Video Modeling and Explicit Instruction: A Comparison of Strategies for Teaching Mathematics to Students with Learning Disabilities

As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital‐based instructional strategy with a limited research base for students with a learning disability is video modeling. Through a single subject alternating treatments design, this study compared the use of video modeling to face‐to‐face explicit instruction for teaching geometry word problems to three secondary students with a learning disability in mathematics. Across 10 sessions of intervention, all three students demonstrated improved performance on all dependent variables with both interventions, while the explicit instruction condition produced slightly greater accuracy scores for two of the three students. The results and their implications for the field of mathematics are discussed.     

Student Views of Computer-Based Mathematics in the Middle Years: Does Gender Make a Difference?

How the use of computers in mathematics classrooms was viewed by students in two middle years mathematics classrooms was the focus of the research described in this paper. The primary data sources consisted of questionnaires, classroom observations supported by videotaping of mathematics lessons, and interviews with two girls and two boys from each class. Thus both qualitative and quantitative methods were used. Girls viewed the computer-based lessons less favourably than did boys. In general, the boys were likely to believe that computers contributed to their experiencing pleasure in these lessons, and to making mathematics more relevant to them. Girls were typically more concerned about whether computers facilitated learning and enabled success in mathematics. The attitudes of students to computer-based mathematics were related to their views of computers.     

Learner perceptions of the introduction of computer-assisted learning in mathematics at a peri-urban school in South Africa

This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners’ perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a period of 4 months to observe the inclusion of a computer centre as part of the teaching of mathematics. Learner perceptions were obtained from (1) individual and group interviews and (2) an actual and preferred version of a learning environment instrument called the Computer-Assisted Learning Environment Questionnaire, which was developed for the South African context. Learners indicated that they considered application of computers as a positive step as it (1) increased their involvement in the mathematics classroom, (2) gave them more exercises in problem solving in mathematics, and (3) provided them with the opportunity to assess their own learning. However, a strong recommendation from this response is for more computers to be made available in order to allow learners to work individually and thereby be able to spend more time using the computers.     

Does computer confidence relate to levels of achievement in ICT-enriched learning models?

Employer expectations have changed: university students are expected to graduate with computer competencies appropriate for their field. Educators are also harnessing technology as a medium for learning in the belief that information and communication technologies (ICT’s) can enliven and motivate learning across a wide range of disciplines. Alongside developing students’ computer skills and introducing them to the use of professional software, educators are also harnessing professional and scientific packages for learning in some disciplines. As the educational use of information and communication technologies increases dramatically, questions arise about the effects on learners. While the use of computers for delivery, support, and communication, is generally easy and unthreatening, higher-level use may pose a barrier to learning for those who lack confidence or experience. Computer confidence may mediate in how well students perform in learning environments that require interaction with computers. This paper examines the role played by computer confidence (or computer self-efficacy) in a technology-enriched science and engineering mathematics course in an Australian university. Findings revealed that careful and appropriate use of professional software did indeed enliven learning for the majority of students. However, computer confidence occupied a very different dimension to mathematics confidence: and was not a predictor of achievement in the mathematics tasks, not even those requiring use of technology. Moreover, despite careful and nurturing support for use of the software, students with low computer confidence levels felt threatened and disadvantaged by computer laboratory tasks. The educational implications of these findings are discussed with regard to teaching and assessment, in particular. The TCAT scales used to measure technology attitudes, computer confidence/self-efficacy and mathematics confidence are included in an Appendix. Well-established, reliable, internally consistent, they may be useful to other researchers. The development of the computer confidence scale is outlined, and guidelines are offered for the design of other discipline-specific confidence/self-efficacy scales appropriate for use alongside the computer confidence scale.     

Challenges of Integrating Mobile Technology into Mathematics Instruction in Secondary Schools: An Indonesian Context

Implementing mobile learning in curriculum-based educational settings faces challenges related to perceived ethical and learning issues. This study investigated the affordances of mobile technologies to support mathematics instruction by teachers. An exploratory study employing questionnaires and semi-structured interviews revealed that, while mathematics instruction can be augmented with mobile learning, the majority of schools in Indonesia have banned student use of mobile phones in classrooms. Teachers are concerned about the improper use of mobile phones that could impact their students' mental well-being and distract them from learning. Most teachers perceive mobile technologies to be disruptive and seem reluctant to use them for teaching delivery. However, teachers are eager to experiment with digital technologies within mathematics instruction. Our findings suggest infusing alternate technologies that fit better with the school's teaching and learning environment. This includes web-based applications that can run on different digital devices ranging from desktop computers, laptops, and tablets, to mobile phones. We propose setting up communities of practice for mathematics teachers to share their instructional repertoire on integrating digital technologies within the classroom.     

Prospective Turkish primary teachers’ views about the use of computers in mathematics education

The use of computers and technology in mathematics education affects students’ learning, achievements, and affective dimensions. This study explores prospective Turkish primary mathematics teachers’ views about the use of computers in mathematics education. The sample comprised of 129 fourth-year prospective primary mathematics teachers from two different universities in Turkey. Data consisting of participants’ written responses were qualitatively analyzed and categorized according to TPACK. Results show that the prospective teachers’ views about computers and their use in mathematics are usually positive. They enjoy working with computers, even though they are only able to perform relatively minor calculations with computers. They stated that improved use of computers can help them to learn and teach mathematics more effectively. However, they did not feel confident about their ability to teach mathematics using computers.     

Teachers, equity, and computers for secondary mathematics learning

The findings presented in this article were derived from a 3- year study aimed at examining issues associated with the use of computers for secondary mathematics learning in Victorian (Australia) schools. Gender and other equity factors were of particular interest. In this article, the focus is on the participating mathematics teachers. Data on their perceived competence levels with technology, and their use of and beliefs about computers for their male and female students’ mathematics learning were gathered. A clear majority of teachers felt comfortable about, and did use, computers for teaching mathematics, and believed that computers helped students’ mathematical learning. Generally, the teachers considered boys to be more confident and capable than girls with computers. The results have implications for pre-service education programs and for the professional development of practicing secondary mathematics teachers.Various findings included in this article have been presented at a range of mathematics education conferences including: AAMT (2003), MAV (2003), and ICME 10 (2004).     

Cognitive Theory and the Use of Computers in the Primary Classroom

Research investigating the role of computers in the primary classroom is closely linked to the body of knowledge concerned with theories of learning and child development. Research is presented as an attempt to provide scientifically supportable reasons why computers are effective in education. Having established a theoretical base for computer use in primary classrooms, this paper then examines the educational application of cognitive theory to classroom instruction.     

Technology use and mathematics teaching: teacher change as discursive identity work

Teacher change towards developing competences for technology use in mathematics teaching has been the focus of current educational reforms worldwide. However, a considerable amount of research denotes the extent to which teachers resist a full integration of technology in mathematics classrooms. The present paper is based on an ethnographic study and focuses on how mathematics teachers – as they participate in an intensive training course – perform identity work whilst collectively articulating meanings concerning the potential of technology-based mathematics learning. By means of discourse theory, we analyse how they try to fix meaning as they engage and interact with varied discourses of ‘change’. Our findings indicate that mathematics teachers' attempts to articulate meaning are organised around discourses that concern directly societal and learning issues of technology use in mathematics teaching.     

Computer Programming

Summary

Computers can be powerful aids to mathematics teaching and learning. Changes brought about by the availability of these tools and the demands of an increasingly technological society impact curricular content and pedagogy in mathematics education as well as the very nature of mathematical thinking and understanding. This article presents ways in which technology is changing mathematics education, guidelines for appropriate technology use in the mathematics classroom, the impact of computers on mathematics learning, common uses of computers in mathematics education, and issues and concerns related to technology use in mathematics.     

Six elements for technology integration in multicultural classrooms

Abstract

Although the number of computers in American schools multiplies, educational inequity remains evident in the area of technology. The socio-economically disadvantaged, the physically disabled, and the culturally and linguistically different have limited knowledge of and experiences with technology. Equitable access to technology requires the infusion of effective multicultural teaching strategies into educational technology use. These strategies must be broad enough to be inclusive of diverse learners, yet specific enough to be valuable as a guide to multicultural teaching. Similarly, they should allow for individual creativity and personal differences in teaching and learning. In this paper, the author proposes and defines six elements for integrating technology in culturally diverse classrooms: cultural awareness, cultural relevance, culturally supportive environment, equitable access, instructional flexibility, and instructional integration. These six elements are based on research on effective teaching of diverse students. They are not exhaustive of good instructional practices for technology use with diverse learners. Nevertheless, the author found their application in the evaluation of 32 technology-integrated units both informative and effective in identifying how teachers integrated computers for diverse learners. The author recognizes the need for further validation of these criteria and for research on effective teacher use of technology in multicultural settings.     

Learning novel mathematical concepts in a computer-enriched environment

There is widespread belief that computers should be used for the teaching and learning of mathematics. Research indicates that computers are primarily used in mathematics classes: (1) to reinforce previously taught concepts, (2) to allow students to construct computer programs to simulate mathematical techniques known to the student and (3) to explore mathematical microworlds encompassing mathematical ideas and concepts normally known to the student. Furthermore, it is said that pre-service teachers should experience the learning of mathematical ideas and concepts of which they had no prior experience in environments in which computers are just one of the resources available for exploring and experimenting with these ideas and concepts. How should these learning environments be constructed so that pre-service teachers are sensitised to the value of doing mathematics in such environments? Is a student's understanding of novel mathematical concepts enhanced when s/he explores it in a computer-enriched environment? An experiment with pre-service teachers was carried out in a college of education for blacks in South Africa. This article describes the insights gained from this experiment.     

Mythmaking and mythbreaking in the mathematics classroom

Constructivism has become a major focus of recent pedagogical reform in mathematics education. However, epistemological reform that is based on the constructivist referent of learning as conceptual change has a very limited viability in traditional mathematics classrooms because of its cultural insensitivity. By contrast, the social epistemology of critical constructivism addresses the socio-cultural contexts of knowledge construction and serves as a powerful referent for cultural reform. From this perspective, the social reality of traditional mathematics classrooms is governed by powerful cultural myths that restrain the discursive practices of teachers and students. The power of the repressive myths of cold reason and hard control is evident in the ways in which they act in concert to create a highly coherent and seemingly natural social reality. Epistemological reform of traditional mathematics classroom learning environments is, therefore, synonomous with cultural reconstruction. Critical constructivism, which has a central concern with discourse ethics and the moral agency of the teacher, draws on the social philosophy of Jurgen Habermas and argues for an alternative culture of communicative action to be established in mathematics classrooms. Teachers are expected to work collaboratively as agents of cultural change in forums beyond their classrooms.Religions, philosophies, arts, the social forms of primitive and historic man, prime discoveries in science and technology, the very dreams that blister sleep, boil up from the basic, magic ring of myth.(Joseph Campbell, The Hero With a Thousand Faces, 1968, p. 8.)     

Computer Literacy as Ideology

Some of the most prominent policies in schools throughout the industrialized world today relate to the rapid introduction of computers. The most common rationale for introducing educational microcomputing is the concept of ‘computer literacy’. It is a concept, however, which is so poorly defined and delineated, and so unclear as to purpose and procedure, that it may best be investigated as a form of ideology. The justificatory arguments for computers in classrooms are primarily vocational or practical. They are based on assumptions that computers will be pervasive in the workplace of the future, or that they are soon going to be ‘everywhere’. The more purely pedagogical arguments are secondary: that learning about computers is a worthwhile experience in and of itself, and that computers can be useful productivity tools for other academic work. Drawing upon empirical evidence from an evaluation of computer use in two Canadian high schools, this paper shows how a critical treatment of computer literacy as ideology raises important issues about the computerization of education. It suggests that educators should question whether they have simply taken the ideology of computer literacy at face value, and whether this almost universal policy has received the critical attention it deserves.     

Student‐teachers’ Use of Computers during Teaching Practice in Primary Classrooms

It is argued that teacher readiness is crucial to the realisation of national goals for educational computer use and that the preparation of student teachers can make an important contribution. This study investigated student‐teachers’ dispositions towards computers and their use of computers in primary‐school classrooms during a final‐year practicum. The student teachers generally viewed computers positively but lacked confidence in their knowledge of computers. While they were nervous about using computers in classrooms, almost two‐thirds did use a computer at least once during a four‐week practicum and were more likely to do so if the supervising teacher modelled such use. The most frequently experienced problems in using computers were organisational. Based on the findings of this study it is suggested that preservice courses should focus on the pedagogical issues associated with computer use and they should provide students with opportunities to observe and practise classroom computing.     

Learning by Exploration in Mathematics Courses: a programme for student teachers

In order to adapt teacher education to new demands in mathematics classrooms, it is necessary to change the courses in mathematics at the university. Teachers’ beliefs about mathematics, learning and teaching has great impact on their teaching. At the University of Göteborg, a co‐operative project has been conducted in order to design a programme based on problem solving in courses taken by prospective Comprehensive School teachers (grade 4‐‐9). The main purpose of the project has been to make student teachers more reflective about mathematics as such, about learning and teaching. Another purpose of the project has been to use a teaching method in a university course‐‐a method which could be applied in a school classroom. The student teachers have worked co‐operatively in small groups of 3‐4 students and the educators role has been that of a facilitator. A preliminary evaluation indicates that student teachers have developed an insight into the complexity of learning and teaching, even though there are variations in this respect. However they still have difficulties in applying the method to teaching mathematics at school.     

Traditional vs. innovative uses of computers among mathematics pre-service teachers in Serbia

This study examined pre-service teachers’ intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers’ experience with computers and their technological pedagogical content knowledge (TPCK). Data collected from 226 participants revealed that the proposed model had a good fit for both traditional and innovative uses of computers. Structural equation modelling suggested that the established TAM variables, together with TPCK and experience, were significant determinants of pre-service teachers’ intentions to use computers in teaching mathematics at both levels. The most dominant determinant of behavioural intention was TPCK, followed by attitude. The proposed model explained 22.7% of the variance in the use of computers in traditional teaching practices and 27.6% of the variance in the use of computers in innovative teaching practices. The implications for mathematics teaching are discussed in the final section.     

Teachers and Computers for Secondary Mathematics

In the first stage of a three-year study in which the effects of using computers for the teaching and learning of mathematics are being explored, a questionnaire was developed and administered to teachers of students in grades 7–10 in a representative sample of co-educational post-primary schools in Victoria, Australia. Using open and closed response formats, the information sought included data on the teachers' professional backgrounds, computer ownership and use, and their beliefs and practices in using computers for the teaching of mathematics. In this article, findings related to ownership, professional development, perceptions of technological skills, beliefs about the efficacy of computer use in mathematics, and data on how teachers are using computers for teaching secondary mathematics are presented and discussed.     

Are We Having Fun Yet? How Teachers Use Manipulatives to Teach Mathematics

Teachers often comment that using manipulatives to teach mathematics is ‘fun!’ Embedded in the word ‘fun’ are important notions about how and why teachers use manipulatives in the teaching of mathematics. Over the course of one academic year, this study examined 10 middle grades teachers’ uses of manipulatives for teaching mathematics using interviews and observations to explore how and why the teachers used the manipulatives as they did. An examination of the participants’ statements and behaviors indicated that using manipulatives was little more than a diversion in classrooms where teachers were not able to represent mathematics concepts themselves. The teachers communicated that the manipulatives were fun, but not necessary, for teaching and learning mathematics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Promoting equity in mathematics teacher preparation: a framework for advancing teacher learning of children’s multiple mathematics knowledge bases

Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction. Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics instruction.