarding «Errors in propo- inaccuracies in the explanation of trans-
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sitions or procedures»: «In procedures, I formations and not in the relationship of
would put the same error as in "Errors in proportionality.
definitions"».
Only six students make any reference
Most of the students who identify con- to the lack of argumentation of the ope-
flicts in procedures refer to the rule of rations. For example, E67 states that:
three: «He crosses out numbers and iso- «The only problem I can see with this
lates «x» in the rule of three confusingly, video is that when simplifying he does
writing small numbers next to big ones not explain this process, it is true that
might give the impression they are powers the video is not about simplification but
(E52)». it could mean students get lost when sol-
ving problems.»
Other students identify procedural
errors: «In the equal quotients method, In relation to other errors, the future
putting the unknown quantity «x» in the teachers fundamentally identify:
38 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
— Errors or inaccuracies in the expres- ing if there is direct proportionality or not,
sion (oral) or language used. it seems imprecise as it only mentions dou-
bling. He should mention «halves match»,
— Unsuitable presentation for primary- «sums match», «differences match», in
other words, using all four operations.
school pupils.
Table 5 shows the frequency of errors
— Difficulties understanding the diffe- detected by the future teachers. We dis-
rences between the methods for solving tinguish between answers that mention
the problem. an error in a somewhat relevant way in
the appropriate category and answers
— Insufficient arguments for arithmetic that are not relevant because they are
transformations. not in the appropriate category, because
the description of the error is not con-
Regarding the «trick» the author of the clusive or is subjective, or because what
video presents, E68 includes the following they include cannot be regarded as an
as an error: error or inaccuracy. In general, the per-
Trick: «To find out whether two mag- centages of students who recognised
nitudes are directly proportional, it is errors and inaccuracies were low. The
enough to establish that the double of one highest related to the justification of the
of them corresponds to the double of the relationship of proportionality, mentio-
other». Although this is a quick way of see- ned by 22 students (23.7%).
year 78, nº 275, January-April 2020, 27-49
Table 5. Errors identified by the students.
Frequency
Irrelevant answer
Errors and inaccuracies in the It is an Inconclu-
revista española de pedagogía
rules and arguments detected by Relevant error but sive or Not Total (%)
the future teachers answer not in the subjective an
category descrip- error
identified tion
Arithmetic-algebraic
1 1 1 4 7 (7.5)
treatment
In rules In definitions 7 3 5 3 18 (19.4)
In propositions-proportions 4 3 5 4 16 (17.2)
When argumenting the rela-
3 8 4 7 22 (23.7)
tionship of proportionality
In
When argumenting
argu- 5 3 3 4 15 (16.1)
transformation
ments
Others 5 2 7 5 19 (20.4)
Source: Own elaboration.
39 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
Section d) of the instructions asked the teachers believed that the mathematical
trainee teachers to identify whether the objects are related in a relevant way and
mathematical objects and the meanings that, as such, the degree of suitability of
are presented in connection in the video. this aspect is high (Table 6). Furthermore,
Apart from two students who did not 63.44% said that the different meanings of
answer this section, 73.12% of the future the objects involved are always connected.
Table 6. Relationships between objects and meanings.
Relationships between mathematical objects Suitability Frequency (%)
All of the propositions
and procedures have an High 68 (73.1)
associated argument
Some of the propositions
Relationships between
and procedures have an Medium 23 (24.7)
objects
associated argument
None of the propositions
and procedures have an Low 0 (0.0)
associated argument
Always High 59 (63.4)
The meanings of the
objects that appear are Sometimes Medium 30 (32.3)
identified and interwoven
Never Low 2 (2.2)
Source: Own elaboration.
year 78, nº 275, January-April 2020, 27-49
According to the results obtained in the jects and meanings), the future teachers
preliminary analyses (variety and repre- had to quantitatively evaluate the degree
sentativeness of the situations-problems of didactical suitability of the video. They
revista española de pedagogía
proposed, variety of representation sys- had to assign a score of 0, 1, or 2 depending
tems, clarity and correctness of the rules on whether they regarded its suitability as
and arguments, connection between ob- low, medium, or high, respectively.
Table 7. Frequency (%) of evaluation of epistemic suitability by components.
Evaluation of the video
Components
0 1 2
Situations–problems 1 (1.1) 40 (43.0) 52 (52.9)
Language 3 (3.2) 37 (39.8) 53 (57.0)
Rules 3 (3.2) 33 (35.5) 57 (61.3)
Arguments 1 (1.1) 42 (45.2) 50 (53.8)
Relationships between objects 4 (4.3) 22 (23.7) 67 (72.0)
Articulation of meanings 2 (2.2) 37 (39.8) 54 (58.1)
Source: Own elaboration.
40 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
Table 7 shows that over half of the stu- 9.5 points. The most common score (in
dents gave the highest mark for relevance 29% of cases) was 10 points. Furthermo-
in each of the epistemic suitability com- re, 9 students (10%) gave the video the
ponents. The aspect with the highest va- maximum score.
luation is the relationship between objects
(72.0% indicated high suitability here) fo- The future teachers were asked to ex-
llowed by correctness of rules (61.3%). plain the reasons for their epistemic sui-
tability scores. Analysing their answers
We can see that the highest score has enabled us to identify the catego-
that can be assigned to the video is 12 ries in Tables 8 and 9, where we distin-
points. The minimum score assigned was guish arguments for a positive evaluation
4 points (one student) and the mean was and arguments for a negative evaluation.
Table 8. Arguments for giving a positive evaluation (n = 93).
Indicator Frequency (%)
Attractive presentation 8 (8.6)
Adequate language 43 (46.2)
Varied language 21 (22.6)
Variety of examples (representative and articulated
26 (28.0)
sample of situations-problems)
Everyday situations-context/connection with real life 27 (29.0)
Appropriate arguments/clear explanations 38 (40.9)
year 78, nº 275, January-April 2020, 27-49
Enough arguments 17 (18.3)
Varied and adequate procedures/methods 23 (24.7)
Coherent/adequate definitions 19 (20.4)
revista española de pedagogía
Articulated meanings 17 (18.3)
Favours reasoning or that pupils construct, perfect, and
use their own representations to organise, record, and 14 (15.1)
share ideas
Appropriate relationships between objects (propositions
15 (16.1)
with associated argument; related methods)
No error in rules or arguments 7 (7.5)
Source: Own elaboration.
The future teachers gave a positive The language used is varied: natural
valuation to the language used and to the (oral and written), symbolic (numerical
arguments used being appropriate and and algebraic), tabular (using tables),
the explanations clear. For example, E14 animation (a child thinking and asking a
gave 2 points to the language component, question, a gif with movement in the re-
saying: sult of the problem), and with arrows es-
tablishing relationships of proportionality.
41 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
… Also, the level of language is clear and However, these components are whe-
simple suitable for the Primary Education re negative evaluations are most often
level it is aimed at. given, referring both to errors in ex-
E22 gives the arguments component pression and language and to unclear
2 points: «I did not think there were any or confusing arguments (Table 9). E38
notable errors regarding the arguments said: «Sometimes it uses language that
and the procedures used in the video. is a bit technical for a primary-school
The arithmetic operations are always child. I think the arguments are good,
accompanied by an argument and justi- but they could be a bit clearer in some
fication. The arguments and procedures of the 4 methods it explains for direct
are clear.» proportionality.»
Table 9. Arguments for giving a negative evaluation (n = 93).
Indicator Frequency (%)
Situations-problems not adequate for primary level 3 (3.2)
Errors in expression/language 11 (11.8)
Language not suitable for primary level 11 (11.8)
Poor representations (little connection, lack of graphic or visual lan-
3 (3.2)
guage)
Difficulty distinguishing methods 4 (4.3)
year 78, nº 275, January-April 2020, 27-49
Excessive arguments 3 (3.2)
Unclear, confusing or fast arguments 19 (20.4)
Propositions with no connected argument 1 (1.1)
revista española de pedagogía
Incorrect or insufficient definitions 2 (2.2)
Definitions not adequate for primary level 4 (4.3)
Procedures not adequate for primary level 3 (3.2)
Procedures unclear or fast 4 (4.3)
Errors in procedures (simplification in rule of 3) 5 (5.4)
Arguments not adequate for primary level 4 (4.3)
Unconnected meanings 12 (12.9)
Lacks situations of meaning construction or own representations 3 (3.2)
The author includes ideas out of context or that might cause confusion
3 (3.2)
(for example, inverse/compound proportionality)
Situations contextualised poorly or only in a mathematical context 4 (4.3)
Source: Own elaboration.
42 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
The analysis as a whole should lead fu- students’ responses into «yes», «yes, but
ture teachers to decide whether the video …» when they make some kind of objection,
seems suitable to them, explaining their and «no». Table 10 includes the frequencies
decision. In this case, we have classified the and percentages of each of these options.
Table 10. Adequacy of the video in the final reflection (n = 93).
In your opinion, is this video adequate? Frequency (%)
Yes 48 (51.61)
Yes but… 38 (40.86)
No 7 (7.53)
Source: Own elaboration.
Of the future teachers, 51.61% consider adequacy of the argumentation. Table 11
the video to be adequate, and they valued summarise the different explanations the
most highly the presence of various ways students used to evaluate how adequate
of solving the problems and the degree of the video is.
Table 11. Arguments when they believe the video is totally adequate (n = 48).
Indicator Frequency (%)
year 78, nº 275, January-April 2020, 27-49
Various ways of solving problems 46 (95.8)
Variety of examples 22 (45.8)
Adequate and detailed explanation 42 (87.5) revista española de pedagogía
Simplifies definitions/presents the most relevant and representative
13 (27.1)
information
Adequate representation/language 26 (54.2)
Useful/motivational 7 (14.6)
Includes tricks/advice 12 (25.0)
Relatable context 10 (10.8)
Inspires reflection on most adequate method 6 (12.5)
43 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
There are no errors 7 (14.6)
Adequate length 2 (4.2)
Attractive presentation, informal tone 5 (10.4)
Source: Own elaboration.
Of the future teachers, 40.86% did not methods used being inadequate for pri-
believe that the video was wholly adequa- mary-level, or it potentially being boring
te (Table 10). They identify as drawbacks for the pupils.
the length, the language, and some of the
Table 12. Arguments that indicate drawbacks («yes but …») (n = 38).
Indicator Frequency (%)
Language not adequate for primary level 11 (28.9)
Arithmetic procedures not explained 4 (10.5)
Excess length 6 (15.8)
year 78, nº 275, January-April 2020, 27-49
Boring or causes pupils to switch off, lacks animations or
19 (50)
visual resources
Causes confusion among the students 6 (15.8)
revista española de pedagogía
Lacks variety of contexts 3 (7.9)
Incorrect explanations 5 (13.2)
Too long and dense for primary school 11 (28.9)
Not all situations/concepts/methods are adequate
12 (31.6)
for primary level
Does not take into account prior knowledge or problems
4 (10.5)
with learning
Contains errors 7 (18.4)
Source: Own elaboration.
44 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
Finally, only 7.5% of the students did 6. Summary, implications, and li-
not believe the video was adequate. They mitations
state that the explanations are not very The aim of this work was to design,
accurate or not at all accurate and the ar- implement, and evaluate a training ac-
guments are inadequate or confusing for tivity for future primary school teachers
primary level. focussed on developing the knowledge
and competence to analyse the episte-
Analysing students’ answers has ena- mic suitability of educational videos on
bled us to detect some conflicts relating proportionality. We started by stating
to the identification of components and why the topic is of interest, given the
descriptors in the analysis of epistemic abundance and availability of videos
suitability, essentially relating to rules that are offered as resources to help
and articulation of meanings. For exam- teach mathematics. However, given the
ple, E32 identifies rules with ways of sol- inconsistent quality and variety of me-
ving a problem and states: «I have given anings in the educational videos (Bel-
trán-Pellicer, Giacomone, & Burgos,
the rules a mark of 2 because they do dis-
2018), there is a need to train teachers
play a wide variety of ways of solving the
in how to evaluate these resources and
problem.»
use them suitably.
Similarly, E56 noted that:
The training activity focusses on pro-
For the rules, I have given a score of 2 viding future teachers with a theory-
year 78, nº 275, January-April 2020, 27-49
(high) for suitability because I agree with based tool for analysing epistemic sui-
how he does the operations in each case tability, that is to say, the mathemati-
where he solves the problems and because cal content presented in a video about
I do not think he makes any errors when proportionality. Preliminary analysis
revista española de pedagogía
doing them. by the researchers of the video revealed
errors and inaccuracies in definitions,
Some students consider that the me- propositions, and procedures, as well as
anings are articulated when various me- shortcomings or inaccuracies in the ex-
thods are used or what is being done in the planations used to justify the procedures
video is justified. For example, E41 said: «I and propositions. Also, the presentation
think that the definition of concepts has a and treatment of a variety of situations-
high level, because it uses various methods problems and the articulation of me-
to solving the problems.» anings of proportionality have major
shortcomings, and so we rated its level
E30 added: «Regarding the articula- of epistemic suitability as medium on the
tion of meanings, the suitability is high low-medium-high ordinal scale. However,
as it constantly explains what each thing the majority of the future teachers, after
being done means.» the training process had been applied, ra-
45 EVMaría BURGOS, Pablo BELTRÁN-PELLICER and Juan D. GODINO
ted the degree of suitability of the video as tent knowledge, in this case regarding pro-
high in almost all components. portionality, increasing the training time
allocated, analysing a larger variety of edu-
The evaluation instrument used, based cational videos, and increasing group dis-
on epistemic suitability components cussion of the results of the analysis phase.
and indicators, considers the variety of
situations-problems posed, the presence
This type of training action, focussing
of different registers of representation,
on the content of the discipline but with
the clarity and correctness of the defini-
tions, propositions, and procedures, and a clear orientation towards knowledge and
the justification for procedures and pro- didactic competences, aligns with works
positions using arguments that are rele- by other authors such as Davis (2015),
vant and adapted to the corresponding where he notes the impact of his concept
educational level. Failure to recognise the study, both when revealing the complexity
absence of some important indicators led of the underlying mathematical ideas and
a high percentage of students (51.6%) to when developing the mathematical ideas
regard the video as an adequate teaching necessary for teaching.
resource without identifying its shortco-
mings. Furthermore, in addition to the epis-
temic element, the didactical suitability
We also observed a degree of inconsis-
theoretical tool includes the cognitive,
tency in the allocation of scores by the par-
emotional, interactional, media, and eco-
year 78, nº 275, January-April 2020, 27-49
ticipants, finding some evaluations with
the maximum score where students iden- logical aspects, which are not considered
tify more drawbacks than in others with in this piece of research. Although it is not
lower scores. While these variations keep relevant to apply some of these aspects to
the case of using didactic resources, in par-
revista española de pedagogía
the overall evaluation coherent, they do
indicate that it is perhaps necessary to de- ticular the aspect of learning achieved, the
fine the criteria more, in order to achieve other aspects could be the subject of analy-
greater uniformity between participants. sis and reflection by the teachers who use
Nonetheless, we have to take into account these resources.
that this is a qualitative evaluation of sui-
tability and that the final number, within
certain margins, is only the summary re- Notes
sult of a more complex process in which 1
The video from the Clasemáticas channel can
the different components of suitability are be viewed at https://www.youtube.com/watch?-
identified. v=o1Mu-lkgv-o
2
The videos suggested can be viewed at:
These results suggest there is a need https://www.youtube.com/watch?v=0Z5DejetHR8
to consider in greater depth the develop- https://www.youtube.com/watch?v=v8KN44iNPls
ment of future teachers’ specialised con- https://www.youtube.com/watch?v=1uAbIb-McLo
46 EVThe issue of didactical suitability in mathematics educational videos: an analysis experiment...
Breda, A., Pino-Fan, L., & Font, V. (2017). Meta
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She has a doctorate in Mathematics from
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temática y Educación Estadística (Theory
48 EVYou can also read
