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An Instrument to Measure An Instrument to Measure Mathematics AttitudesMathematics Attitudes

Presenters: Wei-Chih Hsu Presenters: Wei-Chih Hsu Professor : Ming-Puu ChenProfessor : Ming-Puu ChenDate : 09/15/2008Date : 09/15/2008

Tapia, M. & Marsh, G. E. (2004). An instrument to measurement mathematics attitudes. Academic Exchange Quarterly, 8(2) <http://www.rapidintellect.com/AEQweb/cho25344l.htm>; 2004 Accessed 15.08.2004.

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IntroductionIntroduction

• This article – A report of the development of a new instrument to measure s

tudents’ attitudes toward mathematics.– Determine the underlying dimensions of the instrument by ex

amining the responses of 545 students.

• Attitudes Toward Mathematics Inventory (ATMI).– The reliability coefficient alpha was .97– A maximum likelihood factor analysis with a varimax rotatio

n yielded four factors• self-confidence; • value of mathematics;• enjoyment of mathematics; • motivation.

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Literature review (1/3)Literature review (1/3)

• Conventional wisdom and some research suggest that – students with negative attitudes toward mathematics ha

ve performance problems simply because of anxiety.• One of the first instruments developed was the Dutton Scale (Dutton,

1954; Dutton & Blum, 1968), which measured “feelings” toward arithmetic.

• Aiken (1974) constructed scales designed to measure enjoyment of mathematics and the value of mathematics.

• Some researchers developed scales dealing exclusively with math anxiety.– the Mathematics Anxiety Rating Scale (Richardson & Suinn, 1972), – the Mathematics Anxiety Rating Scale–Revised (Plake & Parker, 1982),

– the Mathematics Anxiety Questionanaire (Wigfield & Meece, 1988).

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Literature review (2/3)Literature review (2/3)• The Fennema-Sherman Mathematics Attitude Scales (19

76)– One of the most popular instruments used in research over the last

three decades.– Consist of a group of nine instruments:

• (1) Attitude Toward Success in Mathematics Scale, • (2) Mathematics as a Male Domain Scale, • (3) Mathematics as a Mother Scale, • (4) Mathematics as a Father Scale, • (5) Teacher Scale, • (6) Confidence in Learning Mathematics Scale, • (7) Mathematics Anxiety Scale, • (8) Effectance Motivation Scale in Mathematics, • (9) Mathematics Usefulness Scale.

– 108 items, and takes 45 minutes to complete. – Subsequent research has questioned the validity, reliability (Suinn

and Edwards, 1982), and integrity of its scores (O’Neal, Ernest, McLean, &Templeton, 1988).

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Literature review (3/3)Literature review (3/3)

• Melancon, Thompson, and Becnel (1994) – Isolated eight factors rather than nine, and they were unable to

find a perfect fit with the model proposed by Fennema and Sherman.

• Mulhern and Rae (1998) – Identified only six factors, – Suggested that the scales might not gauge what they were inten

ded to measure.• Other researchers suggest

– Students may find math to be simply unappealing or socially unacceptable, although they may actually have high aptitude.

• The Attitudes Toward Mathematics Inventory (ATMI) was developed.– Finding a need for a shorter instrument with a straightforward

factor structure.

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Methodology (1/4)Methodology (1/4)• The Attitudes Toward Mathematics InventoryThe Attitudes Toward Mathematics Inventory

– The 49-items • Were constructed in the domain of attitudes toward mathematics to ad

dress factors reported to be important in research.

– Items were constructed to assess • 1.Confidence (Goolsby, 1988; Linn & Hyde, 1989; Randhawa, Beamer, & Lundberg, 1993).

– Measure students’ confidence and self-concept of their performance in mathematics.

• 2. Anxiety (Hauge, 1991; Terwilliger & Titus, 1995). – Measure feelings of anxiety and consequences of these feelings.

• 3. Value (Longitudinal Study of American Youth (1990). – Measure students’ beliefs on the usefulness, relevance and worth of mathe

matics in their life now and in the future.

• 4. Enjoyment (Ma, 1997; Thorndike-Christ, 1991). – Measure the degree to which students enjoy working mathematics and mat

hematics classes.

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Methodology (2/4)Methodology (2/4)

• 5. Motivation (Singh, Granville, & Dika, 2002; Thorndike-Christ, 1991).

– Measure interest in mathematics and desire to pursue studies in mathematics.

• 6. Parent/teacher expectations (Kenschaft, 1991; Dossey, 1992).

– Measure the beliefs and expectations parents and teachers have of the students’ ability and performance in mathematics

• SubjectsSubjects– 545 high school students, 302 boys and 243 girls, enrolled in mathematics hi

gh school classes• 135 freshmen, 153 sophomores, 168 juniors, 84 seniors, and five 8th-grade stude

nts.

• ProcedureProcedure– Teachers administered a 49-item inventory to the subjects during their classes. – Four months later, the inventory was re-administered to 64 subjects who had previou

sly taken the survey.

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Methodology (3/4)Methodology (3/4)

• MaterialsMaterials– The ATMI was originally a 49-item scale. – The items were constructed using a Likert-scale format with the

following anchors: 1 strongly disagree, 2 disagree, 3 neutral, 4 agree, and 5 strongly agree.

– The score was the sum of the ratings.• ResultsResults

– For scores on the 49 items alpha was .96, indicating a high degree of internal consistency for group analyses.

– Of the 49 items, 40 had item-to-total correlations above .50, the highest being .82.

– The mean and standard deviation of the total score were 169.74 and 32.06 respectively.

– The standard error of measurement was 6.07.

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Methodology (4/4)Methodology (4/4)

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Discussion (1/2)Discussion (1/2)

• Four subscales were identified as self-confidence, value, enjoyment, and motivation.

• Scores on the 40-item scale – developed through factor analysis

• showed good internal reliability, and test-retest reliability showed stability over time.

• With only 40 items, the estimated time to complete the deletion of the parent/teacher items was surprising.– These items were dropped because of extremely low item-to-

total correlations, which requires some consideration.

• Attitudinal research should concern more than anxiety and competence.– It is clear that other factors are also important.

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Discussion (2/2)Discussion (2/2)

• Far less attention has been directed to the investigation of student attitudes.– Although there is a body of research about attitudes toward

mathematics, most of it is concerned only with anxiety.

• Use of the ATMI may be important for teachers and researchers– Success or failure in math performance is greatly determined

by personal beliefs. – Regardless of the teaching method used, students are likely to

exert effort according to the effects they anticipate, • Personal beliefs about their abilities, • The importance they attach to mathematics, • Enjoyment of the subject matter, • The motivation to succeed.