The results of this study confirm the tendency visible in national and international evaluations concerning Swedish students’ attitudes towards mathematics education. Although a great deal of effort has been made at the national level to enhance students’ interest in mathematics, the subject was not regarded as one of the most enjoyable at these two schools, and few students looked forward to their mathematics lessons. However, the students were satisfied with their current mathematics education and felt they got enough help in school. Receiving a grant for a mathematics project demands active mathematics teachers and positive school leaders who have the resources to formulate a vision of how they would like to develop the teaching (cf. Johansson, 2001). Hence, it is possible that the schools that take part in the mathematics initiative are not those that lack resources, although one of the schools in our study was under average concerning the proportion of students passing the subject of mathematics in the ninth grade. It is also possible that the teachers at the two schools have already placed higher demands on the quality of their instruction.
Regarding students’ self-confidence, our study supports the results from National Evaluation (Skolverket, 2005) and recent TIMSS-studies, with 75% of the students considering themselves to be good at mathematics. Hence, in this case the goals of the Swedish steering documents seem to have been attained. Earlier research has shown positive correlation between students’ self-perception and their achievement (e.g. Linnanmäki, 2004). Yet, the results in Sweden are getting worse. Could one possible explanation for this be that students are not provided enough challenges in mathematics in school? NU03 reported that more students (30%) find the mathematics tasks they are given too easy, compared to similar studies (17%) from 1992. Almost 60% of the students in our study considered most of the mathematics tasks they are given to be too easy. Confronting only easy tasks may make the students believe they are skilled in the subject. Good self-confidence and the experience of tasks as too easy correlated in our study.
Research has pointed out that in effective mathematics teaching, students need to be given tasks that challenge them (cf. Hiebert & Grouws, 2007).
The hands-on activities that have been advocated in many in-service education projects by, for example, the National Center of Mathematics Education (NCM), and that have dominated many school projects seem to have led to lower expectations placed on students (Skolverket, 2011a). A new national
curriculum was implemented during the study, and it is too early to judge its effects concerning the compulsory school goals. Similar to the earlier Swedish curriculum (Lpo94), there is a heavy emphasis on everyday mathematics.
Expectations on students concerning more abstract mathematics (for example, proof and proof-related items, which students have traditionally experienced as difficult) are low compared to those in Finland and Estonia (Hemmi, Lepik &
Viholainen, submitted). Yet, teachers are given a great deal of freedom to choose relevant activities for students and even problems with every-day connections can be made more demanding. This is important for the teachers to consider when they go on designing their projects.
Our study shows that a majority of the working methods most commonly used in mathematics instruction are also those that the students found the least enjoyable. However, if we choose to look at how instructive the students consider these working methods the view is quite different, as the methods the students found most enjoyable were not always regarded as the most instructive. Many of the schools that received money from the government for local developmental projects in mathematics teaching stated that they wanted their students to experience mathematics as more enjoyable (Skolverket, 2011a). The question is whether this contributes to better mathematics teaching. Studies (e.g. Askew et al., 2010) have pointed out that even countries that display good results in mathematics have trouble with students’ negative attitudes. Do all mathematics lessons have to be perceived as “fun”, or are there other aspects that can motivate students as well, for example higher-level challenges? In future research it might therefore be desirable not only to study how enjoyable students find different working methods. Other aspects such as “anxiety” and “challenging” may also be of importance.
Another question concerns students’ beliefs about what learning mathematics means. We could argue that, although it is important to listen to students’
opinions, it can be hard for them to evaluate their own learning. For example, the communication and shaping of mathematical discourse is stressed as important both in research (cf. Franke, 2007) and in the Swedish steering documents, but group work and work in pairs are not considered equally instructive as individual work by the students in our study. As shown by Boekaerts andCorno (2005), the learning goals a teacher has in mind are not always adopted by the students, which can make it hard for them to evaluate their own learning in relation to the goals. Nevertheless, it is important to consider students’ opinions, since a negative attitude can make them reluctant in learning situations and cause them to avoid challenges (Granström & Samuelsson, 2007). As Franke (2007) asserts, it is the teacher’s responsibility to foster “a discourse environment that both
supports students and helps to create, among them, new identities that include a favorable disposition towards mathematics” (p. 231). In that discussion, the aims of the mathematics teaching should be brought up to the surface so that teacher and students alike are all working towards the same goal.
Granström and Samuelsson (2007) show that students with already positive attitudes towards mathematics education prefer collective discussions over group work, but at the same time this working method reinforces the negative attitudes of students who already dislike mathematics. More research needs to be done in the field of “how classroom practices are negotiated so that they do not have differentially negative impacts on any particular group of students” (Franke, 2007, p. 237). Our study shows that students with more negative attitudes towards their mathematics education find many working methods both less enjoyable and instructive than students with more positive attitudes. These working methods include individual work, work in textbooks and joint review with the teacher, which are also the ones the students perceive to be most frequently used in their mathematics education. Different ways of working are found enjoyable and instructive by different students, and we have to be careful so that we do not teach in a way that has a negative impact on certain students.
Varying the methods and maintaining an open dialogue with students concerning their beliefs about and attitudes towards mathematics education could lead to an increasing number of students that both enjoy mathematics and achieve the goals. Therefore it will be interesting to see whether, and in that case how, this study’s students’ attitudes and beliefs will change after these two schools have completed their mathematics development projects.
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Appendix 1
Statement Mean Standard
deviation t-value Mathematics is one of the topics I
like best in school Cluster 1 2,50 0,88 12,76*
Cluster 2 1,19 0,45
Total 2,17 0,98
I look forward to mathematics
lessons Cluster 1 2,55 0,66 8,88*
Cluster 2 1,56 0,55
Total 2,30 0,77
I will have use for the mathematics
I learn in school Cluster 1 3,62 0,54 7,71*
Cluster 2 2,79 0,81
Total 3,41 0,71
Most of the tasks in mathematics
are too easy for me Cluster 1 2,69 0,76 1,46
Cluster 2 2,49 0,86
Total 2,64 0,79
I am satisfied with the
mathemat-ics teaching I receive today Cluster 1 3,35 0,67 5,46*
Cluster 2 2,67 0,84
Total 3,18 0,77
In school I get enough help in
mathematics Cluster 1 3,49 0,56 7,61*
Cluster 2 2,56 0,73
Total 3,26 0,73
I am good at mathematics Cluster 1 3,05 0,64 6,08*
Cluster 2 2,14 0,92
Total 2,83 0,82
The two clusters responses to statements about attitudes towards mathematics education and beliefs about themselves as mathematics learners. Maximum value is 4 and minimum value is 1. Cluster 1 (n = 129) and Cluster 2 (n = 43). *p <.001
Appendix 2
Enjoyable Instructive
Working method N Mean SD
t-value Mean SD
t-value Individual work Cluster 1 128 3,02 1,07 5,92* 3,91 0,82 3,12**
Cluster 2 43 1,86 1,21 3,40 0,98
Total 171 2,73 1,21 3,78 0,89
Work in pairs Cluster 1 107 3,50 0,99 -0,33 3,38 0,84 0,18
Cluster 2 32 3,56 1,11 3,34 1,18
Total 139 3,51 1,02 3,37 0,93
Group work Cluster 1 99 3,56 1,05 1,78 3,36 0,89 1,65
Cluster 2 33 3,18 1,01 3,06 1,00
Total 132 3,46 1,05 3,29 0,92
Work in textbooks Cluster 1 125 2,93 1,12 6,12* 3,89 0,85 4,31*
Cluster 2 43 1,74 1,00 3,21 0,99
Total 168 2,63 1,21 3,71 0,94
Other material
than textbooks Cluster 1 96 4,24 0,93 0,75 3,52 0,91 0,83
Cluster 2 31 4,10 0,94 3,35 1,14
Total 127 4,20 0,93 3,49 0,97
Joint review with
the teacher Cluster 1 127 3,10 1,03 4,72* 3,98 0,97 4,36*
Cluster 2 43 2,23 1,09 3,19 1,18
Total 170 2,88 1,11 3,78 1,08
Problem-solving Cluster 1 98 3,20 1,26 3,78* 3,48 0,96 3,67**
Cluster 2 37 2,27 1,35 2,62 1,30
Total 135 2,95 1,35 3,24 1,12
Laboratory work Cluster 1 70 3,40 0,98 3,98* 3,37 0,82 3,73*
Cluster 2 24 2,42 1,21 2,63 0,92
Total 94 3,15 1,13 3,18 0,90
Interdisciplinary
thematic work Cluster 1 45 3,33 1,09 3,87* 3,16 0,74 2,77**
Cluster 2 19 2,16 1,17 2,53 1,02
Total 64 2,98 1,23 2,97 0,87
Homework Cluster 1 123 2,09 1,00 5,46* 3,12 0,94 3,84*
Cluster 2 40 1,27 0,75 2,45 1,01
Total 163 1,89 1,01 2,96 1,00
How enjoyable and instructive the two clusters find different working methods.
Maximum value is 5 and minimum is 1. SD stands for standard deviation. *p<.001;
**p<.01