STUDENTS' THOUGHTS ABOUT ICT IN SCHOOL MATHEMATICS

STUDENTS’ THOUGHTS ABOUT ICT IN SCHOOL MATHEMATICS Anne Berit Fuglestad Agder University College In this paper I will report from a survey of students’ thoughts about mathematics, in particular their beliefs about and use of ICT-tools in school mathematics. The survey was conducted within an ongoing project ICT in Mathematics Learning that explore how ICT tools can support inquiry into mathematics in a learning community. The results reveal that most students like to use computers or calculators and feel comfortable using the technology, but a minority of students has problems. There were differences between genders on some issues and between levels in school. The survey is part of a longitudinal study. BACKGROUND AND RATIONALE FOR THE SURVEY Over the last decades the Norwegian Department for Education has made efforts to stimulate use of ICT in schools aiming to give students competence to utilise computers and calculators as tools in their learning and work. In a new curriculum plan for Norway, effective from august 2006, facility to use digital tools is one of five basic proficiencies in all subjects, including mathematics, alongside with ability to read mathematics, express mathematics orally and in writing and perform calculations. In this context digital tools mean computers, calculators and odigital equipment. At upper levels the aim is that students are able use digital tools for problem solving, simulations and modelling, and to judge when their use is appropriate. Similar recommendations were given in the previous curriculum and in other places relating to mathematics teaching, e.g the NCTM Principles and Standards (NCTM, 2000). Recent surveys concerning use of Information and Communication Technology (ICT) in Norwegian schools, reveals ongoing activity using the Internet and communication, but with limited use and influence on learning in school subjects, and in mathematics particularly (Erstad, Kløvstad, Kristiansen, & Søbye, 2005). My impression is that work and research on ICT in Norwegian schools has been on a fairly general level, with limited effort to meet the challenge of ICT in specific school subjects, in particular for mathematics (Erstad, 2004). In an ongoing project named ICT and mathematics learning, the ICTML-project, the aim is to research how ICT can support and improve mathematics learning in school using a developmental research design. The ICTML-project co-operates closely with the LCM-project in developing a learning community involving didacticiansi, teachers and students in school with a focus on inquiry into mathematics (Jaworski, 2004). How can ICT provide situations and support for inquiry into mathematics and mathematics teaching and learning? The research deals with implementation of ICT 2006. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 121-128. Prague: PME. 3 - 121

Fuglestad in mathematics learning and research at all levels of co-operation in the development process and on activities in schools. A longitudinal study is on-going across the two projects, researching students’ thoughts about mathematics and their performance in the subject. Information from the first survey provides a background for further development and later surveys will follow. In this paper I will report from the first survey of students’ thoughts, in particular concerning the use of ICT in mathematics. In this context ICT comprises computers in the years 7 – 10 in schools, and use of graphic calculators in upper secondary schools. The classes in upper secondary schools do not participate in ICTML only in the LCM project. What is going on in the mathematics classes concerning the use of ICT? The purpose of the survey is to describe the present position for a selection of classes in the two projects concerning students’ use of ICT in the classroom and their thoughts about using computers. These results from the survey from the first year in the projects will form a background for understanding of students’ thinking that might influence their work and later we might be able to describe possible changes in their thinking. THOUGHTS ABOUT MATHEMATICS AND ICT Students’ thoughts about mathematics in school cover a wide range of questions connected to the affective domain and partly the cognitive domain. McLeod (1992) describes three components of affect: beliefs, attitudes and emotions. Attitudes deal with questions of liking, and enjoying certain topics. Emotions express joy, frustration, aesthetic responses and similar. Beliefs concern what students believe about mathematics, mathematics teaching, themselves and about their social context. Belief is not precisely defined in mathematics education and we can find several definitions of the concept (Leder, Pehkonen, & Törner, 2002). In this context I will emphasise some considerations about beliefs given by Furinghetti & Pehkonen (2002) who points to belief as connected to the cognitive domain but is subjective knowledge. Beliefs to some extent also include affective factors. The questionnaire prepared for this research encompasses both affective and cognitive elements that can better be described as or formed by the students’ experiences or observations from the classroom, such as which tools and methods are used in the teaching. The subjective element is important in this context; we ask for students’ opinion not for what is the objective truth concerning the statements. Students’ thoughts about computers have been researched also in other contexts and with other methods, for example by Colleen Vale (2005). She found that boys were more positive than girls and thought computers are useful for them. METHODOLOGY AND DATA COLLECTION A questionnaire was used for systematic collection of data concerning students’ thoughts about mathematics in school, teaching, learning and use of various 3 - 122

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Fuglestad resources. This data was collected in order to supplements classroom observations and give background for further observations and issues to address in the developmental research. The questionnaire was given to a selection of classes in the LCM and ICTML projects, with students from grades 7, 8, 9 in compulsory school, later named lower level, and some classes in the first year in upper secondary school. The questionnaire covered a wide range of questions about the subject of mathematics, about teaching and learning mathematics, the students’ competence and experiences in mathematics and so on. The questions were organised in sections with separate headings. A specific section was prepared concerning the use of computers and a few questions about calculators were also included in other sections where this seemed appropriate. I used a few questions from previous projects, including one I have directed relating to ICT in mathematics (Fuglestad, 2005) and some were inspired by other research e.g. Vale (2005). The questions were presented as statements where the students had to tick on a scale 1 – 4 or 1 – 5 with descriptions according to character of the statement, i.e totally agree, agree a little, etc, or never, rarely, fairly often etc.. The questionnaire was administered via the web in order to give ready access for students and easy import of data into Excel and SPSS for further processing and analysis. RESULTS The results were checked for differences between genders and between levels in school, using the Mann-Whitney test for statistical significance. Some differences were found and are reported in the separate sections below. In order to provide an overview the questions are presented in five sections each containing related questions. For the questions concerning computers (101,103-119)ii given to students in grades 7 – 10, corresponding questions concerning graphic calculators (144 161) were given to upper secondary students. In this way I can compare their thoughts about use of ICT i.e. computers or calculators across levels in school. The questionnaire was given to 469 students and about 70% answered. Students’ attitudes towards use of computers in mathematics In this group of statements the students were asked if they liked to use a computer (101), if it is useful for them (104) or if it is important to be able to use a computer in tasks (116). In this section I report only the results from lower grades since the upper secondary schools do not use computers. The answers reveal differences between genders on these questions, with boys expressing they agreed to the statement and girls on average closer to neutral. On all the questions except one the differences were statistically significant, with p < 0.001. The largest differences were found in response to the question asking if they wanted to use computers more in mathematics (107), where 54% of the boys totally agree and 31 % agree a little and for the girls 46% agree totally or a little. PME30 — 2006

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Fuglestad The last question in this group asks students if they prefer to learn mathematics without computers (114). Here the boys disagree and the girls slightly agree, meaning again that boys express liking to use computers for learning mathematics. Quest. totally agree disagree totally Mean Mean Mean number agree a little a little disagree boys girls total N= 101 31,5 41,8 11,5 15,2 2,1 2,6 2,4 165 104 26,8 41,5 21,3 10,4 2,2 2,8 2,5 164 116 24,2 41,2 26,1 8,5 2,2 2,9 2,5 164 107 Boys 53,6 31,0 9,5 6,0 1,8 84 Girls 18,8 27,5 38,8 15,0 3,0 80 Total 36,6 29,3 23,8 10,4 2,4 164 114 Boys 15,5 25,0 32,1 27,4 3,3 84 Girls 24,1 32,9 32,9 10,1 2,7 79 Total 19,6 28,8 32,5 19,0 3,0 163 101 I like well to use computers in mathematics 104 It is useful for me to use computers 116 I think it is important to be able use computers in tasks 107 I wish to use computers more in mathematics 114 I prefer to learn mathematics without computers

Table 1: Results about attitudes in grades 7 - 9. Frequencies in per cent. 1 totally agree, 2 agree a little, 4 disagree a little, 5 totally disagree Experiences with ICT in the classroom Some questions dealt with use of calculators in the classroom (72, 73, 83, 91, 95, 97). Students in all classes were given these questions. There were no significant differences between genders, but significant differences between levels in school. A majority of students answered that they often used calculated answers, 99% in upper secondary schools and 67% at lower grades. There was less use of calculators for investigations and experiments, with 71% in upper secondary school and 57% at lower grades. A majority of students also thought it is important to be allowed to use calculators on all calculations, more important for upper secondary that lower grades, with 61% answering important or very important in upper secondary school. These differences between school grades were significant with p < 0.001. What happens concerning use of computers in the classroom? The students were asked how often the teacher used a computer for introducing a new topic (83). According to the students, this never happens for 77% and rarely for 17% of the students in upper secondary school. It never happens for 42% and rarely for 41% of the students at lower grades. The students were also asked how often they use computers and calculators in the classroom (95, 97). At upper secondary they hardly used computers at all, 80% answered never and 19% rarely. At lower grades they use computers more, but only 30% fairly often or often, and 46% rarely. For calculators the situation is nearly opposite, 83% of the students use calculators often. The results confirm and clarify my observations and what I have learned from contact with schools. It is important to note that the data is not from a representative sample of 3 - 124

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Fuglestad schools in Norway, but from a selection of those participating in our projects. However, it is my impression from other sources that this picture is not far form the reality in general. Further research is needed to confirm this. In connection with questions about frequency of use of different teaching aids, including computers and calculators, the students were also asked to state what other aids they used and what they would like to spend more time on. Very few aids not listed in the questionnaire were offered by students so the list gave a fair picture of what was used, but about 55 students of 184 that answered the question, stated they would like to use a computer and 23 suggested more use of games. Beliefs about use of ICT in mathematics These groups of statements deal with what the technology is used for and how it influences the tasks and learning of mathematics. For upper secondary schools technology here means graphic calculators and for lower grades computers. Students agree that they need to know how to use calculators (37). This is strongly agreed by 74% and agreed by another 20% of the students in upper secondary schools. At this level the use of graphic calculators is compulsory according to the curriculum. In grades 7 – 10 the corresponding frequencies were 36% strongly agree and 37% agree. The students disagree slightly with “Clever students do not need computers to understand” (103, 145). They answer on average fairly neutral to “Since I avoid many errors, I learn easier with computers” (106, 148), with upper secondary students slightly agreeing and lower grades disagreeing. Students think they still need to do mental calculation when they use computers and calculators, but the results on average give only weak disagreement to the statement “I do not need to perform mental calculations since the computer/ calculator does the work” (105, 147). For the statement “I prefer to learn mathematics without computers/calculators” (114, 156) the younger students give on average a neutral answer, but for upper secondary the answer is disagree a little or totally disagree for 72 %. The difference in responses here may be due to the different uses of technology, where a graphic calculator can be regarded as necessary for some of the tasks in upper secondary schools. The difference is also significant with p < 0.001. Concerning the purposes for which ICT can be used, the students think it is not just for checking answers (118, 160), and students in lower grades have significantly stronger (p < 0.001) opinion than the upper secondary students concerning this question. The students agree that computers/calculators are used for investigations and exploring unknown tasks (117, 159) and they can experiment and test out of their own ideas (119, 161). The opinions are expressed slightly stronger at lower grades, but the main trends are the same with more than 60% of the students seeing ICT as a tool for investigations and experiments. PME30 — 2006

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Fuglestad Question totally agree a disagree a totally number agree little little disagree Mean N= 118 low 6,1 12,1 40,6 41,2 4,0 upper 7,8 30,1 34,6 27,5 3,4 Total 6,9 20,8 37,7 34,6 3,7 117 low 20,7 45,7 19,5 14,0 2,6 upper 18,3 35,5 27,5 18,3 2,9 Total 19,6 41,0 23,3 16,1 2,8 119 low 31,3 43,6 22,1| 3,1 2,2 upper 20,4 41,6 23,7 14,5 2,7 Total 26,9 42,5 22,9 8,6 2,5 118 Computers are used only to check answers 117 We use computers to investigate and explore unknown tasks 119 With computers I can experiment and find out of my own ideas

165 153 318 164 153 317 163 152 315

Table 2: Results – kind of ICT use, lower level and upper secondary. Frequencies in per cent. 1 totally agree, 2 agree a little, 4 disagree a little, 5 totally disagree Self assessment concerning ICT What do students think of themselves in relationship to computers and calculators? Some statements dealt with their thoughts about their own ability and experiences concerning calculators. The answers clearly indicate that most students think they can manage well with 89 % indicating they totally agree or agree a little and 83 % stated they are rarely or never unable to use calculators correctly. For lower grades the answers are even stronger. The students only slightly agree to understanding mathematics better with the use of ICT, i.e computers at lower grades or graphic calculators for upper secondary students (108, 150). Most students disagreed to needing a lot of help (109, 151), and slightly disagreed to having to think hard when they use ICT (111, 153). For the statement “I do not understand anything when we use computers/graphic calculators” (115, 157) their answer is even stronger disagreement, and with no difference between the school levels. When tested for gender differences I found significant difference only in response to the statement “I understand mathematics better when we use ICT”, where the boys indicated stronger agreement. Attitudes towards collaboration In our project we encourage collaboration between students, and hope that the students also will appreciate working with their peers using ICT. Three questions also take up this concern. The statements were: “I prefer to work alone on the computer” (110,152), “I do not like others to see on the screen what I work on” (112,154), and the third: “I prefer to work together with others at the computer” (113, 155). The results show that students in upper secondary school on average disagree slightly to the first two statements, and students at lower grades are closer to neutral. A majority of the students also agree a little with the third statement, about working with others. 3 - 126

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Fuglestad COMPUTERS AT FREE TIME Computers are commonly used amongst young people, and students seem to use computers more outside school than in the classroom. In addition to the questions concerning their thoughts about computers and calculators in mathematics the students were also asked about their use of computers outside school, at home or with friends. The results reveal that 71% of students in upper secondary schools, and 54% in lower secondary school use computers daily at home, and further 23% and 26% use computers on weekly basis. About 40% also use computers with friends weekly. Games and use of Internet dominate with 45% – 60%, word processing is used by around 26% and spreadsheets only 10%. The students also indicated other software in use; for playing and downloading music, chat and messenger programs. The results concerning the use of computers corresponds with the main trends in other recent survey of ICT use with Norwegian students (Erstad et al., 2005) SUMMARY AND DISCUSSION I found some statistical significant differences between genders in this study, mainly on some attitude questions. The boys liked computers and agreed that they are useful and clearly stated they want to use computers more in mathematics. In previous projects I have exposed similar differences between genders in response to questions about attitudes towards computers in mathematics teaching (Fuglestad, 2005). These differences can partly be explained by boys often expressing stronger opinions than girls, showing they master computers and like to work on them. I think this is not the full explanation since the boys also use computers more frequently outside school. On other questions the differences were between the students in upper secondary school and lower grades. Some of the differences could be due to the use of different equipment and the fact that students are at different levels in their education. The questions about use of computers in the classroom reveal that there is very little use of computers in upper secondary school and not very much in lower grades either. This confirms the informal impressions gained from visits to classrooms and talks with teachers in meetings and workshops. On the other hand use of graphic calculator is frequent in upper secondary schools, but this is expected because of the requirement in the curriculum plan as is also the need to know how to use them. Considering the projects’ aim to stimulate cooperation and inquiry in mathematics, it is promising to notice that more that 60% prefer to work together and more than 60% of the students regard ICT as a tool for investigations and experiments. CONCLUSION The overall impression is that computers have a motivating effect on students work although this is not strong. The students feel confident and think they can manage well, and do not think that they need a lot of help. The students in general want to use computers more, but expressed no strong expectations to learn mathematics from using computers/calculators. PME30 — 2006

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Fuglestad The results indicate that there is not resistance, but rather a weak positive attitude towards use of computers/calculators in mathematics learning. The students seem not to have a strong opinion concerning collaboration in their work on computers. The results reveal that there is room for development concerning utilising computers for teaching and learning mathematics in the classes and with fairly neutral answers to many questions, there seems little resistance to overcome. Further research in this area is needed in order to evaluate changes in students’ attitudes and beliefs during the course of the projects. I see also need for a survey concerning teachers’ attitudes and beliefs about computers/calculators and students learning and evaluate their influence on students learning. The teachers’ beliefs may have stronger impact than the students’ beliefs concerning use of ICT. References Erstad, O. (2004). Piloter for skoleutvikling. Samlerapport fra forskningen 2000-2003. Oslo: Forsknings og kompetansenettverk for IT i utdanningen. Universitetet i Oslo. Erstad, O., Kløvstad, V., Kristiansen, T., & Søbye, M. (2005). ITU Monitor 2005. På vei mot digital kompetanse i grunnopplæringen. Oslo: Universitetsforlaget. Fuglestad, A. B. (2005). IKT verktøy i matematikk - gutters og jenters valg og holdninger. Trondheim: Nasjonalt Senter for Matematikk i Opplæringen, Norway. (In press) Furinghetti, F. & Pehkonen, E. (2002). Rethinking charaterization of beliefs. In G.Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden Variable in Mathematics Education (pp. 39-57). Kluwer Academic Publisher. Jaworski, B. (2004). Grappling with complexity: Co learning in inquiry communities in mathematics teaching development. In M. Johnsen-Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference for the International Group for the Psychology of Mathematics Education (pp. 17-36). Bergen: Bergen University College. Leder, G., Pehkonen, E., & Törner, G. (2002). Beliefs: A hidden Variable in Mathematics Education. Kluwer Academic Publisher. McLeod, D. B. (1992). Research on Affect in Mathematics Education: A Reconceptualization. In D.G.Grouws (Ed.), Handbook for Research in Mathematics Education (pp. 575-596). New York: Mac Millan Publ. NCTM (2000). Principles and Standards for School Mathematics. Reston,Virginia: National Council of Teachers of Mathematics. Vale, C. M. (2005). Student views of computer-based mathematics in the middle years: Does gender make a difference? Educational Studies in Mathematics, 287-312. i ii

Didactician is used to mean researcher or doctoral student at the university college Numbers in parenthesis refer to items in the questionnaire

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