Factors that encourage or inhibit computer use for secondary mathematics teaching (1).
Computers are now commonplace in classrooms across Australia and there is steady pressure on teachers to incorporate them into their teaching. In contemporary Australian mathematics curricula in most states, there is also the expectation that teachers will use technology--computers and calculators--in their teaching of mathematics at all levels. For example, in the overview of the Victorian curriculum, the Curriculum and Standards Framework II [CSF] (Victorian Curriculum and Assessment Authority [VCAA], 2001a), the following is found:</p> <pre> The CSF encourages full use of the flexibility and value for teaching and learning programs provided by the increased application of information and communications technology (ICT) ... The CSF acknowledges that through the effective use and integration of ICT students are quickly developing new capabilities and that teachers have greater choice in creative teaching, assessment techniques and connections to students learning at home. </pre> <p>An Information and Communications Technology (ICT) chart (Victorian Curriculum and Assessment Authority, 2001b) accompanies the Mathematics CSF. The ICT chart reveals that students at levels 5 & 6 (grades 7-10) are expected to use and develop the following ICT applications and skills: file management, graphics, multimedia, electronic communication, data-logging, database, spreadsheet, desktop publishing, simulation/modeling, graphics calculators, and Computer Algebra Systems [CAS].
Similar statements about technology use and expected benefits to students' learning are found elsewhere in the world. For example, in the U.S., one of the six principles underpinning the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000) is the technology principle:</p> <pre> Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. (p. 11) </pre> <p>In the reality of school settings, it seems important to know which factors promote and which factors serve to hinder mathematics teachers from bringing these technologies into their classrooms. Exploring this issue, with a focus on computers for the learning of mathematics at the secondary level, was among the main aims of a 3-year study on which the findings reported in this article are based. To address this research aim, a survey questionnaire comprised of closed and open-ended items was used as the main data gathering instrument. The questionnaire was administered to grade 7-10 mathematics teachers from a representative sample of co-educational secondary schools in urban and rural Victoria across the three Australian educational sectors--government, Catholic, and Independent (i.e., non-Catholic, non-government). The survey was administered in 2001 and again in 2003. In both years, teachers from the same schools were invited to participate and, to avoid school bias (the schools differed in enrollment numbers), only one teacher at each grade level in each school provided data. The items designed to gather the necessary data included in the survey instrument were developed from earlier research findings in the field, a summary of which is presented in the next section.
Factors Encouraging and Hindering Computer Use in Schools
Bringing computers into classrooms can have profound effects on teachers. Goodson and Mangan (1995) claimed that computers challenge teachers' technical abilities, place new demands on their time and energy, and require them to adopt significant changes in their teaching strategies. In the U.S., Smerdon et al. (2000) found in their study that only half of the public school teachers who had computers available in their schools used them for classroom teaching and learning. The teachers' perceptions of the barriers to computer and Internet use for instruction were also examined. Most frequently, the teachers reported lack of release time to learn how to use computers or the Internet (82%), lack of time in the daily schedule for students to use computers in class (80%), and insufficient numbers of computers (78%) as the major barriers. In an earlier large-scale U.S. study, Hadley and Sheingold (1993) had reported a similar, related set of barriers to computer use that teachers identified. These included: lack of appropriate software or information about it; teachers' self-doubts, lack of interest or knowledge about computers; inadequate numbers of computers; and lack of maintenance, support, advice, and upkeep. In a fairly recent large Australian study, Finger, Russell and Russell (1999) found that most of the participating teachers had very high levels of basic computer skills, with a much lower proportion reporting advanced skills. Although 90% of the teachers agreed that information technology was worthwhile for teaching and learning, several barriers to its effective implementation were identified including hardware and software costs, and insufficient maintenance and technical support.
Factors Encouraging and Inhibiting Computer Use in Mathematics Classrooms
Studies on computer use among mathematics teachers have also been conducted, and barriers to computer use for the teaching of mathematics identified. The findings are consistent with those for computer use in general (as discussed above). In the U.S., secondary mathematics teachers indicated that they did not use computers because they lacked experience and access to educational software, lacked knowledge about appropriate ways to use computers to enhance mathematics learning, and lacked professional training in using computers in mathematics instruction (Manoucherhri, 1999). In the UK, Andrews (1999) noted that mathematics departments had poorly developed policies on computer use, few schools had coherent strategies for staff development, the teaching commitments of information technology (IT) coordinators prevented them from assisting colleagues, and schools had less than the 10 hours of weekly technical support that is considered a minimum to maintain a school computer system.
According to Norton's (1999) Australian research, some computer (technology) coordinators claimed that mathematics teachers under use available computer resources. They use difficulty of access as an excuse to mask other reasons that include: lack of knowledge of suitable software; concerns about changes to their role as teachers; lack of time to plan computer-based mathematics learning; concerns about not covering the syllabus; and computer phobia. Much earlier, in Victoria, Zammit (1992) identified factors that encouraged or discouraged the computer use of mathematics teachers in seven Victorian secondary schools. Classroom computer users were defined as those who used computers at least once a term (there are four terms in the school year) with their students. Compared to today, this level of usage defined for a user may seem minimal; for that era, however, it was not. The teachers were asked to classify themselves as users (n=102) or non-users (n=250) and then to rank-order a set of factors, provided by the researchers, that encouraged or hindered their use of computers for mathematics teaching. Users indicated that access to computers and the availability of software were the strongest encouragers for them to begin using computers. The next three highest ranked factors were: self-motivation to keep up to date, the need for students to learn to use technology, and a supportive computer coordinator. Both users and non-users were asked to rank seven factors that inhibited their use of computers. Zammit's (1992) overall rankings are shown in Table 1.
As Table 1 shows, users reported being primarily hindered by difficulties of access to a computer room; non-users were hindered most by their own lack of confidence and skill with computers.
In the present study, it was of interest to see which factors contemporary Victorian secondary (grade 7-10) mathematics teachers identified as encouraging or inhibiting computer use in their classrooms, and to determine how these differed from the sets of factors reported in earlier research studies (e.g., Zammit, 1992; Manoucherhri, 1999) as described above.
AIMS, PARTICIPANTS, AND METHODS
The aim of the component of the 3-year grant by the Australian Research Council (ARC) described in this article was to determine factors that secondary teachers consider encourage and/or discourage the use of computers in their mathematics classrooms. One subsidiary aim was to compare the findings with those reported internationally and those from earlier Australian studies. Since data were to be gathered from teachers from the same schools in 2001 and 2003, there was also the opportunity to note any changes in the sets of identified factors that might emerge.
In 2001, 96 grade 7-10 teachers participated. This sample of teachers taught mathematics in a representative sample of 28 coeducational, secondary schools across the three educational sectors--government, Catholic, and independent--in urban and rural Victoria. To avoid school or grade-level bias, not more than one teacher from each grade level per school was involved. The same schools were invited to participate again in 2003. The 2003 teacher sample size was reduced to 75 because, for a variety of reasons, five of the schools declined the invitation to participate. In both years, the questionnaires were completed anonymously. Thus, there is no clear information about the exact composition of the teacher cohorts, although it is highly probable that several of the teachers completed the survey in both 2001 and 2003. Other than knowing that the same schools participated in both years, no other assumptions are made about the composition of the teacher cohorts in the results presented here.
For this study, a survey questionnaire instrument entitled, You, Your Students, Mathematics and Computers, was developed and used. The same instrument was administered in both 2001 and 2003. Questionnaire items were based on pertinent research findings as described above, with some items also drawn from relevant previously published scales tapping similar constructs, or modified versions of them (e.g., Galbraith & Haines, 2000; Leder & Forgasz, 2002; Vale, 1998). Open and closed response formats were used. Data scored included those with categorical-response formats (e.g., Yes / No), Likert-type response formats (e.g., 5-point scales from Strongly Agree [SA]--Strongly Disagree [SD]), and others. Items were clustered under the eight headings listed below (brief descriptions and/or sample items are included):
1. About you: Background information (e.g., Gender? Years teaching mathematics?)
2. About you and computers (e.g., Own a computer at home? Perceived levels of competence?)
3. Computers in your school: (e.g., How are computers organized in your school?)
4. Teaching and learning mathematics: Beliefs about learning mathematics (e.g., Do computers assist people's understanding of mathematics?)
5. About your students and computers in this mathematics class: (e.g., Have your students used computers this year? How often?)
6. About using computer software for mathematics: Lists of software provided (e.g., Used this year? Previously? Would you like to use?)
7. Your reasons for using / not using computers to teach mathematics: (e.g., Encouraging / discouraging factors?)
8. Anything else
This article focuses on the teachers' responses to Section 7 of the questionnaire (i.e., Your reasons for using / not using computers to teach mathematics). The exact wording of the survey questions developed to identify factors that encouraged or discouraged teachers from using computers for mathematics teaching were similar. The open-ended items read, "What factors encourage(d) / [discouraged] you to use / [from using] computers to teach mathematics? Please list." (Some examples were supplied).
In both 2001 and 2003, the open-ended responses were analyzed using the categories from previous research findings as a guide. A grounded approach (Strauss & Corbin, 1990) was adopted for the other responses in order to group and categorize them. The frequencies and proportions of responses in each category were calculated. In each year, the coder repeated the exercise some 3 months after the initial categorizations to check the reliability of the classification process. In each year, the repeat procedure produced approximately 98% agreement with the original classifications.
RESULTS AND DISCUSSION
To put into context the teachers' perceptions of the factors that encouraged and discouraged their use of computers for mathematics teaching that were found in the present study, it seems important to report the teachers' self-ratings of computer competence. In Section 2 of the questionnaire (i.e., About you and computers), the teachers were asked to rate their current computer skills and confidence when faced with using a computer for teaching mathematics. A large proportion of the teachers (89% in 2001; 81% in 2003) rated their computer skills as at least average, with about half (53% in 2001; 48% in 2003) indicating that they felt fairly competent; none of the teachers reported not wanting to turn the computer on. Over half of the teachers in 2001 (58%) and over two-thirds in 2003 (68%) felt confident when faced with using a computer for teaching mathematics; a further 36% in 2001 and 27% in 2003 indicated that they were at least prepared to have a go. In summary, it can be said that the teachers were generally supportive of the idea of using computers in their mathematics teaching and that most were confident and comfortable enough with their computer skills to at least try. Although not statistically significantly different ([chi square] test, p>.05), there were indications that the teachers' levels of competence and confidence were slightly higher in 2003 than in 2001.
Factors that Encouraged Teachers' Use of Computers for Mathematics Teaching
Not all teachers answered the question about factors that encouraged their use of computers for mathematics teaching. In 2001, 75 of the 96 teachers (78%) answered the question and provided lists of factors; in 2003 there were responses from 62 of the 75 teachers (83%). For both 2001 and 2003, the categories identified and the frequencies and relative percentages of responses in each category are listed in Table 2. The order reflects the relative rankings of the factors for the 2001 responses. It should be noted that many teachers listed more than one factor; hence, the sum of the percentages in Table 2 is greater than 100%.
It can be seen from Table 2 that the three most frequently mentioned encouraging factors in 2001 and in 2003 were related to software, access to the hardware, and teachers' skills and confidence. While the most frequent response in 2001 was that the software was seen as of high quality, fun, motivational, relevant, and varied for students (41% compared), it was ranked third with a 29% response rate in 2003. The most frequent response in 2003 was the availability of computers and/or computer laboratories (40%); this was ranked second in 2001 by 37% of the teachers. Teachers' confidence, experience, skills, or enjoyment of computers comprised the third most important factor in 2001 (32%) and was ranked second in 2003 (37%).
Student enjoyment was mentioned by a higher proportion of teachers in 2003 than in 2001 (23% compared to 8%) while factors, such as being encouraged by the school (e.g., by mathematics coordinators or others) and technical support, were also considered important by some. This set of encouraging factors and the relative rankings are similar to those reported by computer users in Zammit's (1992) study: access to computers, the availability of software, self-motivation to stay up-to-date, the need for students to learn to use technology, and a supportive computer coordinator were the five top-ranked (researcher-supplied) categories. Representative comments from teachers in the present study about factors that encouraged their use of computers for mathematics teaching are presented below:
[Key to abbreviations: M=Male, or F=Female teacher; Metro=Metropolitan, or R=rural school; Gov=government, Cath=Catholic, or Ind=independent school; Gr.=Grade].</p> <pre> Good programs/software/Web sites out there (2003, M, Gr.8, R, Gov). The computers are available for use and students like to use them (2001, M, Gr.8, Metro, Gov). I can use a computer. Mathematics coordinator supports the use of computers. We have enough computers. We have technical back up. I am interested in using computers (2003, M, Gr.10, Metro, Gov). The (my) school placed a high priority on the use of computers. The maths coordinator supported me and gave me confidence to use computers, personally and in the classroom. Other enthusiastic and capable staff members gave help. Our school has technical staff back up (2001, F, Gr.8, R, Gov). Have had computer training. Use of computers/technology is encouraged at the school. There is good technical support.
Computer labs well equipped (2003, F, Gr.7, Metro, Gov). </pre> <p>Factors that Discouraged Teachers' Use of Computers
Eighty-seven of the 96 teachers (i.e., 91%) in 2001 and 54 of the 75 (i.e., 72%) in 2003 responded to this item, citing a number of factors that discouraged them from using computers for teaching mathematics. The categories identified, and the frequencies and related percentage response rates in each category are shown in Table 3. The order of the listing of the factors reflects the relative rankings of the 2001 responses.
As can be seen in Table 3, the overall rankings of the most prevalent discouraging factors identified by the teachers were similar over the 2 years. Access to computers and/or computer laboratories was the most prevalent inhibiting factor according to 60% of the teachers who responded to the item in 2001 and 67% in 2003. In 2001, the perceived need for professional development, and technical problems, lack of technical support, and old equipment were ranked an equal second as discouraging factors by 31% of the teachers. In 2003, professional development issues, as well as time-related issues, were ranked an equal second as inhibitors to computer use by 22% of the teachers.
Representative comments from teachers about barriers to their use of computers for teaching mathematics are presented below:</p> <pre>
[Computer] Labs are used for keyboarding and info tech classes
95% of time. Very difficult to get lab when you have classes.
Lack of experience. Time is always a problem. I teach 24 periods
and never have enough time to do everything I would like to
(2001, F, Gr.10, R, Gov). I need more exposure to software packages available. The school needs to buy and educate the teachers to use them (2001, F, Gr.9, Metro, Gov). I have not had the opportunity to view what is available. I am
not aware of other maths teachers that use computers in class
(except for research) (2003, F, Gr.7, R, Cath). Don't have the time to get students to effectively use computers and complete set course work. Find it difficult to keep students
on task. Too often they go on Internet or email rather than do
activity I assign them (2003, F, Gr.8, Metro, Ind). Don't have the computer skills. Very difficult to get access to
the computer. Lack of knowledge of programs (2003, M, Gr.7/8, R, Gov). </pre> <p>It was again interesting to compare the range and rankings of the inhibiting factors emerging from the responses of contemporary Victorian mathematics teachers in the present study with those presented to Victorian teachers by Zammit (1992) over 10 years ago (see Table 1). In both studies, lack of access to computers was the highest ranked factor. The majority of Zammit's (1992) other categories were also identified by teachers in the present study, albeit expressed slightly differently, or in a slightly different rank order. In the present study, a number of highly ranked factors, not used in the Zammit (1992) study, also emerged, including: professional development concerns, a wider range of time related factors, and lack of technical support.
There are several important findings from this study. First is the uncanny similarity in the sets of categories of encouraging and inhibiting factors that emerged from the analyses of the pertinent open-ended responses. Factors that served to encourage many mathematics teachers appeared to act as barriers to computer use for others, for example, access to or availability of computers. Also, the most prevalent encouraging and inhibiting factors that emerged were strikingly similar to those reported in earlier research studies on computer use for education generally (e.g., Finger, Russell, & Russell, 1999, in Australia; and Smerdon et al., 2000, in the U.S.) and for computer use for mathematics teaching more specifically (e.g., Manoucherhri, 1999, in the U.S.; and Zammit, 1992, in Australia). The latter finding with respect to computer use for mathematics teaching in Victoria is particularly important in that it suggests that while there may have been many changes over the intervening years with respect to the importance attached to technology use in Victorian schools, little appears to have changed in terms of the identified barriers to the use of computers for mathematics classroom teaching. Considering that over a decade separated the present findings gathered from mathematics teachers in 28 Victorian schools from those reported by Zammit (1992) from 7 Victorian schools, it seems somewhat remarkable that the set of barriers identified were so alike. With computer numbers in schools having increased over that decade, it could be argued that the access difficulties identified in this study are likely to stem from a situation in which demand outstrips supply, rather than simply a shortage of hardware--this shortage was more likely to be the explanation in 1992, although this may still be true in some settings. It should be noted that in Victoria, the State government target for 2001 was a computer-to-student ratio of 1:5; it was reported that the average ratio attained had exceeded that figure and was, in fact, 1:4.31. (State of Victoria, Department of Education and Training, 2002).
It was interesting to note that the relative prevalence of the most encouraging factors identified by the teachers in the present study changed slightly over the two administrations of the survey questionnaire, whilst the order of the factors identified as most prevalent in hindering teacher computer use was more similar. The reasons for these patterns cannot be determined from this study and invite further investigation.
As reported by the teachers and recorded in Table 3, institutional factors--access to hardware, software issues, professional development needs, and particular time constraints--appear to outweigh personal factors, e.g., confidence, competence, and other time-related issues, in preventing teachers from using computers in their mathematics teaching. This augurs well for the future with respect to anticipated levels of computer competence among new, younger, mathematics teachers as they enter the profession.
In the Victorian context, it was particularly surprising to find that the need for students to use or to master graphics calculators (mandated in some grade 12 mathematics subjects) did not feature more highly as a reason mitigating against teacher use of computers (only encouraged in curriculum documents). With the advent of CAS calculators as the soon to be mandated hand-held technology in Victoria, it may be that computer use for mathematics learning will decline as teachers confront the need to master this new technology and the challenges it may present to their pedagogy.
With expectations high that students in Victorian schools will use various technologies as tools in their mathematics learning, it was encouraging to find that contemporary mathematics teachers appeared generally supportive and confident in wanting to use computers in their classrooms. The findings reported here direct attention to areas that require further attention to enable teachers to use computers more in their teaching. In particular, greater access to hardware, more technical support, the availability of high quality software, and ongoing professional development were the significant issues identified by the teachers.
While factors that encourage and discourage computer use for mathematics teaching were identified in this study, there was no evidence gathered to shed light on whether computer use actually enhances students' mathematics learning. Elsewhere, other findings from the main ARC study have been presented indicating that about two-thirds of the teachers and a much lower proportion of their students believe that computers do assist students' understanding of mathematics (see, for example, Forgasz, 2003). The findings presented in this paper appear consistent with the teachers' optimism with respect to the positive effects of computer use on student learning. More evidence is needed, however, to enable conclusions to be drawn regarding whether these beliefs can be supported. Thus, to put forward suggestions on how best to address the identified barriers to the use of computers in mathematics classrooms, it also seems sensible to learn more about the factors associated with computer use for mathematics learning that result in the enhancement of student learning outcomes--both cognitive and affective. Could it be, for example, that students with particular needs benefit more than others from computer use? Are some software applications more effective than others in promoting mathematical understandings and/or motivation to learn mathematics? There is some evidence from other dimensions of this research project that the visual power of computer technology enhances some students' understanding of particular mathematics concepts, for example when using The Geometers' Sketchpad and Graphmatica (a freeware application used for graph plotting, downloadable from http://www8.pair.com/ksoft/index.html--see Forgasz, 2003). Knowledge about which aspects of computer use enhance learning outcomes would aid in focusing efforts to improve computer access and the types of software that should be used, and would direct attention to more specific professional development needs for teachers.
In summary, there is room for further research to determine which factors associated with computer use for mathematics learning should be the focus in order to have the desired positive impact on students' mathematics learning outcomes.
This project was funded through the Large Grant scheme of the Australian Research Council [ARC].
My thanks are extended to Nike Prince who assisted in the collection and analysis of the data included in this article.
Andrews, P. (1999). Some institutional influences on secondary mathematics teachers' use of computers. Education and Information Technologies, 4(2), 113-128.
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(1) An earlier version of this article was accepted for presentation as a refereed paper at the annual conference of the Australian Association of Research in Education, 2004, Melbourne.
Table 1 Mathematics Teachers' Rankings of Barriers to Computer Use (Users and Non-Users): Adapted From Zammit (1992) [NB. 1 = Highest Ranked Factor] Factor Rank: Users Rank: Non-users Difficulties of access to computer room 1 4 Not enough computers for individual use 2 5 Not enough time to review software 3 2 adequately Quality of software 4 6 Lack of confidence and skill with 5 1 computers Computers not a high priority in subject/ 6 3 department Students lack keyboard skills 7 7 Table 2 Factors Encouraging Teachers to Use Computers: 2001 (N=75) and 2003 (N=62)--Rank Order, and Frequency and Percentage Response Rates 2001 2003 Response category Rank N (%) Rank N (%) Software: quality, variety, motivation, 1 31 (41%) 3 18 (29%) fun, relevance Availability of computers and/or 2 28 (37%) 1 25 (40%) computer laboratories Teachers' confidence, skills, 3 24 (32%) 2 23 (37%) experience, enjoyment Supportive mathematics coordinator 4 18 (24%) 7 8 (13%) School (e.g., policy, provision of 5 14 (19%) 6 9 (15%) appropriate facilities, the principal etc.) Technical back-up, support 6 11 (15%) 5 10 (16%) Develops students' mathematical skills 7 9 (12%) 8 6 (10%) Students enjoy using computers 8 6 (8%) 4 14 (23%) Other staff members 9 5 (7%) 14 1 (2%) Computers are a teaching tool 10 4 (5%) 10 4 (7%) Develops students' computer skills 11 4 (5%) 9 5 (8%) Lap-top computer program 12 3 (4%) 13 2 (3%) Professional development 13 3 (4%) Develops students' job skills for 14 1 (1%) =11 3 (5%) future Other categories with less than 4% 15 3 (4%) =11 3 (5%) response rate Table 3 Factors Inhibiting Teachers From Using Computers: 2001 (N=87) And 2003 (N=54)--Rank Order, and Frequency and Percentage Response Rates 2001 2003 Discouraging Factors Rank N (%) Rank N (%) Access to computers and/or 1 52 (60%) 1 36 (67%) computer laboratories Need professional development and =2 27 (31%) =2 12 (22%) time for professional development Technical problems, lack of =2 27 (31%) 5 8 (15%) technical support, old equipment Time: students to cover syllabus, 4 21 (24%) =2 12 (22%) acquire basic skills, set up computers; teachers to prepare lessons Software: availability, appropriate, 5 22 (25%) =6 7 (13%) relevant Lack of experience, confidence, skills 6 19 (22%) 4 10 (19%) Student discipline, attitudes, 7 5 (6%) =6 7 (13%) behaviors Graphics calculators 8 5 (6%) =9 1 (2%) Not part of math course 9 1 (1%) 8 5 (9%) Students lack keyboard skills 11 =9 1 (2%) Other categories with less than 4% 10 1 (1%) 11 1 (2%) response rate
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|Publication:||Journal of Computers in Mathematics and Science Teaching|
|Date:||Mar 22, 2006|
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