Research questions 1c and 2c explored the teacher effectiveness subclass of teacher attitudes and beliefs, and were as follows:
Q.1c With respect to mathematics, what similarities and/or differences exist between fourth class teacher attitudes and beliefs in Ireland and Northern Ireland, as reported in TIMSS 2011?
Q.2c How do teachers in Ireland and Northern Ireland describe the role of teacher attitudes and beliefs in student learning and achievement in mathematics?
Question M2a-e on the TIMSS 2011 Teacher Questionnaire required teachers to indicate how confident they felt in relation to a range of classroom practices. A three point Likert scale was used, with options ranging from very confident to not confident. Table 4.16 below shows the results. Northern Irish teachers were significantly more confident than Irish teachers with respect to every classroom practice apart from answering students’ questions about mathematics, for which the difference was not statistically significant. A possible explanation for this may be that TIMSS 2011 teachers in Northern Ireland were more experienced and may therefore have felt more confident about their teaching. In addition, teachers in Northern Ireland benefitted from more mathematics-related professional
development, which may have boosted teacher confidence in teaching the subject. Although it is not explored in the TIMSS data, qualitative interviews showed that P6 teachers in Northern Ireland had more consecutive years of experience teaching P6 in comparison with their Irish counterparts (see table 3.6). If this was an unobserved factor within the TIMSS 2011 data, it may also explain why Northern Irish teachers were more confident than Irish teachers.
Table 4.16 How confident teachers feel in relation to a range of classroom practices (M3e)
Maths Confidence Ireland Northern Ireland Statistical Significance How confident teachers
feel to: Very Conf. Some- what Conf. Not Conf. Very Conf. Some- what Conf. Not Conf. Chi- Square P- Value M2a: Answer Students’
Questions about Mathematics 89.6% 10.4% 0.0% 88.6% 11.4% 0.0% 1.784 0.182 M2b: Show Students Variety of Problem Solving Strategies 67.2% 32.2% 0.6% 80.3% 19.7% 0.0% 165.581 <.001 M2c: Provide Challenging Tasks for
Capable Students 61.6% 35.0% 3.4% 70.8% 28.5% 0.7% 104.033 <.001 M2d: Adapt Their Teaching to Engage Students’ Interest 65.9% 32.4% 1.7% 75.2% 24.1% 0.7% 77.743 <.001
M2e: Help Students Appreciate the Value of
Learning Mathematics
64.5% 34.3% 1.2% 70.9% 29.1% 0.0% 77.743 <.001
During qualitative interviews, teachers were asked about the attitudes and beliefs that were important for promoting student learning and achievement. Two teachers in Northern Ireland pointed out that a confident teacher attitude towards mathematics was important for promoting positive student outcomes in mathematics. This echoes the finding by Stipek et al. (2001) that teacher self-confidence is significantly correlated with student self-confidence. Interestingly, both teachers linked teacher
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confidence to teacher mathematics knowledge and surmised that if a teacher is lacking in their mathematical knowledge, they will not communicate a confident attitude towards mathematics within the classroom, which will in turn impact negatively upon students. For example, Michael (School D, Northern Ireland) said:
… the teacher who is maybe not as confident, it will show with the kids. Because as you go up the school … you could be caught out if you don’t know your stuff.
Similarly, Geraldine (School C, Northern Ireland) noted:
Some teachers really lack confidence in maths … and for example the teachers further down the school [teaching younger classes], who are very capable say “I haven’t done that [angles] for ages!”
In fact, confidence was linked to mathematics interest, attitudes and motivation by teachers and this is discussed in detail in section 4.5.2 of this chapter, which discusses factors that hinder teachers in promoting student achievement. However, to synthesise interviewee views regarding confidence, it was perceived that confidence is influenced by teacher mathematics knowledge. It was also perceived that if a teacher is lacking in confidence regarding mathematics, they may hold a negative attitude towards the subject or have less interest in it, which in turn could lead to them being less motivated in their teaching of the subject. The synergy between teacher knowledge, confidence and teaching of mathematics described here is consistent with findings by Geist (2015), who links teacher perceptions about their mathematics knowledge to their confidence about their mathematics ability and in turn to their mathematics teaching approach.
One of the most notable findings regarding teacher attitudes and beliefs, was the notion that the attitude communicated by the teacher towards mathematics was picked up and replicated by their students. This is notable, as the literature to date has been unclear about the way in which teacher attitudes or beliefs impact upon their
classroom practices and, in turn, on student outcomes. Interestingly, the data revealed that the classroom practice of communicating a positive, enthusiastic attitude towards mathematics resulted in students adopting a more positive attitude themselves. This is substantiated by several studies which find correlations with teacher and student attitudes (Stipek et al., 2001; Geist, 2015). Furthermore, it is notable that students were reported to perform better in mathematics when their teacher communicated this strong positive attitude towards the subject. For example, Geraldine (School C, Northern Ireland) noted that parents have “said to me that their child has learnt more because of my enthusiasm for it [mathematics].” However, it may be the case that teachers who have a strong mathematics background and communicate positive attitudes towards mathematics to their students also engage in other classroom practices that promote student achievement. For example, Una (School C, Ireland) reflected that her enthusiastic attitude towards mathematics motivates her to devote time to mathematics teaching for one hour every day. She explained:
I do maths every day without fail. If there is nothing else done I will do it. Nevertheless, communicating a positive attitude towards mathematics, unlike many other classroom practices, is linked definitively by multiple interviewees to increased student achievement and it is therefore noteworthy. However, further research in this area is needed to substantiate these anecdotal reports.
Another interesting finding revealed in this study was the strong link between a teacher’s mathematics background and past experiences, and their attitudes and beliefs with respect to teaching mathematics. This is described in detail in the teacher background section of this chapter (section 4.2.3). To summarise, however, the data revealed that teachers who had positive past experiences and backgrounds with mathematics held very positive attitudes towards mathematics and communicated their love and enthusiasm for mathematics within the classroom. On the other hand,
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teachers who had negative past experiences with mathematics held strong attitudes that the students in their own class should not be subjected to similar negative experiences. This translated into classroom practices that involved these teachers making extra efforts to make mathematics enjoyable, interesting and understandable.