Context
According to Hammersley & Scarth (1993) it is important to understand the context in which a report is produced (p.217). Fenema et al carried out their research in the United States of America in 1990. The subjects were 38 female 1st grade teachers from 24 elementary schools. Tiedemann carried out his research 10 years later in 2000 in a North German city. The subjects were 52 3rd and 4th grade teachers of which 5 were male. It is not clear from the research papers how they both chose their samples. However, it seems likely that both used a form of cluster sampling. Denscomb (1998) states that the logic behind cluster sampling is that, in reality it is possible to get a good sample by focussing on naturally occurring clusters of the particular area the researcher wishes to study and schools are a good example of a naturally occurring cluster. (p.14). Cluster sampling comes under the heading of probability sampling which is based on the idea that people or events that are chosen are done so because the researcher has an idea that these will be a representative cross-section of people in the population being studied. Denscomb (1998) adds that cluster sampling can save a great deal of time that would have been spent travelling to various research sites throughout the land. However, he states that one must remember the aim is to achieve a representative cluster and this could be obtained through random or stratified sampling (p.13). Fenema et al (1990) chose to study only female teachers; this may be because this is an accurate representation of the population, if there were little or no male 1st grade teachers. If they had particularly chosen to research female teachers attributions and beliefs this would have been stated somewhere in the research paper. Tiedemann however, had 5 male teachers within his sample of 52. It could be presumed that if a stratified approach was used, male teachers therefore, represent approximately 10% of teachers in the population he studied. Denscomb (1998) acknowledges that random sampling is likely to provide a representative cross-section of the whole, however he adds that stratified sampling has a significant advantage over random sampling in that the researcher can assert some control over the selection of the sample in order to assure that key people or factors are covered by it and are representative of how they are in the wider population (p.13).
Purpose
Fenema et al (1990) states that research had not investigated whether or not teachers hold different beliefs about girls, boys and mathematics. Therefore their study aimed to identify successful and unsuccessful mathematics students and the accuracy of their identification; teacher’s attributions of the causes of successes and failures of girls and boys and teachers’ beliefs about the characteristics of their best girl and boy mathematics students (p.56). They did not hypothesise about what they expected to find, but outlined a set of questions they wanted to answer. Tiedemann (2000) research title is very similar to that of Fenema et al’s (1990) and he quotes Fenema et al’s (1990) research in his review of the literature. His aim is not to re-test their findings, but to test for perceptual bias in teacher beliefs about gender in their teaching of mathematics at elementary schools (p.194). Tiedemann (2000) believes that it is still difficult to draw any conclusions with confidence. He is however working 10 years later and uses research conducted after Fenema et al’s (1990) to make a hypothesis of what he expects to find in relation to teachers attributions and beliefs.
Bell (1999) identifies that it is useful to make statements about relations between variables as it provides a guide to the researcher as to how the original idea may be tested and they can attempt to find out whether it is so among the subjects in the sample (p.25). Cohen & Manion (1994) agree that hypotheses and concepts play a crucial part in the scientific method, also known as positivism, defined as all genuine knowledge is based on sense experience and can only be advanced by means of observation or experiment. Positivism, however, has been challenged from many quarters (p.11), Cohen & Manion (1994) quote Kierkegaard’s (1974) theory of existentialism saying that people should be freed from objectivity and having to discover general laws to explain human behaviour, but instead consider ones’ own relationship to the focus of the enquiry, which is the capacity for subjectivity (p.23). Tiedemann (2000) states an underlying assumption of his study, that there is no difference in gender achievements or teacher beliefs in mathematics. Cohen & Manion (1994) criticise embarking on a study having pre-interpreted the world to be researched as the assumptions of the researcher can influence upon the results (p.25).
Methods
Both Fenema et al (1990) and Tiedemann (2000) used questionnaires to gather data. Fenema et al (1990) used two types of questionnaires, one being a structured individual interview the other a non-direct questionnaire, in their research. Denscomb (1998) states that a structured interview, which involves tight control over the format of the questions and answers, is similar to a questionnaire that is administered face to face. He adds that structured interviews lend themselves to the collection of quantitative data, which was the type of data Fenema et al (1990) did gather. There are issues to consider when deciding to conduct a questionnaire directly. Denscomb (1998) states that research shows when questioning people face-to-face informants respond differently depending on how they perceive the person asking the questions. In particular the informant’s answer may be tailored to match what they feel fits in with what the researcher expects from them or to what they perceive to be the researcher’s point of view (p.116). As already stated the researchers assumptions of the study can affect the outcome. For example in Fenema et al’s (1990) structured interview the teachers might not readily admit that the pupils lack of success is due to them not providing the support for the child even if it is their belief. In the case of Tiedemann (2000) his underlying assumption that there is no difference in gender achievements or teacher beliefs in mathematics could be perceived by the informant who modifies their response to this expectation. Cohen & Manion (1994) cite Kitwood’s (1977) critique of direct contact questionnaires; he states that there is a trade off between reliability and validity. If the researcher develops an atmosphere where the respondent feels at ease the more likely they are to disclose true information which is necessary to the validity, however reliability is enhanced by rationalisation, but when the interviewer becomes rational and calculating the less likely the situation will contain a human element and the more calculated the response is likely to be (p.282). Denscomb (1998) reflects on both types stating that questionnaires, which are conducted without direct contact, remove the impact of face-to-face interaction (p.88). Cohen & Manion acknowledge the bias that can impact upon direct interaction, but “it allows for greater depth than is the case with other methods of data collection” (p.272). By Fenema et al (1990) using both types of questionnaires, they have experienced the advantages of both. Tiedemann (2000) used only the non-direct contact and therefore his study as Cohen & Manion (1994) stated could lack greater depth and a human element.
Fenema et al (1990) and Tiedemann (2000) employed similar styles of questionnaires to collect data about teachers’ attributions. Both used a non-direct questionnaire, which contained statements about the pupils that the teachers had to estimate on a scale. Fenema et al’s (1990) sex-role stereotype questionnaire was an adaptation of another researcher’s method of data collection. The 20 descriptors, concerning characteristics of the teachers best mathematics pupils, contained 2 opposing statements, the teachers responded from high agreement to the right phrase to high agreement with the left phrase.
The structured interview and questionnaire used by Fenema et al (1990) and the questionnaire used by Tiedemann (2000) all contained closed questions where the answers are restricted to options supplied on the questionnaire. Denscomb (1998) acknowledges both the advantages and disadvantages of closed questions. He states that the structure of such a questionnaire provides the researcher with information which is of the same length and that can be easily compared, quantified and analysed. In the case of both research papers where the results were of a statistical nature, it would seem closed questions were the most suitable to use. Denscombe (1998) notes the disadvantages saying there is less scope for respondents to supply answers which reflect the exact facts of true feelings of a topic and as a result of this the respondents may become frustrated by “ not being able to express their views fully in a way that accounts for any sophistication, intricacy or even inconsistencies in their views” (p.101). Fenema et al’s (1990) questionnaire overcomes some of the limitations of closed questions by allowing teachers to rank their agreement with the phrases from 1 to 5, enabling them to strongly agree with one phrase by marking 1 or 5, or to indicate a modification by marking 2, 3 or 4. Tiedemann’s (2000) questionnaire similarly is structured to allow teachers to respond on a three-point scale of true, not true and partly true. However Bell (1999) cautions against the use of ambiguous words such a partly true, which may mean something different to each respondent (p.121).
In Fenema et al’s (1990) attribution interview each teacher chose their 4 most successful mathematic students and 4 most un-successful students to attribute the cause of their success or failure. The paper does not state the criteria for how the students were classified as most or least successful, this information however is crucial to understand the teachers’ beliefs of what constitutes success or failure in mathematics, which is central to the research question. Tiedemann (2000) however states the criteria of a successful or failing mathematics student. He chose three bands of performance level that the students would fall into, 2 from the upper level, 2 from medial and 2 from the lower performance level. These bands were derived from performance grades attributed to the children in a similar way children in the UK are levelled from performance in QCA or SATs tests. One of Fenema et al’s (1990) objectives however was to discover how accurate the teachers were in selecting their most and least successful students. This was done by testing all 314 girls and 368 boys taught by the teachers and matching the results to the accuracy of the teachers’ choices. Therefore, it was important that the teachers chose the students as it gave a greater insight into whether they were able to identify their most and least successful students. However, it is important to note that there will always be the issue of whether the test results of the students are wholly valid. The test questions were read to the students by a trained tester. This immediately puts visual learners or children with poor memory at a disadvantage. According to Felder & Silverman (2002) visual learners remember best what they see - pictures, diagrams, flow charts, time lines, films, and demonstrations, verbal learners however get more out of words, spoken or written and therefore could have an advantage in this form of spoken test. Dyslexic students may also be put at a disadvantage from this style of test. These children, who are often able mathematicians, according to the British Dyslexia Association (2002) tend need more time when completing mathematical activities due to contributing factors such as poorer short-term memory and slower writing speeds. They can also have problems with auditory processing. Fenema et al’s (1990) test had a time limit, again putting some children at a disadvantage.
Results
Fenema et al’s (1990) and Tiedemann’s (2000) results opposed each other in two particular aspects. Fenema et al (1990) concluded that in both the most and least able categories, teachers attributed girls’ success and failure to effort considerably more so than for boys. Tiedemann (2000) however found that teachers thought that girls profited less from additional effort than boys and had to exert relatively more effort to achieve the level of actual performance in mathematics. Under the category of ability, both research papers contrasted each other in their findings. Tiedemann (2000) states that teachers attributed failure in girls more to low ability, whereas Fenema et al (1990) found that boys success was attributed more to ability than girls’ success. When analysing the results obtained by both parties one must take into account the differences in their research methods and contexts. The researchers did not study children of the same age, in fact the children in Fenema et al’s (1990) research were 3 to 4 years younger than in Tiedemann’s (2000). The research was conducted in differing countries and Fenema et al’s (1990) sample size (pupils) was double that of Tiedemann’s (2000). Denscomb (1998) reflects on issues when using a sample of 300 or less (Tiedemann’s (2000) being 312). He states that extra attention needs to be paid to the issue of how representative the sample is and caution is needed about the extent to which generalisations can be made on the basis of the research findings (p.24). Does this mean therefore that Tiedemann’s results are less viable than Fenema et al’s (1990) due to his sample size? This would have to be investigated in relation to how representative his sample was. Fenema et al (1990) may have a larger sample but there is no information on how representative it is. Denscombe (1998) also states the smaller the sample the simpler the analysis should be, in the sense that the data should be subjected to fewer subdivisions (p.24). Tiedemann however divides his questionnaire in 6 categories containing 21 items; according to Denscomb (1998) this can ‘dilute’ results (p.24). The issues of bias and validity in terms of Fenema et al’s (1990) interview should also be taken into account. As previously discussed these issues can affect results and more information on how the interview was conducted is needed before an analysis of its reliability can be conducted.
To close, it is difficult to draw clear and unequivocal conclusions from both these sets of research, although Fenema et al’s (1990) study follows more of the advice for gaining reliable results, such as more than one method of data collection and a large enough sample size. Bell (1999) states that in the analysis, interpretation and presentation of data, care has to be taken not to claim more for results than is warranted. Li (2001) states that when studying all the literature, including both the research papers analysed here, on gender-related beliefs in teachers, the results are inconclusive.
Bibliography
Bell , J. (1999) Doing Your Research Project Bucks: OUP
Cohen, L. & Manion, L. (1994) Research Methods in Education London: Routledge
Denscomb, M. (1998) The Good Research Guide Maidenhead: OUP
Li, Q. (2001) Teachers’ beliefs and gender difference in mathematics: a review Educational Research Vol. 41 No. 1 pp. 63-76
The British Dyslexia Association (2002) Mathematics and Dyslexia - 01/06/03
Tiedemann, J. (2000) Gender-Related Beliefs of Teachers in Elementary School Mathematics Educational Studies in Mathematics Vol. 43 pp. 191-207
Felder, R. M. & Silverman, L. K. (2002) Learning Styles and Strategies - 01/06/03
Fenema, E. Peterson, P. L. Carpenter, T. P. & Lubinski, C. A. (1990) Teachers’ Attributions and Beliefs About Girls, Boys and Mathematics Educational Studies in Mathematics Vol. 21 pp. 55-69
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Hammersley, M. & Scarth, J. & (1993) Beware of wise men bearing gifts: a case study in the misuse of educational research in Gomm, R. & Woods, P. (ed) Educational Research in Action London: Chapman Ltd
