Addressing math anxiety in the classroom

Abstract

In today’s educational systems, students of all levels of education experience math anxiety. Furthermore, math anxiety is frequently linked to poor achievement in mathematics. The purpose of this study is to examine the causes of math anxiety and to explore strategies which pre-service teachers have identified to overcome math anxiety. The methodology included conducting surveys with 70 pre-service teachers in Canada and completing a critical analysis of the data to provide an overview of the causes of math anxiety. These data indicate that pre-service teachers have encountered math anxiety in many situations. These causes include: lack of self-confidence, fear of failure; teaching styles; ineffective learning practices, and non-engagement of students. Furthermore, these data indicate that facing math anxiety have empowered the participants to devise strategies which have enabled them to overcome math anxiety. The author suggests that an improved understanding of math anxiety hold implications for all students and educators of mathematics.

Keywords

Assessment practices engaging students in learning math anxiety pre-service teachers teaching and learning strategies

Introduction

In today’s educational systems, many pre-service teachers have faced math anxiety. They are determined to find strategies to address math anxiety. This research begins with an examination of the definition of math anxiety, investigates the causes of math anxiety in pre-service teachers at a small Canadian university, and identifies strategies to overcome it.

In this article, I draw on the responses from a survey of 70 pre-service teachers. Specifically, I use two models as a conceptual framework, drawing a contrast between the traditional delivery method and the constructivist approach to teaching mathematics. In order to conceptualize this study, I will first present an overview of the theories and practices of math anxiety, record the responses from the survey through a series of tables, and complete a critical analysis to investigate the complex and multifaceted nature of the experiences of the participants.

Conceptual framework

Given the focus on the causes of math anxiety as identified by the participants, I have defined math anxiety as it is discussed in research literature. As a conceptual framework, the Traditional Classroom delivery method has informed the process of examining the causes identified by the participants of the study. These causes have been organized into the symptoms and emerging themes of math anxiety.

To address the participants’ emphasis on finding strategies to overcome math anxiety, I have used the Constructivist Teaching theory as the conceptual framework for this study. I have analyzed the participants’ suggestions for overcoming math anxiety, from a personal approach, and as future teachers.

Math anxiety: Research theories and practices

What is math anxiety? Math researchers define math anxiety as a ‘feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in ordinary life and academic situations’ (Hopko et al., 2003, p. 648). This could be a mild tension to a strong fear of mathematics. Ashcraft explains that students that suffer from math anxiety will avoid situations where they have to perform math calculations. ‘Unfortunately math avoidance results in less competency, exposure and math practice, leaving students more anxious and mathematically unprepared to achieve’ (Ashcraft, 2002, p. 184). Richardson and Suinn remind us that math anxiety is characterized by ‘fear about performing mathematics and is associated with delayed acquisition of core mathematics and number concepts and poor math competence’ (1972, p. 553).

According to Sheila Tobias (2013), ‘math anxiety is a response, over time, to stress in the math classroom where tests are frequently given under time pressure, in the home where there is competition with siblings, or at the workplace’ (Posamentier, Smith, & Stepelman, 2010, p. 3). Ashcraft and Humbree have indicated that ‘although it is not yet determined what factors make learners feel anxious when confronting mathematics, learners with higher mathematics anxiety show a strong tendency to avoid learning mathematics, hold negative attitudes towards mathematics, and have weak self-confidence in doing mathematics’ (in Wei, 2010, p. 10). Moreover, research literature informs us that ‘in general, there is little empirical research about the causes of math anxiety’ (Geist, 2010, p. 24).

Causes of math anxiety

From research literature, math anxiety is frequently linked to the teaching style of mathematics in the classroom. Mathematics in many classrooms has been based on a traditional delivery method, with a focus on development of skills. This traditional delivery method consists of the following elements:

Begins with parts of the whole – emphasizes basic skills

Strict adherence to fixed curriculum

Textbooks and workbooks

Instructor gives/students receive

Instructor assumes directive, authoritative role

Assessment via testing/correct answers

Knowledge is inert

Students work individually. (Source: Traditional Delivery Method, 2013)

With this approach, teachers use directed instruction, with the power of authority. Students passively receive information, and do not question the teacher’s authority. Knowledge is taken from the fixed curriculum and textbooks, with little time for questions or an understanding of the process. Students work individually to try to find correct answers; there is no time for group work and discussion. Too often, this means memorization and rote recitation rather than active concept based learning (Cates & Rhymer, 2003).

Another prime factor that causes math anxiety has been teacher behavior. The types of teacher behavior were investigated by Jackson and Leffingwell (1999). They identified the grade level at which math anxiety first occurred in students. They found that it is usually evident early on in primary grades. There is a focus on success and getting results, instead of on understanding. This creates math anxiety for students and result in lack of self-confidence for students:

Peter Lacey, Association of Teachers of Mathematics, in the UK, explains how teachers are constrained by a system focus on targets and attainment levels. Answers are either right or wrong, teaching methods focus on quick recall and mental math, and on answers given in front of the class. These strategies do not build self-confidence. The pressure is to get children to a certain level, rather than focus on understanding (Brian, 2012, p. 2)

Students often develop math anxiety in schools, frequently as a result of learning from teachers who are themselves anxious about their mathematical abilities. Research indicates that many teachers feel uncomfortable teaching mathematics because they do not like math themselves, or they believe they are not good at math themselves (Burns, 1998; Stuart, 2000). In fact, many teachers who have math anxiety will pass it on to their students. Math anxiety does not come from math itself, but from the way math has been presented to teachers when they themselves were students (Stuart, 2000). To compensate for their weak math skills, all too often, teachers will use a right and wrong answer approach:

Math is usually taught as a right and wrong subject and as if getting the right answer were paramount. In contrast to most subjects, mathematics problems almost always have a right answer. Additionally, the subject is often taught as if there were a right way to solve the problem and any other approaches would be wrong, even if students got the right answer. When learning, understanding the concepts should be paramount, but with a right/wrong approach to teaching math, students are encouraged not to try, not to experiment, and not to take risks. (Stuart, 2000, p. 330)

Furthermore, math is often taught as if students have the same ability, preferred learning style and pace of working (Boaler, 2002). There is little consideration of individual styles and behaviors. With this approach, teachers begin to focus on repetition and speed or ‘timed tests’ as important tools for improving mathematical prowess and skills (Popham, 2008; Scarpello, 2007; Thilmany, 2004; Tsui & Mazzocco, 2007). Also, research indicates that adding time requirements to tasks does increase anxiety and creates a negative attitude toward mathematics (Ashcraft, 2002; Popham, 2008; Tsui & Mazzocco, 2007). Instead of helping math students become more efficient at problem-solving and understanding concepts, these approaches have produced students that rely more on rote memorization and have increased the math anxiety of students.

Strategies to overcome math anxiety

As an initial step, teachers need to recognize some of the symptoms and indicators of math anxiety in their students, such as students drawing a blank on a test or exam; or the notion that incorrect answers are bad, and correct answers are good. ‘The emphasis must be placed on the process rather than the product’ (Posamentier et al., 2010, p. 3). The emphasis on the process is firmly established in the Constructivist teaching approach.

Constructivist teaching is based on the belief that:

learning occurs as learners are actively involved in a process of meaning and knowledge construction as opposed to passively receiving information. Learners are the makers of meaning and knowledge. . . This theoretical framework holds that learning always builds upon previous knowledge. Because all learning is filtered through pre-existing schemata, constructivists suggest that learning is more effective when a student is actively engaged in the learning process rather than attempting to receive knowledge passively. (Constructivist, 2013)

The Constructivist Classroom consists of the following elements:

Begin with the whole – expanding to parts

Pursuit of student questions/interests

Primary sources/manipulative materials

Learning is interaction – building on what students already know

Instructor interacts/negotiates with students

Assessment via student works, observations, points of view, tests. Process is as important as product

Knowledge is dynamic/change with experiences

Students work in groups. (Source: Thirteen Ed Online, 2004)

The characteristics of constructivist teaching include actively engaging students, and having activities that are interactive and student-centered. The teacher facilitates the learning process, encouraging students to take risks, to be responsible and to be critical and independent thinkers. The constructivist classroom is a space for active engagement of students. The teacher is a facilitator who interacts with the students; the teacher begins with the whole and expands to the specifics. Students begin with their prior knowledge and build upon what they already know. Students are encouraged to ask questions and pursue their interests. Students work in groups and use manipulative materials as primary sources. Knowledge is dynamic and changes with the experiences they have. The focus is on the process and on understanding, instead of getting the right answer. Assessment practices include student work and projects, observations, conferences, anecdotal notes, checklists, diagnostic interviews, and tests. All of these approaches validate diverse learners (Van de Walle, Folk, Karp, & Bay-Williams, 2014 [2006]).

Overcoming math anxiety means that we need to examine the classroom environment, and how we teach mathematics in the classroom. Addressing anxiety and self-esteem of children, and improving their confidence and related attitudes to math are crucial. Especially important is making math relevant to real-life contexts, and linking to students’ interests. Both Dewey (1938) and Piaget and Inhelder (1969) emphasized the importance of experience and actively engaging students in the educational process. Children are not blank slates to be filled. ‘Therefore children learn best when they are allowed to construct a personal understanding based on experiencing things and reflecting on those experiences’ (Constructivist, 2013). Vygotsky (1978) suggested that learners can be assisted by working with others who are ‘more knowledgeable. A range of knowledge may be out of reach for the individual to learn alone, but is accessible if the learner has the support of peers or more knowledgeable others’ (Van de Walle et al., 2014 [2006], p. 6).

This reminds us how important it is to have a research focus on the math experiences of students in the classroom. I acknowledge the importance of this research with its focus on addressing math anxiety and developing strategies to overcome it. I want to contribute to this literature of narrative research by examining the life educational experiences of these pre-service teachers in the Canadian context. It is important to know what challenges they have faced, and what strategies they have created to overcome these challenges with regard to math anxiety.

Methodology

This study was conducted at a small Canadian university. Participants consisted of pre-service teachers who were taking methodology courses in mathematics, in preparation to become math teachers. These participants were students in the author’s math methodology courses at the elementary, middle school and secondary levels. In conversations with the author, and from reflective journal responses, they had identified math anxiety as an issue in their own learning experience of mathematics. They were concerned about their future teaching experiences and wanted to learn how they could address math anxiety with their students.

Surveys were conducted with 70 pre-service teachers. All indicated a willingness to participate in these surveys. I have selected these individuals as a result of the diversity of their backgrounds and their willingness to have success in teaching mathematics to students, at all levels of public education. These individuals represented a) diverse math backgrounds; b) diverse levels of mathematical knowledge; c) various levels of math anxiety. Seven of the students were from First Nations’ communities, and one student was from the African Canadian community. All of the participants in this study had indicated that they had learned mathematics in a traditional classroom.

Students were given a questionnaire about their experience of math anxiety and asked to respond anonymously. The questionnaire was made up of open-ended questions using a process similar to an interview process. This method provided a structure to obtain information about their experience of math anxiety, with the opportunity for participants to respond, stating why they felt the way that they do. This questionnaire was designed from Seidmann’s (1991) approach who used an interview process to explore the experiences of the participants, their educational experiences and their interactions with other individuals. This qualitative approach conforms to education research practice. ‘Qualitative researchers aim to gather an in-depth understanding of human behavior and the reasons that govern such behavior. The qualitative method investigates the why and how of decision making, not just what, where and when’ (Qualitative Research, 2012, p. 1).

The goal of this research is to have the participant recount her/his experiences within the topic under study. Questions that have guided the data collection and analysis are:

(1) Have you ever had math anxiety? If so, at what grade level did you first experience it?

(2) If yes, please describe your math anxiety situation.

(3) What are the causes of your math anxiety? What do you think caused math anxiety?

(4) What strategies have you used to help you overcome math anxiety?

(5) What strategies would you suggest as future teachers to help your students overcome math anxiety?

The data collected have been compiled into themes of the causes of math anxiety identified by these pre-service teachers, and their strategies to overcome it.

Participants

The sample is composed of 70 pre-service teachers enrolled in a 16-month BEd program. All the participants were enrolled in math methodology courses. They were between the ages of 20 and 30. Nearly all indicated that they had suffered math anxiety at some point in their lives. They were near the end of their pre-service training to become teachers. They had completed their practical part of the course in classrooms, teaching elementary, middle school and high school levels and were enrolled in a final mathematics methodology course. Some of the students had Bachelor’s degrees in Science with a focus in mathematics; or a Bachelor’s degree in mathematics. Other participants had taken one or two university courses in mathematics. Some students were very knowledgeable of mathematics; others had very little math knowledge. All of the participants wanted to discuss the causes of math anxiety, and how they could prevent this in their own classrooms, as they began their teaching careers (Figure 1).

Figure 1.

Demonstrates the number of participants and their first experience of math anxiety.

Research findings

Based on the responses from the surveys, the data have been compiled into themes emerging from math anxiety descriptions of the participants, causes of math anxiety, and personal and teacher strategies suggested by the participants.

Emerging themes

In the survey, participants were asked to describe their math anxiety situations. In some cases, students described symptoms of math anxiety; in other cases, they shared what had caused their math anxiety. From these responses, these themes emerged. Thirty-one participants described their physical and emotional symptoms; 12 participants shared their feelings of frustration and confusion; 11 felt very stressed and began to shut down, and stop listening. Figure 2 demonstrates the number of participants who identified each of the themes.

Figure 2.

Symptoms of math anxiety.

Causes of math anxiety

There are many causes of math anxiety. This anxiety begins with the student and can be increased or decreased, depending on the situation. Figure 3 demonstrates some of the causes for math anxiety identified by the participants. These are grouped into themes from the responses of the students.

Figure 3.

Causes of math anxiety.

In column one, 23 participants connected math anxiety to lack of self-confidence; in column two 17 made links to fear of failure; in column three, 28 connected to teaching styles; in column four, 24 linked math anxiety to students’ lack of knowledge and in column five, 10 identified student non-engagement as a cause.

Personal strategies

Participants indicated several personal strategies to overcome math anxiety. Figure 4 demonstrates the number of responses for each category. In many cases, more than one participant had chosen these categories.

Figure 4.

Personal strategies.

In in column one, 13 students indicated that they used methods of relaxation; in column two, 16 students found ways to build self-confidence; in column three, 31 students identified the importance of practice in mathematics; in column four, 20 students emphasized the importance of study and homework; and in column five, 28 students explained how important it was for them to get help when they needed it.

Teacher strategies

In Figure 5, participants identified strategies which they would like to use in their future careers. The first two columns emphasize how they would support students in learning mathematics. The remaining columns represent diverse teaching strategies and engaging students. In column one, 32 participants identified encouraging risk taking; in column two, 28 participants emphasized the importance of opportunities for practice of mathematics; in column three, 45 responses support diverse teaching strategies and assessment practices; in column four, 34 students indicated the importance of presenting math at a slow pace; and in column five, 14 participants focused on the importance of engaging students.

Figure 5.

Teacher strategies.

Discussion

This discussion is an analysis of the responses of the participants. The analysis is divided into three sections: the causes of math anxiety, personal strategies to overcome math anxiety, and strategies which the participants intend to use as future teachers.

Causes of math anxiety

The causes of math anxiety are numerous and varied. In many cases, they are connected to the classroom environment. For 23 participants, math anxiety was developed when the students lacked self-confidence. According to the participants’ responses, this was caused by failure in math classes at many levels, or at home. This could have also been caused when students were not encouraged to try to do the mathematics by teachers. Sometimes this occurred when family members or teachers gave the impression that math was easy, when the student was struggling with math. Or, the opposite could have occurred, in that students would constantly hear that math was difficult; that one or both parents were not good in math, engraining the socialization process, that if a parent could not do math, then the student would probably not be good in math either. In fact, studies have shown that ‘the mother’s attitude and encouragement toward mathematics was a significantly important factor to children having a positive attitude toward mathematics, and was linked to positive achievement in mathematics’ (Scarpello, 2007, p. 27). The importance of family socialization and attitudes were key factors in increasing or decreasing math anxiety.

As indicated by 17 students, a fear of failure caused a great deal of anxiety. As part of the traditional classroom, students often worked individually. In this setting, the students thought there was only one right answer, or only one way to get the right answer. Students felt a lot of stress when they thought that they had the wrong answer; they didn’t know how to do the mathematics to get the right answer, or to whom they could turn to get help.

In the traditional classroom, the teaching style was a major cause of anxiety. When the teacher was too focused on completing the curriculum and all the curriculum outcomes; only using textbooks and workbooks as resources; or emphasizing computation and skills, then anxiety built for the students. If the teacher didn’t take the time to see if all students understood, many students became anxious, and were not able to do the math successfully. Students recognized that the teacher set the pace. When the pace in the math classroom was too fast, when the focus was on memorization, or knowing or applying the formulae, instead of focusing on understanding the math concepts, participants indicated that math anxiety developed.

Twenty-eight participants indicated that in their traditional classrooms, the teacher assumed a directive authoritative role. The teacher gave the information and provided steps on how to solve the math problems; the students received the knowledge. Anxiety occurred when students were afraid to ask questions, thinking that their questions were not intelligent. Some students indicated that when they would raise their hands to ask a question, they would sometimes be ignored by the teacher, or not be given a direct answer. As a result, the student would stop asking questions, and became more confused with the mathematics. All students, regardless of grade level, had math anxiety when they were put on the spot to answer questions. They felt anxious when they were placed under time constraints to get the math completed. One student explained that she knew how to do the math, and was usually good in math, but when the teacher insisted that the problems be solved quickly, and that the process be written on the board, she had a blank, and couldn’t even start the math problem. She was so afraid to give the wrong answer, or be ridiculed for not knowing how to do the problems, that she stopped trying, with math anxiety taking over.

Competition caused a lot of anxiety. In some cases, students spoke about teachers who lined up students and expected them to respond orally for mental math questions and computations. Furthermore, some teachers insisted on speed in answering the mental math questions. Students explained that if they had had a pencil and paper, they would have been able to answer the questions. During this competitive process, when students had a wrong answer, students felt a great deal of anxiety in that they felt inferior in front of their friends, who might have had the right answer.

Tests and exams caused a lot of math anxiety for the students. Students sometimes would draw a blank when faced with an exam. At times, students acknowledged that they were not well prepared; either they had not attended all classes or had not completed all the assignments. At other times, students stated that they had crammed for the exams, and had not kept up on their work. In some cases, they had completed the work without fully understanding the process of doing the mathematics. As a result, when faced with an exam, they didn’t know where to start a question or how to complete the work. This caused a great deal of math anxiety for the students.

In some cases, students felt math anxiety when the teacher didn’t have a thorough knowledge of mathematics and insisted on doing math only one way, his/her way. Goulding, Rowland, and Barber (2002) suggest that ‘there are linkages between a teacher’s lack of subject knowledge and ability to plan teaching material effectively’ (p. 691). When students could see that the math teacher didn’t like mathematics, and didn’t really want to teach mathematics, this caused math anxiety. They felt that it was as if the teacher believed that a lot of students couldn’t do math, and this message was passed on to the students. In all cases, students had math anxiety, when the teacher was not approachable, and they felt that they couldn’t ask questions.

At university, students faced math anxiety. Frequently, the classes were large and the professors moved at a fast pace. They didn’t provide time for questions. Sometimes the students had difficulty understanding the professor, or he presented the mathematics by writing quickly on the board without much explanation. These practices caused math anxiety for the students. At other times, students felt math anxiety when they saw other students being able to do the math, when they didn’t know how to do the math themselves. Sometimes, they had enrolled in courses for which they lacked the fundamentals or were not prepared. In some cases, the prerequisites of the level of mathematics for the courses were not clearly indicated. One student indicated that, in the beginning, all was well in the course that he registered for. As the course progressed, the assignments required an advanced knowledge of mathematics which he didn’t possess. This caused a lot of math anxiety.

Personal strategies

To address this math anxiety, these students used a variety of strategies. They had learned how to address physical and emotional symptoms; how to confront frustration and how to overcome the fear of failure; and how to become engaged in learning and to increase their knowledge in mathematics.

According to the participants responses in Figure 4, 13 students had developed ways to relax, either by breathing exercises, by listening to music, or by simply convincing themselves to calm down. Sixteen students had developed ways to build self-confidence. These included: making connections to previous knowledge; going from easy to difficult problems and building upon small successes; and telling themselves that they could be successful at math. Thirty-one students indicated the importance of staying organized; of reviewing notes and practice, thereby strengthening the basics. Twenty students stated the importance of studying and doing homework; of learning processes and memorizing formulae; of not falling behind. Twenty-eight students identified the importance of getting help: from teachers, from peers, and from family members. Some indicated that they used the internet when they didn’t understand.

A strategy mentioned by all the students was the support they received from family members and the extended family. They spoke of the emotional support offered by both parents. Parents and siblings who were good in math, or simply loved math, provided an important encouragement if a student found math difficult. From day one in the lives of students, their parents have been very supportive, helping them to develop their self-confidence and self-esteem.

Many First Nations and African Canadian students spoke of community support. In some cases, these students who were unable to receive help in math at home, were tutored by community members. All students shared that simply knowing that someone could help them reduced math anxiety. In some cases, when students were struggling, math tutors could make the difference in their being successful. All of these factors reduced math anxiety.

Teaching strategies

The teaching strategies have been grouped according to topics: supporting the learner; diverse teaching strategies; assessment practices; and engaging students.

Supporting the learner

Many pre-service teachers emphasized how the process of learning mathematics had changed. In the past, the focus had been on completing work sheets, using formulae to solve problems, following and applying the steps to solve problems, outlined by the teacher. In many cases, students were expected to know only one way to solve a problem; if the students did not know this way, they would not be able to be successful. Research literature informs us that most recently:

doing mathematics means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, checking to see if your answers make sense. (Van de Walle et al., 2014 [2006], p. 11)

This is linked to a constructivist teaching approach, where the focus is on the process, where students create meaning and knowledge, and where the students are actively engaged.

As indicated in Figure 5, 32 participants identified encouraging risk-taking as an important factor in learning mathematics. They indicated that as future teachers they would support learning mathematics by implementing key factors of an interactive learning environment which include: encouraging each student to express his/her ideas with the potential to contribute to everyone’s learning; ensuring that students recognize that there are multiple ways to solve problems, and that each student can choose his/her own method; and making sure that mistakes are not covered up but provide an opportunity to learn. All of these approaches would build self-confidence and are found in research literature which informs us that acknowledging the correctness of a solution depends on the mathematical sense it makes (Hiebert et al., 1997). In these situations, the teacher interacts with the students, negotiating with them to design their own solutions. As a result, students are empowered to construct their own approaches, rather than rely on the teacher as the authority. For them, as future teachers, they believed that would be crucial for constructing an inviting, creative learning environment.

Creating understanding was critical in reducing math anxiety (Hiebert et al., 1997). In the study, students indicated that using a variety of resources to learn mathematics was fundamental in the process. These resources could include textbooks; videos; math games; manipulatives, and using technology. This variety of resources responded to the diverse needs of the students, and links to the constructivist classroom where resources are not limited to the curriculum and textbooks. When students are confronted with a situation, students have shared that they have often found it helpful to use a picture or model. In some cases, where the problem was abstract or complex, students found that creating an experiment and seeing what happens, could be useful. Going through these processes helped students to have mathematical understanding not by rote, but by ‘associating to many other existing ideas in a meaningful network of concepts and procedures’ (Van de Walle et al., 2014 [2006], p. 23).

Twenty-eight participants emphasized the importance of practice in mathematics. They acknowledged that to engage students in mathematics requires activating prior knowledge, and to become reflective by providing explanations and justifications for their answers. An important learning strategy was to link math topics to one another, and to connect with their own knowledge from previous courses. When students faced challenging questions or problems, they discovered that by connecting to another area in mathematics in which they were familiar enabled them to begin the process of solving the problem. This resulted in their not feeling helpless and in acknowledging that there are many diverse ways to solve math problems. This process encouraged creativity on their part. Students had less math anxiety when they could take ownership of the learning process.

Once understanding was established, these 28 participants recognized that finding ways to understand math concepts and practice math skills were crucial in the development of math knowledge. They identified the importance of keeping up to date in their math assignments. Being well prepared for tests and exams was important. When students were shown how to prepare for tests/exams and how to write tests/exams to be successful, this reduced some math anxiety. Reviewing their notes and formulae prior to an exam; learning how to identify types of math problems; learning the process; and practising the steps required to solve these problems were fundamental to their learning. However, when students knew that the test was only one way of many ways in which he/she would be assessed, math anxiety was greatly reduced, because students knew that they could demonstrate their knowledge and understanding in diverse and multiple ways.

Diverse teaching styles

Participants in the study identified key components of the constructivist teaching approach. Participants responded that math knowledge is dynamic and changes with experiences. As a result, it is extremely important to get to know their students and plan lessons and activities that support the interests of their students; to focus on the process of doing mathematics and ensuring that students understand. All of these contribute to the constructivist classroom and reduce math anxiety.

Setting up a constructivist learning environment where there is a spirit of inquiry, trust and expectation, reduces math anxiety. An important focus is active engagement in learning. Chapin, O’Connor, and Anderson (2003) wrote:

when a teacher succeeds in setting up a classroom where students feel obligated to listen to one another, to make their own contributions clear and comprehensible, and to provide evidence for their claims, that teacher has set in place a powerful context for student learning. (p. 9).

Students spoke of the importance of collaborative learning in the math classes. Working in groups, where students have opportunities to talk about mathematics, where the ideas of all students are respected and listened to, students are able to share their thinking, and work through a variety of steps to a solution. Having peers with whom they could discuss and practise math was extremely useful, rather than working alone. In this group environment, being able to ask questions, and have them answered immediately by peers, reduced math anxiety.

In Figure 5, 45 participants spoke of the diverse teaching strategies of their math teachers. They shared how they could recognize teachers who have a good knowledge of math and a passion for teaching it. These teachers passed on their enthusiasm to their students and motivated them to want to learn mathematics. These teachers encouraged multiple ways to solve math problems, which encouraged self-confidence in their students. They also identified teachers who recognized that knowledge is dynamic and who encouraged understanding the math concepts. Students shared that understanding was improved when the topics of mathematics were broken down into parts and when lots of examples were given. In these classes, students felt comfortable to ask questions whenever they did not understand. The teachers would take the time to respond in a direct manner, and encourage their students to stop them and ask questions as the math was being taught. This focus on understanding and on the process of building up their math knowledge worked to relieve math anxiety.

Many students spoke of the importance of having teachers believe in them, and tell them that they could do the mathematics, and celebrate the small successes of students. They indicated that teachers who were approachable and who took an interest in their students played an important part in relieving math anxiety. Students spoke about one educator they had during the learning process. They shared that this educator used to say ‘students don’t care what you know unless you show them that you care about them’. This was all that was needed for students to go on and want to learn more. As a result, many students became successful in learning mathematics.

Participants also acknowledged the teachers who took the time to show how mathematics was related to real-life situations, and how important it was for students not to drop mathematics, or take a lower level of mathematics. By so doing, these teachers provided students with the information they needed to be able to go on and advance to career choices, which would not have been possible without having the required courses in mathematics.

Assessment practices

As part of the diverse teaching strategies, 11 of the 45 participants wrote about assessment practices as a means to reduce math anxiety. In the constructivist classroom, assessment practices are much more than tests and exams. Knowledge is assessed in a variety of forms. Process is an important as the product, or the right answer. Many assessment practices were suggested by the participants in the study.

Having a variety of assessment practices helped to remove math anxiety from students. These activities included having discussions either during the work or once the work was completed. As students discussed together and went through the process of solving a task or playing a game, teachers could see how students understood the process, and how they approached the task. The teacher could determine whether a specific concept was understood, much better from listening to the discussion, than from a written test. Data gathered from listening could:

provide significantly greater insight into students’ thinking than any written test can provide. Data from student conversations and observations of student behavior can be recorded and used for the same purposes as written data or for evaluation. (Van de Walle et al., 2014 [2006], p. 29)

Participants identified performance indicators, such as rubrics, as excellent ways to enable the student to know what is expected of them. It is an excellent self-check for the teacher to ensure that the task designed by the teacher is accomplishing its purpose. When performance indicators are in place, unexpected methods and solutions happen. It is very helpful for students to know that they can demonstrate their understanding of mathematics in their own way, without having to try and figure out the teacher’s way of thinking and doing. This alleviates a great deal of math anxiety for students.

Participants identified how they were engaged in mathematics through the assessment practices. There are several observational tools which are useful in the process. These include: conferencing, anecdotal notes, observation rubrics, checklists for individuals and for all students. By using a variety of tools, teachers are demonstrating to students where they are in the process of learning mathematics, and are empowering them to use a variety of methods to solve problems. Other important methods in assessing students include journal writing, providing writing prompts and ideas, and encouraging students to use drawings and diagrams to illustrate their work. Having diagnostic interviews, where students have the opportunity to share what they know and where they are struggling, provides an excellent way to relieve anxiety for math students (Van de Walle et al., 2014 [2006]).

A portfolio is an excellent way for students to show their work and take pride in their accomplishments. This builds self-esteem and self-confidence so that students are willing to take risks, and deepen their understanding of mathematics. Student self-assessment is a first-rate way for students to excel. Stenmark (1989) stated that:

the capability and willingness to assess their own progress and learning in one of the greatest gifts students can develop. . . Mathematical power comes with knowing how much we know and what to do to learn more. (p. 26)

Engaging students

When thinking about engaging students, 14 participants indicated that journal responses, learning centers with hands-on activities, and strategic lesson plans were effective ways to engage students.

Participants indicated that they felt that journal responses enabled students to discuss diverse strategies for solving math problems and for understanding math concepts. When the students were encouraged to share what worked for them, and the areas that they continued to struggle with, the teachers could then use this information to prepare effective lesson plans. They could be a means to build self-confidence and empower students, and lessen math anxiety. Given here is a journal response written to the author towards the end of the Elementary math methodology course. It provides a glimpse of how math anxiety can be addressed. The student wrote:

As we approach the end of the semester I have been reflecting on the lessons which I have learned. I walked into this Math course with anxiety and fear. After spending only a few short months learning Elementary math, I feel as though I have learned enough to teach for years. I have learned about the importance of partner and group work. We have shared our ideas and problem solving techniques with each other and as a class. I have become engaged with the entire class, and have learned different learning styles.

In this math course, I have experienced something I have never experienced in a math class before: success. I enjoyed myself and learned not only about my peers but also about how I learn math best. I will carry the strategies you have taught us, and what you have shared with us to every math class that I teach. I began this course feeling anxious and scared; I leave this course feeling confident and educated.

The strategies to which this student is referring are those from the Constructivist Classroom (Thirteen Ed Online, 2004).

The participants believed that having lesson plans that provided a constructivist teaching environment would address math anxiety. They designed a structure for these lesson plans. They suggested that the process would be divided into three parts: before, during and after (Van de Walle, et al., 2014 [2006], pp. 26–27). In the beginning part, they would name the topic and the outcome; then ask a question of the day which would link to prior knowledge and students’ interests. Learning would be interactive with a focus on the process. In some cases, they would present the lesson by using a story to introduce the topic; they would have the students work in pairs or a group, using problem-solving as the process to do the math. Students would be encouraged to discuss strategies, and ask questions. In another situation, the teacher might use learning centers with a variety of strategies for students to experience. Mathematical understanding would be constructed and demonstrated in numerous ways: by graphs, tables, diagrams, symbols, manipulatives, words, and real-life examples. In the ending section, students would present their results to the class. Assessment practices would be student work, observations, portfolios, conferences, journals, diagnostic interviews, and testing (Van de Walle et al., 2014 [2006]). Participants indicated that by having these components in their lessons, students would be empowered to take risks, and would be actively engaged in learning mathematics.

Conclusion

For many readers, the perspectives of these pre-services teachers might be a first glimpse of the causes of math anxiety faced by students in the math classroom. All pre-service teachers have identified the positive impact of educators. It is time to stop and consider the many strategies they have identified: diverse learning and teaching strategies; assessment practices; family and community support; making connections to prior knowledge; and the importance of actively engaging students in the math classroom.

All students need to become aware of the challenges and strategies for success of math students. As educators, we need to be examining the obstacles and challenges identified by these pre-service teachers to begin to consider their implications for all students. We need to consider how their strategies for success can impact upon all students and we need to learn from these shared experiences. It is important for all students, and in particular for students who face math anxiety, to hear these comments, to know that there are students in similar situations, and that there are educators who are really concerned with removing math anxiety from the math classroom.

‘With encouragement from the teacher, a nurturing environment, and permission to proceed at one’s own pace, math anxious students can be helped to eventually eliminate math anxiety from their lives’ (Posamentier et al., 2010, p. 3)

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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