Teachers\u27 Conceptions of Mathematics and Intelligent Tutoring System Use

The purpose of this mixed-methods study was to investigate the relationship between teachers’ conceptions of mathematics and their use of intelligent tutoring systems for mathematics instruction. Intelligent tutoring systems are adaptive computer programs which administer mathematics instruction to students based on their cognitive state. A conception is a mixture of beliefs and knowledge. The participants in this study were 93 junior high school mathematics teachers from three school districts in the Midwest. Data were gathered using a two-part online survey. The first part of the survey contained questions about their use of intelligent tutoring systems, graphing calculators, Desmos and dynamic geometry software. The second part of the survey contained Likert questions from the teachers’ version of the Conceptions of Mathematics Inventory. Desmos is a website providing interactive classroom activities and a user-friendly graphing calculator. Dynamic geometry software is a class of interactive geometry programs. The quantitative analysis revealed no statistically significant interactions between teachers’ conception scores and intelligent tutoring system use, or between teachers’ conception scores and how intelligent tutoring systems were used. There were statistically significant interactions between teachers’ conception scores and their use of graphing calculators, Desmos, and dynamic geometry software. The qualitative analysis revealed that teachers used intelligent tutoring systems for differentiation. Teachers used graphing calculators, Desmos, and dynamic geometry software for visual, computational, and exploratory purposes. Teachers exclusively using intelligent tutoring systems to incorporate technology should also incorporate technology which promotes student exploration

Hand-Held Calculators And Mathematics Achievement: What the 1996 National Assessment Of Educational Progress Eighth-Grade Mathematics Exam Scores Tell Us

The purpose of this study was to analyze the 1996 National Assessment of Educational Progress data to identify the relationship between calculator use and student performance on the National Assessment of Educational Progress Mathematics Assessment. This general purpose includes several sub issues. In addition to being interested in the overall relationship between use and National Assessment of Educational Progress achievement (including the effort to control for spurious factors), this study examined the contextual factors that moderate the impact of calculator use. Similarly, it analyzed the relationship between calculator use and student performance on calculator-allowed and calculator-restricted items, as well as the ability of students to recognize whether the use of a calculator was appropriate when responding to a math problem. Findings indicate that significant differences in achievement exist between students who regularly use calculators and those who do not use calculators. Even when controlling for various contextual factors that moderated this relationship (e.g., gender, socioeconomic status, parents\u27 level of education, students\u27 National Assessment of Educational Progress achievement level), it was found that the more frequently students use a calculator the higher their scores tend to be. The results also show that when not allowed to use calculators, the more frequent calculator users continue to score higher than those who do not use calculators. Finally, using calculators does not automatically equate to calculator dependence, and, in fact, the more often students use a calculator the more adept they are at applying it properly and withholding it when inappropriate. Based on the findings of this study, the use of a calculator in mathematics classes should improve students\u27 ability to learn mathematical concepts and apply calculator technology in an appropriate manner when solving mathematical problems

Computer education: new perspectives

Computer technologies were introduced into educational contexts over two decades ago and while there is some argument about the extent to which computers have realised their potential, they have undoubtedly had a significant impact on education. A look into any school will reveal computers being used widely by clerical staff, teachers and children. It is clear that computers are here to stay, but it is less clear as to how effectively they are being used in the learning process. Teachers not only need to use computers but they need to use them well, and in order to do this they must understand what computer technology can offer and the ways in which such technology can be used in teaching and learning

Virtual Manipulatives Used by K-8 Teachers for Mathematics Instruction: Considering Mathematical, Cognitive, and Pedagogical Fidelity

This study examined teachers’ uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson summaries in which classroom teachers described their uses of virtual manipulatives during school mathematics instruction. The findings indicated that the content in a majority of the lessons focused on two National Council of Teachers of Mathematics (2000a) standards: Number & Operations and Geometry. Virtual geoboards, pattern blocks, base-10 blocks, and tangrams were the applets used most often by teachers. The ways teachers used the virtual manipulatives most frequently focused on investigation and skill solidification. It was common for teachers to use the virtual manipulatives alone or to use physical manipulatives first, followed by virtual manipulatives. One important finding of this study was that teachers used the virtual manipulatives during the main portion of their lessons when students were learning mathematics content. These results represent an initial exploration of teachers’ current use of virtual manipulatives in K-8 classrooms

Simulations For Financial Literacy

Financially literate consumers are empowered with the knowledge and skills necessary to make sound financial decisions that ensure their long-term economic well-being. Within the context of the range of cognitive, psychological, and social factors that influence consumer behavior, simulations enhance financial literacy by developing consumers’ mental models for decision-making. Technical communicators leverage plain language and visual language techniques to communicate complex financial concepts in ways that consumers can relate to and understand. Simulations for financial education and decision support illustrate abstract financial concepts, provide a means of safe experimentation, and allow consumers to make informed choices based on a longitudinal comparison of decision outcomes. Technical communicators develop content based on best practices and conduct evaluations to ensure that simulations present information that is accessible, usable, and focused on the end-user. Potential simulation formats range from low- to high-fidelity. Low-fidelity simulations present static data in print or digital formats. Mid-fidelity simulations provide digital interactive decision support tools with dynamic user inputs. More complex high-fidelity simulations use narrative and dramatic elements to situate learning in applied context

THE "POWER" OF TEXT PRODUCTION ACTIVITY IN COLLABORATIVE MODELING : NINE RECOMMENDATIONS TO MAKE A COMPUTER SUPPORTED SITUATION WORK

Language is not a direct translation of a speaker’s or writer’s knowledge or intentions. Various complex processes and strategies are involved in serving the needs of the audience: planning the message, describing some features of a model and not others, organizing an argument, adapting to the knowledge of the reader, meeting linguistic constraints, etc. As a consequence, when communicating about a model, or about knowledge, there is a complex interaction between knowledge and language. In this contribution, we address the question of the role of language in modeling, in the specific case of collaboration over a distance, via electronic exchange of written textual information. What are the problems/dimensions a language user has to deal with when communicating a (mental) model? What is the relationship between the nature of the knowledge to be communicated and linguistic production? What is the relationship between representations and produced text? In what sense can interactive learning systems serve as mediators or as obstacles to these processes

Evaluating the impact of electronic voting systems on university mathematics teaching and learning

This thesis presents an evaluation of the impact of the use of Electronic Voting Systems (EVS) on mathematics teaching and learning, based on the research question: What are the views of academic staff on the impact of EVS use on their mathematics teaching; and how has EVS use influenced student engagement and learning approach to mathematics? To answer the question, a descriptive survey of academic staff, and semi-structured interviews with students were conducted; data from these studies were supplemented by classroom observations of EVS use, relevant documentary evidence, and preliminary studies conducted. Survey data was analysed via quantitative techniques; while the annotated interview transcripts were analysed via thematic analysis, and the application of an integrated theoretical framework. The validity, reliability and replicability of both studies were also established. The findings show that feedback is viewed as the single, most beneficial impact of EVS use, as it enables instructors, through formative assessment, to identify student misconceptions, which then helps instructors to focus on the identified problem areas. EVS has also positively impacted student emotion, behaviour, and cognition. EVS use helps focus student attention, enhances participation and interactivity, and enables students to cognitively engage with learning material. The adoption of an integrated theoretical framework helps to characterise, and to reveal qualitative differences in student learning approaches. Also, the use of specific EVS question types tends to induce specific learning approaches in students. Implications of the findings include the need for EVS-using instructors to have clearly defined pedagogical objectives and well-designed questions, and for learners to re-adapt their mathematical ideas in response to EVS feedback. Findings also show the need to incorporate instructional measures that would promote both procedural and conceptual learning approaches in students, and to perhaps rethink the role of calculator usage and guesswork in student approaches to learning. The requirements for technologies that may replace EVS, the need to align assessment with instructional practices, and for instructors to undergo further EVS training and/or form mathematics-specific support group(s) are also highlighted

Review of the use of technology in Mathematics education

This research is intended to inform the Mathematics Course Advisory Committee (CAC) of the Western Australian School Curriculum and Standards Authority (SCSA) about appropriate and effective use of digital technologies in Mathematics courses for upper secondary school students and in examinations that contribute to students’ Australian Tertiary Admissions Rank (ATAR)..

A primary numeracy : a mapping review and analysis of Australian research in numeracy learning at the primary school level : report

The outcome from this project produces a database of over 185 projects and 726 publications relating to numeracy research to systematically &lsquo;mapped&rsquo; Australian research on primary school numeracy over the last decade. The database incorporates research summaries and findings that are easily accessible to teachers and teacher educators, and act as a valuable tool for determining further research directions. The project report examines the available research and organises the discussion of the research findings under a set of themes and sub-themes. Some summarised examples from the report reveals that: * Effective teachers of numeracy: - have high expectations of their students; - focus on children&rsquo;s mathematical learning, rather than on providing pleasant classroom experiences; - provide a challenging curriculum; - use higher-order questioning; - make connections both within mathematics and between mathematics in different contexts; and - use highly interactive teaching involvement with students in class discussion. * Effective professional development programmes: - provide teachers with the time and appropriate resources to enable them to reflect on their teaching; - provide continuing support and encouragement while teachers explore possibilities and trial new strategies in their classrooms; - involve teachers in school-based and wider networks; - are of sufficient duration to allow significant changes to habitual beliefs and practices; and - create opportunities for the exploration of theory-practice relationships.<br /

Beyond written computation

This collection of papers based on research into aspects of number is a result of a writing conference held on Rottnest Island, near Perth, Western Australia. The concept of the conference emanated from Alistair Mcintosh and Len Sparrow and was based on two similar meetings organised by Cal Irons and Bob Reys. All papers in this book were discussed at the Rottnest conference and subsequent changes were made by the authors based on comments and recommendations from the peer group who attended the conference