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Researching the AttitudesTowards Mathematics in BasicEducationMiriam Cardoso Utsumi & Clayde Regina MendesPublished online: 02 Jul 2010.

To cite this article: Miriam Cardoso Utsumi & Clayde Regina Mendes (2000)Researching the Attitudes Towards Mathematics in Basic Education, EducationalPsychology: An International Journal of Experimental Educational Psychology, 20:2,237-243, DOI: 10.1080/713663712

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Educational Psychology, Vol. 20, No. 2, 2000

RESEARCH NOTE

Researching the Attitudes Towards Mathematicsin Basic Education

MIRIAM CARDOSO UTSUMI, UNICAMP, Brazil

CLAYDE REGINA MENDES, PUC ± Campinas, Brazil

ABSTRACT The objective of this study was to check attitudes towards mathematics and to

analyse if there are differences in attitudes that could be attributed to the type of school, gender,

grade, age, the frequency in which mathematical problems were understood, the amount of days

dedicated to the study of mathematics, school failure, whether help on the completion of

homework was offered and to the self-perception of mathematical performance. A total of 209

students of the 3rd and 4th Grades of basic education in the private school system in

Campinas, SaÄ o Paulo, Brazil, were surveyed. They responded to an attitude towards

mathematics scale and to a questionnaire for their characterisation, during school hours and in

the absence of their mathematics teacher. The average ® gure on the attitudes scale was 52.718,

with a standard deviation of 11.837. Signi® cant statistical differences were found ( a 5 0.05)

in the attitudes according to the type of school, the frequency in which the subjects understood

the mathematical problems solved in the classroom, grade, age and to the self-perception of

mathematical performance.

Currently, the Brazilian education system is divided into: basic education, middleeducation and higher education. Children are expected to stay in school for 4 years soas to ® nish the ® rst and second cycles (1st to 4th Grades), another 4 years to ® nish thethird and fourth cycles (5th to 8th Grades) of basic education and a further 3 years to® nish middle education; adding up, therefore, to a total of 11 years.

Nevertheless, for a number of reasons, ranging from the lack of openings into publicschools, a series of school failures and even the need for premature engagement in thework force to contribute to family income, many children are not able to ® nish middleeducation.

There is a belief that the subjects of Portuguese and mathematics are the ones thatconstitute the most repeated failures, which generates negative attitudes towards thesesubjects and, in many situations, repellence as well.

The in¯ uence of a few affective variables, especially attitudes, has received specialattention from educators, mainly after Brazil (1998) published the Paraà metros Curricu-

ISSN 0144-3410 print; 1469-5820 online/00/020237-07 Ó 2000 Taylor & Francis Ltd

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238 M. C. Utsumi & C. R. Mendes

lares Nacionais (National Curriculum Parameters), which af® rmed that the anxietypresent in learning situations can generate an unfavorable attitude, which could resultin an impediment to learning.

In other countries, the concern for the in¯ uence of affective variables in learning ismuch older, having been intensi® ed after Aiken (1961) organised a Scale of AttitudesTowards Mathematics, which was later revised by Aiken and Dreger (1963).

This scale has been widely accepted by researchers who study attitudes towardsmathematics, because it is an instrument that measures only the attitude towards thesubject itself, disregarding the teacher’s performance or the type of mathematicalactivity proposed.

According to Klausmeier (1977):

¼ the word attitude is used to mean not only the variegated emotional statesof individuals, as well as identi® able public entities, which are used tocommunicate signi® cances among individuals that speak the same language.(p. 413).

The term attitude presents many de® nitions that often complement each other; accord-ing to Thurstone (1928, quoted by GoncË alez, 1995):

¼ attitude is the total sum of inclinations and human feelings, prejudices ordistortions and preconceived notions, ideas, fears and convictions regarding acertain matter. (p. 17).

In this study, we will consider the de® nition presented by Brito (1996), according towhom:

¼ attitude can be de® ned as a personal inclination, idiosyncratic, present inall individuals, directed to objects, events or people, that takes on a differentdirection and intensity according to the experiences each individual has had.Besides, it presents components from the affective, cognitive and motordomain. (p. 11).

It seems that there is not a consensus in the scienti® c literature about the existingrelations between performance and attitudes, while some research does not ® ndevidence of signi® cant relations between performance in mathematics and attitudestowards this subject (Kulubya & Glencross, 1997); others (Kloosterman & Cougan,1994; Ma, 1997; Norwich, 1994) have con® rmed the existence of strong relationshipsbetween affective variables and school performance.

It is thus believed that the teachers and the school in general should give specialattention to these variables, including, in its planning, objectives that aim to developattitudes in students that are more positive, especially towards mathematics.

According to Leikin and Zaslavsky (1997), group activities can be a way to make thedevelopment of positive attitudes feasible. In a study conducted by these researcherswith four classes of students with poor school performance in Grade 9 (equivalent tothe 1st grade of Brazilian middle education), one of these classes was selected to be thecontrol group, in which the teaching of mathematics was processed in the traditionalmethod, while, for the others, a co-operative work methodology in small groups wasused. Data collection was done through classroom observation, student reports on theirown activities, interactions and attitudes towards the experimental method, and anattitude questionnaire. The results have shown that in the small co-operative groups

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Attitudes Towards Mathematics 239

there was an increase in student participation, creation of a larger number of opportu-nities for the exchange of information and an increase in positive attitudes.

Given these considerations, the objective of the present study was to verify theattitudes towards mathematics and to analyse whether there were differences in attitudethat could be attributed to the type of school, gender, age, how often mathematicalproblems were understood, the number of days dedicated to the study of mathematics,school failure, whether the students received help with their homework and theself-perception of mathematical performance.

Method

Subjects

The participants of this study were 209 students from the 3rd and 4th cycles (6th, 7thand 8th Grades) of basic education in a school from the public system and from aschool from the private system in the region of Campinas, SaÄ o Paulo, Brazil.

Instruments

A Scale of Attitudes Towards Mathematics (Aiken, 1961; Aiken & Dreger, 1963),which was translated, adapted and validated by Brito (1996), is of the Likert type andis made up of 20 items, 10 of which are positive feeling statements and 10 of negativefeelings, with values that may vary from 20 to 80. In addition to this scale, aquestionnaire was also employed with questions that aimed to characterise the subjectsof the research.

Procedure

The Scale of Attitudes Towards Mathematics and the questionnaire, with questionsabout the subjects, were ® lled in during class time and in the absence of the mathemat-ics teacher.

Results

The public school was responsible for 53.6% of the sample and the private one for46.4%, with 56.9% of the subjects being male and 43.1% female.

The age of these subjects ranged from 11 to 19 years of age (average 5 13.29 years),with a standard deviation of 1.56 years.

The average value in the attitude scale was 52.718, which means that the attitude ofthese subjects towards mathematics was a positive one.

When the subjects were grouped according to the school they attended, the analysisof variance, t (204) 5 2.38, p 5 0.018, indicated that the students attending publicschools have signi® cantly more positive attitudes than students in the private school.

Most of these subjects (60.8%) were not helped in their studying or completion ofhomework assignments in mathematics and, amongst those who were helped, mostwere assisted by family members living in the same place as the subject.

Cooper et al. (1998) highlighted the fact that attitudes and parent participation in thehomework assignments can be transmitted to the children, having an effect theireducation. A study conducted by these researchers with 700 triads, each composed of

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240 M. C. Utsumi & C. R. Mendes

one student (from the 2nd to 12th Grade), his or her father and teacher, made evidentthat the amount of homework assignments completed by the student were strongly andpositively linked to their school performance, especially in the higher grades.

In the present study, nevertheless, being helped or not in the completion of home-work assignments did not in¯ uence the subjects’ attitudes towards mathematics in astatistically signi® cant manner, t (199) 5 2 1.30, p 5 0.195.

Walberg et al. (1985) have synthesised the research of the time that indicated thatcompletion of homework assignments had a positive effect on learning.

In some recent research, Balli (1998) stated that homework assignments are import-ant to help the student practise and reinforce the concepts learned in the classroom,but, as indicated by studies, this importance does not seem to have been perceived bythese subjects, as 35.8% stated that they studied mathematics on not one single day aweek.

The subjects’ attitude towards mathematics was not in¯ uenced by the number ofdays dedicated to the study of this subject, F(4, 196) 5 1.912, p 5 0.110.

Despite the little dedication to the study of mathematics, 88.5% of the subjects statedthat they understood the mathematical problems posed in the classroom always or mosttimes. Mathematics was the subject most often mentioned as the subjects’ favourite,whereas history was the one most often mentioned as least favourite.

The variance analysis, F (2, 202) 5 25.792, p 5 0.0000, has revealed that the fre-quency with which subjects understood the mathematical problems posed in theclassroom was related in a statistically signi® cant why to the subjects’ average inthe scale of attitudes, which means, the more often the subjects understood themathematical problems posed in the classroom, the better their attitude towardsmathematics was; or even vice versa, that is, the better a subject’s attitude towardsmathematics the more often he or she understood the mathematical problems posed inthe classroom.

It was observed that the female subjects had slightly more positive attitudes towardsmathematics than the male subjects, which is not commonly stated in related literature,although this difference is not statistically signi® cant, t (204) 5 2 0.14, p 5 0.88.

These results are in accordance with the work of Ma and Kishor (1997), in whichthey grouped and summarised, through meta-analysis, the ® ndings of 113 pieces ofresearch about the relation between attitudes and mathematical performance. They didnot ® nd signi® cant differences between attitude and mathematical performance attribu-table to gender, but they observed the existence of a relation of dependence betweenschool grade and ethnic af® liation of the subjects to these variables.

In relation to grades, the subjects from the 6th Grade had, on average, attitudes thatwere more positive towards mathematics than the subjects on the 7th and 8th Grades,and this difference is statistically signi® cant, F (2, 203) 5 6.597, p 5 0.0017.

Whether or not they had failed a grade previously in¯ uenced the attitude of thestudents in this sample towards mathematics; the variance analysis, t (202) 5 2 3.20,p 5 0.002, has indicated that the students that have never failed a grade had attitudesthat were signi® cantly more positive than the ones expressed by the subjects that hadalready failed at least one grade previously.

Age seems to be a factor that in¯ uenced the attitudes of the subjects in this sample,as the variance analysis, F (5, 198) 5 3.516, p 5 0.005, has shown signi® cant differencesin the attitudes, with the subjects that were 16 years of age or older expressing morenegative attitudes (average 5 46.778, standard deviation 5 9.723) than the ones ex-pressed by the subjects that were 11 or 12 years old, the averages being respectively:

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Attitudes Towards Mathematics 241

average 5 60.083 (standard deviation 5 9.080) and average 5 56.000 (standard devi-ation 5 12.289).

When the subjects were grouped according to the self-perception of mathematicalperformance, the variance analysis, F (3,196) 5 38.418, p 5 0.000, showed the exist-ence of signi® cant differences among the groups. The Turkey-HSD test indicated that,as the self-perception of mathematical performance improved, so did the subjects’attitude towards this subject.

Conclusion

This study has revealed that, for this sample, there were no statistically signi® cantdifferences in attitudes towards mathematics associated to gender. Even though thisfact is not very common in the related literature, it seems to show advancement in therelationship between mathematics and female attitudes, being a means to demystify theidea that mathematics is a male domain.

Streitmatter (1994, quoted by Loef¯ er, 1997) showed in his studies that teacherstend to give more attention and help to male subjects, so that they can learn tocomplete their assignments, whereas, when dealing with female subjects, there is atendency that the teachers will themselves complete the assignments. Furthermore,male subjects are criticised for their lack of effort more frequently, while the femalesubjects are criticised for their lack of skill.

Based on similar results, Loef¯ er (1997) pointed out the need to monitor the learningenvironment, to attempt to avoid this and other gender-related prejudices, suggestingthat co-operative environments be used, as they provide suf® cient support for womento overcome the physical and emotional risks needed for acquiring new skills, as well asto recognise and assert their competence.

Turner et al. (1998) stated that negative feelings are common in mathematics classeswhere students frequently report being confused about the complexity and the precisionof the subject. These negative qualities in the teaching of mathematics are assumed toin¯ uence the performance of the students in mathematics and, later on, their choice ofcareers related to the area of pure sciences.

In accordance with these researchers, the present study has shown that, as schoolingprogresses, attitudes towards mathematics become less positive, a fact that may beassociated with the decrease in the understanding of the subject or of the contenttaught.

The documents of the National Council of Teachers of Mathematics (1989) empha-sises the importance of promoting positive attitudes and interest hand-in-hand with theunderstanding of mathematical concepts. In this way,

¼ understanding how teachers create positive climates for learning and motiva-tion in mathematics has considerable pedagogical importance as well asimplications for students’ mathematical involvement. (Turner et al., 1998, p.733).

A few studies (Hornibrook et al., 1997; Jacobs et al., 1996; Leikin & Zaslavsky, 1997;Loef¯ er, 1997) have suggested that a way to improve performance and attitude towardsmathematics is working in co-operative groups, where the students help each other.

That way, to try to increase the students’ understanding of the subject and, maybe,to halt or hamper the decrease of positive attitudes towards mathematics as studentsmove up to higher grades, the authors of the present study believe that some kind of

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242 M. C. Utsumi & C. R. Mendes

intervention programme, based on differentiated activities and in solving problems,should be adopted by teachers.

Acknowledgements

MCU has a teaching degree in Mathematics, is taking her Ph.D. in Education, in thearea of Mathematical Education and at the time this study was developed, received® nancial support from the FundacË aÄ o de Amparo aÁ Pesquisa do Estado de SaÄ o Paulo(Research Assistance Foundation of the state of SaÄ o Paulo).

CRM has a teaching degree in Mathematics, is post-doctorate in Education, in thearea of Mathematical Education.

Correspondence: Miriam Cardoso Utsumi, Caixa Postal 183, CEP 13140± 970, PaulõÂ nia,SaÄ o Paulo, Brazil. Email: mutsumi@zaz.com.br; or Clayde Regina Mendes, Rua DomBosco, 75-Apto 124, CEP 13070-060, Campinas, SaÄ o Paulo, Brazil. E-mail:clayde@acad.puccamp.br

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