Publisher: University Of Education of Freiburg

Author: Matthias Zeller, Bärbel Barzel, Paul Drijvers

Language: English

Institution: University of Education

Department: Institute for Mathematics

City: Freiburg, Germany

Abstract: Results on Learning of Algebra from the CAYEN project 1. In lessons using the black-box-approach (in which the equation is unknown), CAS pupils who were taught with an emphasis on math principles mastered new challenges in algebra well and were able to work independently. 2. Use of CAS makes it possible to get an overview of a topic at the beginning, simply by trying out new commands. Thus, with CAS it is easily possible to learn many aspects of a mathematical topic in parallel. 3. In our analysis of pupils’ written comparisons of graphic, numeric and symbolic representations, in the CAS-group we noticed many positive comments about advantages of algebra. An effect was that they were more motivated to use algebra and inserted it more often in open tasks. 4. CAS pupils master the transition from arithmetic to algebra more easily. CAS students accept the output of the calculator as a common means of expression and realize the relevance of algebra. Furthermore, early in the curriculum they perceive the versatility of algebraic work in contrast to arithmetic approaches. By using CAS the pupils learned many commands and algebraic transformations; it did not matter that they could not do them all in a technology-free way. By contrast, GC-pupils sometimes had difficulties in accepting that the same underlying rules are valid in algebra and arithmetic. They argued that their calculators should be able to handle expressions with variables, if the same rules would be valid. 5. CAS-pupils’ argumentation concerning algebra included more mathematical arguments and was more objective than the argumentation of the GC-pupils. 6. We observed that the thoughts of pupils using CAS were on a high algebraic level and included reference to many concepts.

Reference: Report

Keywords: TI-Nspire, CAS, Germany, Algebra

Document Content: General claims These are general claims about benefits of CAS, drawn from the project literature review. The CAYEN study provides some kinds of confirming evidence for many of them. 1 CAS supports the development of conceptual knowledge. 2 Technology-independent math competencies may still be acquired when using CAS. 3. The use of mathematical language is activated by use of CAS 4. Technical skills (of using CAS) complement mathematical competencies meaningfully in the sense of instrumental knowledge. 5. CAS supports a unified and principle-based treatment of mathematical topics (as opposed to the common tendency to teach math topics in a highly fragmented way). 6. CAS supports the integration of open-ended tasks and the use of multiple individual ways of solving them. 7. Use of CAS can help teachers to use more student-centered methods. The lessons can be more flexible, allowing students to be more self-directed. This frees the teacher to give more attention to individual students. However, at the beginning, these new lesson types require more preparation effort.

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/283/final_ti_report.pdf

Year: 2009

Publisher: York University

Author: Margaret Sinclair, Ron Owston, Herb Wideman, Amanda Allan

Language: English

Institution: York University

Department: Mathematics Education

City: Toronto, Canada

Abstract: The TI-Navigator project was a mixed methods study to investigate use of the TI-Navigator in grade 9, 10 and 11 mathematics. The study began in 2006 and continued into 2009. The key questions for the research were: 􀂃 What are the effects of TI-Navigator use on student achievement in Grade 9/10 applied/academic mathematics? 􀂃 What are the effects of its use on the attitudes of Grade 9/10 applied/academic math students towards mathematics? 􀂃 What are the effects of its use on teaching practice? 􀂃 What support do teachers need to use such technology effectively? The study involved 15 teachers and 546 students in year one. In year two, the study involved 611 students (454 students from the implementation year (2006-2007), and 158 new students) and 16 teachers. In the third year of the study, 219 students were followed into grade 11. These students were selected because they enrolled in either a university prep mathematics course (U) or a university/college-prep mathematics course (U/C) in the first semester.

Reference: Report

Keywords: TI-Navigator, TI-84, Canada, Grades 9, Grade 10, Grade 11

Document Content: Year one The first year of the study incorporated several elements: the delivery of professional development by TI instructors, developing a variety of instruments, administering surveys and pre- and post-tests, observing selected classes, meeting with student focus groups, interviewing teachers and department heads, and arranging for additional teacher support. There were several challenges during the year. Technical difficulties slowed the process of implementation considerably, and the presence of a teacher who used the TI-Navigator on a fairly regular basis in one of the six classes at the control school created an unexpected problem. As a result, we concluded that drawing firm inferences about the effects of the TI-Navigator on student achievement based on this year was not advisable. In our year one report, we presented and analysed the collected data to provide a rich picture of the study participants and their environment in preparation for our subsequent years’ work. We treated this first year as a study of implementation, and began the second year by repeating the attitudinal surveys and pre-tests; we then followed students through grades 10 and (in some cases) into grade 11. Year two In the second year of the study we continued to investigate how teachers made use of the TI-Navigator in their classrooms and whether use of the TI-Navigator is beneficial to students in early secondary mathematics. In particular, we focused on helping teachers in the experimental schools extend their implementation via class discussions. By the start of year two, seven of the eight study teachers at the experimental schools had relatively strong technological backgrounds. We found that all teachers gained additional confidence in use of TI-Navigator, although one was still tentative about general use and troubleshooting by the end of the year. LearningCheck and Quick Poll were the most commonly used Ti-Navigator applications but all study teachers used activities recommended by colleagues or shared at the PD sessions. Several of the observed teachers who had followed a traditional pedagogy showed some movement towards a more constructivist teaching style. Although they did not hold full class discussions, they did engage students in analysing responses and considering the source of errors. These strategies were stressed in the three days of professional development provided to the participating teachers during year two. While teachers were very positive about the effects of TI-Navigator use on students –noting that students enjoyed the activities and were motivated to participate – the statistical analysis of pre- and post-test data showed that the treatment had a significant positive effect only in the case of the academic classes. Academic students who participated in focus group interviews reported that they enjoyed using TI-Navigator (though students in one class were frustrated by the teacher’s ongoing difficulties with set up). We noted that students in the observed academic classes were engaged by the activities and that in one of the classes, student participation was accompanied by a noticeable energy. No statistically significant difference was found between the control and experimental student groups for applied stream students in year two. However, despite these results, we contend that applied students did benefit from the use of TI-Navigator in other ways. We noted that students in the two observed applied classes were actively involved in the mathematics activities; applied students who participated in a focus group indicated that they enjoyed the technology and particularly appreciated being able to share answers anonymously. Year three Two teachers at each school agreed to continue participating in the study in year three (although one teacher at the control school opted out of observations), and in the 2008- 2009 school year we followed 219 students into Grade 11. The project in this final year of the study consisted solely of pre-test/post-test analysis and classroom observations. Quantitative analyses of third-year data showed no significant group differences in test scores; however, we believe that the third year of the study contributed important qualitative data. We theorized three roles for TI-Navigator in the classroom – as support for sharing, checking, and modelling. Using these categories, we analysed the practice of the study teachers and found evidence that most teachers had used TI-Navigator for sharing and checking but had not taken advantage of its modelling capabilities. Drawing on Hoz and Weizman’s (2008) theory of teacher conceptions, we carried out a case study examination of the practice of three teachers. This revealed that those teachers who were most successful in moving towards a classroom connectivity approach already possessed (or were developing) views of mathematics as a social construct, and mathematics teaching as engaging students in doing and discussing mathematics. General findings The results of the student baseline survey indicated that although there were a number of instances of statistically significant differences, the control and experimental students had many of the same experiences of and attitudes toward mathematics. In particular, responses suggest that for both groups, mathematics had been taught in a very traditional manner. Students reported that very little use was made of computers for demonstrating ideas or student work, and students rarely engaged in mathematics projects or used an overhead projector to demonstrate their work. The teacher baseline survey indicated that overall, the study teachers were very experienced, and fairly traditional in approach. Most had used graphing calculators and the CBR/CBL and a majority had used Geometer’s Sketchpad, but use of other technologies was sparse. An interesting finding is that proportionally more teachers used Geometer’s Sketchpad with applied classes than with academic classes. Some teachers had used algebra tiles, a strong number had used co-operative learning strategies, and a few had implemented assessment strategies that went beyond tests and quizzes. These, and the very positive responses to the questions on the PD survey with regard to in-class mentoring suggested that while some teachers were interested in adopting new approaches, they likely required more support than is generally provided. Teachers at the experimental schools were asked to provide feedback on the professional development provided by TI during the first year. Some teachers responded that the summer and fall PD sessions did not provide sufficient help with implementation. On the other hand, the prep-time and in-class assistance with a mentor provided by Texas Instruments received positive comments; teachers indicated that good ideas and technical help were provided and that materials developed for their classes were helpful. The mentor reported that the support resulted in a gradual improvement in the handling of technical aspects of Navigator use, and in the incorporation of TI-Navigator in the curriculum. In particular he found that the in-class help encouraged the teachers to use the technology in different contexts. For year two, teachers requested training grounded in the Grade 10 curriculum, particularly sessions that were activity-based but included more time for practice. This suggestion was incorporated into the training provided in year two of the study. The technical aspects of implementation were difficult for most, but by the end of year one both students and teachers were reasonably comfortable with the system. At the same time, these teachers had not yet fully embraced the pedagogy that TI-Navigator can enable. Links to other strands and contexts were infrequent and discussions that engaged all students in analysing the images sent to the TI-Navigator, or pulling together the outcomes of the day’s activity, were not held. Significant progress in these areas was noticed in the second and third years as teachers gained confidence and experience. One focus group meeting was held with students from one of the experimental schools. The students were very positive about the use of technology. One said that calculators make math easier, although another believed that they make some people lazy. A third student said that it was faster to do tests – and fun to be able to analyse everyone’s answers. Three of the students felt that the technology had not affected their understanding – because “the teacher still teaches you”, but one noted: “on the screen you can see how others have done so it’s helpful. [The] teacher goes over the wrong answers so that we can understand where we went wrong.” Another commented that it helps to be able to “see it.” Despite the technical difficulties, teachers from the experimental schools gave very positive responses during interviews conducted at the end of year one. Overall, the six teachers said that they enjoyed using the TI- Navigator. Some of the benefits mentioned by one or more teachers were: TI-Navigator assisted them to better structure their lessons, using LearningCheck and Quick Poll helped them determine whether the students understood the material; and use of the TI-Navigator helped in meeting the diverse needs and abilities of students in the classroom. A number of teachers expressed the belief that more students were actively involved in learning. Teachers said that it was time consuming to learn to use the technology seamlessly and to reorganize their lessons to accommodate the use of the TI-Navigator; however, all teachers were enthusiastic about continuing the project with one stating “I don’t see that we have to improve anything. It was a good experience for me and for the students”. Another said “I love it! It helps me make [math] more interesting”. The project team interviewed the department heads as well. Both of the department heads at the experimental schools regularly used the TI-Navigator system in their classes and were very positive about the benefits to teachers and students. With regard to implementation, one of the department heads noted that incorporating technology into lessons requires a willingness to change one’s pedagogy – something that was a problem for some study teachers. The other department head offered a similar idea but from a different perspective; i.e., the positive aspect of TI-Navigator use is that it forces teachers to reflect on different on alternative ways of presenting material. During the first year, both heads acted as role models and provided significant support for the new users. They provided materials and advice, visited teachers’ classrooms to assist and to troubleshoot technical problems, and invited the teachers to watch them teach with the TI-Navigator. Although schools were not chosen on the basis of school-based expertise with TI-Navigator, it is difficult to imagine how the project could have progressed without the continuous onsite help provided by these two dedicated, and knowledgeable, department heads. Recommendations The collected data and our experience in the first year of the study provided insights into the nature of TI-Navigator implementation by “typical” teachers and the support they require in order to experience success. We found that need for support falls into two categories – technical, and pedagogical. We suggest that professional development sessions for such teachers need to include additional practice time on technical skills, and also that teachers may require customized materials developed specifically for their curriculum. In subsequent years of the study, we found that use of Navigator can encourage a more open pedagogy (i.e., one that is in line with NCTM precepts) when teachers believe that mathematics is socially constructed and that mathematics teaching must involve students in investigating and discussing mathematics. For this reason, we believe that professional development that focuses on changes in beliefs and attitudes may be the most significant factor in helping teachers use this technology.

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/282/TI-Navigator study final report Oct 09 - Sinclair.pdf

Year: 2012

Publisher: T3 France

Author: T3 France

Language: French

Institution: Texas Instruments

Department: T3 France

City: Paris, France

Abstract: This case study reports on trials of TI-Nspire mobile handhelds in mathematics and science classes of 12 Lycees in 10 cities in France, involving 17 classes and 480 students. The goal was to evaluate impact on teaching, and on classroom culture. This pilot project is part of an ongoing series of similar projects throughout Europe since 2008. Cette solution s’inscrit pleinement dans les programmes de mathématiques en France qui demandent à intégrer au maximum les TICE et ce, sans dédoublement de classe.

Reference: Report

Keywords: TI-Nspire, France, Lycee, Case Study

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/281/Bilan ClassNum_Maths_Sciences_Web.pdf

Year: 2011

Publisher: Malmö University

Author: Per-Eskil Persson

Language: English

Institution: Malmö University

Department: Mathematics and Learning

City: Malmö, Sweden

Abstract: Research of technology used in mathematics education has been mainly focused on the calculators. Therefore it has been of great value, as in this study, also to study how teachers and students can use laptops with TI-Nspire technology and software, with or without concomitant use of handheld devices. Of particular interest has also been examining possible changes in teachers' teaching experience, the students' problem-solving methods and the students' math¬ematical learning and deeper understanding of mathematics, and other outcomes of education in this technological learning environment. Eight classes of students in theoretical programmes at upper secondary level in southern and central Sweden, as well as their teachers, were using TI-Nspire CAS in a regular course, Mathematics A or Mathematics B, during a whole semester. They used the software and/or handhelds continuously during the course and also, where appropriate, implemented the national test on laptops. Experiences of students and teachers, concerning opportunities and the positive sides as well as obstacles and problems, agree well. Almost all showed significant progress during the study, both in terms of management of technology in the math work, and when it comes to integrating it into a high-quality learning environment. A majority of the students testified about the positive impact that the use of technology had on their view of mathematics and of what mathematical activities would include. This raised at a great extent their interest in the subject and gave them more confidence towards mathematics. Perhaps the most important results of this study are how TI-Nspire software on laptops could be used in regular education in courses at upper secondary level. Its various possibilities, of technical, mathematical and conceptual nature, have had the opportunity to appear in this relatively long study. But also the various obstacles and risks of this type of technology were identified, and teachers' approaches to them have been reported. They agree that CAS represents a difficulty, especially for low-performing students, but also carries an incredibly pow-erful potential in mathematics. Experiences from the use in the national tests were positive, and the barriers that existed for the use of laptops could in practice be eliminated. Special attention has been given in the study to the question if the combination of handheld unit and computer has added something extra to education. The results indicate that there are several reasons to consider this technical solution, such as the hand units being better in certain situations; for quick calculations, for tests and in other subjects; while computers presenting an advantage for working with graphs or to solve larger problems and finally to document them. This indicates that implementation of new technology must always be preceded by a careful analysis of how it is meant to be used in education in practice.

Reference: Report

Keywords: CAS, computer, digital, high school, laptop, national test, technology, TI-Nspire, upper secondary, Case Study

Document Content: Also available in Swedish. http://dspace.mah.se/handle/2043/12582 (English) http://dspace.mah.se/handle/2043/12552 (Swedish)

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/280/Teaching and learning with TI-Nspire - Persson 2011.pdf

Publisher: University of Louisville

Author: Barbara R. Buckner

Language: English

Institution: University of Louisville

Department: Department of Teaching and Learning

City: Louisville, KY

Abstract: The purpose of this study was to determine the effect of TI-Nspire graphing calculator use on student achievement and on teacher behavior variables of planning, teaching, and assessing. This study investigated the teaching of functions by teachers using the TI-Nspire graphing calculator versus teachers using a non-graphing scientific calculator. A review of the literature found that the emergence of calculators and computers has changed the way mathematics is both done and used (Ellington, 2006; Thorpe, 1989; & Kieran, 1992). Research also showed that students can effectively use a graphing calculator as an instructional tool to make and understand different types of representations (Choi-Koh, 2003; Colgan, 1993; and Drijvers & Doorman, 1996). Other studies have shown how graphing calculator use has engaged students in higher level thinking skills (Dessart, DeRidder, Charleen, & Ellington, 1999; Ellington, 2006; Graham & Thomas, 1998; Keller & Hirsch, 1998; Huntley, Rasmussen, Villarubi, Sangtong, & Fey, 2000; & Ronau et al., 2008). Since it is a relatively new tool, there is a limited amount of research on the classroom use of the TI-Nspire. The TI-Nspire is designed to link together multiple-representations within a single problem, so the concept of functions is an ideal context within which to study the impact of the TI-Nspire. This was a quasi-experimental study. The researcher gathered and analyzed pre-test, post-test, and post post-test data on student performance on function concepts. The study included a 90 minute classroom observation of each class as well as document analysis of weekly questionnaires, daily lesson plans, and daily assessments. Vignettes employed classroom observations, document analysis, and thick description to triangulate the results of the qualitative analysis. During the summer prior to this study, all teachers attended 12 hours of training over the course of two days with a National Texas Instruments Instructor in which they were trained to use the TI-Nspire graphing calculator. Teachers were then given a TI-Nspire, TI-Nspire emulator and access to online Atomic learning video training (Atomic Learning, 2011), to continue their exploration of the TI-Nspire. The week prior to the study, the teachers attended another day of professional development activity taught by a Texas Instruments Trained Cadre member. This “Function Focused Session” was six hours long and provided review on the TI-Nspire, specific training about teaching the function concept with the TI-Nspire, and time to create lesson plans and activities for this study. During the two weeks of treatment and two weeks of follow up, teachers met once a week for “Weekly Touchdown Sessions,” a 90 minute meeting held after school to complete a weekly questionnaire, turn in lesson plans, assessments, and receive further professional development on the TI-Nspire. Providing a trained Texas Instruments Instructor on a weekly basis to answer questions, assist in providing direction for the following week, and meeting weekly with the teachers to complete questionnaires were vital strategies necessary to support teachers with this new technology tool and to assure their fidelity in treatment implementation and control maintenance. All professional development sessions were taught by Texas Instruments trained Instructors. The results from four teachers, each with one treatment class using the TI-Nspire and one control class using a non-graphing scientific calculator, were significant on the pre-test with the control group having a higher mean score than the treatment group and statistical significance on the post post-test with the treatment group having a higher mean score than the control group. While there was a statistically significant effect of Teacher Zeta on the post-post test in comparisons with the other teachers, most of the teacher effect was controlled for within the design of the study. To control for teacher effect, all teachers taught both a treatment and a control class. For each teacher, one of their two algebra classes was randomly assigned to treatment and the other was then assigned to control. There was not enough power in the data to properly analyze the effect of socioeconomic status and special education. This study supports the use of TI-Nspire graphing calculators in Algebra classrooms while studying the concept of functions. This study shows that, while using the TI-Nspire graphing calculator, the use of multiple representations and higher Depth of Knowledge activities can be used to improve student achievement, and impact classroom teaching, and lesson planning. While this study shows the impact of the TI-Nspire graphing calculator for the concept of functions, further research is needed to continue evaluating the impact of the TI-Nspire across additional mathematics topics.

Reference: Thesis

Keywords: TI-Nspire, Algebra, 9th Grade, Kentucky

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/279/Teaching Functions with TI-Nspire - Buckner 2011.pdf

Year: 2012

Publisher: Texas Instruments

Author: Foshay, Rob

Language: Other

Institution: Texas Instruments

Department: Research

City: Dallas, TX

Abstract: This is a PowerPoint presentation summarizing the most important current research on TI-Nspire and TI-Navigator (collectively referred to as the interactive math/science classroom), of interest internationally.

Reference: AV media

Keywords: TI-Nspire, TI-Navigator, Math, Science

Document Content: Translated into Chinese by Yanmin Wu.

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/277/0228-Research on the IMC - Overview 2012-trans_Yanmin.ppt

Year: 2011

Publisher: MNU

Author: Heimann, Rebekka, Liebner, Frank, Besser, Lukas

Language: German

Institution: University of Leipzig

City: Leipzig, Germany

Abstract: During seven chemistry lessons students from grade 9 and 10 conducted three chemical experiments. They used the calculator TI-Nspire and different sensors for recording data and providing the corresponding graphs. Central aims of the study were to find out what students think about the use of the hardware and software, what advantages and disadvantages they see and how useful the obtained graphs are for them to interpret the experiments and find out general rules. The study included 350 pupils from 7 different schools in 4 different federal states of Germany.

Reference: Journal article

Keywords: TI-Nspire, Case Studies, Case Study, Science, Chemistry, Germany, Sensors, High School

Document Content: The study was carried out in cooperation of Prof. Dr. Rebekka Heimann from the University of Leipzig, Mr. Frank Liebner from the Löbau High School, the German T3 Project and Texas Instruments.

Attachments: http://www.ti-researchlibrary.com/Lists/TI Education Technology Research Library/Attachments/276/Calculators in Chemistry Lessons - Heimann - MNU_6_2011_349-356.pdf

Publisher: Springer

Author: Alison Clark-Wilson

Language: English

Institution: University of Chichester

Department: Mathematics Education

City: Chichester, UK

Abstract: New digital technological tools offer increasingly complex functionalities with the facility to combine and manipulate multiple mathematical representations within a single software package. However, little is known about how teachers begin to integrate such technologies into their classroom practices. It can be argued that, without a deeper understanding of the teachers’ learning processes, it will be difficult to envisage how teachers can be supported in their professional development in order to meet the future needs of their more digitally aware students. Within the context of a research project that focused on the introduction of the Texas Instruments’ TI-Nspire handheld and software package to English classrooms (Texas Instruments, 2007), this chapter will outline the instrument utilisation schemes developed by the teachers as evidenced by the classroom activities they designed for their students. It continues to show how the analysis of an individual teacher’s utilisation schemes provides an insight into their learning trajectory within the context of the study. The chapter concludes by outlining some possible areas for future research.

Reference: Book part

Keywords: TI-Nspire, Algebra, Geometry, Use Cases

Document Content: The author has developed a diagrammatic representation of use cases for TI-Nspire, mapping from numeric, syntactic or geometric problems onto calculator functions: numeric-measured, numeric-calculated, numeric - tabulated, syntactic, graphical-coordinate points, graphical-function graph, geometric. This is a book chapter: Clark-Wilson, A. (2012). Integrating multi-representational software into mathematics teaching -- trajectories of teachers' practices. Visual Mathematics and Cyberlearning. D. Martinovic and V. Freiman. The Netherlands, Springer. 1: 300. The book is scheduled for publication in summer 2012.