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Why Teach Mathematics? -- A Study with Preservice Teachers on Myths around the Justification Problem in Mathematics Education

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Title: Why Teach Mathematics? -- A Study with Preservice Teachers on Myths around the Justification Problem in Mathematics Education
Language: English
Authors: López-López, Alberto (ORCID 0000-0002-1745-4266), Aguilar, Mario Sánchez (ORCID 0000-0002-1391-9388), Castaneda, Apolo (ORCID 0000-0002-7284-8081)
Source: International Journal of Mathematical Education in Science and Technology. 2022 53(8):2102-2114.
Availability: Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 13
Publication Date: 2022
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Preservice Teachers, Misconceptions, Mathematics Education, Student Attitudes, Foreign Countries, Mathematics Instruction, Thinking Skills, Cognitive Development, Mathematics Skills, Positive Attitudes, Mathematics Teachers
Geographic Terms: Mexico
DOI: 10.1080/0020739X.2020.1864489
ISSN: 0020-739X
1464-5211
Abstract: In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within such arguments. The study is based on semi-structured interviews with 19 preservice mathematics teachers from Mexico. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (1) mathematics is related to the development of mental or thinking skills, (2) mathematics is useful for daily life, and (3) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (1) the myth of reference, (2) the myth of participation, (3) the myth of importance, and (4) the myth of cognitive development. The report concludes by discussing the results and pointing out some future research routes.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1366502
Database: ERIC
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  Value: <anid>AN0159177047;imt01aug.22;2022Sep20.08:41;v2.2.500</anid> <title id="AN0159177047-1">Why teach mathematics? – A study with preservice teachers on myths around the justification problem in mathematics education </title> <p>In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within such arguments. The study is based on semi-structured interviews with 19 preservice mathematics teachers from Mexico. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (<reflink idref="bib1" id="ref1">1</reflink>) mathematics is related to the development of mental or thinking skills, (<reflink idref="bib2" id="ref2">2</reflink>) mathematics is useful for daily life, and (<reflink idref="bib3" id="ref3">3</reflink>) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (<reflink idref="bib1" id="ref4">1</reflink>) the myth of reference, (<reflink idref="bib2" id="ref5">2</reflink>) the myth of participation, (<reflink idref="bib3" id="ref6">3</reflink>) the myth of importance, and (<reflink idref="bib4" id="ref7">4</reflink>) the myth of cognitive development. The report concludes by discussing the results and pointing out some future research routes.</p> <p>Keywords: Justification problem in mathematics education; myths; pre-service mathematics teachers</p> <hd id="AN0159177047-2">1. Introduction</hd> <p>The study reported in this manuscript is closely linked to the so-called <emph>justification problem in mathematics education</emph> (Ernest, [<reflink idref="bib6" id="ref8">6</reflink>]; Niss, [<reflink idref="bib14" id="ref9">14</reflink>]). The justification problem in mathematics education refers to the discussion of the reasons and arguments for providing mathematics education to the students of a particular society. According to Paul Ernest ([<reflink idref="bib6" id="ref10">6</reflink>]), the justification problem in mathematics education concerns the following questions:</p> <p>Why teach mathematics? What is the philosophy of mathematics education in terms of the purposes, goals, justifications, and reasons for teaching mathematics? How can current mathematical teaching plans and practices be justified? What might be the rationale for reformed, future or possible approaches for mathematics teaching? What should be the reason for teaching mathematics, if it is to be taught at all? (p. 33)</p> <p>In spite of not being commonly addressed as an object of explicit discussion nor as a research object, the justification problem is very relevant for mathematics education. Niss ([<reflink idref="bib14" id="ref11">14</reflink>]) put forward three reasons that could justify its relevance: first, the scholarly reason, which refers to all the resources – material and human – that are invested in the massive task of teaching and learning mathematics in society, and also to the fact that this task deeply affects a large number of people; for such reasons, to investigate the motivations and arguments that sustain the teaching of mathematics in society should be considered a legitimate and relevant research object. Second, the implications reason which is related to the fact that the structure and organization of mathematics instruction are a reflection of the justification and goals of mathematics education that different agents have. For example, the number of mathematics lessons per week can echo the goals of the political and administrative system that governs an educational institution; similarly, the type of exercises and tasks that students are exposed to could be a reflection of the goals of their mathematics teacher. Thus, identifying and revealing the arguments for and purposes of mathematics education contributes, among other things, to a healthy and explicit discussion of the reasons and goals of mathematics education among the forces that shape the mathematical education that our students receive. Finally, the discussion preparedness reason which is related to how unusual it is for us, mathematics educators, to explicitly discuss the justification and goals of mathematics education; hence, identifying and discussing these issues would prepare us to hold the same kind of discussion with other actors who may have a genuine interest in – and doubts about – the justification of mathematics education, such as students, parents, educational authorities, politicians, and even colleagues from other disciplines.</p> <p>However, the identification and discussion of the arguments that justify mathematics education and its purposes is not an enterprise free of obstacles. For instance, Ernest ([<reflink idref="bib6" id="ref12">6</reflink>]) claims that there are 'a number of myths and fallacies about mathematics and its teaching which act as obstacles to the clarification of the aims and the justification of mathematics teaching' (p. 36). These myths or fallacies are considered as obstacles because they are a kind of widespread misconception that can contribute to distort the discussion of the justification problem. An example of such myths identified by Ernest ([<reflink idref="bib6" id="ref13">6</reflink>]) is the statement: 'Girls and women generally underachieve at mathematics'. Another complication to address the justification problem in mathematics education is that, usually, the arguments and reasons for mathematics education are tacit and not well defined. As Niss ([<reflink idref="bib14" id="ref14">14</reflink>]) puts it: 'reasons [for mathematics education] are implicit, indirect, fuzzy and vague, and form part of a complex conglomerate of other reasons, societal and group interests, cultural and political ideals, and so on' (p. 12). In sum, if we want to reveal the reasons and arguments that justify the teaching of mathematics in a certain period of time within a given society, it is necessary to engage in an investigative work in which we try to unravel such reasons and arguments – in official documents, in curricular plans, in actual mathematics lessons, in the perceptions of educational and political actors – but it is very likely that in this inquiry process we find myths related to the teaching and learning of mathematics, like those identified by Ernest ([<reflink idref="bib6" id="ref15">6</reflink>]). In this study we decided to focus on a key actor in the teaching-learning process such as the mathematics teacher; in particular, we investigate the arguments that future mathematics teachers provide when they are asked questions related to the justification problem in mathematics education. Thus, the study reported in this article is guided by the two following research questions:</p> <p></p> <ulist> <item> What arguments are invoked by preservice mathematics teachers when they are asked about the justification problem in mathematics education (i.e. why mathematics is taught)?</item> <p></p> <item> Are the arguments put forward by the preservice mathematics teachers constituted by myths related to the teaching and learning of mathematics?</item> </ulist> <p>To clarify how these research questions were empirically addressed, we will later describe the research method followed. Before that we will explain in more detail the concept of myth, and we will introduce some myths reported in the literature and related to the problem of justification in mathematics education, which provide us with a conceptual framework that allows us to identify and classify the myths present in the arguments of the preservice mathematics teachers who participated in the study.</p> <hd id="AN0159177047-3">2. Myths about mathematics, its teaching and learning</hd> <p>Myths are related to the notion of belief (Philipp, [<reflink idref="bib16" id="ref16">16</reflink>]), since myths can be considered as shared beliefs between groups of people. Thus, the study on myths reported here could be framed in the research area of mathematics teachers' beliefs. There are previous studies in this research area on teachers' beliefs about the nature of mathematics (e.g. Ernest, [<reflink idref="bib5" id="ref17">5</reflink>]) and about school mathematics (e. g. Beswick, [<reflink idref="bib2" id="ref18">2</reflink>]), but teachers' beliefs about <emph>why</emph> we teach mathematics remain unexplored. In this research we approach the study of teachers' shared beliefs through the notion of social representation.</p> <p>The concept of social representations was developed to understand the common and everyday knowledge of people about a social object (Moscovici, [<reflink idref="bib13" id="ref19">13</reflink>]). In particular, the common knowledge that is produced by individuals in the social processes of daily life while interacting with others. This notion refers to the representations of reality that are formed and communicated between groups of people. This research is related to the common knowledge about the social object 'mathematics teaching' that is constructed and shared among some preservice teachers.</p> <p>We interpret myths as a kind of social representation (Moscovici, [<reflink idref="bib12" id="ref20">12</reflink>]), as an understanding that a social group has about something considered important or relevant to the group. However, in the case of the myths about the teaching and learning of mathematics, this collective understanding is not completely accurate: as mentioned before, myths are widespread misconceptions about mathematics, its teaching and learning. Paul Ernest ([<reflink idref="bib6" id="ref21">6</reflink>]) even considers them as constituents of a regime of truth, in the sense of Foucault ([<reflink idref="bib7" id="ref22">7</reflink>]); such regimes of truth are produced by discourses that are accepted as truth – although they may not be necessarily true – which are perpetuated without being questioned.</p> <p>Some authors have discussed myths related to the justification of mathematics and its relevance. Next we provide an overview of such myths, which constituted a conceptual framework for the study.</p> <p>Paul Ernest ([<reflink idref="bib6" id="ref23">6</reflink>]) identifies 12 myths associated with mathematics and its teaching which act as obstacles to the clarification of the aims and justification of mathematics teaching. He classifies the myths into four categories:</p> <p></p> <ulist> <item> Myths related to the nature of mathematics and school mathematics (for example, 'Mathematics is a value-free and culture-free set of intellectual tools').</item> <p></p> <item> Myths related to the role of mathematics in society (for example, 'Mathematics is very useful, and more maths skills are needed among the general populace in industrialised societies').</item> <p></p> <item> Myths related to the perceptions of mathematics (for example, 'Mathematical ability is more or less the same as intelligence').</item> <p></p> <item> Myths related to success at school mathematics (for example, 'Failure to achieve success at school mathematics is due to cognitive deficits on the part of the learner').</item> </ulist> <p>Paul Dowling ([<reflink idref="bib4" id="ref24">4</reflink>]), for his part, develops an analysis mainly based on mathematics textbooks where he identifies five myths associated with mathematics: the myth of reference, the myth of participation, the myth of emancipation, the myth of the construction and the myth of cyberspace. However, due to its connection to the justification problem in mathematics education, and because they are reaffirmed and propagated through school mathematics, in our study we only used the first two myths, the myth of reference and the myth of participation.</p> <p>The myth of reference refers to the elevated status assigned to mathematics over other forms of human expression. This myth tends to create a division between intellectual and manual activity, where the former is paradigmatically represented by mathematics and conceptualized as an activity of a higher order than manual tasks. This privileged position gives mathematics the 'right' to generate comments upon other types of activities. In the words of Dowling:</p> <p>it is as if the mathematician casts a knowing gaze upon the non-mathematical world and describes it in mathematical terms. I want to claim that the myth is that the resulting descriptions and commentaries are about that which they appear to describe, that mathematics can refer to something other than itself. I shall refer to this myth as the myth of reference. ([<reflink idref="bib4" id="ref25">4</reflink>], p. 6)</p> <p>Some textbooks reinforce this myth through tasks where mathematics is embedded in settings making reference to a semi-reality (Skovsmose, [<reflink idref="bib18" id="ref26">18</reflink>]), and where mathematics is depicted as underlying many daily non-mathematical situations and as useful for modelling and solving everyday problems – like doing domestic shopping, although often this representation seems forced or even artificial.</p> <p>The myth of participation highlights the usefulness of mathematics for the daily lives of students. According to Dowling ([<reflink idref="bib4" id="ref27">4</reflink>]), this argument about the utility of mathematics helps to justify its existence in the curriculum: 'Mathematics justifies its existence on the school curriculum by virtue of its utility in optimizing the mundane activities of its students. This is the myth of participation' (p. 9). As with the myth of reference, the myth of participation could be reinforced through tasks contained in textbooks where mathematics helps to find the solution to everyday problems, supposedly relevant and familiar to the students.</p> <p>David Kollosche ([<reflink idref="bib11" id="ref28">11</reflink>]) identifies another myth related to mathematics when he analyzes students' responses when questioned about the importance of school mathematics lessons in their lives. The myth is called the myth of importance and refers to the narrative shared among students that the mathematics that they study at school will be useful for them in the future, even if such a future is not clear enough and tangible: 'the goals which justify the educational enterprise in mathematics are positioned in a utopian space which will never be realised' (p. 636). The promise underlying the myth of importance, that mathematics will be important in a future life, can play different roles; for example, it helps alleviate the symptoms of irrelevance that students experience in their mathematics lessons when they ask themselves or their teacher 'what is this useful for?'. Also, it relieves the teacher of the responsibility of providing explanations about the usefulness of mathematics in students' present lives:</p> <p>it is much easier to prophesy that a specific mathematical content will be needed in a distant future than to prove how it promotes cultural competence, an understanding of the world or even critical thinking in the here and now. (p. 641)</p> <p>The overarching nature of the myths of reference and participation identified by Dowling ([<reflink idref="bib4" id="ref29">4</reflink>]) leads to intersections with other myths. For example, the myth identified by Ernest ([<reflink idref="bib6" id="ref30">6</reflink>]) that 'mathematics is very useful, and more maths skills are needed among the general populace in industrialised societies' (p. 37) could be considered as a manifestation of the myth of reference; similarly, the myth of importance proposed by Kollosche ([<reflink idref="bib11" id="ref31">11</reflink>]), where students are promised that mathematics will play an important role in their future lives, could be considered to be a particular case of the myth of participation – although Kollosche ([<reflink idref="bib11" id="ref32">11</reflink>]) argues that the myth of importance 'not only provide[s] the ideological basis on which the learning of mathematics can be legitimised individually, it also erects the boundaries of the relevance discourse' (p. 641). As explained next in the Method section, these intersections between myths posed some difficulties for the categorization of arguments that were overcome with the implementation of an investigator triangulation.</p> <hd id="AN0159177047-4">3. Method</hd> <p>To investigate the arguments around the justification problem in mathematics education, a group of 19 preservice mathematics teachers who voluntarily agreed to participate in the study were interviewed. At the time of conducting the interviews, these preservice teachers were enrolled in a normal school (a teachers' college) located in the State of Mexico, in south-central Mexico. These future teachers receive training based on general knowledge of pedagogy and topics related to the practice of mathematics education, such as lesson planning and classroom practices. This education is intended to prepare high school graduates to become mathematics teachers at the lower secondary level. Several of them come from families where teaching is a tradition, that is, their own parents and close relatives are or have been teachers. The group of participants consisted of ten women and nine men in a 19–22 years age range.</p> <hd id="AN0159177047-5">3.1. Data collection</hd> <p>Semi-structured interviews with preservice mathematics teachers were conducted and audio-recorded as the main empirical data of the study. The participants were informed that the interview data would be used for research purposes and that their participation should be voluntary. The interviews lasted an average of four minutes and were conducted by the first author of the article. The interviews were conducted in a school classroom during the regular class period in the months of November 2017 and February 2018.</p> <p>To conduct the semi-structured interviews, an interview guide was used. The guide for the interviews was tested and refined after a pilot application with a preservice mathematics teacher. During the pilot application it was confirmed that the justification of mathematics is commonly done on utilitarian grounds (Dowling, [<reflink idref="bib4" id="ref33">4</reflink>]; Pais, [<reflink idref="bib15" id="ref34">15</reflink>]), that is, it is argued that mathematics is taught because it is useful. In consequence, the interview guide included questions to delve into the utility argument in the event that it appeared during the interviews. Thus, the final version of the interview guide consisted of two main guiding questions (MQ) and two auxiliary questions (AQ) to deepen the answers to the main questions:</p> <p></p> <ulist> <item> MQ1 – Why teach mathematics?</item> <p></p> <item> AQ1 – Do you think mathematics is important? Why?</item> <p></p> <item> MQ2 – Do you think mathematics is useful? Why?</item> <p></p> <item> AQ2 – Provide an example where mathematics is useful.</item> </ulist> <hd id="AN0159177047-6">3.2. Data analysis</hd> <p>The audio recordings of the interviews were subjected to a two-level analysis. At the first level, a thematic analysis was performed (Braun & Clarke, [<reflink idref="bib3" id="ref35">3</reflink>]) in which the initial generation of codes and the definition of themes was carried out collectively among the authors of the study. Examples of the codes generated during the first level of analysis and related to the usefulness of mathematics are: 'shopping', 'construction', 'decision-making' and 'mental activities'. Through this thematic analysis all the justifications given by the preservice teachers were identified and grouped into themes. For instance, the codes 'shopping' and 'construction' were grouped under the theme 'Mathematics is useful for daily life'. Such themes provide an answer to the first research question and are presented later as categories in the Results section.</p> <p>In the second level of analysis, the categories of myths about mathematics that were identified in the literature (Dowling, [<reflink idref="bib4" id="ref36">4</reflink>]; Ernest, [<reflink idref="bib6" id="ref37">6</reflink>]; Kollosche, [<reflink idref="bib11" id="ref38">11</reflink>]) were used as lenses to try to identify myths in the arguments of the preservice mathematics teachers; the identification of these myths responds to the second research question. An investigator triangulation was implemented (Rothbauer, [<reflink idref="bib17" id="ref39">17</reflink>]), in which each researcher independently tried to identify if any of the arguments provided by the student teachers could be classified as one of the myths associated with the mathematics identified in the literature, namely: the twelve myths identified by Ernest ([<reflink idref="bib6" id="ref40">6</reflink>]), the myths of reference and participation proposed by Dowling ([<reflink idref="bib4" id="ref41">4</reflink>]), and the myth of importance suggested by Kollosche ([<reflink idref="bib11" id="ref42">11</reflink>]). Later, the researchers met to compare their classifications; if there was discrepancy or doubt about how an argument should be categorized, an explicit discussion was organized to reach a consensus on its interpretation. Discrepancies occurred when trying to categorize an argument that could be classified as two different types of myths simultaneously, that is, arguments that stood at the intersection of myths as was mentioned at the end of section 2; however, these discrepancies were not systematic.</p> <hd id="AN0159177047-7">3. Results</hd> <p>The results are presented in two sections. First, the results in answer to the first research question are presented; they refer to the arguments invoked by preservice mathematics teachers when asked a question related to the justification problem in mathematics education. Next, the myths identified in the arguments of the future teachers are explained, in order to answer the second research question. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (<reflink idref="bib1" id="ref43">1</reflink>) mathematics is related to the development of mental or thinking skills, (<reflink idref="bib2" id="ref44">2</reflink>) mathematics is useful for daily life, and (<reflink idref="bib3" id="ref45">3</reflink>) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (<reflink idref="bib1" id="ref46">1</reflink>) the myth of reference, (<reflink idref="bib2" id="ref47">2</reflink>) the myth of participation, (<reflink idref="bib3" id="ref48">3</reflink>) the myth of importance, and (<reflink idref="bib4" id="ref49">4</reflink>) the myth of cognitive development.</p> <hd id="AN0159177047-8">3.1. Arguments invoked by preservice mathematics teachers when asked why teach mathematics</hd> <p>The arguments provided by the prospective teachers when asked about why mathematics is taught can be divided into three main categories: (<reflink idref="bib1" id="ref50">1</reflink>) mathematics is related to the development of mental or thinking skills, (<reflink idref="bib2" id="ref51">2</reflink>) mathematics is useful for daily life, and (<reflink idref="bib3" id="ref52">3</reflink>) mathematics fosters positive attitudes and emotions.</p> <hd id="AN0159177047-9">3.1.1. Mathematics is related to the development of mental or thinking skills</hd> <p>Twelve preservice teachers argue that mathematics is taught because it helps to develop different mental or thinking skills, for example: logical reasoning, reflection, decision-making, creative thinking, spatial intelligence, information processing. The following excerpts from the interviews illustrate this type of argument:</p> <p></p> <ulist> <item> '[Mathematics] develops a great skill within the brain to better understand things, analyze them, and understand them in a better way. [...] This helps us to make a better decision'.</item> <p></p> <item> 'So that students have a better logical reasoning and can better understand cognitive processes, to transit from the concrete to the abstract and to have a better intelligence within the space'.</item> <p></p> <item> 'Adolescents, which is where we focus, they can develop certain skills or certain processes or acquire certain processes or certain cognitive schemes that help them in aspects of their daily lives'.</item> <p></p> <item> '[Mathematics] helps us to process the information better, to have more concrete but well-defined answers'.</item> </ulist> <hd id="AN0159177047-10">3.1.2. Mathematics is useful for daily life</hd> <p>Another frequent argument (mentioned by 17 teachers) is to affirm that mathematics is taught because it is useful for different aspects of daily life. When this argument is deepened and interviewees are asked to provide examples of everyday situations in which mathematics is useful, contexts such as shopping, cooking, personal finances, housing construction and school, are mentioned. This is illustrated next with some interview transcriptions:</p> <p></p> <ulist> <item> 'You use it [mathematics] for responsible purchasing, to manage your own bills, your own personal savings, to save, to quantify your income and expenses'.</item> <p></p> <item> 'When going to buy something, we can do it in a faster way by multiplying how much a piece of clothing costs by the other, and then we have a result'.</item> <p></p> <item> '[Mathematics] is very basic in everyday life, from a merchant to the home life, for example to prepare food'.</item> <p></p> <item> 'If at some point they [the students] go to a shop, they need to add, subtract, even fractions. They should know eh [...] I do not know, to build a house they need volumes, they need areas, they need fractions at some point, they need to be able to get all those calculations [...] so I think it is very important and it is necessary, I believe that this is a good example for the daily life of a student and any other person'.</item> </ulist> <hd id="AN0159177047-11">3.1.3. Mathematics fosters positive attitudes and emotions</hd> <p>Although it did not appear as frequently as the arguments that constitute the two previous categories, five future teachers argued that mathematics is taught because it promotes positive attitudes and emotions:</p> <p></p> <ulist> <item> 'Knowing mathematics helps you as a person, as well as feeling like someone big, someone that many people admire'.</item> <p></p> <item> 'With mathematics secondary students would know a way to multiply faster. They make them skilful and have better attitudes'.</item> </ulist> <hd id="AN0159177047-12">3.1.4. Mathematics is not relevant for everyday life, but ...</hd> <p>It is important to note that two prospective teachers acknowledged that mathematics – or at least part of it – may be irrelevant to students' daily life; however, the same future teachers found a way to solve this gap in the utility argument by providing other arguments about its usefulness, as illustrated in the following transcripts:</p> <p></p> <ulist> <item> 'Maybe they are not so useful for life, to multiply and all that stuff, but [it is useful] to be able to understand things more because we can reason better'.</item> <p></p> <item> 'I am not saying that that everything you see in the school in connection to mathematics is going to be put into practice, but I think that the most basic stuff like arithmetic and algebra, you can use it everywhere'.</item> <p></p> <item> 'It is not that [the student] use it [mathematics] very much in everyday life, it is because it develops her cognitive processes'.</item> <p></p> <item> 'If I teach them trigonometric functions, it is not that they are going to apply them at home or somewhere, but that knowledge allows them to advance in their academic education, then it is not that they are [mathematics] absolutely applicable, but yes, they are useful'.</item> <p></p> <item> 'Often the problems that arise in school are fictitious, but if we really transpose them to real life, we may not use them that way, but we do use the experience we already had by solving this problem, when solving another problem that maybe is not completely mathematical, but it does require those skills'.</item> </ulist> <hd id="AN0159177047-13">3.2. Are the arguments put forward by the preservice mathematics teachers constituted by myth...</hd> <p>Some of them are. In particular, the presence of the following myths was identified in the preservice teachers' arguments: (<reflink idref="bib1" id="ref53">1</reflink>) the myth of the reference, (<reflink idref="bib2" id="ref54">2</reflink>) the myth of participation, (<reflink idref="bib3" id="ref55">3</reflink>) the myth of importance, and (<reflink idref="bib4" id="ref56">4</reflink>) the myth in which mathematical ability is considered to be more or less the same as intelligence. In the following, each of the identified myths will be illustrated with transcripts from the interviews.</p> <hd id="AN0159177047-14">3.2.1. The myth of reference</hd> <p>The idea that mathematics is a discipline with an elevated status – a status of omnipresence and almost omnipotence – is present in all the preservice teachers involved in this study. During the interviews the idea that mathematics can function as a commentator of other less elevated disciplines was manifested.</p> <p></p> <ulist> <item> 'Mathematics is related to everything we do. If we want to see it from the school perspective, then mathematics is related. For example [...] in a poem it must have a sequence in the verses, and in the prose and everything. If we see it from [the point of view of] science and biology then all the chemical components and all that'.</item> <p></p> <item> 'Mathematics is everything. That's why everything was built. It is the reason why we can have a world like this one. It is the origin of everything'.</item> <p></p> <item> 'When I started to play an instrument, I did not know what fractions were, but they were giving me an idea, I had to go on counting, then I said "OK, I'm going to count" and they told me later: "did you know that they are fractions? Did you know that you are using fractions?"'.</item> </ulist> <hd id="AN0159177047-15">3.2.2. The myth of participation</hd> <p>Seventeen teachers refer to the usefulness of mathematics to make the mundane life of students more efficient. This type of beliefs can be considered as part of the myth of participation:</p> <p></p> <ulist> <item> 'Well, I've always considered that, in everyday life, something that students apply a lot is the fourth proportional. And it can be applied, I mean, from the simple, when we go to the shop [...] I think that topic is the one that helps students the most in their daily life'.</item> <p></p> <item> 'If mathematics is present in decision-making, the student develops himself more, and he makes good decisions in his daily life'.</item> </ulist> <hd id="AN0159177047-16">3.2.3. The myth of importance</hd> <p>The prophecy that mathematics will play an important role in the future life of students manifested itself in some of the arguments of five future mathematics teachers. David Kollosche ([<reflink idref="bib11" id="ref57">11</reflink>]) states that this promise that mathematics will be useful in a non-tangible future is the basis of the myth of importance. The following transcripts suggest the presence of such a myth in the arguments:</p> <p></p> <ulist> <item> 'Yes, yes, mathematics is very useful, I can give you an example from class. This, a student I asked me: "teacher, why are mathematics useful?". I simply asked him: "what do you want to study?", "I want to be an industrial engineer, I want to be this", "then it is necessary to use mathematics to be able to excel at it"'.</item> <p></p> <item> 'Mathematics is essential for life. Every day it is used. You can find mathematics in any aspect of your life, you will study it throughout your education'.</item> <p></p> <item> 'Students throughout their lives, whenever they are, always are going to use mathematics'.</item> <p></p> <item> 'Our students may want to continue pursuing a degree, and a degree requires mathematical knowledge'.</item> </ulist> <hd id="AN0159177047-17">3.2.4. The myth in which mathematical ability is considered to be more or less the same as in...</hd> <p>As illustrated by the interview transcripts presented in the section 'Mathematics is related to the development of mental or thinking skills', there is a tendency among preservice teachers to suggest that studying mathematics produces different cognitive gains in students, such as logical reasoning, creative thinking, spatial intelligence, etc. – which is an unfounded claim that is not necessarily true. Twelve teachers expressed this idea during the interviews.</p> <hd id="AN0159177047-18">4. Discussion</hd> <p>We have inquired into the arguments that preservice mathematics teachers provide when they are asked about why mathematics is taught, that is, when they are asked about the justification problem in mathematics education. The results show that preservice teachers' arguments can be grouped into two main categories: (<reflink idref="bib1" id="ref58">1</reflink>) mathematics is taught because mathematics is related to the development of mental or thinking skills, and (<reflink idref="bib2" id="ref59">2</reflink>) mathematics is taught because it is useful for daily life. Only a small proportion of teachers argue that mathematics is taught because it promotes positive attitudes and emotions.</p> <p>The claim that the study of mathematics develops a myriad of cognitive abilities in the individual can be contentious. First of all, what mathematics are referring to? Do all mathematics produce those cognitive gains? What evidence is used as a basis for making this kind of statement? The alleged correlation between the study of mathematics and the development of cognitive abilities seems to be a social representation, an idea shared among several future mathematics teachers that, as we will argue later, could constitute a myth about the teaching of mathematics.</p> <p>The results of this study coincide with those obtained by David Kollosche ([<reflink idref="bib11" id="ref60">11</reflink>]) in the sense that practically all of the prospective mathematics teachers interviewed 'stick to the narrative of the general relevance of mathematics for life' (p. 638) when trying to argue why mathematics is taught. In addition, just like the examples proposed by the students participating in the study by Kollosche ([<reflink idref="bib11" id="ref61">11</reflink>]), the examples of useful of mathematics in daily life provided by the preservice teachers are reduced to a small set of activities – shopping, cooking, managing personal finances, building houses – where only elementary mathematics is used, or practically no mathematics is used at all, as in the case of the shopping situations in which the payment systems are increasingly automated, thus reducing the need to perform arithmetic calculations.</p> <p>It is important to note that there was a faction of the preservice teachers who seemed to catch a glimpse of the irrelevance of mathematics in students' daily life when they acknowledged that mathematics may not be as relevant as expected. However, as a kind of defense mechanism that is activated in such situations, these preservice teachers found ways to continue justifying the relevance of mathematics teaching: they talked about the cognitive advantages that mathematics supposedly produces, or about the important role mathematics will have in the future education of the students. This mechanism can be associated with the process of <emph>anchoring</emph> described in the theory of social representations, through which new ideas or phenomenon – including those problematic or troubling – are related to a well-known phenomenon or context in order to make sense of them (Höijer, [<reflink idref="bib9" id="ref62">9</reflink>]). Kollosche ([<reflink idref="bib11" id="ref63">11</reflink>]) identifies a similar mechanism in students when they perceive the potential irrelevance of mathematics for their own lives. He interprets this mechanism as an ideological patch with specific functions: 'on the one hand [it] covers the symptoms of irrelevance and allow[s] the students to enjoy mathematics in the hope of a bright but opaque future' (p. 638). Perhaps in the case of preservice teachers this ideological patch has a similar function. It allows them to ignore the potential irrelevance of mathematics for their students, and thus continue with their preparation as a mathematics teacher without experiencing concerns or doubts about the possible irrelevance of mathematics.</p> <p>We also inquired whether the arguments for the relevance of mathematics teaching put forward by the prospective teachers were constituted by myths. Evidence was found of the presence of four myths in their arguments: the myth of relevance, the myth of participation, the myth of importance, and the myth of cognitive development.</p> <p>There is a widespread presence of the myth of reference among the preservice teachers who participated in this study. On the one hand, no preservice teacher questioned the relevance of mathematics – not even those who catch a glimpse of its potential irrelevance – and many of them assigned it a high status that is reflected in affirmations such as 'Mathematics is everything. That's why everything was built. It is the reason why we can have a world like this one. It is the origin of everything'. Mathematics is perceived as a higher form of thought, which allows us to free ourselves from less desirable forms of thought – like intuition – as mentioned in the following argument from one of the interviewees: '[Mathematics] allows us to quantify phenomena that we know or we access to by simple intuition [...] once you quantify it you can make decisions that are based on a quantification and not on an intuition'.</p> <p>Although not as widespread as the myth of reference, the myth of participation also emerged in some of the student teachers' arguments when they asserted that mathematics is useful for the daily life of students. The examples that support these arguments are questionable – like the claim that the fourth proportional is the mathematical notion that 'helps students most in their daily lives' – and ignore the criticisms that have been made about the use-value argument (Pais, [<reflink idref="bib15" id="ref64">15</reflink>]), such as the difficulty of transferring knowledge that is learned in school to non-school contexts (Jurdak, [<reflink idref="bib10" id="ref65">10</reflink>]).</p> <p>This study confirms the existence of the myth of importance identified by Kollosche ([<reflink idref="bib11" id="ref66">11</reflink>]) in students. As previously shown, several teachers use a discourse in which it is promised that mathematics will play a role in the future life of students. The fact that this myth is present in both students and future teachers could be an indication of the important role it plays in alleviating the symptoms of the irrelevance of mathematics that students and teachers may experience.</p> <p>Another myth identified is called the myth of cognitive development, which is closely related with one of the myths identified by Paul Ernest ([<reflink idref="bib6" id="ref67">6</reflink>]) in which 'mathematical ability is more or less the same as intelligence' (p. 37). This myth presumes an almost direct correlation between the study of mathematics and the development of certain mental or thinking skills; however, there is no conclusive scientific evidence to show that this is the case. Although cognitive science has advanced in determining the brain areas that are activated during different mathematical activities, like analyzing equations or evaluating the validity of a mathematical statement (e. g. Amalric & Dehaene, [<reflink idref="bib1" id="ref68">1</reflink>]; Zeki et al., [<reflink idref="bib19" id="ref69">19</reflink>]), the evidence gathered is not enough to support the assertions related with this myth.</p> <p>We believe that there is still much work to be done to understand the scope and the different traits of the justification problem in mathematics education. In this study we have focused on analyzing the arguments of future mathematics teachers about this problem, but teachers are not the only actors associated with this problématique. It is possible to develop a research programme that makes use of different methodological and theoretical approaches, focusing on revealing and analyzing the arguments that different agents – politicians, parents, educational authorities, curricular plans, textbooks, etc. – put forward to justify the teaching of mathematics in a particular society. The theoretical approach adopted in this study would allow us to consider different social actors, from varied cultures and backgrounds, but sharing different social representations about the teaching of mathematics to a greater or lesser extent.</p> <p>In the case of the preservice mathematics teachers who participated in this study, it is important that they become aware of the existence of myths in their arguments; it is important to understand why they are considered myths, and what their implications are. A didactic intervention focused on expanding the knowledge of prospective mathematics teachers about the myths associated with the justification problem could contribute to develop a <emph>political conocimiento</emph> (Gutiérrez, [<reflink idref="bib8" id="ref70">8</reflink>]), which ultimately affects in a positive way the mathematical education that our students receive.</p> <hd id="AN0159177047-19">Disclosure statement</hd> <p>No potential conflict of interest was reported by the authors.</p> <ref id="AN0159177047-20"> <title> References </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113 (18), 4909 – 4917. https://doi.org/10.1073/pnas.1603205113</bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">2</bibl> <bibtext> Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in Mathematics, 79 (1), 127 – 147. https://doi.org/10.1007/s10649-011-9333-2</bibtext> </blist> <blist> <bibl id="bib3" idref="ref3" type="bt">3</bibl> <bibtext> Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3 (2), 77 – 101. https://doi.org/10.1191/1478088706qp063oa</bibtext> </blist> <blist> <bibl id="bib4" idref="ref7" type="bt">4</bibl> <bibtext> Dowling, P. (1998). The sociology of mathematics education. Mathematical myths/pedagogic texts. The Falmer Press.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref17" type="bt">5</bibl> <bibtext> Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249 – 254). Falmer.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref8" type="bt">6</bibl> <bibtext> Ernest, P. (1998). The justification problem in mathematics education. In J. H. Jensen, M. Niss, & T. Wedege (Eds.), Justification and enrolment problems in education involving mathematics or physics (pp. 33 – 55). Roskilde University Press.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref22" type="bt">7</bibl> <bibtext> Foucault, M. (1980). Power/knowledge. Selected interviews & other writings (1972–1977). Pantheon Books.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref70" type="bt">8</bibl> <bibtext> Gutiérrez, R. (2013). Why (urban) mathematics teachers need political knowledge. Journal of Urban Mathematics Education, 6 (2), 7 – 19. https://doi.org/10.21423/jume-v6i2a223</bibtext> </blist> <blist> <bibl id="bib9" idref="ref62" type="bt">9</bibl> <bibtext> Höijer, B. (2011). Social representations theory. A new theory for media research. Nordicom Review, 32 (2), 3 – 16. https://doi.org/10.1515/nor-2017-0109</bibtext> </blist> <blist> <bibtext> Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world, situated, and school contexts. Educational Studies in Mathematics, 63 (3), 283 – 301. https://doi.org/10.1007/s10649-005-9008-y</bibtext> </blist> <blist> <bibtext> Kollosche, D. (2017). The ideology of relevance in school mathematics. In A. Chronaki (Ed.), Mathematics education and life at times of crisis. Proceedings of the Ninth international mathematics education and society conference (pp. 633 – 644). University of Thessaly Press.</bibtext> </blist> <blist> <bibtext> Moscovici, S. (2000). Social representations. Explorations in social psychology. Polity Press.</bibtext> </blist> <blist> <bibtext> Moscovici, S. (2004). La psychanalyse, son image et son public [The psychoanalysis, its image and its public]. Presses Universitaires de France.</bibtext> </blist> <blist> <bibtext> Niss, M. (1996). Goals of mathematics teaching. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 499 11 – 47). Kluwer.</bibtext> </blist> <blist> <bibtext> Pais, A. (2013). An ideology critique of the use-value of mathematics. Educational Studies in Mathematics, 84 (1), 15 – 34. https://doi.org/10.1007/s10649-013-9484-4</bibtext> </blist> <blist> <bibtext> Philipp, R. A. (2007). Mathematics teachers' beliefs and affect. In F. K. Lester, Jr. (Ed.), Second Handbook of research on mathematics teaching and learning (pp. 257 – 315). Information Age Publishing.</bibtext> </blist> <blist> <bibtext> Rothbauer, P. M. (2008). Triangulation. In L. M. Given (Ed.), The Sage encyclopedia of qualitative research methods (pp. 892 – 894). Sage.</bibtext> </blist> <blist> <bibtext> Skovsmose, O. (2001). Landscapes of investigation. Zentralblatt für Didaktik der Mathematik, 33 (4), 123 – 132. https://doi.org/10.1007/BF02652747</bibtext> </blist> <blist> <bibtext> Zeki, S., Romaya, J. P., Benincasa, D. M. T., & Atiyah, M. F. (2014). The experience of mathematical beauty and its neural correlates. Frontiers in Human Neuroscience, 8, 68. https://doi.org/10.3389/fnhum.2014.00068</bibtext> </blist> </ref> <aug> <p>By Alberto López-López; Mario Sánchez Aguilar and Apolo Castaneda</p> <p>Reported by Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib14" firstref="ref9"></nolink> <nolink nlid="nl2" bibid="bib16" firstref="ref16"></nolink> <nolink nlid="nl3" bibid="bib13" firstref="ref19"></nolink> <nolink nlid="nl4" bibid="bib12" firstref="ref20"></nolink> <nolink nlid="nl5" bibid="bib18" firstref="ref26"></nolink> <nolink nlid="nl6" bibid="bib11" firstref="ref28"></nolink> <nolink nlid="nl7" bibid="bib15" firstref="ref34"></nolink> <nolink nlid="nl8" bibid="bib17" firstref="ref39"></nolink> <nolink nlid="nl9" bibid="bib10" firstref="ref65"></nolink> <nolink nlid="nl10" bibid="bib19" firstref="ref69"></nolink>
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  Data: Why Teach Mathematics? -- A Study with Preservice Teachers on Myths around the Justification Problem in Mathematics Education
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  Data: <searchLink fieldCode="AR" term="%22López-López%2C+Alberto%22">López-López, Alberto</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-1745-4266">0000-0002-1745-4266</externalLink>)<br /><searchLink fieldCode="AR" term="%22Aguilar%2C+Mario+Sánchez%22">Aguilar, Mario Sánchez</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-1391-9388">0000-0002-1391-9388</externalLink>)<br /><searchLink fieldCode="AR" term="%22Castaneda%2C+Apolo%22">Castaneda, Apolo</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-7284-8081">0000-0002-7284-8081</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Mathematical+Education+in+Science+and+Technology%22"><i>International Journal of Mathematical Education in Science and Technology</i></searchLink>. 2022 53(8):2102-2114.
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  Data: Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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  Data: 10.1080/0020739X.2020.1864489
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  Data: In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within such arguments. The study is based on semi-structured interviews with 19 preservice mathematics teachers from Mexico. The results show that the arguments of the future teachers to justify the teaching of mathematics can be divided into three categories: (1) mathematics is related to the development of mental or thinking skills, (2) mathematics is useful for daily life, and (3) mathematics fosters positive attitudes and emotions. On the other hand, a presence of myths was identified in the arguments of the prospective teachers, namely: (1) the myth of reference, (2) the myth of participation, (3) the myth of importance, and (4) the myth of cognitive development. The report concludes by discussing the results and pointing out some future research routes.
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