Exploring the Affective Domain in Math: Enhancing Attitudes
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Introduction
Research attention continues to be directed at attitudes to learning mathematics. My genuine interest stems from my professional experience of teaching secondary mathematics for over 15 years, and hence a genuine interest in students' attitudes to learning the subject and how I can contribute to changing that to enhance their learning and experience of mathematics at least at school.
A phrase often heard in the corridors and playground has eventually found its place in the classroom and it's almost difficult to hide any frustrations when met with the most unexpected but obvious response ‘Sir I hate maths’, ‘Sir I don’t like maths’. Some even go further to outline and explain how their parents have expressed their hatred for the subject and even how members of their family have done the same. Some however on further probing responses such as; ‘I will not need this bit of maths in future and hence I hate it ‘‘sir please tell me where am I ever going to use this type of maths in my life’’.
The relationship between students' attitudes and parents is moving towards the mathematical researcher and making the mathematical researcher that is based on the recommendation. It applies to the access and makes the memorization with the positive technique that is applicable to serve and make the mathematical factor to overcome the problem (Russo et al. 2020). Math attitude refers to the beliefs and emotional responses that assist in changing behaviors and measurement. It is applicable to assess and improve the mathematical attributes that help to solve and provide support to overcome the perceived achievement to reduce the mathematical anxiety and conduct the meta-analysis. The achievement in the mathematical attributes applies to the access and makes the broader decision to overcome the diversification and changes in the attributes of mathematics. It is required to support and provide the mathematical evaluation that is making the prediction to overcome the problem and access the scaled question to make the analysis on the mathematical structure (Mejía-Rodríguez et al. 2021). It is putting more emphasis on achieving the mathematical credential that is forming the changes with the prediction in the overall dignity and applicable to solve the issue.
This article explores the affective domain as a concept in studying and understanding attitudes towards learning mathematics and how that can be improved for classroom practitioners.
McLeod(1992) refers to the affective domain as the wide range of beliefs, feelings and moods that are generally regarded as going beyond cognition and highlights how affective issues play a central role in teaching and learning mathematics. Observations made by both teachers and students talking about mathematics centre around like or dislike or hatred of mathematics. Feelings and moods like anxiety, confidence, frustration and satisfaction which are all used to describe responses to mathematical tasks are referred to as attitudes even though with some limitations. It is making the evaluation by bringing new changes in the mathematical coincidences that are applicable to improve and make the credential in the achievement to reduce the mathematical anxiety. Zhong & Xia (2020) have stated that the positive effect of mathematical success is dependent on the scale question that is applicable to accessing and maintaining dignity in business improvement. It is liable to set and predict the overall credential that is applicable to overcome the problem and set attributes to improve the overall standard and credentials in the business (Attard, & Holmes 2022). The role of a metaphor for organizing and making the improvement in the constructivist approach to language that is required for the individual construction to make the limitation for knowledge and language. It is applicable to access and makes the intellectual instruction that is reliable to set and improve the overall diversity in accessing and making the system.
Data Sources
In an attempt to seek some answers for mathematics teachers, this article is written in four sections, with each section attempting to answer key research questions related to effect and mathematics education. The search for relevant literature was conducted on Google scholar, a useful tool for carrying out such exploratory searches, even though with limitations (Jasco, 2005). Searches were also carried out in other specific academic databases such as EBSCO, and PROQUEST among others, for academic journal articles and publications on affect and mathematics education, and on attitudes to learning mathematics generally. This includes publications which are both qualitative and quantitative in nature between 1975 and 2020. Undertaking searches on multiple databases allows a multi-conceptual and disciplinary approach to relevant and broader research to be found (Jasco, 2005).
What is the effect? How is affect connected to learning mathematics?
What does attitude to learning mathematics mean?
The meaning of effect carries a certain level of clarity and ambiguity, and its use and meaning have largely been borrowed from the field of psychology. Affect is for emotion, and feeling etc, behaviour is for actions, and cognition is for thoughts and reasoning. Whether, positive attitude and reflection towards this learning explore more than 17% that Americans were suffering from. This highlights the uniqueness and the divergence of effect and cognition. Spinoza, a philosopher used the term 'affects' for central aspects of humanity concerned with motivation, feeling and emotions but the traditional viewing of affect as feeling and thinking together can be traced back to Aristotelian theory during the 16th century in the Rhetoric 2, even though heavily contested in classical Greece at the time.
In psychology, "Affect" can be defined as the underlying experience of having different types of emotion, feeling, mood, attachment, or urge to take different actions. In 1992, in his study McLeod, has been described "Affect" as the experience of emotions and feelings.
In the case of mathematics education, "affect" basically explores different dimensions. Affect in the mathematical study also elements the affective domain such as anxiety, motivation, engagement, identity, attitudes and beliefs. Russo et al. (2020) has been stated that, mathematics mainly uses to provide an effective and efficient strategic way of building psychological discipline. It further encourages mental rigour within the human mind as well as enhances the power of logical reasoning among them. According to the opinion of Li & Schoenfeld, (2019), mathematical knowledge uses to play a crucial role in case of developing an understanding of other scientific studies and aspects as it allows one to think diversifically and relates to all the scientific and logical studies. The author also added that Math also allows the human being to understand different forms of art even music.
Descartes's (1596-1650) famous slogan ''cogito ergo sum'' meaning ''I think therefore I am'' draws attention to the dualism between body and mind in a way that suggests we can investigate a person’s thinking, their rationality without accounting for their feelings or emotions. However, if emotions such as happiness, sadness, fear, anger, disgust shame, pride, desire, and tension wellbeing with several components (Sutton& Wheatly, 2003) and is defined by Damasio (2003) as subconscious physiological fluctuations giving rise to conscious feelings, and by Ekman(2003) as innate, overt, responses to situations, then why can’t this affect how I think or reason? Some emotions are mental states (Hargreaves, 1998) and can change quickly, can be felt and are seen as less cognitive than attitudes (Philips, 2007).
Within a person, the attitude toward learning, underlying and practising mathematics is the factor that learners use to organise predisposition to think, perceive, feel, and behave toward mathematics. ATM is another aggregated measure of “a liking or disliking mentality toward learning mathematics". Moreover, a positive attitude towards learning has been able to influence the level of performance and provide efficiency to predict independent of factors. This tendency will further generate the feeling of engaging in or avoiding the study of mathematics or mathematical activities. This is a belief that leads one to presume the subject in the parameter is good or bad.
In a classroom that teaches mathematics, the affective domain is concerned with students' perception of mathematics, their feelings toward solving problems, and their attitudes about school and education in general. Personal development, self-management, and the ability to focus are key areas. A negative attitude among the learners while developing an understanding of mathematics will further limit the performance of learners in the case of building understanding or clearing concepts. Negatuvbe attitude among the learners is also responsible for shaping the level of motivation among them that further restrain the learning and understanding process.
The attitude among the learners, in case of changing through learning, further occurs when these “learned responses” were getting shaped and modified by the previous knowledge and future experiences. According to the conclusive remark of Li & Schoenfeld, (2020), self-observation and reflection, raising consciousness or awareness and implicit or explicit instruction while implementing the learning strategies of mathematical approaches as well as emotional management, uses to play a significant role in learning. The attitude that has been imposed on the students has a significant role in shaping the attitudes students have regarding the study of mathematics. This statement presented by Russo et al. (2019), is evidencing that both the psychological and actionable "affect" uses to share a connection toward learning mathematics.
While researching the attitude toward learning mathematics, Zhon & Xia, (2020) has been evaluated that this attitude is mainly get affected by the factors such as influences from parental guidance, effective support from the teacher and classroom instruction. This study also has been stated that a positive attitude among students while learning math can lead them toward the scope of higher achievement. On the other hand, it can be stated that as per the view of Attard, C., & Holmes, (2022), as the factor of logical responding has been enhanced among the students due to the practice and learning of maths, will be more helpful for the to broaden the opportunity for the students, to understand other significant subjects presented in their existing school syllabus.
According to the opinion of Mejía-Rodríguez, Luyten, & Meelissen, (2019), high scope for achievement in the both the academic and professional career is relatable with each other as theory have been dealing with the most effective factors pf professional career. Understanding mathematics can help students pursuing higher studies. It will lead them to perform better financial activities and control the financial risks. Therefore when they get to know that they can perform and manage their financial activities as well as logoixcally expand that will further lead them toward a professional life with a better financial position, this results in a more effective and favorable attitude among them regarding the understanding of mathematics. The attitude of the students regarding math is easily effective in affecting the overall achievement by modifying or reshaping the thinking or assumption of mathematics. Self-confidence, value, motivation, anxiety even the factor of enjoyment is also affecting factors when the learner is surrounded by the subject of math, therefore, these factors are clearly reflected and visible within an attitude student.
McLeod’s reconceptualization based on the work of Mandler (1984) suggested that the important factors in research on the affective domain should include beliefs, attitudes and emotions even though used to describe a wide range of affective responses to mathematics. The table below shows this:
Beliefs according to McLeod are largely cognitive in nature and may be developed over relatively long periods of time while emotion may involve little cognitive appraisal and may appear and disappear rather quickly. Does this suggest that beliefs may be harder to change than emotions? I am also not sure which one must change first to affect the other. If a learner of maths hates maths due to their held beliefs that maths is not needed for example or they may need maths in life, perhaps presenting maths to such through real-life examples may change this long-held belief but how does that change their emotions? Is it automatic that once this learner accepts that they may need maths in the real life the emotional state changes straight away? At which point do their emotions change and for how long?
What does attitude to learning mathematics even mean?
In small scale studies involving open-ended questioning set out to find out if people actually panic about mathematics and how they coped with maths anxiety. Buxton pointed out that panic as a type of feeling may relate to a variety of situations, both desperate cries for survival, and less serious ones, all evoke similar reactions. Buxton, drawing on a link between panic and learning mathematics highlights ‘panic’ as the point where normal logical responses cut out, the point where people perform significantly less well than they are capable of.
The mental state of math anxiety is one of the most common and significant cognitive among students when they have been dealing with the subject matter of Mathematics. As the students have to deal with huge logical reasoning as well as a diverse mindset in case of solving a single problem of math they find it hugely difficult. As stated by the opinion of Dindyal et al. (2021), this mindset sometimes can be triggered by a few external factors such as influences from parental guidance, effective support from the teacher and classroom instruction. Positive attitudes to the component have also created an effect of the learning ability and credibility that increase knowledge and factors. Learning theory and attitude learned different principles that occur in the case of classical components and selection among different possibilities. If they had to face huge pressure from their parents or teachers in case studying math it might be proven harmful to their cognition. On the other hand, Gandolfi, Ferdig, & Kratcoski, (2021) has pointed out the factor of genetics or heredity as the major responsible factor for math anxiety. The author also added that those students also have been dealing with anxiety while studying or learning math are genetically victimised by poor logical reasoning. In contradiction to this, Dindyal et al. (2021) has been stated that, when learners have identified their shuddering ones are terrified with their performance in maths, it them then develop a fear or feeling regarding the difficulty of maths in this subject.
I will agree with Buxton fully based on my teaching experience in the classroom, even though his research was not conducted in a structured classroom environment. It involves the experiences of adults, his conclusions have a direct impact on teaching and learning mathematics: first the presence of an authority figure, someone making judgements about how and what you are doing can create panic. The second is the emphasis maths teachers place on speed as well as perception i.e. ‘doing maths under pressure’ can create panic, and the last is doing maths in a public place such as a classroom, which can arouse panic. All of these lead to the formation of some form of attitude towards the learning of mathematics and in this regard, the type of taking strategy pedagogy employed plays a significant role in forming such attitudes. It may also be that the school and the department’s policy on teaching and learning eg having starter activities that must be completed in a set time say 5 minutes made of questions which students may not be familiar with can cause anxiety.
The sense of belonging and the sense of self-efficacy within one who is expert in math mainly can be considered as compatible and connected to each other. These two uses share a directly proportionate relationship with each other, as the increasing level of self-efficacy is able to higher the sense of belonging in one, while if one gets a higher sense of belonging among them it will further enhance their rate of self-efficacy. Therefore, it can be stated that, when one is dealing with the subject of mathematics, it will further give birth to the movement mentioned four major factors.
It has been observed that learners of the subject related to mathematics need to retain practical cognitive and emotional abilities. Mathematics learning is not just practicing and memorizing the concepts of mathematics. It also demands a constructive attitude with respect to the subject in terms of persevering challenges. Along with that positive outlook related to the challenges embedded with learning mathematics can be amended. The studies have suggested that attitude plays a major significant role in terms of learning mathematics. Thus, the learning and performing aspects of students in contrast to mathematics have been emphasized based on the degree of attitudes.
In contrast to the scenario, the degree of attitude in learning mathematics emphasizes student perceptions, problematizing teaching and embodied design of learning mathematics. Attard and Holmes (2022) have investigated the perception of students and teachers with respect to the blended learning practice in mathematics classes. The researchers have explored that in terms of gaining successful learning outcomes with respect to the mathematics attitude factor the learner has a great degree of dependency. The learner comprised of a lack of a positive attitude has to go through a lot of hardship during the process of learning. As a result of this scenario, the performance of learners on the grounds of mathematics is broadly impacted.
The authors have suggested that the development of a consciousness related to willingness to learn is critically essential for accurate learning of mathematics. Besides that, it has been also coined that this type of approach has a critically significant role in terms of the ability to endure problematic tasks. On the other hand, Mazana, Suero Montero, and Olifage (2019) have explored and evaluated the learner attitude in the field of learning mathematics. The researchers have coined out that a few factors broadly influence the learning aspects related to mathematics. Those factors are prior experience and knowledge, culture and ability or quality of the teacher. The researchers have explored that learners enriched with prior experience and knowledge in the ground of mathematics have reserved a positive attitude. This type of aspect has a great degree of impact in terms of learning mathematics.
Besides that, Mazana, Suero Montero, and Olifage (2019) have also argued that teachers related to the concerned subject have a major role in terms of making the learning process interesting. It has been observed that a skilled and effective teacher with a distinct teaching capability can make the teaching process much more joyful and attractive for the learners. As a result of this scenario, a positive attitude is build in contrast to the learning trait can be developed that can facilitate the successful learning of the concerned subject. The study has emphasized that female learners of mathematics have comparatively less positive attitudes in terms of learning mathematics. Along with that, it has been also found that learning mathematics is not innate in nature. However, it has been shaped by different factors those are experience, knowledge and quality of the teacher.
The study by Abrahamson et al. (2020) has emphasized the future perspective of embodied design in the field of mathematics. Thus, it can be stated that learning and teaching aspects related to mathematics have been contrasted within the study. Therefore, in contrast to the scenario, it can be stated that embodied design retained a high potential in order to positively influence the attitudes of learners toward learning mathematics. The enhancement is being set to predict the overall credit scale of the business through the equilibrium that is making the conceptual segmentation with the attributes of the value proposition. Based on the context, motivation, creativity and engagement aspects of learners have been associated with embodied design. Thus, it can be argued that embodied design includes distinct threads of incorporating manipulative, gestures and physical movements in contrast to the learning of mathematics.
Due to the concerned approach, learners can retain tangible and more concrete methods in order to experience mathematics in a highly engaging and accessible manner. Therefore, the authors have strongly emphasized that embodied design can play a critical role in the learning process of mathematics. In contrast to the scenario, it can be stated that learning the concerned subject will become enjoyable, relevant and interesting for the learners.
Li and Schoenfeld (2019) have argued that traditional approaches in order to teaching mathematics usually prioritize the transmission of skills and knowledge over infusing required attitudes with respect to the subject. It has been found that problematize teaching mostly leads to point of view of the learner in terms of fixed and unchanging subjectivity. The teaching perspective is set to improve the overall standard and make the decision to hence the learning prospect for the students. These findings parallel the characteristics of emotions expressed by teachers identified in the quality of teaching literature. Due to such reasons, a major impact on the learners with respect to the lacking the potential in terms of innovation and creativity can be recognized. Besides that, problematizing teaching encompasses a highly creative and critical approach in terms of grooming learner attitudes.
In view of the scenario, it can be argued that learners can reserve highly beneficial aspects in terms of strengthening the learning of mathematics. It has been observed that Li and Schoenfeld (2019) have suggested that opportunity of engaging students with open-ended problems needed to be considered. This can help in the process of establishing a positive attitude towards the learning aspects related to the subjectivity of mathematics. Along with that, in view of the concerned approach, interdisciplinary perspectives and world context also can be incorporated. Hence, learning and performing aspects of students in contrast to mathematics based on the degree of attitude can be improved. The learning of the students with respect to mathematics has been broadly affected by numerous factors and attitude is one of those. An increased epistemological dimension related to the cognitive sciences broadly fosters innovative approaches. Therefore, the attitude of learners in contrast to the learning of mathematics can be robustly improved by fostering a degree of positive attitude among the learners.
How can we study attitudes to learning mathematics, and how can we improve or change these in a mathematics classroom?
I selected a few of these keywords below: measuring scales, teachers' attitude, students' attitude, engagement, tools, questionnaires, surveys, student responses, quality of teaching and learning, schools attitude and many more. What this tells me is that studying attitude to learning mathematics and aiming to improve this attitude is not an easy task and is a concern for many. It is setting a metaphor for the intellectual instrument that is usually expressing and explaining the abstract to understand the subject through the references of another subject. Chen, (2019) stated that the attributes are one of the nonlinear relationships that are applicable to make the shortcuts to reveal and make the intellectual schemes to enlighten a certain aspect of a concept set that is required to be addressed.
A negative attitude among the learners while developing an understanding of mathematics will further limit the performance of learners in the case of building understanding or clearing concepts. However, Gresham, & Burleigh (2019) stated that it is applicable to make the identification for the metaphor to improve the mathematical attributes by making involvement in learning the mathematical concept and options for creating attributes to improve the metaphor theory. It is applicable to the access and makes the involvement of different mathematical approaches that are reliable to solve and improve the performance through research questions (Dindyal et al. 2021). It is making positive attitudes towards the learning of mathematics that has the responsibility to solve and hence the participants for growing the representation of the mathematical attributes. The valuable question is being set to make the maximum variability to improve the dignity and set a nationwide higher attribute to the mathematical representation.
Figures-1
The above is indicative of a simple set of questions rooted in the beliefs and attitude of learning maths but based on the researchers' beliefs of learning mathematics. This appears qualitative in nature and judging by the level of maths suited for primary school learners. Learning theory attributes is making the dignity in the way us of different attributes that helps to solve and make the acquisition of the performance. It is liable to set and predict the instrumental contribution that has the liability to set the standards and improve the overall dignity of the attributes (Zachariou et al. 2019). It is making the border decision to improve the conductivity and liability to solve and improve the performance (Marbán, & Mulenga, 2019). The causal relationship is being set to perfect the overall performance and improve the standard of work. It is having the force to improve the standard and set an expected outcome that is applicable to set and improve the performance of the mathematical attributes. However, it is important to make the conceptual evolution of the qualitative relations with different elements that are being set to predict the credential and improve the dignity of the expected value and outcome.
The responses from the above survey were then used to construct figure 4 which is then used to inform the teaching and learning of mathematics.
Figures-2
The above survey used to study attitudes to learning mathematics is quite simple compared to other surveys, for example, the Likert scale, which has been defined as, ‘a method of ascribing quantitative value to qualitative data, to make it amenable to statistical analysis. Papavlasopoulou, Giannakos & Jaccheri (2019) has stated that most teachers acknowledge the positive changes from the emotions such as enjoyment and pride when the learners are actively improving the overall standard that is experiencing negative emotions with disappointment that is associated with the student's disengagement with the perceived lack of learning. The critical evaluation is applicable to the access and making the border decision to improve the critical role and make the enhancement in performance Gandolfi, Ferdig & Kratcoski (2021). The educational setting is applicable to the access and makes the major concern on the changes with the subject's perspective. However, it is important to set and predict the overall standing with the performance and mathematical perspective. It is improving and making better considerations based on the standard work and dignity of the attributes. Both teaching and learning prescribe are being set to predict the major concern on the changes that are liable to set and make the credential in the mathematical attributes. The overall engagement is being set to predict the overall dignity and the censored performance.
It is making the learning approach with the commercial bodies that focus on improving the overall density of the learning to achieve sustainability in the classroom. The exploring is reciprocal links between teachers' quality and the emotion of the students that is applicable to improve the overall performance. It is making a broader decision that is based on the evaluation of changes through credentials in the educational system (Mejía-Rodríguez, Luyten & Meelissen, 2021). Teacher confidence in mathematics is linked with the highest level of valuation that is enhancing overall dignity and improves the standard of work. It is making the border decision that is applicable to solve and resolve the attributes to make the cognitive decision on their valuable session. It is set to make the broader decision to improve the overall standing with the diversification in the performance. It is liable to set and hold students' focus on the teaching prospect that is applicable to improve the learning prospect and can make the decision with the evaluation of changes. It is making an improvement in the overall dignity and establishing standard work. The improvement in the business is liable to set the credential for the business performance and make the engagement with the broader preserve.
Some including Turner (1993), have argued about the language used in the Likert scale-type questionnaires may pose problems with translation, but this applies to all forms of questionnaires and instruments of data collection if they are written in another language or has to be translated for the purposes of analysis. Also, problems with ensuring the validity and reliability of the data from such questionnaires have been reported by Reid (1990) while Hatch and Laxaraton (1991) criticise Likert scale measurements for use with small-scale data as not necessarily produce to the normal response. While open-ended type questions have been hailed (Nunn, 1992) as one that will lead to normal results, I suppose it depends on the level of depth of the nature of the open-ended questions. The Whiting survey described above has used some level of open-ended questions but was targeted at primary school children who may not be able to fully complete an in-depth open-ended questionnaire.
However, it is important to improve the overall standing with the preliminary evidence that is based on the mathematical perspective. It is liable to set and make the passion for business improvement. It is applicable to set and make the credential in improving the overall sustainability and decision-making in mathematical learning (Zhong & Xia 2020). It is applicable; to set a positive attitude towards the licensing system that is making the credential in the teaching. The learning prospect is set to predict the overall stability and performance of the positive attitudes toward learning. However, it is important to set and make the credential in mathematics anxious to solve the issue and overcome the problem through the learning prospect.
It is applicable to the access and improves overall dignity with the degree of self-confidence that is alive to set and enhance the overall standard. Making the border diversification based upon the changes that are improving the overall perspective. Moreover, it is important to set overall stability with the credential to set teaching questionnaires (Chen, 2019). It is also important to hence the learning perspective with the relative literature that is enhancing the stability of making the decision to enhance the overall standard and dignity of the business. The demanding changes are applicable to set and make the credential in the overall perspective that is being set to make the broader decision with the liability to improve the mathematical changes.
Assuming the definition of attitude to be multidimensional and going beyond just a simple emotional disposition such as like or dislike, Di Martino &Mellone (2005) presents a different way of studying attitude to learning mathematics in low-interest mathematics and poor achieving classroom for a period of 12 months. Their methodology based on their theoretical position on attitude presented results which were difficult to analyse compared to other ways of measuring attitude such as using the Likert scale. It included open-ended questionnaires, direct classroom observations, semi-structured interviews and analysis of students' reports, and thoughts on the activities carried out. It is set to make positive attitudes in learning mathematics that enhance the performance and solving the issue of the students. However, it is important to solve the issue and learn the problem from the credential teaching perspective (Attard & Holmes, 2022). It is important to set and overcome the problem with the relative enjoyment of teaching different subjects that is reliable to solve the mathematical induction. It is important to set and make the credential in a mathematical perspective to improve the overall performance. Moreover, it is applicable to set and make the overall sustainability through learning behavior and relative enjoyment of teaching different subjects (Russo et al. 2020). The overall effects of one instrumental change are enhancing the prospecting and making the growth through learning mathematical and enhancement in mathematics.
Analysing over 1304 mathematical essays from primary, middle and secondary schools, Zan & Dimartino (2008) identifies three main core themes relating to attitude to mathematics from students point of view:
a) the emotional disposition towards mathematics are specifically expressed with ‘I like/dislike mathematics’, b) the perception of not being or being able to succeed at mathematics is expressed with ‘I can do it /I can’t do it, c) the vision of mathematics expressed with’ mathematics is ...’
They further assert that essays very often show that even when mathematics is perceived as useful, the perception is not necessarily associated with a positive emotional disposition, such as ‘’even though it is a useful subject, I don’t like it ‘but also quick to mention that the description of pupils’ attitude towards mathematics is not enough to highlight their emotional disposition i.e. negative or positive towards mathematics, but rather the vision and self-efficacy beliefs the emotional disposition is associated with. Self-efficacy beliefs appear pervasion when to comes to developing attitudes to maths. This view changes the view that teachers attitude contributes to the learner’s attitude towards learning mathematics (Marches, 2011), however, a positive teacher attitude goes a long way to help learners build positive attitudes. This highlights the weight positive teacher beliefs and attitude about their learners carry in terms of learners’ attitudes toward learning mathematics.
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Conclusion:
I started this article in an attempt to havea deeper understanding of a concern I have had some time now.This concern stems from the fact that some of my students constantly show what I call negative attitude to mathematics by asking questions such as, why are we learning this? When will I need this? I hate maths! I don’t like maths among others. I posed the following questions to guide me to understand my concerns and to find a way to address them:
What is Affect? How is affect connected to learning mathematics?
What does attitude to learning mathematics actually mean?
How can we study attitude to learning mathematics?
How can we change or improve this attitude to learning mathematics in a classroom?
Through a search on the literature I have come to understand affect as complex area for researchers especially those in mathematics education. The field of psychology and neuroscience have made more advances in understanding the affective domain and has contributed significantly to the understanding of affect in mathematics education, field of psychology has deepened understanding in the explanations of terminology and methodological approach of studying affect including in mathematics education, neuroscience has made a case for the connection between the affective factors as key for the survival of our species. Attributes such as creativity, problem solving and decision making are connected in very complex ways that brings emotions and rational thinking closer than ever thought. Emotional thought encompasses processes of learning, memory, and decision making in social and non- social contexts. Within the domain of the emotional thought, creativity plays out and both creativity and responses aspect of creativity are informed by rational thought and high reason.
The affective domain includes beliefs, emotions, attitudes and recently values and is used to refer to a wide range of affective responses to mathematics.Even though there are many studies on attitude to learning mathematics ittends to be researched alongside beliefs and or emotions.
The formation of attitude towards mathematics may happen in different ways in the classroom. Buxton (1981) highlights the following ways: the presence of an authority figure. The thought of a teacher making judgements about what a learner is doing right it wrong can lead to the breaking of thought patterns and hence the formation of some form of attitude towards the subject, the second relates to the circumstance that arouse panic is the focus teachers places on speed, doing maths in a hurry.Since the classroom is a public place many students feel exposed if they are not able to do mathematics or the aspect of mathematics which is being taught eg. This can also lead to the arousal of panic which as mentioned earlier interrupts the thoughts patterns and hence may lead to the formation of some form of attitude towards the subject.
Having an emotional reaction towards a particular aspect of mathematicrepeatedly may lead to the development of an attitude such that if a learner panics about doing algebra every time algebra is taught, for reasons I suspectincluding those mentioned by Buxton (1981), then this get embedded in the subconscious and becomes automated each time there is an algebra lesson. Once this happens some learners are then able to transfer this emotional reaction in algebra for example to other aspects of maths such as geometry.
Prior to this article my own definition of attitude has been one of either negative or positive as I have been led to construct through my classroom experience. The literature highlights a deeper definition, one that I share, that allows attitude to be studied deeper as per Zan &Di Martino (2008) proposed the following three definitions.
The simplest definition is one that simply describes attitude as positive or negative which was my own definition before this essay.
A multi-dimensional definition which recognises three components in the attitude ie emotional response, beliefs about the subject and behaviour related to the subject.
A bi dimensional implicit definition which sees attitude towards mathematics as patterns of beliefs and emotions associated with mathematics
Other researchers including Klum (1980) argue that there may not a single definition of attitude that fits all situations rather a working definition which sees attitude as functional to the researcher posed problems.This definition draws a difference between the meaning of attitude as applied in psychology and in mathematics education.Ruffell, Mason &Allen (1988), simply sees attitude as a construct of the observer.
The attitude a learner uses to pay while learning mathematics is mainly get shaped by different cognitive elements such as their own or surrounding beliefs and even the mental processes are also responsible for this attitude. However, as per the perspective of Gresham & Burleigh, (2019), the significance of cognitive processes within a person in their attitude toward mathematics has not been a well-researched area yet, it still requires a lot of information to clear the vague concepts.
More recent studies on attitude to learning mathematics seems to be based on some theoretical perspective such as assuming the definition in one of the 3 afore mentioned definitions depending on observer’s or researchers’ issue. Most includes using a set of questionnaires for quantities analysis and or using measuring scale like the Likert scale, in interpreting attitude, to using small scale interviews, to using students’ essays for qualitative analysis. Earlier studies, often from psychology on attitude has been criticised for focussing too much on the instruments of measurement and not based on a theoretical position.
According to the above study regarding the "conceptual exploration of attitudes towards learning mathematics," it can be concluded that the attitude among the students regarding learning maths can be proven both helpful and harmful in meeting the learners' goal. Negative attitude among the learners is also responsible for shaping the level of motivation among them that further restrain the learning and understanding process. Both the psychological and actionable "affect" uses to share a connection toward learning mathematics. The preliminary change is making the credential in the overall educational context that is liable to set and improve the performance of the learning prospect. Therefore, it can also be stated that, the final result of "helpful and harmful" actions is mainly dependent on the positive or negative attitude among the students.
Changing attitudes to learning mathematics involves a good collaboration with classroom practitioners and researchers. Students often panic about maths for reasons already discussed which teachers needs to be aware of and then create the necessary classroom environment to try to reverse the issue.
The case for the link between the affective domain and cognition has been clearly made by research as discussed in this article. It seems at an early age, learners of mathematics are less likely to have emotional disposition if mathematicsis presented in a problem-solving way or if they can relate to where they will need mathematics and how it relates to the real world. But not having an emotional disposition toward mathematics does not necessarily mean you will do well in maths or succeed at maths?
I guess the definitions and the meaning of being successful inmathematics then becomes crucial, a problem for the focus of another article In hind sight, my quest to understand my students’ attitude which I had narrowly and suspiciously defined as being either ‘positive’ or ‘negative’ towards mathematics,could have begun by looking at a specific aspect of mathematics such as attitude towards mathematical investigations or geometric proofs as attitude towards mathematics in general seem very broad, nevertheless, I have been enriched with specialist knowledge on Affect and learning mathematics in a different way prior to starting this essay, which will contribute to my own professional development and that of many.
References:
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