Use of Technology in Teaching and Learning Mathematics - Research Paper Example

Qualitative Research Name Institution course Lecturer Date Use of Technology in Teaching and Learning Mathematics- a focus on Australia Introduction The use of technology in schools and in the teaching and learning of various subjects such as Mathematics is a practice that is highly being adopted. This is mainly due to the need for instructors to always ensure that they constantly develop new methods as well as media that will effectively design, develop, construct knowledge, stimulate thinking and deliver student information. Mathematics is one key subject through which Information and Communications Technologies such as calculators, computers, calculator and computer device features. Another reason is the realization by many educational institutions and organizations of the potential offered by the adoption of technology. The adoption of these technologies is mainly done for instructional functions or purposes. Many research studies have been undertaken to scrutinize the adoption of technology in mathematics, the process of implementation, acceptance by teachers, its role in improving education as well as its effects. One reason for this is the ever increasing complexity in the various mathematical needs of the entire work force. Conducted studies have used different methods of research design, data collection and analysis and as a result have presented varying findings. This paper looks at the various researches that have been carried out on the use of Technology in Mathematics in Australian schools with focus being on the method of research design, collection of data and method of data analysis as well as the presented findings. All information was obtained by peer reviewed journal articles and other empirical study reports accessed from the internet, Pro Quest and the Educational Research Databases that include ERIC. The selected journal articles are those between the years 1998 and 2009. Key Words: Technology, ICT, teaching, mathematics education, learning, ICT in Australian Schools, examination, role of Technology. Study Sample Objectives/Research Question Methodology: Research Setting Methodology: Data Collection & Analysis Findings Yates, M. S. (2006) Flinders University in Adelaide, Australia. Norton, S. & Cooper, T. J. (2008) Griffith University and Queensland University of Technology. 127 (29 males, 98 females) experienced elementary school teachers from 21 schools (those operated by DECS (Department of Education and Children’s Services) and that introduced the South Australian Curriculum Standards and Accountability Framework (SACSA) that promoted ICT use. The teachers were of varying ages and qualifications 1 teaching Principal 3Teachers from 3 different schools 20 students from 1st to 7th grade from a school in Queensland Projects were undertaken in varying group ages: Students 4 to 7 years: Designing a sundial 1 to 3 years: Designing a package 3 to 4 years: Designing a bug catcher 5 to 7 years: Designing proportional puppets To assess the beliefs of the teachers about mathematic teaching and learning after the implementation of SACSA. To assess the teaching practices of experienced teachers in mathematics To find out how many mathematic curriculum reforms the teachers have experienced. To identify the relationship between the teachers’ beliefs on teaching as well as learning mathematics and the current practices in relation to the reforms. To study the perceptions of teachers on teaching Technology and Mathematics and on the process of implementation. The teachers were provided with surveys in their respective schools through post between October and the month of December, 2005. The teachers had previously been asked to use a constructive approach and ICT in the teaching of mathematics beginning 2001 to 2005. The survey incorporated the use of rating scale- research- instrument to study the various beliefs of teachers about mathematics, learning and teaching of mathematics as well to measure their present pedagogical practices related to mathematics and experiences with mathematics curriculum reforms. A case study was conducted with the researchers acting as active participants together with the teachers. This was to investigate on the results on the designed curriculum project required to trail the application of design practice as a key tool for the integration of mathematics and technology teaching. Data collection period = 4 years. Qualitative/Ethnography: Use of surveys Analysis: Data collected form the survey reports were entered into SPSS. The 20 belief items obtained were analysed using Principal. The relationship between the teachers’ beliefs and their practices in teaching mathematics was assessed using Analysis of Variance (ANOVA). Data Collection period = 9 weeks. Qualitative: observation of Classroom activities for the students and teachers. Data was recorded using field notes, audio tapes and video tapes. Semi-structured interviews conducted on teachers. Lesson plans, unit plans and students’ work were collected to define instructional and regulatory discourse. Analysis: Focused on instructional and regulatory discourse. Data was analysed for all recurring evidence that was then used to describe instructional and regulatory discourses used in carrying out technological projects. A relationship exists between the beliefs of teachers and the curriculum reform experience as well as practices in mathematics. Teachers with more years of experience were exposed to more curriculum reforms. They recorded higher level of ICT use in class as well as higher need to have constructive information on mathematic learning by students. The teachers’ beliefs were not in any way related to their ages, years of experience or education qualification. Teachers who strongly felt the beauty of maths recorded higher usage of manipulative than worksheets during mathematics lessons. The teachers indicated that the use of technology in teaching mathematics harnessed the enthusiasm of the students and helped them to be more constructive and creative. Through technology, students found purpose/ value in mathematics and recorded more class participation. Study Sample Objectives/Research Question Methodology: Research Setting Methodology: Data Collection & Analysis Findings Goos, M. & Bennison, A. (2006) University of Queensland Thomas, M. O. (2005) University of Melbourne Forgasz, H. J. (2004) Monash University Scott, A., Downton, A., Gronn, D. & Staples, A. (2008) Australian Catholic University. Patahuddin, M. S. (2008) University of Queensland Clark, J., Aldous, C. & Davies, J.( 2005) 456 schools in the thirty three education districts in Queensland. (257 government schools and 199 private schools). The number of surveys sent out to the school depended on the number of students enrolled as indicated in the website: For < 100 students-1 survey given to the teacher heading the mathematics department. 100- 299 sudents-2 surveys 300- 799 student- 5 surveys >800 students- 10 surveys. Pilot respondents: 10 secondary mathematic teachers. 30 teachers from 20 secondary schools in Victoria. Year 1: 29 schools: 7th to 8th grade students and their respective teachers.11th grade students Year 2: 3 schools; 10th grade students and teachers Year 3: 24 schools; 1613 7th to 10th graders A beginner primary school undergraduate teacher. 2 teachers: 1who is a HUI (High Use internet); highly uses the internet for professional development as a math teacher. 1 who is LUI (Low Use Internet); the teacher does not use the internet for teaching mathematics though he or she is willing to. 20 Parents 28 Teachers 33Secondary and primary school students undertaking ICT, science and mathematics in 4 rural schools (3 governments & 1 catholic school) within the South Australian. How frequently do teachers at Queensland schools use graphic calculators, the internet and computers in teaching mathematics in secondary schools? How confident are the teachers in using graphic calculators, the internet and computers to tech mathematics? To what level of extent does technology use by the teachers in terms of confidence and frequency relate to their various pedagogical beliefs, experience, knowledge, technology access as well as opportunities to develop professionally? Identify the relationship that exists between the teachers’ application of technology in mathematic teaching and the 3 factors that affect this ( opportunities to develop professionally, access to the technology and pedagogical beliefs, experience and beliefs) To identify the role that technology plays in mathematics. To identify effective teaching practices in technology use for mathematic learning. Research Questions What is the technology the technology that is currently being used to teach mathematics? Can the use of technology be useful in learning statistics and calculus? How can mathematic teachers effectively interact with the various forms of technology to advance the learning of mathematics? What social, cultural, equity and demographic issues can be identified in patterns of technology use? To identify students’ access to technology and find out if any equity issues exist in relation to the access. Measure the attitudes that students have towards mathematics, computers and use of computers in learning mathematics as well as to identify if there any differences in the attitudes in relation to the equity factors. How are novice undergraduate primary teachers using technology to teach mathematics? How effectively are they teaching? Drivers and inhibitors of internet use for professional development of teachers and for mathematics teaching. Identify the various prospects and problems related to the teaching and learning of science, technology as well as mathematics in the rural regions of South Australia. The teacher heading the mathematics department was provided with the surveys which he or she was supposed to fill out. The surveys required them to describe how frequently they used technology to teach mathematics, which topics they used them on, reasons for use as well as answer questions on the students’ use of the various forms of technology during assessment. The department head with more than one survey distributed the others to their colleagues in the department to fill out. The surveys were piloted on ten secondary mathematic teachers before distribution. Follow up observations and interviews were conducted on 30 teachers who volunteered for the study. Surveys were used to collect data on technology use and the attitudes that the teachers had on its use. Case studies were also conducted. Lesson plans, teachers’ diaries, questionnaires and interviews were used to obtain on teacher’s pedagogical practices and attitudes as well as the school and department practices and processes. Surveys conducted during the first and third year with in depth case studies being conducted in the classrooms during the second year. Distributed survey questionnaires for year 1 and 3 contained questions about schools’ computer organization and their use in learning mathematics, students’ access of computers at their homes. Data from students was obtained based on various equity issues that included; gender, ethnicity, socioeconomic status and ones school’s geographical location. Another important factor was the student’s rating and grade levels in mathematics. The one hour mathematic lesson was recorded digitally, to identify how beginner career teachers used technology during a lesson on capacity utilising Interactive White Board, calculators and PCs. Each of the two teachers was observed while teaching in their classes for a period of 2 weeks and interviewed for a 4 week period. There were continued email exchanges between the two teachers and the researcher after the period of observation. Teachers filled out questionnaires by giving information regarding their various professional backgrounds, internet use for professional development, teaching as well as learning mathematics. Informal interviews were conducted on the two teachers to clarify the various questionnaire questions as well as to verify what had been observed by the researchers. Each group of teachers, students and parents was interviewed independently.School principal were also allowed to take part. Students were questioned on what was the most difficult and what was the most enjoyable for them in every subject area, the relevance of these subjects to their individual future lives as well their views on all matters within school and the surrounding community. Teachers gave information regarding their backgrounds, what was most enjoyable and most difficult to teach, the various issues that relate to the rural setting of the school. Parents were questioned on their backgrounds, the future aspirations they have for their daughters and sons, reasons for selecting the specific schools and the school’s strengths and weaknesses that could affect the learning of maths, technology and science. They also gave information on the various community aspects that might affect the learning progress of their children. Teachers and parents gave recommendations on necessary actions and changes. Data Collection Surveys were posted heads of maths departments in the secondary schools to be filled out by the mathematics teachers. The attitudes of teachers towards the use of technology was assessed using a Likert type scale indicating 1 for ‘strongly disagree’, 5 for ‘strongly agree’ and 3 for ‘undecided’. Analysis: Analysis was done based on the 20% (89) surveys that were returned. The relationship between the use of technology by the teachers and the 3 factors that affect this use was analysed by performing chi- square tests on the obtained frequency distributions from the cross tabulated responses on the items assessing the frequency of technology use. Data Collection National surveys were distributed to the teachers. This contained open and close ended questions. Case studies were also used. Classroom observations and interviews on the teachers were conducted and data recorded using field notes and video tapes. Lesson plans, teachers’ diaries, questionnaires and interviews were used to obtain all data necessary. Analysis: Quantitative and qualitative methods of data analysis were used to analyse the questionnaire data. Data Collection period = 3 years Survey questionnaires were distributed to be filled out by the 7th and 8th graders during year 1 and 3. Case studies were conducted during the 2nd year and on the 8th grade classes. Analysis: The students’ level of mathematics achievement was assessed using a 5 point scale rating from 1- weak to 5-excellent and the results analysed. The survey questionnaires used 8 Likert type attitude items. The response formats range from strongly agree- strongly disagree. For every item cluster principle-components factor as well as reliability check analysis was done to find out if the various items produced a uni dimensional scale. Mean scores obtained for the 3 attitude scales for the identified equity factors were compared through t-tests (independent groups) or ANOVA (one way). Chi square tests tested the statistical significance for every equity factor. Data Collection Classroom lessons were digitally recorded. Analysis: The digitally recorded data was analysed using current classroom observation protocols and schedules. Each researcher was provided with a Product Pedagogy Framework to ensure consistency. After familirializing themselves with the schedule, every researcher individually filled out the PP schedule using the scoring- system with a range of 0- 5. 1 represented minimal dimension evidence while 5 showed a strong presence. Data Collection: Period- 18 months Used an ethnographic method with data collection methods that included interviews, participant observation, questionnaires, email communication, websites favourite to the teachers (as stipulated in the teacher’s computer bookmarks) and other non written as well as written sources. Class lessons were video taped. Field notes were also taken. In depth case studies were conducted on each teacher. Analysis: Analysis was done using the Zone Theory (Goos, 2007). Data Collection: Focus Group Discussions were conducted during the first phase. Interviews were conducted on each individual group of parents, students and teachers. Analysis: Quantitative and qualitative methods of data analysis were used to analyse the questionnaire data. Most schools recorded high usage of calculators Teachers use technology more frequently while teaching senior classes than in the junior classes. Calculators are used more among the seniors while computers are more frequently used with the juniors. Teachers were reported to be more confident while using computer applications such as the internet and computers than in the use of graphic calculators. 63.5 percent of teachers were found to have used technology in teaching mathematics while 36.5% had not. 73% of the teachers were willing to make use of computers more frequently but did not have enough access to them. They also lacked confidence and skills. Indicated ranges of technological teaching practices included the use of computers and computer programs such as PowerPoint. The highest level of computer usage was recorded during statistics lessons followed by graphical work. Little use was recorded during geometry, trigonometry, calculus and algebra classes. 90% of all teachers recorded a use of calculators in their lessons. An equal number of male and female students had average socio economic backgrounds (60%), 22% spoke a different language, not English, at home while 2% were Aboriginal. The mean score for the mathematics achievement was 3.61 with differences occurring in terms of gender. Most students rated their score as being average or even better. Every school had computer resources despite its geographic position. 52% of students had used CDROMS during their mathematic lessons, 63% had used computers that particular year. 97% of students had access to at least 1 computer at home. 7th graders, NESB (Non English Speaking Back Grounds) students, male students and those who rated their mathematics performance as being excellent recorded a more positive attitude to mathematics than those in the other equity categories. Equity issues were therefore associated with 7th to 10th graders ownership of personal computers with attitudes towards computers, mathematics and computer use for learning mathematics. The geographic location and SES had an implication on students’ attitudes towards mathematics and on computer ownership. Students were found to enjoy activities done on the Interactive White Board. The various teaching practices enhanced the development of supportive and positive school environment and thus enhanced learning. The activities were found to be relevant. Intellectual quality of learning mathematics was found to be limited. An engaging, interesting lesson that is students centred and that integrates the use of ICT will not automatically enhance more understanding of mathematics. HUI teacher: The teacher tried to enact her various pedagogical beliefs using the third zone (ZPD). There is a positive relationship between the teacher’s ZFM (first zone ) curriculum element and her various beliefs and knowledge (ZPD) A strong overlap exists between the teacher’s beliefs and knowledge (ZPD) and her professional development. The teacher views her professional context in terms of ZPD/ZPA relationship. LUI teacher: The LUI teacher identified time as one of the inhibitor to internet use in teaching mathematics.ZFM was found to be favourable but his pedagogical beliefs and teaching approaches (ZPD) acted as a hindrance to optimal internet use. The teacher’s professional development is viewed in terms of ZFM/ZPD relationship. His professional context and beliefs influences him t seek PD to enable him function more efficiently and effectively. Resources do not necessarily guarantee successful teaching and rich learning. The availability of internet in the schools has most definitely not been wholly optimised through teaching. The Zone of Free Movement cannot necessarily be regarded as the teachers’ real environment but rather as a way through which teachers view and interpret the surrounding environment. Teaching resources do not out rightly enhance an environment for mathematic learning that is technologically rich. Internet and computers are only tools likely to restrict or enrich learning. Students indicated mathematics and technology as being enabling factors in the selection of university courses such as engineering, applied science and sciences. Most mathematic teachers in rural schools do not have sufficient skills to incorporate technology. Many of these teachers have no previous experiences. There was a positive response to the overall usage of ICT in the schools. Availability of technical support and internet access were indicated as being the major challenges with the existing filtering mechanisms being regarded as the major hindrances to internet access. Students felt comfortable with ICT use both in school and at home and recorded high home ownership levels as well as use. Emerging issues here included lack of technical support and continuous PD (professional development). They felt that having one identifiable individual within the school to support them as well as enhance PD was an effective model. Equity and diversity issues were found to be unique for each school researched. Generally, access inequities were regarded as being the major issues of concern in remote and rural schools. Teachers reported lack of access to PD as being their greatest hindrances. With distance and the availability of TRT as being the greatest barriers. Part two Goos & Bennison (2004) focus on studying the use of technology in the teaching and learning of mathematics in secondary schools. The paper brings out survey findings of a research carried out to investigate on mathematic teachers’ usage of the internet graphic calculators and computers in secondary schools in Queensland. With the current move in Australia requiring schools to integrate the use of ICT in their curriculums, the author feels that there is need to investigate the nature as well as extent to which teachers actually use these technologies and to identify the various factors that drive or inhibit the effective integration of the technologies into mathematics teaching and learning. The findings according to this study indicated that most schools recorded high usage of calculators. Teachers were found to use technology more frequently while teaching senior classes than in the junior classes. Calculators are used more among the seniors while computers are more frequently used with the juniors. Teachers were also reported to be more confident while using computer applications such as the internet and computers than in the use of graphic calculators. The authors focus on the major forms of technologies that include the internet, computers and graphic calculators, a focus that differs from many other researchers who focus on only one form of technology. In this way, the study considers the major forms of mathematical technologies. The selected sample of 456 schools in the thirty three education districts in Queensland (257 government schools and 199 private schools) is representative and therefore appropriate for the provision of reliable and valid findings. It is also appropriate that the number of survey questionnaires were distributed depending on each school’s overall population and depending on the number of students enrolled as indicated in the website. The process, methods and instruments of data collection that include observation of Classroom activities for the students and teachers, use of semi structured interviews, use of field notes, audio tapes and video tapes were also appropriate and effective for producing valid and reliable findings. There is need for further research to be done to find out how as well as under what particular conditions teachers gain knowledge on how to effectively and efficiently make use of technology in teaching mathematics. Forgasz, (2004) the study aimed at identifying students’ access to technology and find out if any equity issues exist in relation to the access as well as to measure the attitudes that students have towards mathematics, computers and use of computers in learning mathematics as well as to identify if there any differences in the attitudes in relation to the equity factors. According to done research findings related to the various attitudes towards the use of computers and other forms of technology in education, inequities exist in terms of access and usage. It is such findings that created the basis for this research. The findings obtained indicated that 7th graders, NESB (Non English Speaking Back Grounds) students, male students and those who rated their mathematics performance as being excellent recorded a more positive attitude to mathematics than those in the other equity categories. Equity issues were therefore associated with 7th to 10th graders ownership of personal computers with attitudes towards computers, mathematics and computer use for learning mathematics. The geographic location and social economic status had an implication on students’ attitudes towards mathematics and on computer ownership. Students were also less convinced that computers enable them to understand mathematics more. This was as compared to their teachers. Female students recorded a lower level of conviction than males. The sample made up of 1613 students from different grades and from 24 different schools in the state of Victoria can be said to be representative of the whole as its composition was based on the various equity factors such as social economic status, language back ground, gender among others. The author uses survey questionnaires that were posted to the schools, a reason why the number of schools that sent back the questionnaires was lower. As a way of ensuring that all the questionnaires were returned, the researchers should have delivered the questionnaires and later collected them after they were filled out. The use of case studies was one way through which the researchers were able to obtain first hand information though this was only used during the second year. This same method as well as active participation should have been used during the first and second year. The findings obtained from this research brings out a number of questions that include; what are likely to be the longterm effects of computer use on mathematics on the attitudes of the students and on their class participation, will the different effects promote or challenge the use of such technology in mathematics as well as the desired outcomes? It is important that the identified issues related to equity in the use of computers to teach and learn mathematics be addressed as a way of optimising students’ learning of mathematics. References Angrist, J., & Lavy, V. (2002). New Evidence on Classroom Computers and Pupil Learning. The Economic Journal, 112, 735–765. Clark, J., Aldous, C. & Davies, J. (2005) Science, Technology and Mathematics Teaching and Learning in Rural South Australia: Problems and Prospects. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Forgasz, H. J. (2004) Equity and Computers For Mathematics Learning: Access and Attitudes. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Retrieved 12 October 2010. Goos, M. & Bennison, A. (2004). Teachers’ use of technology in secondary school mathematics classrooms. Paper presented at the annual conference of the Australian Association for Research in Education, Melbourne, 28 November-2 December. Retrieved 12 October 2010 from Goos, M. (2007). Supporting an investigative approach to teaching secondary school mathematics: A professional development project. Paper presented at the 30th annual conference of the Mathematics Education Research Group of Australasia, Melbourne. Norton, S. & Cooper, T. J. (2008) Teaching Mathematics and Technology through Design Practice. Mathematics Education Research Journal. 14, 37 59. Patahuddin, S. M. (2008) Use of the Internet for Teacher Professional Development and for Teaching Mathematics: Supports and Inhibitors. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Retrieved 12 October 2010. Scott, A., Downton, A., Gronn, D. & Staples, A. (2008) Engagement versus Deep Mathematical Understanding: An Early Career Teacher’s Use of ICT in a Lesson. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Thomas, M. O. (2005). Technology Use and the Teaching of Mathematics in the Secondary Classroom. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Yates, M. S. (2006) Elementary Teachers’ Mathematics Beliefs and Teaching Practices after a Curriculum Reform. PME 30(5):433-440. Read More