Research into the Negative Responses to Mathematics

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The purpose of this report is to analyze the main cause of mathematics panic in colleges and to offer solutions and give recommendations to the Head of the Department of Mathematics and Statistics at Curtin University. By reviewing professional literature, scholarly journals, and accredited websites a better understanding of the causes and effects of mathematics anxiety, this report will achieves the purpose by analyzing and concluding the prior research and give solutions that aimed at these issues. In addition, the nature of the mathematics in general will also be considered and relate mathematics to professional life.

The report will firstly go into an overview of the issues in mathematics teaching and learning before dealing with the problem of the math panic in colleges. A general overview of the nature and social perspective of mathematics will be discussed, which will then lead to a scrutiny of what universities should do to help to direct students' attitude and understanding of mathematics.

1.2 Background and recent findings

Because of its utility and importance, learning mathematics is described as a necessity for a person's full development in the 21st century (Kogce et al. 2009, 291). However, the popular image of mathematic as difficult, abstract, not very practical, and largely masculine, etc. Therefore, math panic appears in vary level of schools. Mathematics anxiety is introduced firstly by Dreger and Aiken in 1957 and it is defined as "a sequence of cognitive, affective, and behavioral responses to a perceived self-esteem threat which occurs as a response to situations involving mathematics" (Birgin et al.2010, 1).

Mathematics anxiety is prevalent among the college students population (Zakaria and Nordin, 2007, 27). According to Google-counting, mathematics anxiety emerges in schools especially "in college" has 26,000 occurrences (Brown 2008, 61-92). In addition, Birgin et al. (2010, 1) have found that negative attitudes to mathematics or mathematics anxiety is a barrier in learning mathematics and attending careers which require mathematics. As a result of mathematics anxiety, impacts like "avoidance of mathematics, distress, and interference with conceptual thinking and memory processes" may even extend negatively in adult life.

2.0 Causes & effect of mathematics anxiety

Mathematics anxiety has been found that may be affected by many causes, including "mathematics, educational and curriculum-related issues, parental attitudes, values, and expectations toward mathematics" (Baloglu and Kocak 2006, 1325-1335).

Numerous researches have analyzed the causes of mathematics anxiety and the results are different from each other. Zakaria and Nordin (2008, 27-30) have claimed that low mathematics achievement usually accompany the occurrence of mathematics anxiety. A student may be defeat by his/her own fear that result from constant failure in mathematics and make him/her to believe that he/she can never do well on it. Furthermore, it is also suggested that the main cause of mathematics anxiety has been in teaching methods because most mathematics courses "did not encouraged reasoning and understanding". It is also believed that attitude towards mathematics can be one of the reasons of math panic (Kogce et al. 2009, 291). The attitude or value can be affected by teachers or parents. In addition, time pressure in mathematics test should also be considered when refers to causes of math anxiety. The pressure created by time limitation is the combination of stress may lead to uncertainty about how to do the task and fear of failure (Buxton 1990, 153).

Figure 1. Relationship between anxiety and self-efficacy (Source: Hoffman, B. 2010)

As displayed above in Figure 1, the standardized scores showed a regressive relationship between mathematics anxiety and students' self-efficacy in solving simple mathematics problems. It is clear that as anxiety increases, self-efficacy falls which indicates a strong correlation between these two items.

2.1 Value and attitude

One of the reasons for mathematics anxiety is attitude towards mathematics. Students' attitudes or values toward math usually come from teachers and parents. Some researches held by universities show that students perform better when doing exercises in mathematics classes without teachers than the students under teachers' supervision. Additionally, Buxton (1990, 155) have argued that teachers should not restrict student's thinking by saying "this is not the way that written in books" or keep giving the right answer without leading the students to think independently. Otherwise, students may feel boring and confusing and their motivation to seek mathematics problems solving opportunities may be decreased and cumulate into fear and avoidance.

Parents' expectations as much as teachers' may also give students pressure in mathematics. Parents usually stand in a position to judge their children and fail to resolve the view with explicit statements. For example, some parents show disappointedly on face when children understand slowly in mathematics. Therefore, children may feel even harder to overcome the problems due to lower confidence and this turns into anxious and avoidance.

2.2 Lack of understanding

According to Zakaria and Nordin (2008, 27-30), a lack of understanding is one of the main causes of mathematics anxiety and "that understanding based learning is more effective than drill and practice". For most students, the first time when they are afraid of solving math problems is when they cannot understand the concepts in classes. Therefore, their self-confidence of learning mathematics may decline and they lose interest to overcome the problems. Lower achievement results and a prejudicial attitude towards mathematics may result from this kind of self-perceptions, which can affect their perspective of learning mathematics (Hoffman 2010, 276-283).

2.3 Time pressure

Many students suffer anxiety when it refers to be giving a certain extent of time to finish certain commitment (Hoffman 2010, 276-283). This can be one of the factors when discussing about the causes of mathematics anxiety. For example, students who familiarized to solving problems without time limitation might feel anxious if they are told to solve problems quickly.

Furthermore, according to some studies, the emotional responses of students become intense frequently when students work on math problems over an extensive period of time (Buxton 1990, 153). In other words, it is claimed that the more time students spend on solving math problems, the more anxiety they suffer. Most students failed in their mathematics exams due to wasting too much time by worrying about the time restriction and cannot complete all the questions. According to Hoffman (2010, 276-283), the Test Anxiety Inventory (TAI) and the Fennema-Sherman Mathematics Anxiety Scale (MAS) were co-operating for the Problems Test of mathematics anxiety. The students were required to respond to all the items by giving enough time. The students finished all the questions within 30 minutes, although no time limit was set. According to this study, it can be suggested that problem solving time restriction can be one of the factors that results in mathematics anxiety.

However, Hoffman (2010, 276-23) suggests that "high anxious individuals may actually have faster problem-solving times". Students may want to finish the task as soon as possible when they are prompted feelings of anxious or worry during the solving mathematics problems. This may result in faster completion of problems, even though possibly at the loss of accuracy.

3.0 Mathematics & gender

There is a hypothesis assumes that women have more mathematics anxiety than men due to less experience with mathematics. As a result, Hoffman (2010, 276-23) points out that female are less likely to seek opportunities to solve mathematical problem and even mathematics careers, and tend to avoid jobs to do with computers and technology that link to mathematics. However, many studies failed to substantiate considerable gender differences in math panic, even though numerous studies support the view that female have more math anxiety than male (Baloglu and Kocak 2006, 1325-1335).

3.1 Gender Stereotype

According to Hoffman (2010, 276-83), although ability may be the cause of performance differences, the pessimistic attitude to a high achievement shows females did not 'try as hard' when solving mathematics problems. Some studies suggest that more male than female enroll in the higher level of courses in mathematics (Meece, Wigfield, and Eccles 1990, 60-70).

Gender stereotype, one of the reasons why females are much passive in learning mathematics, seems to be the most persuasive one. Gates (2001, 53) explains that gender stereotype that masculinity associate with reason while femininity with alternative approaches is the cause of gender differences in mathematics anxiety. This difference can affect their feelings in relation to mathematics problem solving. According to Gates' study, 'masculine' subject such as mathematics and physics are seen as 'difficult' by female but 'interesting' by male. Therefore, female students may have the panic of learning mathematics because they perceive it as being difficult although they are interested in this subject.

In contrast, Hembree's meta-analysis claimed that the "negative behaviors associated with mathematics anxiety" were more marked in males than females. In addition, present research found that the influence of mathematics anxiety on the achievements of males when solving math problems is stronger than females (Hoffman 2010, 276-283).

4.0 Teaching mathematics in college

"Mathematics anxiety is prevalent among the college students population (Zakaria and Nordin, 2007, 27)." According to Google-counting, college students have 26,000 occurrences of math panic which is the highest among schooling.

Zakaria and Nordin (2008, 27-30) further stated that the main factor of mathematics anxiety is teaching methodologies. For example, a report of Gabriella and Paul Rosenbaum Foundation called The Effect of Singapore Mathematics on Student Proficiency in a Massachusetts School District:  a Longitudinal Statistical Examination shows in figure 2 that after introduced the teaching syllabus of Singapore mathematics (SM), the mathematics performance of students with Coded MCAS, who used to perform bad in this subject improved much better as overall.

Moreover, it is predicted that more than 50% of the students are underprepared when they enrolled in mathematics courses in college (Baloglu and Kocak 2006, 1325-1335). Therefore, teachers in colleges should stand in a position of guiding and rectifying.

Figure 2. Percentage of students with Coded MCAS, with and without SM (Source: Goldman et al. 2009)

4.1 What universities offering currently

Teachers nowadays make use of teaching aids and resources such as graphics and models to help students understand mathematical theories and principles (Gates 2001, 53). Resources are important because they can provide an image or representation of the number concepts and facilitate the understanding of abstract nature of mathematics. It is argued that using concrete resources in the process of learning mathematics can positively "increases students' mathematics achievement and their attitudes towards mathematics" (Kogce et al. 2009, 291).

However, the problem is whether these resources really help understanding. For instance, resource like counters can be used to help students count but the fact is a big number of students cannot do mental calculation and they focus too much on the aspects of mathematics of counting. What's more, another common situation in university mathematics classrooms is that not all students feel easy to learn mathematics with the help of the resources and aids and some of them fail to connect different aspects of math even with the help of numerous graphs and diagrams. Accordingly, Gates (2001, 125) have suggested that a two-way interactions between teachers and students should be strongly considered. Some students may accept the learning method given by teachers and never think by their own and consider whether the present method is the best for them.

4.2 Computer as teaching aid

Modern technology today is used in most universities help teachers to teach students. Computer should be one of the most useful technological tools in mathematics classrooms. Gates (2001, 167) have demonstrated that whether the use of computer is effective or not in mathematics is influenced by the classification of roles of teachers and computers. Computers should be a teaching aid by teachers and controlled by teachers.

Computers used as teaching aid provide a number of advantages to release students from some difficulties during the learning of mathematics and reduce their mathematics anxiety. For example, computer nowadays is used commonly as an 'electronic blackboard' for exposition and presentation. As a source of various information through internet, teachers can search considerable extend information to help to improve students understanding of knowledge. Furthermore, Gates (2001, 168) has also stated that in the form of exercises and games, students can practice mathematics skills and improve their coherence of different aspects of this subject. In addition, vivid images and demonstration by the use of computer resources may increase students' interest and reduce their panic of the difficulties. A perfect example of computers helping learning math is the Integrated Learning Systems (ILS). This system not only sets exercises but also marks the work, evaluates and records progress, and lead students to further advance work (Gates 2001, 169).

5.0 Mathematics in our life

Most people study mathematics until they lose interest or until they find it too hard for them. Low achievement or failure is one situation that making people reject learning a subject, and believe it's not worth to try. However, mathematics is actually important to our life. Selby (1995) has explained how mathematics works in our daily life separately for various aspects. For example, counting by hand or with a calculator is necessary when people calculate weights or amounts like money which appears in daily life. Just like solving mathematics problems step by step, wrong numbers that show in one step of a calculation process would make all the rest incorrect. Moreover, when filling the tax forms, people need to calculate with arithmetic followed the providing instructions step by step. Therefore, arithmetic as one part of mathematics that taught in schools is useful and related to our life.

Additionally, people may argue that aspects like Algebra and geometry which may use with formulas and theories are not related to our life. However, people should "understand formulas or computation methods needed for loans, pensions and investments, for shop keeping or buying and selling with markups or markdowns" Selby (1995). What students learn in mathematics classes in schools is about understanding how the formulas work and being reasonable. By knowing these, it will offer people more options during earning, financing or investing money. What's more, statistics, further topic in mathematics, is very popular nowadays.  Statistics is useful in the measurement or estimation of numbers and the error or variation in the estimates. Such as in the situation of calculating data for productivity or the price of products, statistics used to imply important information from values like average number.  Therefore, as Gates (2001, 24) stated mathematics is a "powerful tool" in the world that we live.

6.0 Conclusion

It is clear that the causes of mathematics anxiety can be identified as, namely, students' values and attitude to mathematics which can be influenced by teachers, parents and even society; students' understanding of mathematics concepts in classes; and time limitation in mathematics exams. There is a figure below helps to illustrate how anxiety develops and affects students' learning of mathematics. From pursuit to avoidance, there may be a lot of reasons such as students find out they are not gifted at mathematics so they refuse to learn anymore, or female students may feel learning this subject is not appropriate for them due to gender stereotype. From confidence to anxiety, unpleasant experience may be the main cause. This experience may include lack of understanding result in failure in solving problems; blamed by parents or teachers as low achievements or being compared with gifted students; time limitation causes stress in exams, etc. All theses causes above may lead to failure in mathematics performance and turn back to even serious avoidance and anxiety.

Figure 3. Math Anxiety Dynamics (Source: Strawderman, W. 2004)

In addition, there is a strong correlation between gender differences and math panic that males are more likely to attend advanced mathematics courses than females. It has been considered due to gender stereotypes except abilities. However, mathematics is used everywhere in our life and careers. From individual bills and expenses calculation to taxation and financing, we need mathematics as a guide to live a more quality life.

7.0 Recommendations

After analyzing the relevant issues in this report, various recommendations to the Head of the Department of Mathematics and Statistics have been developed due to extensive research presenting the impacts of mathematics anxiety on college students. These recommendations are possible solutions to and help students to be more confident in their own ability to understand mathematics and to promote mathematics in the 21st century. The following suggestions can be undertaken to reduce mathematics anxiety and increase students' achievement:

Teacher should develop an encouraging learning environment, free from tension and threatening of embarrassment or humiliation. This may reduce the students' anxiety about being judged by teachers while making mistakes or failing to understand. Mathematics teacher should demonstrate a caring attitude to their students to help them overcome mathematics panic.

Test taking strategies should be given appropriately might help students to raise their achievement and reduce their anxiety of mathematics test.

Students should put themselves under an exam atmosphere when they doing mathematics homework regularly. Therefore, when they solving problems in exams, time pressure will be reduced and students may feel more confidence.

Activities in classes should include both independent and group work. Group work helps students to exchange their ideas with pales and reflecting their understanding to teachers. Therefore, their problems can be solved immediately or they may realize that others have the same problem as they do.

Teaching aids and resourced should be used effectively. Make a connection of mathematics in schools and new technologies.

Small classes like tutorials should be increased instead of leaving multitudinous homework to students to finish after classes. Once students confused or do not understand during their studying, they cannot get solutions immediately and they may lose the motivation to continue. Increasing hours of tutorials may solve this problem effectively.

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