NORMATIVA DE OBLIGADO CUMPLIMIENTO DIN 53857

Considerable thought was given to choosing the survey instrument used with this study. In the first instance an investigation from the literature was

conducted to ascertain what scales to measure affect were available for use and what constructs and/or sub-constructs of affect did they aim to measure. It was important to choose an instrument whose validity could be defended and whose reliability was sound (Leder and Forgasz, 2002:98). A valid measure is one that measures the construct it is expected to measure. Scales are

measured for validity in the literature. Factor analysis can be used to construct a questionnaire that measures an underlying variable and hence it would appear to support the validity of the scale (Field, 2005:619).

What is common amongst all of these scales is that the measurements that were developed by the research community were to a large extent developed for use with mathematics students and all were examined for their reliability and validity. Nunnaly in Chamberlin (2010:171) regards a 0.80+ internal consistency level as one that provides a sound instrument for the mathematics education community. More recently a maximum level of 0.90 is recommended as higher may indicate that some items in the scale are redundant (Tavakol et al.,

2011:54). Many of the self-report questionnaires would are constructed to use a Likert-scale format.

Instruments used to measure affect include:

1. Observations in mathematics’ classrooms usually carried out by researchers

2. Checklists

3. Questionnaires using Likert scales 4. Interviews of individuals

5. Focus groups

6. Collected dialogue, reflections, journal entries (Leder and Forgasz, 2002:101).

The most common instruments used in studies on measuring beliefs and attitudes showed that questionnaires and interviews and journal entries

predominated (Leder and Forgasz , 2006:411). One criticism of the instruments developed is that they are rarely created for the individual teacher to use in the classroom and a view is expressed that affective instruments should also be easy to implement (Chamberlin, 2010:177).

Later research has questioned the validity, reliability and integrity of the Fennema-Sherman Mathematics Attitude Scale scores (Tapia, 2004:1). Chamberlin (2010:173) cautions that estimates of reliability and validity of scales may become less stable over several decades due to for example changes in word meanings. The Fennema-Sherman scale was used

extensively for many years to measure students’ attitudes to mathematics. This makes the scale unsuitable for use with this study due to the passage of time as validity and reliability of an instrument should be established for the particular group on which the instrument is used. More recently the scale ‘Attitudes Towards Mathematics Inventory (ATMI)’ was designed to measure students’ attitudes to mathematics that the researcher believed must be a shorter

instrument than the 108 items in the Fennema-Sherman scale (Tapia, 2004:19). Four sub-scales were included in the ATMI scale and they included self-

confidence, value, enjoyment and motivation where the value category was designed to measure students’ beliefs on the relevance of mathematics to their lives now and in the future (Tapia, 2004:17). The ATMI scale was designed to be used with adolescents (Tapia, 2004:21). Only a small section of this scale was suitable for the measurement of students’ beliefs and hence was not considered suitable for use with this study.

The Academic Emotions (AEQ) was used alongside four self-developed scales measuring characteristics of the classroom environment. The authors (Frenzel et al., 2007:483) argued that students’ perceived learning environments are significantly related to emotional and social outcomes. The study conjectured that teachers were able to influence and mould students’ value beliefs in the subjects that they taught describing the teacher’s enthusiasm for their subject as emotional contagion (Frenzel et al., 2007:493).

The Experience Sampling Method (ESM), the authors claims, allows insight into motivations, attitudes and beliefs associated with an individual’s behaviours (Leder and Forgasz, 2002:105).

Kloosterman (2002:262) combined the collection of data through the use of a questionnaire and student interviews. In analyzing the outcomes from his study Kloosterman maintains that the interview instrument proved to be more effective than Likert scales in assessing students’ beliefs, attitudes and overall motivation.

The growing body of research indicating the importance of students’ beliefs about mathematics and its learning prompted the development of the

The development of the scale was also prompted by the lack of integration of different categories of beliefs in previous studies (Andrews et al., 2007:211). An instrument was developed consisting of a number of factors and sub-factors to measure students’ mathematics-related beliefs. The focus in the MRBQ scale was on belief systems, relevant categories of beliefs and the way they relate to each other (Op’t Eynde and De Corte, 2003). This instrument was further developed and refined and yielded four conceptually different and reliable scales (Diego-Mantecon et al., 2007: 229). The questionnaire uses a 6-point likert scale to assess students’ beliefs.

The MRBQ scale was developed at the University of Leuven, Belgium by Op ‘t Eynde and de Corte in 2003 (Diego-Mantecon et al., 2007:229). The

questionnnaire was developed for use with fourteen year old Flemish students which suggests it could be appropriate for use with this current study. The instrument was refined subsequently and was shown to yield four reliable factors, each with at least two reliable sub-factors. The study to test the

instrument for transferability between cultures was carried out in England, Spain, Northern Ireland and Slovakia which resulted in the conclusion that the scale was sensitive to context (Andrews et al., 2007:209).The MRBQ has four factors as identified by the results of a principal components analysis which refines and reduces items in a scale to form a smaller number of coherent factors (Pallant, 2007:179). They are:

Beliefs about the role of their own teacher.

Beliefs about their own competence in mathematics. Beliefs in the relevance of mathematics.

Beliefs in mathematics as an inaccessible subject.

Cronbach’s alphas for these factors were 0.92, 0.89, 0.65 and 0.69 respectively (Op ‘ Eynde and Hannula, 2006:123). Cronbach’s alpha values, usually

between 0 and 1 (though occasionally negative), give the average correlation among all the items that make up the scale (Pallant, 2007:6). The higher values indicate greater reliability.

A 6-point scale was used as the scale developers believed that forcing a positive or a negative answer from respondents would lead to better quality data (Diego-Manetcon et al., 2007:3). A 6-point Likert scale is used in the questionnaire with responses to questions scoring from strongly agree (1) to strongly disagree (6).

The 6 points are equidistant from one another. The total for each of the factors is the sum of each of the items scores. Questions are generally positively worded except for the last category (Beliefs in mathematics as an inaccessible subject) being negatively worded. An example of a positively worded item is ‘My teacher tries to make the mathematics lessons interesting’ (Beliefs about the role of their own teacher). In negatively worded items the scoring is reverse scoring from strongly agree (1) to strongly disagree (6). An example of a

negatively worded item is ‘If I cannot solve a mathematics problem I quit trying’ (Beliefs in mathematics as an inaccessible subject).