Bringing Numbers to Life: a Study in Synaesthetes’ Relationship to Mathematics

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Malmö Högskola

Matematik och Lärande

Natur, Miljö, Samhälle

Examensarbete

15 högskolepoäng

Bringing Numbers to Life: a Study in

Synaesthetes’ Relationship to Mathematics

När talen får liv: en studie i synesteters relation till matematik

Kim Granvik

Lärarexamen 270 poäng Matematik och lärande

Examinator: Per Schubert

Examineringsdatum: 2013-12-20 Handledare: Tamsin Meaney

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Abstract

Synaesthesia is a phenomenon where several senses and impressions interact, for example numbers may appear in colour. There has been some research on the consequences of number synaesthesia, but the purpose of this paper is to investigate the synaesthetes’ own experiences. Using qualitative interviews, I focus on three major areas in relation to synaesthetes’ personal perspective: synaesthesia and cognition; synaesthesia and emotions, attitudes and identity; and synaesthesia and mathematics. The results suggest that synaesthetes can relate to what some research has shown about how synaesthesia works, but that people’s individuality must always be kept in mind.

Abstrakt

Synestesi är ett fenomen där flera sinnen och intryck samspelar, till exempel kan siffror upplevas i färg. En del forskning har gjorts kring konsekvenserna av siffer-synestesi, men syftet med den här uppsatsen är att undersöka synesteters egna upplevelser. Med hjälp av kvalitativa intervjuer fokuserar jag på tre huvudområden i relation till synesteters personliga perspektiv: synestesi och kognition; synestesi och känslor, attityder och identitet; och synestesi och matematik. Resultaten tyder på att synesteter kan relatera till vad en del forskning har visat angående hur synestesi fungerar, men att människors individualitet alltid måste has i åtanke.

Key words:

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1. Introduction

There are many different things that can affect a person’s view on mathematics, both on an emotional and a cognitive level. I was about twenty years old and had already been in mathematics teacher education for a year when I realized I had a form of synaesthesia: I perceived numbers, and certain letters, words and shapes, in colour. Thinking about it, I realized that I had always had this “additional sense”, but I had not paid any attention to it and had therefore been unaware that I had it. Yet I also realized that it had always affected me, and the way I viewed numbers and letters, subconsciously. I remembered, for example, how I had always experienced it as strange that three times eight equals twenty-four, and now I could see that this feeling probably had something to do with the colours I have always subconsciously associated with those numbers; it felt illogical to me that something bright red could come out of something green and blue. Similarly, I understood that the reason I had confused the city of Lund with the city of Ystad well into my late teens, was probably because I perceive both their names as a clear beige. As I started paying attention to the colours I associated with different numbers, shapes, letters and words, I began to better understand why I viewed certain numbers and parts of mathematics the way I did. On the whole, it was a positive experience, and my relationship to mathematics and numbers became richer with this new understanding. Then it started to make me frustrated that I had not realized this feature in myself sooner, and I wondered if it would have made my mathematics studies in school even richer if I had then been fully aware that I was synaesthetic.

After I myself became aware of my synaesthesia and I realized how much richer my mathematical identity and my relationship to mathematics and numbers became once I started to understand my synaesthetic perceptions, I began to wonder if other people had had similar experiences. But before I could start investigating other synaesthetes’ perceptions and form a research question, I felt that I needed to find out more about how synaesthesia works and what research has shown to be the consequences of number synaesthesia.

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2. Background

Here I present previous research on synaesthesia and its consequences in order to narrow down my area of interest. I also discuss attitudes towards synaesthesia, and mathematical identity.

2.1. What is Synaesthesia?

Ramachandran and Hubbard wrote in 2001 that synaesthesia “is still sometimes dismissed as bogus” (p. 4). In their article, they present a list of what they claim are common arguments as to why synaesthesia should not be considered a real thing; for example, it has been argued that synaesthetes are drug addicts, have a very vivid imagination, or are simply remembering early childhood memories of seeing coloured numbers and letters. Ramachandran and Hubbard (2001) then present arguments why these claims do not hold, among other things questioning why only a handful of people would appear to be remembering these alleged childhood memories. In this section, further evidence is provided from previous research that synaesthesia is a real phenomena.

2.1.1. Experiencing Synaesthesia

Synaesthesia is usually described as a phenomenon, experienced by some people, where a certain sensory impression (such as sounds, writings, or touch) triggers the experience of an additional impression (such as colours, geometrical shapes, or tastes) (Mills 1999; Ramachandran & Hubbard 2001; Cohen Kadosh, Tzelgov & Henik 2005; Mächler 2009; Ghirardelli, Mills, Zilioli, Bailey & Kretschmar 2010; Cawley 2010; Simner 2012; Ward 2012). Simner (2012) and Ward (2012) refer to the trigger impression as the “inducer” while calling the additionally experienced impression the “concurrent”, citing Grossenbacher and Lovelace (2001) as the founders of these terms. The synaesthetic experiences are also referred to as “photisms” (Ghirardelli et al. 2010) and come automatically, without the synaesthete being able to consciously control it (Mills 1999; Cohen Kadosh et al. 2005). It is important to note that a synaesthetic impression does not replace the inducer, it is merely an

additional impression (Simner 2012; Ward 2012). Synaesthetic experiences have been

compared to looking through a window pane; you can see what is beyond the glass, but you can also see your own reflection in it (Mächler 2009).

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Many different forms of synaesthesia have been reported; according to Simner (2012), the latest count is 61. Relevant for this paper are the types of synaesthesia that have to do with numbers; that is to say, when the inducer is a number. To some people, numbers take on a specific colour. Ghirardelli et al. (2010) refer to this as “colour-digit synaesthesia”, although Ward (2012) and Ramachandran and Hubbard (2001) include numbers and letters together in what they call colour synaesthesia”. In this paper, I use the term “grapheme-colour” for synaesthesia with coloured numbers and letters and “number-“grapheme-colour” for synaesthesia with coloured numbers. I am not using Ward’s version “colour-digit” because most authors appear to place the inducer first in the different synaesthesia labels. There can also be a difference between numbers and digits, which I will be discussing later, and this is another reason for using the term “number” rather than “digit”. Another form of synaesthesia related to numbers is “OLP” (ordinal linguistic personifications), which means that linguistic elements, such as numbers, letters, or days of the week, are perceived as having sexes and personalities (Simner 2012). There is also “number-form synaesthesia”, where numbers are perceived as having fixed positions in space relative to each other and/or to the synaesthete’s body (Gertner, Henik & Cohen Kadosh 2009; Ward 2012). Previous research, presented by Gertner et al. (2009), has shown that non-synaesthetes also use some kind of inner number-line representation when comparing numbers; test participants are normally quicker to tell which one out of two numbers is the numerically larger one if the numerical distance between them is bigger, which suggests they think of the numbers as having positions on a line. However, non-synaesthetes seem to be creating this number line subconsciously and can adapt it to the purpose of the situation – for example imagining the numbers arranged circularly when dealing with clocks – while synaesthetes consciously always perceive the same spatial representation when handling numbers.

A notable thing is that synaesthetes appear to agree on concurrents “more than would be expected by chance” (Ward 2012, p. 63). For example, synaesthetes who perceive letters as coloured often perceive A as red (Mächler 2009; Ward 2012) and for those who see numbers in colour, the colours tend to get darker the larger the number’s numerical value is (Ward 2012). This fact can be seen as one argument for why synaesthesia is not simply “bogus”.

According to Mills (1999), the most common form of synaesthesia is “coloured hearing” (p. 181), meaning that the inducer is a sound and the concurrent is a colour. However, the general opinion seems to have changed since this article was conducted. Ramachandran and Hubbard (2001) claim that grapheme-colour is the most common form and Simner (2012) supports this, presenting a number of sources suggesting that 88% of all synaesthetic inducers

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are linguistic. Ward (2012) also agrees with this, saying that “[t]he most common synesthetic inducers are linguistic in nature [and t]he most common synesthetic concurrents are visual in nature” (p. 51). From this, it can be concluded that number-colour synaesthesia is probably among the more common types. How common synaesthesia in general is, though, remains an unanswered question; Ramachandran and Hubbard (2001) present two different studies giving numbers as far apart as 1 person in 20,000 and 1 in 20, while claiming that their own findings suggest 1 in 200. Cawley (2010) presents two other studies, one saying synaesthesia occurs in 1 person out of 25,000 and another saying 1 in 22. Cawley (2010) suggests that the great variety in numbers may be the cause of different definitions of synaesthesia.

2.1.2. Defining Synaesthesia

The word “synaesthesia” originates from the Greek syn and aisthesis or aesthesia, which translates to “union” or “joining” and “senses” or “sensation” (Mills 1999; Simner 2012). However, a more precise definition of synaesthesia remains a matter of debate. One of the most fundamental criteria to determine if a person has synaesthesia has for a long time been consistency over time; people are asked about their concurrents and then asked again at a later occasion (Simner 2012; Ward 2012). Synaesthetes tend to be 80-100% consistent (Simner 2012; Ward 2012), while controls are 20% consistent according to Simner (2012), or 30-50% consistent according to Ward (2012). In other words: if people show high enough consistency with their photisms, they are classified as synaesthetes. Although, Simner (2012) claims that there is a grey area of people who say they have synaesthetic experiences, but are not consistent enough to be statistically classified as synaesthetes, and she questions whether consistency is a reliable method for determining synaesthesia in a person.

Part of the discussion about synaesthesia seems to focus on whether synaesthesia is sensory or conceptual. Ramachandran and Hubbard (2001) argue that their “psychophysical experiments were the first to prove conclusively that synaesthesia is a genuine sensory phenomenon” (p. 27), although they also mention that cognition probably has some influence on how synaesthetes perceive things. Ward (2012), on the other hand, suggests that “[s]ynaesthesia could be regarded as an example of an individual difference in cognition” (p. 51) and that we should study it not only to understand synaesthesia itself, but we should also use it “as a tool to understand cognition more generally” (p. 69). Ghirardelli et al. (2010) also claim that studying synaesthesia can help develop “theories of cognition and perception” (p. 176).

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Simner (2012) criticises the common definition of synaesthesia as a “merging of the senses” and instead suggests a definition based on neurological foundations, rather than behavioural ones. Using letter-colour synaesthesia as an example, Simner (2012) asks the question whether it is the concept or the physical shape of a specific letter that triggers the experience of a colour. She presents research suggesting it is mainly the concept (for example, changing the font of a letter does not seem to change synaesthetes’ colour perception of it), which indicates that synaesthetic experiences are based on cognition, rather than sensory experiences. Other research supports this hypothesis. For example, Mills (1999) studied a person who experienced colours for numbers, both when the numbers were spoken and when they were presented in writing. Mills (1999) argues that this suggests the synaesthetic experience is “based on a ‘concept’ of a digit rather than the actual physical stimulus” (p. 189). There are, however, findings suggesting that the visual features seem to play a certain part; grapheme-colour synaesthetes tend to perceive graphemes of similar shapes (e.g. 3 and E) as having similar colours (Simner 2012). However, a further argument that synaesthesia is mainly linked with cognition is that number synaesthetes have reported that their synaesthetic experiences are linked to the decimal system (Mills 1999; Ward 2012); for example, only the numbers 0-9 tend to have unique colours, while numbers with two or more digits have colours that are a combination of the single digits (Mills 1999; Ward 2012).

On the subject of neurology, Simner (2012) presents several sources saying that letter-colour synaesthetes show activity in the brain’s letter-colour section when processing linguistic elements. Ramachandran and Hubbard (2001) argue that number-colour synaesthesia is caused by a cross-wiring between the brain areas that recognize colours and graphemes, which are located right next to each other. Synaesthetes show a different brain activity than control participants when stimulated with common inducers (Ramachandran & Hubbard 2001; Ward 2012, Cohen Kadosh et al. 2005); even trained controls, who have been taught to connect numbers with different colours, have not shown the same brain activity as synaesthetes (Cohen Kadosh et al. 2005).

In summary, it can be concluded from the research presented above that synaesthesia is indeed a real phenomenon, which can be explained neurologically.

2.2. Consequences of Number Synaesthesia

Several researchers have made different types of experiments to examine how synaesthesia affects a person’s ability to handle numbers. One of these types of experiments consists of a

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modified “Stroop test”. In the original Stroop test, participants are being shown colour names printed in colours that are either congruent or incongruent to the word’s meaning (e.g. the word GREEN printed either in green or another colour, like yellow) (Mills 1999; Cohen Kadosh et al. 2005; Ward 2012). When asked to name the colour, ignoring the written word, participants have proven to be slower when the colour is incongruent to the word (Mills 1999; Cohen Kadosh 2005). In a synaesthetic Stroop test, participants deal with coloured numbers.

Mills (1999) made a case study, exposing a 22-year old with various forms of synaesthesia, among them number-colour, to a modified Stroop test, where she was presented with numbers printed in black or in colours either congruent or incongruent to her personal synaesthetic impressions and was asked to name either colour or digit. Mills (1999) explained that since the subject saw the colours of the printed figures as well as perceiving her synaesthetic colours, she experienced a conflict when the two colours did not match, and this caused her to respond slower during mismatched conditions.

Ghirardelli et al. (2010) aimed to extend the experiment done by Mills (1999), along with others, which all suggest that synaesthesia affects a person’s ability to process numbers. Using one-digit numbers only, Ghirardelli et al. (2010) presented a 21-year-old synaesthetic subject (who appears to be the same person used in a study by Mills et al. 2009, although if the authors have any specific reason for using the same person, they do not give it) and different control groups of the same age with a number of simple arithmetic equations and asked the subjects to determine whether each equation was true or false. The numbers were either black, coloured according to the synaesthetic subject’s perceptions, or coloured incongruently to these. It turned out that the synaesthete usually responded quicker, and with higher accuracy, when the digits where coloured according to her synaesthetic perceptions, while the control groups were better with black digits. The authors point out that the results agree with previous research and help to confirm the theory that synaesthesia does affect the processing of numbers, and that the study “serves to remind us how dynamic synesthesia can be” (p 188).

Cohen Kadosh et al. (2005) present further research that has shown that synaesthetes are slower at naming the colour of a coloured grapheme if the actual colour is incongruent with their own perceived one. They further claim that there have been no reports on whether colours can evoke numbers in synaesthetes, the same way that numbers evoke colours. However, with an experiment of their own, Cohen Kadosh et al. (2005) show that

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synaesthesia is not completely unidirectional; seeing a colour can actually, as they say, “influence numerical cognition in synesthetes” (p. 1770).

In an experiment by Gertner et al. (2009), three number-form synaesthetes with different spatial representations of numbers, along with two control groups, were presented with pairs of figures presented horizontally or vertically to each other and were asked to determine which of the figures had the highest numerical value. The figures’ positions in relation to each other were either congruent or incongruent; congruence for non-synaesthetic control groups meant – based on previous research – that figures with a higher numerical value were positioned to the right of, or above, the other figure, while congruence for the synaesthetic subjects was individually adapted according to their perceptions. Gerter et al (2009) explain “the distance effect”: people have proven to respond quicker when asked which of two figures have the highest numerical value if the numerical distance between the digits is bigger. According to Gertner et al. (2009), the distance effect has, by many, been argued to prove the theory that everyone has an inner mental number line, while others argue that it does not. However, the experiment made by Gertner et al. (2009) revealed that the synaesthetes showed tendency to a distance effect only when the figures appeared congruently to their own perceptions (two of the three also showed a noticeable difference in response time, responding faster when the numbers’ positions were congruent to their perceptions), while the control groups always showed a tendency at a distance effect – this despite the fact that one of the control groups was English and the other Hebrew, meaning that whether the control subjects normally read from left to right, or from right to left, did not seem to make a difference. The authors state that the results show how it can be difficult for number-form synaesthetes to adapt their spatial number representations, and that possible consequences may include difficulties to perform a vertical multiplication if the person has a horizontal number representation.

2.3. Attitudes towards Synaesthesia

In the articles I have read for this paper, I have seen various attitudes towards synaesthesia reflected in the language of the authors. This is important to discuss in relation to my research question regarding synaesthetes’ own thoughts about their synaesthesia and its effect upon their relationship to mathematics.

Cawley (2010) shows what appears to be a very positive view of synaesthesia, calling it a little known type of “giftedness” (p. 574) and emphasizing the importance of discovering

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synaesthetic children and helping them to develop their synaesthetic senses. Mächler (2009), being a synaesthete himself, talks about synaesthesia as a part of one’s identity and points out how important it is that people know about synaesthesia, while giving a lot of personal thoughts and experiences. Mills (1999) also shows a relatively positive attitude in her article, calling synaesthesia “an interesting and important topic” and using the neutral word “phenomena” when referring to it (p. 181).

However, others display what could be interpreted as a more negative attitude. Ward (2012) twice uses the word “difference”, saying that synaesthesia is “an individual difference in cognition” (p. 51), and that synaesthetic experiences are caused by “functional and structural differences within the brain” (p. 58). The word “difference” might seem neutral and harmless at first, until the question is asked: “different from whom?” The answer would probably be “different from the majority” or perhaps “different from the ones expected to read this article”. Ward may of course not have a negative attitude towards synaesthesia, but I argue that labelling something as “different” is not far from labelling it “abnormal” and this might lead the reader to think about synaesthesia in a negative way. “Different” also connotes the feeling that “there are ordinary people, and then there are synaesthetes”.

The most extreme case when it comes to a negative attitude against synaesthesia being reflected through the language is Ramachandran and Hubbard (2001), who call synaesthesia “a curious condition in which an otherwise normal person experiences sensations in one modality when a second modality is stimulated” (p. 4, my emphasis). Once again, Ramachandran and Hubbard (2001) may not think about synaesthesia as a negative thing, but I feel it necessary to point out how their language can be interpreted in a way that makes the reader think synaesthesia is to be viewed as something abnormal and undesirable. The words “otherwise normal” are used by Ramachandran and Hubbard (2001) at one more point to describe synaesthetes (p. 16). These words undoubtedly hide the claim that synaesthesia is something abnormal. Reading the word “normal” as something that is a part of majority, this is not an untrue claim about synaesthesia; however, I claim that with our cultural meaning of the word “abnormal”, it does not only refer to something that stands outside majority, but to something that is unnatural and undesired. I would also like to point out a few other choices of words that Ramachandran and Hubbard (2001) make: at one point, they say “synaesthesia and certain other neurological disorders” (p. 5, my emphasis), which could clearly be interpreted as indicating that synaesthesia is to be considered a disorder. When discussing the neurological causes of grapheme-colour synaesthesia, Ramachandran and Hubbard (2001)

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adult’s, thereafter arguing that grapheme-colour synaesthesia might be the result of these connections enduring as the child grows up, due to “a failure of pruning (or stabilization) of these prenatal pathways” (p. 10, my emphasis). They also claim that synaesthesia is caused by “a mutation causing defective pruning and cross-activation” (p. 28, my emphasis). With the words Ramachandran and Hubbard (2001) choose to use, it could easily be interpreted that synaesthesia is to be viewed as a defect, an undesired abnormality, proof that the brain failed to develop correctly.

Since other people’s attitudes can be important – critical, even – for the shaping of our own, I believe it is important to keep the above in mind when discussing synaesthesia as part of one’s identity.

2.4. Belonging in the Mathematics Classroom

I regard my synaesthesia as part of my identity, and in particular as part of my mathematical identity, but I have never heard of synaesthesia being mentioned in a mathematics classroom. Boaler, Wiliam and Zevenbergen (2000) argue that it is important for young mathematics students to develop a sense of identity, but that this necessity is often overlooked. One significant part of finding one’s identity is findng and identifying with a group; identity with a group has been argued to be correlated to a person’s self-esteem (Boaler et al. 2000, Thornberg 2006). It has been said that as children start to mature into adolescents they start to become more aware of what group they belong to, and this group identity grows and develops with them (Boaler et al. 2000). Thornberg (2006) provides a number of definitions for a “group”, among them suggesting that a group can emerge from the individuals’ need for each other, or from the need to complete a task, something that might occur in a mathematics classroom.

Based on a number of interviewes with students, Boaler et al. (2000) state that many students make connections between their attitude to mathematics and the type of person they see themselves as; they might have a negative attitude towards mathematics because they are a “history person” or a “language person”. This suggests that identity plays a significant part in the mathemaics classroom. Boaler et al. argue that students learn how to behave in the mathematics classroom; “[t]hey learn how to be a mathematics student” (p. 3), suggesting that there are certain expectations of how to be and behave in the mathematics classroom. According to the study presented by Boaler et al. (2000), students of both England and the US “believe mathematics to be rigid and inflexible, and in particular, a subject that leaves no

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room for negotiation of meaning” (p. 1). Boaler et al. further states that if the sense of identity that a student develops in relation to mathematics corresponds to the mathematical discourse in the classroom, the student is more likely to continue studying mathematics, and also that “[t]he students’ enjoyment of mathematics [is] largely related to the extent to which they [identify] as a mathematics learner” (p. 7). Adapting the claims by Boaler et al. (2000), it can be assumed that if synaesthesia has no place in the mathematical discourse, synaesthetes might feel left out since their identity may not correlate to the mathematical discourse. It is also likely that synaesthetes will suppress or even not notice their own perceptions until at a later age due to lack of confirmation, as it was in my case.

Awareness of ones own understanding and thinking is generally referred to as “metacognition”. It has been argued by previous researchers that metacognition is very important for learning and development (Hartman 1998, Yunus and Wan Ali, 2008) and that it is closely linked to motivation (Yunus and Wan Ali 2008). It has also been said that being aware of one’s own thinking and understanding in mathematics helps one to be successful in the subject (Özsoy 2011).

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3. My Study

3.1. Aim and research question

When I decided to write about number synaesthesia, I had almost only myself for a reference point and was therefore somewhat uncertain what approach to take. After reading up on research, however, I decided that what interested me was something that I found missing from almost all studies that I read, namely, the synaesthetes’ own perspective. The studies presented above show that synaesthesia is most likely linked to cognition, and that it can sometimes act as an interference when the synaesthete handles numbers. They also show various attitudes towards synaesthesia, some of them very negative. What very few of the studies above do, however, is ask the synaesthetes themselves how they feel about their synaesthesia, emotionally as well as in relation to numbers and mathematics.

I decided, based upon what I had read and have presented above, that there were three areas with seemed relevant and which interested me: synaesthesia and cognition; synaesthesia and emotions, identity and attitudes; and synaesthesia and mathematics. I therefore phrased the following question:

How do number synaesthetes view their own synaesthesia, cognition wise, emotionally, and in relation to mathematics?

3.2. Methodology

To answer this question, I decided to make a qualitative interview study. One reason for not making a quantitative study was that there are few number synaesthetes in the general population, which made a quantitative study practically complicated. However, the main reason for choosing qualitative research methods was that I was interested in the subjects’ point of view on a close level, and according to Bryman (2008), this is one of the main reasons for conducting a qualitative research. I was also taking inspiration from Boaler et al. (2000), who used interviews in their study aiming to understand mathematics students’ point of view, which is similar to what I myself intended to do. In an attempt to get into my interviewees’ personal viewpoint, I did not tell them anything beforehand about the research on synaesthesia that I had studied, wanting them to give an image of how they viewed their synaesthesia in relation to themselves and not to researched facts.

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I found three people with number synaesthesia who were willing to be interviewed, and I put together an interview guide for a semi-structured interview, hoping for opportunities to also ask improvised follow-up questions based on the interviewees’ answers and comments. The interviewees were informed of the purpose of the interview and that they were participating of their own free will and could withdraw at any time, they were guaranteed anonymity (but were also given the opportunity to choose their own code names) and gave their signed consent, all according to the ethical guidelines provided by Vetenskapsrådet* (2002). The interviews were recorded with the permission of the participants, who were given the opportunity to read the transcripts.

For my analysis, I am not using only one theory, but relating back to all previous research presented in my background. Bryman (2008) says that all that can really be provided for the analysing of qualitative research are “broad guidelines” (p. 538), yet he describes two methods for the analysing of qualitative research: analytic induction and grounded theory. In analytic induction, he explains, one collects data after a hypothesis has been made concerning one’s research question; if a case is encountered which does not fit the hypothesis, one either reformulates the hypothesis to fit all the data collected or reformulates the hypothesis and continues collecting data. Grounded theory, Bryman (2008) describes as “by far the most widely used framework for analysing qualitative data” (p. 541). Quoting Strauss and Corbin (1998), Bryman (2008) says that “grounded theory has been defined as ‘theory that was derived from data, systematically gathered and analyzed through the research process’” (p. 541). He also explains that grounded theory is a method where the collection of data, the analysis, and the eventual theory interact with each other during the research process.

I feel that neither of these methods apply to me. I do not have a hypothesis before I begin the research because I want to keep an open mind to what my interviewees tell me. Neither do I intend to form a theory out of the data I collect, mainly because it is a small study from which a general theory can not be derived. Instead, I looked at what I have read about my subject – synaesthesia – and determined on three major areas of interest: synaesthesia and cognition, synaesthesia and emotion, and synaesthesia and mathematics. During my analysis, I intend to relate back to the research presented in my background section and look for connections between what my interviewees tell me and what researchers have found.

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3.3 Participants

The three people who participated in the study were 27 year old “Jim”, who works part time as a substitute teacher but has a Master’s degree in the history of ideas and teaching and looks for some kind of academic job, 36 year old “Leo”, who teaches piano but wants to be a casino dealer, and 56 year old “Mia”, who works with mathematics teacher education.

3.4 Reliability and Validity

Since this is a small study only with only three participants it can not be relied on for general theories, but only give an idea of how synaesthetes might perceive their own synaesthesia. The people participating in the study have not undergone any kind of test to determine their synaesthesia (like a consistency test), but are simply self-identified.

Bryman (2008) talks about the importance of seeing through the eyes of the people studied when engaging in qualitative social research. Being a synaesthete myself, I hoped to have an advantage with this, since I might have a more direct understanding for my interviewees’ point of view than someone without synaesthetic experiences. Although, I was also aware that I may be blinded by my own synaesthetic perceptions, ask questions related to me and my experiences, and thereby miss out on things that the interviewees perceive very differently from myself.

It should also be mentioned that I was vaguely familiar with one of the participants – Leo – before the interview, which might have had some effect on how the interview went.

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4. Interview Guide

This is the interview guide I used for my interviews. The questions are written in bold italics and comments in plain font.

GENERAL BACKGROUND

This is to get an idea of who the interviewees are in terms of mathematics and how much they know about synaesthesia. I hope that this information will help me analyse the answers from the focused interview, and also that it will help the interviewees to enter a relaxed “talking mode” before going into the deeper questions.

What do you do?

Do you use mathematics/numbers at work? What upper secondary program did you take?

Have you studied mathematics since upper secondary school?

Describe your experiences of mathematics class from school. How did you like the subject? How did you like the teacher? etc.

Tell me what you know about synaesthesia.

FOCUSED INTERVIEW

Here I begin with personal questions about how the interviewees perceive their own synaesthesia and how they feel about it. I then move on to more cognition based questions about how the interviewees feel that their synaesthesia affects them when they handle numbers. I finish up with a question about synaesthesia in school, linking back to the beginning of the interview.

Describe your own synaesthesia. What type? How strong?

I hope this will, except tell me what type of synaesthesia the interviewees have, give me an idea of how aware the interviewees are about their synaesthetic experiences. This might tell

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me something about how big an impact it really is for them and to what extent they view their synaesthesia as part of themselves.

When did you become aware of your synaesthesia?

OR: When did you have your experiences “labelled” with the name “synaesthesia”?

How?

I might phrase this question a little differently depending on the situation. I hope to be able to link this back to my discussions about identity. (Boaler 2000; Mächler 2009)

Do you tell people that you have synaesthesia? Is it something that you are “open” with?

I hope to be able to link this back to identity and attitudes. (Ramachandran and Hubbard, 2001; Mächler, 2009; Cawley 2010)

Possible follow up questions:

How do people usually react when you tell them about your synaesthesia? What do you feel the overall attitude towards synaesthesia is?

Do you feel that people in general know that synaesthesia exists?

How do you feel today that your synaesthesia affects your relationship to, and your dealing with, numbers?

Do you think it affects you when dealing with numbers without you being directly aware of it?

I hope to find out if the interviewees feel that they are experiencing the effects of synaesthesia that the research I present in my background section shows (Mills 1999; Cohen Kadosh et al 2005; Gertner et al 2009; Ghirardelli et al. 2010; Ward 2012). Possibly, this could also be linked to attitudes/emotions.

Do you feel that your synaesthesia is an advantage or a disadvantage when you deal with mathematics and numbers?

The purpose of this question is to get an even clearer picture of how the interviewees feel that their synaesthesia affects them, mainly cognition wise. Like with the previous question, I hope to link this to research done on the consequences of synaesthesia. Possibly, this could also be linked back to identity.

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If yes: Did you notice any difference in how you related to mathematics after you

understood that you had synaesthesia?

If no: Did you notice any difference in how you related to numbers you encounter in

everyday life after you became aware that you had synaesthesia?

If the interviewee was always aware: dig more in the two previous questions.

The purpose of this question is to get an even clearer picture of how the interviewees feel that their synaesthesia affects them, mainly cognition wise. I want to find out if discovering their synaesthesia affected how they viewed their own cognition. Possibly, this question will not even be necessary, since the interviewees may already have mentioned it at this point; if so, they could be asked if they have anything to add on the subject.

Do you think number synaesthesia is an advantage or a disadvantage in today’s Swedish school? Why?

This links back to the beginning of the interview when the interviewees were asked how they liked the subject of mathematics. Now they have, hopefully, throughout the interview, thought a lot about their own synaesthesia from various angles, and they are asked to think about school mathematics with that in mind.

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5. Results and Discussion

All interviewees turned out to have one thing in common: they all had some link to education. However, the thing that really struck me after I had finished all three of my interviews was how very different the three individuals were from each other, especially in the way they viewed their own synaesthesia.

5.1. Various Perceptions

All the interviewees know what synaesthesia is, even though they do not show any deeper scientific knowledge of it, and they appear to be very aware of their own synaesthesia, but they all have different relationships to it.

Jim has number-colour synaesthesia; when describing it he says: “It’s not like I see the colour, it’s just that…it feels…the same as when I see that colour when I think of a certain number.”* As mentioned previously, it has been pointed out by other researchers that the synaesthetic impression does not completely take over the original inducer (Simner 2012, Ward 2012) and I feel that Jim here describes this in his own way. Jim also says that his awareness of his synaesthesia, and his realization that it was something not everyone has, grew over time. Today, he views it mainly as something that makes handling numbers more aesthetically pleasing to him than it might be to non-synaesthetes.

Leo has several types of synaesthesia; his number-colour synaesthesia was the one he noticed first and the one he says is the strongest for him, but he also connects colours to vowel sounds and musical notes, and he says he sometimes senses faces and poetic messages in the four-digit combinations of digital clocks. He has been aware of his number-colour synaesthesia since seventh grade, but did not get the name “synaesthesia” for it until upper secondary school. Being vaguely familiar with Leo since before the interview, I know that he is very spiritual, and he tells me during the interview that he has a spiritual relationship to his synaesthesia; he explains a theory he has about why synaesthetic experiences occur, based on objects’ energy, and also says that he needs to be in a meditative state to be able to make certain synaesthetic connections, like the poetic messages connected to the digital clock face. Leo is aware that synaesthetic impressions are involuntary, as is mentioned in the background by Mills (1999) and Cohen Kadosh et al. (2005), but compares synaesthesia to the visual sense: “Right now I can close my eyes and then I don’t see anything,” he says. He further

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explains that he “disconnects” his synaesthesia – like closing his eyes – when handling numbers in calculations since he thinks it would be impractical in that kind of situation to have too many impressions to handle, some of which would be completely irrelevant for the task at hand; as he puts it: “equations don’t care whether it’s about purple or red.” As we have seen presented by Ghirardelli et al. (2010) as well as Gertner et al. (2009), synaesthetic experiences can indeed be an interference when handling numbers and calculations, at least if the numbers are in any way presented incongruently to the synaesthete’s experiences. Leo continues: “But at any time I can turn that sense on, and then I see; it’s like opening my eyes – I can’t choose what I see. I see you, I see a locker,” he says, pointing to me and the locker behind me. “In the same way I kind of see a whiteness on the figure of one. I don’t think I’ll ever be able to change that; it’s been the same all years.” Here he suggests that his photisms are consistent – which is one of the main criteria for determining synaesthesia (Simner 2012; Ward 2012).

Mia has been aware of her synaesthesia since a young age, but did not learn that it was called synaesthesia until she was an adult. She too has number-colour synaesthesia, but in addition she has spatial-form synaesthesia as well; she perceives the numbers 1 to 100 as a colourful line that bends off in different directions. She believes this mental number line is her way of “sorting reality” but states that she probably did it subconsciously at a young age, that she had no control over which colours certain numbers would have or in which direction they would turn, but that it has been unchanging her entire life, thereby also suggesting that she fits the consistency criteria. She views her synaesthesia as just another of her senses; “It’s actually very undramatic; it just is this way,” she says.

5.2. Synaesthesia and Cognition

The interviews with Jim and Mia gave me some interesting insights into the connections between number synaesthesia and number cognition which can be related back to what I have read and presented in my background, and also to my own experiences. Leo, however, had a different view on his synaesthesia.

After the interview with Leo is finished, I tell him a little about the research I have found about synaesthesia, and that one of the debates around synaesthesia has focused on whether it is a phenomenon linked to cognition or sensory experiences. Leo then tells me that he believes the visual impression of the number is what gives him the synaesthetic experience, rather than his understanding of it. The way he talks about synaesthesia as being completely

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irrelevant when solving mathematical problems supports this statement. Although, he says a few things that make me think cognition has played a certain role to his synaesthetic perceptions; he tells me that the digits 1 to 5 to him had very clear colours from the start, but that the colours of the remaining digits took some time to appear. I also find out that numbers of more than two digits to Leo appear as multicoloured depending on the individual figures’ colours. All this indicates that his synaesthetic perceptions are linked to the decimal system (only the single digits 1-0 have unique colours, and Leo divides the digits into fives – half tens), which would be a cognitive connection as according to Mills (1999) and Ward (2012). However, it is Leo’s own perceptions that are of interest for this paper, and he perceives his synaesthesia as being purely sensory, in accordance to what is argued by Ramachandran and Hubbard (2001).

Jim and Mia, on the other hand, clearly relate their synaesthesia to their understanding of numbers. Jim points out more than once that there is a difference between digits and numbers. He says that numbers consisting of two or more digits to him often have complex colours that are not only a combination of the separate digits’ colours. As an example, he says that the number 16 has a colour that is close to the colour of 4, since 16 is a multiple of 4, and that he experiences the same thing for other multiples. That a number’s factors affect the synaesthetic impression of it is something I can relate to myself, and it is definitely something that is linked to cognition. Jim points out that this only happens with lower multiples, when he immediately knows that the number is a multiple. None of the researchers presented in my background discuss the phenomenon of a number’s factors affecting the synaesthetic perception of it, but it would have been interesting to see what Ward (2012) and Ghirardelli et al. (2010) would have to say about it since they both point out how synaesthesia could help us to better understand cognition in general. Jim also tells me that his synaesthesia sorts numbers into odd and even ones, with odd ones taking on warm colours like red and yellow and even ones appearing in cold colours like blue and green, also something that can be said to be connected to the numbers’ mathematical meaning and the synaesthete’s understanding of this.

Jim has worked a bit with the hexadecimal system, and I ask him how his synaesthesia works then. He says that he gets more or less the same synaesthetic experience in the hexadecimal system as he does in the decimal system, but that the experience is not as immediate since he first has to translate the hexadecimal symbols in his head. This is a clear sign of Jim having a cognitive view of his synaesthesia; once he has understood the meaning

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figures. This can be compared to Mills’ study (1999), where a person experienced colours for digits both in written and spoken form, indicating, according to Mills (1999), that she reacted to the concept of the digit.

Mia too says her figures do not necessarily have the same colours if they stand as part of a bigger number as when they stand alone, which would suggest the visual impression is not what triggers her colour experience. When I ask her directly if she thinks her synaesthesia is connected to her cognition, she replies “Yes, I think so.” When she describes the form of her spatial number line, I can tell it is linked to the decimal system, and she comes back to this later, saying that since “something happens at every ten,” her mind must have created this particular pattern when she came to understand the decimal system. I ask if she feels that her synaesthesia helps her see patterns and connections between numbers and she replies that it probably does and that she likely created this coloured line representation as an aid.

5.3. Synaesthesia and Emotions, Identity and Attitudes

Since several articles about synaesthesia has portrayed it as something strange, or even abnormal, I wanted to know how my interviewees felt about this. I asked them if they were open with being synaesthetic, how people normally reacted when they told them, and I probed several comments the interviewees made about how they felt about their synaesthesia on an emotional level.

It becomes clear to me that all three interviewees understand that synaesthesia is viewed by many as something strange, yet they are all open about it, although Jim and Mia both point out that it does not come up in conversations very often. Without me having specifically asked for positive or negative attitudes, Jim tells me that no-one he has told about his synaesthesia has “thought [him] strange in a negative way for it,” indicating that he almost expects exactly that, or would at least understand it if someone thought so. Instead, he says people generally find it “strange but a bit interesting.” Mia says that people usually find it very strange and surprising that she sees numbers in colour and they cannot “see the point of it,” as she puts it, though she does not interpret this as a negative reaction. Leo claims that many people he meets can after some thinking relate to synaesthetic experiences and “understand that there are connections” and find their own, even though he cannot recall meeting anyone who has experienced the same “intensity” and “conviction” as he does. He says he has never met anyone who has thought badly about synaesthesia, but points out that he might have a social circle that is generally more open. Again, he makes a connection

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between synaesthesia and spiritualism, suggesting that non-spiritual people “who do not believe in life after death and spiritual dimensions or energy” might find synaesthesia “irrational.”

Mächler (2009) discusses synaesthesia and identity in his article, saying that many synaesthetes he has talked to did not want to identify with the term “synaesthesia” at first. He suggests that this could be because synaesthesia is so often presented as something very strange and exotic. “Thus, hearing about this ‘strange phenomenon called synaesthesia’ many synaesthetes construct false ideas about synaesthetic perception, because what they perceive seems to be normal for them and they do not consider this to be special” (Mächler p. 9). In my interviews, Jim and Mia are both very clear to point out that synaesthesia is what is normal to them, without using those exact words. Jim tells me about an article he read about synaesthesia in middle school: “Perhaps it was presented as a little more exciting and alien than I perceived it, because, why, I was used to it,” he says, laughing a little. This is very much like the scenario Mächler (2009) describes.

When I ask Jim if his growing consciousness of his own synaesthesia has affected his attitude towards mathematics, he says that “it is difficult to say since [he] cannot put [his] finger on when [he] realized that not everyone experienced this.” Notice how he says that he eventually understood how not everyone was like him, rather than that he was not like everyone else, indicating that he uses himself as the starting point – the “norm” if you will. I ask Mia the same question, and she, too, points out that she cannot tell if her synaesthesia affects her relationship to numbers and mathematics since she cannot know what it would be like to be without it. When telling the story of how she discovered her synaesthesia, she says she did not know that not everyone saw numbers and other graphemes in colour, why she thought it simply was that way. She then tells me that her sister had similar synaesthetic experiences and when they suddenly started talking about it she told Mia that her friends did

not see things in colour, which they both found very strange. “We thought they were the

strange ones, so to say,” Mia tells me, suggesting, with this phrasing, that she now understands that she is usually the one regarded as the “strange one”. Leo also makes indications that his synaesthetic experiences are what is normal to him; “For me number one is white, for example. Everyone who thinks anything else is stupid,” he jokes. When he starts describing the rest of his numbers, I cannot help but laugh as I think, from my own perceptions, that he is describing them wrong, and he suggests we have an argument about it after the interview.

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As has been mentioned in the background, finding an identity, and a sense of belonging to a certain group, is very important for young people, especially considering their self-esteem (Boaler 2000, Thornberg 2006). Mia says she views her synaesthesia as part of herself, though not precisely as part of her mathematical identity. The way she talks about connecting with her synaesthetic sister suggests a need for confirmation. Leo also probes this area, mentioning that as he noticed his number-colour synaesthesia in his early teens, he began to ask his friends if they had similar experiences. He further tells me that when he discovered that a boy whom he had a crush on also had number-colour synaesthesia with colour associations very similar to his own, he almost felt like they were soul mates. With this, Leo shows a need for confirmation and finding someone to relate to, which might be interpreted as a need to find an identity and a group. On the other hand, when he talks about how he disconnects his synaesthesia when dealing with calculations, he says that synaesthesia to him is “an apparatus in [his] brain, not in [his] person,” indicating that he sees himself as separated from his synaesthesia. Although, when he describes his perceptions of the different digits, it becomes clear that they affect his relationship to the numbers. He explains that his synaesthetic perceptions of the different digits developed over time; the colours of the digits 1-5 were very clear from the start, but it took some time before he could see the colours of 6-0, and when he did, the colours were quite complex. He says he finds this fascinating, although when he talks about it he sounds more frustrated than fascinated; in any case, there are definitely emotions linked to this. Jim also probes the area of emotional relationships to numbers; as mentioned previously, he sees his synaesthesia as something that makes handling numbers more aesthetically pleasing than it might have been otherwise. As an example, he says that he “really [likes] the number 12” and explains that its factors 3 and 4 are the digits that give him the strongest colour impression.

5.4. Synaesthesia and Mathematics

Most people in Sweden today probably associate “mathematics” with the school subject. I asked all my interviewees about their experiences from mathematics education in school in order to get an idea of how well their experiences match what researchers say and of how synaesthesia might fit into today’s mathematics classroom.

When asked about mathematical activities, Jim tells me that he does not encounter mathematics on a daily basis but enjoys simple calculations like the ones that show up in his leisure time activities such as roleplaying. Leo, who, as mentioned above, teaches music

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points out that “the music is very mathematical” and also tells me that he currently studies mathematics on his own out of pure interest, and Mia of course deals with mathematics daily since it is a big part of her profession.

All my three interviewees remember their mathematics education as very inflexible, just the way it is described in Boaler et al’s (2000) study, and they talk about it with little enthusiasm. Mia, who is the oldest interviewee, describes the mathematics education she had as a child as “extremely traditional,” consisting of lectures followed by practice tasks. As far as I can tell, with my experiences from my teacher education, a lot of mathematics education in Sweden is still following this teaching pattern. Jim describes feelings of confusion and insecurity from the mathematics studies in his earlier school years, saying that he often found it difficult to understand which rules were necessary or not – like in which order the factors in a multiplication should stand – and he says that he often did not understand if the ways the teachers wanted him to think were relevant or not. He further describes how he, as he started seventh grade, got a new teacher whom he felt showed a better confidence in his mathematical abilities and provided him with teaching that suited him better, which turned his attitude towards the subject in a more positive direction. Although, Jim says that even though he did not like studying mathematics in school in his earlier years, he “could still think that mathematical things were interesting,” and tells me how he started experimenting with different positional numeral systems in middle school and that he found it joyful. Leo describes the school subject of mathematics as “not sympathetic,” saying that he often wanted to do things his own way but was told off by the teachers: “’No, this is how you do it’ – that was the general mentality,” he says.

I ask my interviewees if they believe synaesthesia could be an advantage or a disadvantage in today’s mathematics classroom. Mia, being involved in mathematics education, points out that colours are often used in education for younger children, for example as coloured blocks to represent ones, tens, hundreds and so on, and she suggests that synaesthesia might become a distraction in those cases. Although, she also talks about her own colourful number line as something she probably created subconsciously as a helpful tool for understanding the number system. Leo thinks synaesthesia might be an interference when handling calculations: an understandable viewpoint since he does not regard his synaesthesia to be linked to his cognitive senses. However, he points out that synaesthesia might be of help in the history classroom since it could help one to memorize numbers. Jim also mentions number memory, saying that his synaesthesia “probably affects the way he remembers numbers.” Regarding

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that “it probably depends on one’s awareness of it,” whereupon he continues by suggesting that it might be possible to turn one’s synaesthesia into an advantage. He also suggests that it is probably a good thing to be aware of one’s synaesthesia and that not everyone has it. For one whose synaesthesia is related to cognition, this might be very true considering what was said in the background section about awareness of one’s own understanding being important for development (Hartman 1998, Yunus and Wan Ali, 2008). Jim continues to say that synaesthesia could possibly be turned into an advantage, but adds that “it feels like such a very individual thing,” thereby summing up my overall impression of the three interviews.

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6. Summary and Conclusion

Research has shown that number synaesthesia can have a certain influence on a person’s number processing, thereby affecting the person’s cognitive senses. It has also been shown that being aware of one’s own thinking and understanding is important for the learning process as well as for motivation and success. Different researchers have presented different attitudes towards synaesthesia; some present synaesthesia as a gift that needs attention and confirmation, while others portray in a way that could be interpreted as it being an abnormality and a defect. Lastly, it has been shown that a sense of identity plays an important role when one studies mathematics.

In my own study, I met three people who were very different in the way they viewed their own synaesthesia, showing that there is not simply one true answer to the question what it means to be synaesthetic. Focusing on the three major areas cognition, emotions and identity, and mathematics in relation to synaesthesia, I learned that synaesthesia can affect a person’s relationship with numbers, evoking feelings of pleasure as well as frustration, that it can be seen as a way of sorting reality, as an apparatus that can be switched off, and even as a spiritual thing. I learned that confirmation and finding a sense of belonging can indeed be very important and I was reminded that people who are by others often viewed as strange still usually view themselves as normal.

Because this study only investigated three people’s viewpoints, I would recommend further research concerning number synaesthetes’ own view on their synaesthetic perceptions and what they mean to them, perhaps with the aim of finding ways to help synaesthetes understand their synaesthesia better and use it as an advantage.

Despite the small extent of the study, however, it reminded me once again that all people are different, something that must always be considered when teaching, which is why it is the thing from this study that I first and foremost take with me. Synaesthesia is one thing that can affect a person’s relationship to, and understanding of, numbers and thereby also mathematics, but my study serves as a reminder that even two people with the same label – in this case “synaesthesia” – can still be very different as individuals, which we must always remember when we teach.

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