This qualitative study documents case studies on use of TI-Nspire by teachers who are using the new Scottish Curriculum for Excellence.  The main research question is: Do teachers find that the use of dynamically linked multiple representations enhances their students’ relational understanding of the mathematics involved in their lessons or not, and what evidence do they provide to support their findings?

In this technology-oriented age, teachers face daily decisions regarding the use of advanced digital technologies—graphing calculators, dynamic geometry software, blogs, wikis, podcasts and the like—to enhance student mathematical understanding in their classrooms. In this case study, the authors use the Technological, Pedagogical, and Content Knowledge (TPACK) model in conjunction with a five-stage developmental model, which can be used to describe growth in TPACK to describe the initial attempts of a teacher, Jane, to develop TPACK as she learns and attempts to integrate an advanced teaching technology into her classroom, namely the TI-Nspire graphing calculator. The study tracks her struggles to reconcile some traditional beliefs about how students learn with her desire to be responsive to what she perceives as affordances of advanced digital technologies. Main data collection methods were journal writing, observations, document analysis, and interviews. Using the five-stage developmental model, we saw that this experience helped Jane to move among different stages. This study showed that the TPACK model with the five-stage developmental model can be a beneficial tool for researchers to study teachers' professional growth and is also a valuable tool for teachers to reflect on their own growth.

The Phase 2 ALN research yielded the following key findings:
• TI-Nspire Navigator is an important component of the ALN resource suite that complements other TI resources (i.e. ALN and TI-Nspire)
• The research found a marginally significant increase in learning associated with TI-Nspire Navigator, above and beyond TI-Nspire and ALN. (This result may be an underestimate of the full impact, due to implementation variation and other factors inherent to the research.)
• The ALN resource suite influenced teacher pedagogy to emphasize deeper learning for students
• Teachers believe that the ALN resource suite contributed to increased student engagement and supported deeper student learning
• In comparison with their less experienced peers, teachers with more experience with TI-Nspire and TI-Nspire Navigator:
▫ Were more likely to shift their pedagogy to include more high-level instructional activities
▫ Reported that their students were more engaged and learned more
▫ Had students who learned more math
• Teachers who used the technology more frequently also reported that their students were more engaged and learned more math

Pre-/post-comparisons showed gains in perceived experience from the beginning to the end of the course. However, the number of students who felt nervous about the prospect of using graphing calculators increased.

The pupils were able to see for themselves the ‘product of prime factors’ representation of any integer they chose, use the results that they had found, and see if they had correctly prime factorised a number without any intervention.

Summary Slides for Case Study #15.  This is a preliminary report on this study.

By using the handheld, the students made the connections much quicker and seemed to understand the concept of how equations relate to lines and how they relate to the slope and vertical intercept.

Students took the state exam, the FCAT (Florida Comprehensive Assessment Test), March 2009…FCAT year-to-year score comparisons are made using a special DSS scale. In Mr. Armbrister’s two classes, the average DSS score improved by an impressive 256 point…,”

The students have been using their own TI-NspireTM handhelds since September 2008 and I started to use TI-NspireTM NavigatorTM with them in May 2009. In this lesson sequence I used the File transfer, Screen Capture,  Live Presenter features and I plugged in the GoTemp probe to my TI-NspireTM handheld to do the data collection.
In this activity Screen Capture was an essential tool to enable me to pick out a graph I wanted to discuss with the class and this also told the students that it is their contribution and not the teacher’s who does everything all the time. With TI-NspireTM NavigatorTM the students were part of the contribution in a completely different way and it felt as though they appreciated their increased involvement. The value of letting the students discover different parts of maths is enormous and I think it will trigger off new approaches from the students that I don’t know yet. It is very exciting, I think, and maybe also a bit scary?

The students have been using their own TI-Nspire handhelds since September 2008 and I started to use TI-Nspire Navigator with them in May 2009.  I used the File transfer and Screen capture features during the lesson. The TI-Nspire file also included some question that I was able to analyse using Class Analysis after the lesson.
The activity was excellent for the students to find out that angles subtending the same arc are equal or that the angle subtending the arc at the centre is twice the angle subtending the arc. The use of the Screen Capture view and being able to collect the students TI-NspireTM files enabled me to get a very good idea of the students’ learning during the lesson. There were a few students who would have benefited from more time on the exploratory tasks – they were less confident to answer the questions - whereas others were able to progress very quickly. Most of the students were able to generate the required theorems which meant we could move onto to justifying and proving them in the subsequent lessons.

The students, who are all following a technological programme, have been using their own TI-NspireTM handhelds since September 2008 and I started to use TI-Nspire Navigator with them in May 2009. 
Initially, there were a number of students who were unsure about how to generate a linear function to go through a given coordinate point and by using the Screen Capture view they were able to see how to get started. It also let me see who needed my support. The Quick Polls encouraged all of the students to give their opinion and, from this I was able to see students change their point of view as they listened to my explanations and the other students’ reasoning. The students showed that they were beginning to really understand why a particular coordinate point lay on a particular straight line and how to find the equation of a straight line through a given point

Scholengemeenschap Sophianum is a state secondary school in the Netherlands. I have been using TI-Nspire handhelds and software with my students since September 2007 and TI-Nspire  Navigator since May 2009. In this lesson I used the File transfer, Screen Capture and Live Presenter  features.
In this lesson my students had needed to think mathematically by considering the properties of special cases and counter examples. These were made more obvious to the whole class due to the number of different screens that could be displayed at one time with Screen Capture. Using TI-Nspire Navigator  in this lesson enabled my students to see each others’ work and this prompted a much wider discussion in the classroom than would normally happen when the students only work with the student seated next to them.

Davison Church of England High School for Girls is a state secondary school and I have been using the TI-Nspire handhelds with this class periodically since July 2007. In May 2009 I began to use TI-Nspire Navigator and in this I used the Screen Capture features.
The use of the Screen Capture view did allow the students to begin to make the obvious connections between the different types of transformations and the effect of these on the graphs. Most of the students were able to connect the vertical translation of functions by adding a constant to their existing knowledge of changing the value of c in linear functions of the form y=mx +c.

TI-Nspire technology made possible a whole new way of teaching with major improvements in performance on the new NY State Regents exam.

The class was mostly paperless, and had no textbook.  Everything was distributed electronically via the TI-Nspire Handhelds and class web site.

This Geometry educator saw gains on quizzes and a chapter test in comparison to results from teaching the same unit the previous year without TI-Nspire technology

Dr. Lapp gives an example of how he posed a problem to his students and they used multiple representations to solve the problem, building their own deeper understanding of the behavior of functions.

Ms. Gagnon finds TI-Nspire CAS manipulation and calculation capabilities to be easier to use than other geometry software. Both she and her students were familiar with the representation modes of most use in Geometry within a week of use.

Using TI-Nspire, at midyear Ms. Hoyt had 2 to 4 times as many students in the “Basic” or “Proficient” level, compared to other teachers’ classes not using TI-Nspire

“...“the ability to see multiple representations at one time really enhanced my students’ understanding… students were able to actually draw several lines of best fit on the screen and call up the equation to see how they were slightly dfferent.”

Blue Coat School is a state secondary school for students aged 11-18 years in Walsall, UK.  This class have used the TI-NspireTM handhelds previously and this was the first time I had also used TI-NspireTM NavigatorTM with them. In this lesson I used Screen Capture.
The TI-NspireTM NavigatorTM Screen Capture view enabled students to communicate their findings and consider alternative solutions - some students’ curve families were larger/different to other students’ curve families. TI-NspireTM NavigatorTM gave me continual updates on the progress the class was making so that I could target interventions better. Also students could ‘see’ that other students were progressing in ways that were different to them.  Some students had clearly got screens that matched my hand-drawn diagram of a family of curves better than other students.  This made them aware that the possibility existed of solving the task (as others in the room had clearly done so)

A qualitative case study in France of six 10th second grade classes using TI-Nspire handhelds with Computer Algebra System (CAS) found that:
-Teachers in the project developed an effective model for pedagogical resource in the TI-Nspire environment, including a .TNS file in combination with a unit-based pupil worksheet, a teacher sheet and a scenario for use, explaining the possible use of ICT.
-The document structure served as a local temporary record of the activities being performed in class, thus supporting teaching, assessment and research
-Collaboration was essential to develop learning progressions and learning activities, by adapting the shared resources.
-Collaboration is supported by an online shared workspace for teachers.
 
Using one such learning activity in geometry:
-Pupils were observed to become engaged in the assignment and remained engaged for the full two hours of the session
-Cognitive complexity of the same learning activity had been underestimated by its designers
-Pupils did not spontaneously examine different approaches to the problem, but required the teacher to highlight relationships
 
Student opinion surveys showed:
-Over 96% of students had a computer at home, and 75% used it daily, and amongst the small part of pupils knowing dynamical geometry, most had experience with cabri.  But they still cited as advantageous the extreme portability and dynamic applications of TI-Nspire.
-Regular in-class use of TI-Nspire facilitated ease in mastering the tool, and difficulties of use were rapidly overcome.
-As the year progressed, the calculator was seen more as a tool available in the class
-As the year progressed, student emphasis was far more on the possibilities for symbolic calculation and new potentials for problem solving, rather than the features of the device.

A qualitative study of TI-Nspire Navigator use in seven classrooms in five European countries found the teachers:
- developed new and supported existing formative assessment practices using screen capture & presenter;
-providing teachers with additional insight to enable them to provide thoughtful interventions during the lesson;
-promoting purposeful classroom discourse to enrich the teacher’s awareness of students’ existing mathematical knowledge;
-developing strategies for students’ peer assessment and self assessment.
-enabled the development of innovative mathematics tasks;
-focusing students’ attentions on making mathematical generalisations through generative questioning
-creating “shared learning space”
-generating the mathematical data to initiate the task

With the ever changing landscape of American education, it is vital for schools to provide teachers and students with the latest forms of technology that can foster a positive learning environment for all students. The advancements that have occurred in technology and education have greatly helped both students and teachers have success in the classroom. In addition, with the increase in diverse learners and varying achievement levels found in each classroom, it is crucial for teachers to be able to modify their lessons and differentiate instruction so that all learners can achieve. One specific advancement in technology and education has been the Texas-Instruments product, the TI-Nspire Navigator. The TI-Nspire Navigator is a wireless device that connects to the back of the students’ calculator. Connection occurs through a router and a laptop. Once connected, the teacher can send the students questions, quizzes, or data to the calculator instantly. At that point, students respond to the question by sending their results back to the teacher. The information is displayed on the laptop in an organized form. It is the goal of this study was to determine how the TI-Nspire Navigator affects student achievement in the classroom.
Specifically, this study analyzed the use of the TI-Nspire Navigator in two mathematics classrooms – one 9th grade Algebra Regents class and one 10th grade Algebra Extended Class containing special education students. Data was collected over a six week period, through student and teacher surveys, quiz/test results, and teacher observations. The researcher analyzed and observed how student achievement changed when the TI-Nspire Navigator was incorporated into the classroom. Furthermore, data was collected to observe its role in increasing student achievement for not just the general education student, but the special needs student as well.

The purpose of this action research study was to determine whether a more frequent integration of the TI-NspireTM into the pedagogy for my Advanced Algebra class would enhance the students’ achievement and increase their comfort with, usage of, and knowledge of graphing calculators in general and the TI-NspireTM in particular. I also wanted to determine students’ perceptions about the use of TI-NspireTM graphing calculators and technology in the teaching of Advanced Algebra. Pre- and post-surveys of the students were used to measure the students’ comfort with, usage of, and knowledge of graphing calculators in general and specifically the TI-NspireTM graphing calculator. Achievement was measured by students’ ability to reach scores of 89% on quizzes and tests. Students’ perceptions about the use of TI-NspireTM graphing calculators and technology in the teaching of Advanced Algebra were measured using a questionnaire at the end of the study. End of project interviews with participants and teacher journaling were also part of the study. Integration of TI-NspireTM graphing calculators into my pedagogy did have a positive effect on enhancing my students’ achievement on exams while also increasing their comfort with, usage of, and knowledge of graphing calculators in general and specifically the TI-NspireTM graphing calculator. I was also able to determine that my students had positive perceptions regarding the TI-NspireTM and the use of technology in the teaching of Advanced Algebra.

Students in the TI-Nspire group tended to use more graphical representations. This study provides preliminary evidence that technology-enhanced instruction can influence students’ use of multiple representations while solving mathematical word problems.

The use of mathematics analysis software (MAS) including handheld scientific and graphics calculators offers a range of pedagogical opportunities. Its use can support change in the didactic contract. MAS may become an alternative source of authority in the classroom empowering students to explore variation and regularity, manipulate simulations and link representations. Strategic use may support students to direct their own learning and explore mathematics, equipping them to share their findings with the teacher and the class with more confidence. This paper offers a framework for examining the impact of the use of MAS on the didactic contract. Lessons were observed in 12 grade 10 classes, with 12 different teachers new to MAS. MAS technology was used with a variety of didactic contracts, mostly traditional. The framework drew attention to many ways in which the teaching differed. Analysis of the didactic contract must consider both the teaching of mathematics and of technology skills, because these have different characteristics. In all classes, both teachers and students saw the teacher as having a responsibility to teach technology skills. Students saw technology skills as the main point of the lesson, but the teachers saw the lesson as primarily teaching mathematics—one of the mismatches which may need negotiation to adapt didactic contracts to teaching with MAS.

This document (attached) has the purpose to underline the value of CAS from teaching, learning and assessment point of view and all theses are supported from a long list of research references.

The M³ pilot project, initiated by the Bavarian State Ministry for Education and Culture, forms the context for this research study. The long-term project constitutes an authentic development environment. Therefore the observations from the study can easily be generalized to what is actually happening in the classroom.
The following research question resulted from the concerns of the ministry and from prior research on the use of handheld devices. "What are the effects of long-term handheld use in a realistic research field and what factors influence these effects?" This research question is divided into several sub-questions and each has been investigated using quantitative and qualitative methods.

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.

In the 1990s, handheld technology allowed overcoming infrastructural limitations that had hindered until then the integration of ICT in mathematics education. In this paper, we reflect on this integration of handheld technology from a personal perspective, as well as on the lessons to be learnt from it. The main lesson in our opinion concerns the growing awareness that students’ mathematical thinking is deeply affected by their work with technology in a complex and subtle way. Theories on instrumentation and orchestration make explicit this subtlety and help to design and realise technology-rich mathematics education. As a conclusion, extrapolation of these lessons to a future with mobile multi-functional handheld technology leads to the issues of connectivity and in- and out-of-school collaborative work as major issues for future research.

Draft:  Do not reference or quote without the expressed, written permission of the Authors.

Thirty-five teachers teaching advanced topics in high school mathematics were engaged in a year-long intensive professional development project intended to increase their Mathematical Knowledge for Teaching in the area of discrete mathematics.  Project activities embodied a models and modeling perspective on pedagogy and learning.  Results showed that participating teachers’ content knowledge improved significantly in discrete mathematics, their classroom practice improved significantly.  Additionally, participating teachers’ students outperformed their counterparts in a matched-control group in achievement. Results provide evidence of the effectiveness of mathematical modeling for developing teachers’ mathematical knowledge for teaching, and on improving secondary mathematics teachers’ practice.

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.

Facilité de prise en main et d'utilisation: Les élèves prennent en main et utilisent la calculatrice et le logiciel et s'en servent dans leur travail en classe et hors la classe

Utilisation de la calculatrice par les élèves suivant des modes diferents:
-- calculatrice comme cahier de brouillon
-- calculatrice comme répertoire de notes
-- calculatrice comme lieu de stockage et de mémoire
-- calculatrice comme lieu d'expérience et de simulation
Dans les déclarations des élèves, les liens entre les apprentissages des mathématiques et l'usage de la calculatrice
apparaissent fortement.

Evolution des usages de la calculatrice pour la compréhension
des notions mathématiques du programme

Le développement instrumental ne se fait pas de façon linéaire, mais des phases de repli surviennent lorsque
les rétroactions ne sont pas comprises par les élèves et les enseignants

Abstract:
Im Rahmen eines Unterrichtsprojekts in der zehnten Jahrgangsstufe konnten Schüler zunächst für drei Monate mit einem iPod Touch (mit Mathematik-Apps) und später über mehrere Monate mit dem TI Nspire CAS arbeiten. Im Anschluss erfolgten Beurteilung und Vergleich beider Geräte durch die Schüler hinsichtlich ihrer Eignung für den Mathematikunterricht.

Abstract: In the context of a classroom project in the tenth grade, students worked initially for three months with an iPod touch (with math apps) and later for several months with the TI-Nspire CAS. Afterwards the students carried out an assessment comparing both devices regarding their suitability for teaching and learning mathematics.

published in a conference report: in: Beiträge zum Mathematikunterricht, Vorträge auf der 46. Tagung für Didaktik der Mathematik, Matthias Ludwig und Michael Kleine (Hrsg.),
URL:      http://www.mathematik.uni-dortmund.de/ieem/bzmu2012/

Since fall 2007 Symbolic calculators (CAS-calculators) have been allowed in
national tests in Upper Secondary mathematics in Sweden. But their usage
in Swedish mathematics education is limited. One research question is: Are
modern CAS-calculators difficult to learn, for final year Science students in
Upper Secondary school? A second question is: What does the students think
about using CAS-calculators? I have observed mathematics students, a 3rd
year Science class, with theories according to Nielsen (1993). The five subquestions
that are measureable are: 1) Is the CAS-calculator easy to work
with?, 2) Is the CAS-calculator efficient to use?, 3) Is it easy to remember
the commands?, 4) Does the students make few errors?, and 5) what does the
student think about the CAS-calculator, is the experience pleasing?. When
collecting the material I used both observations of the 11 students, and questionnaires.
The two CAS-calculators that were used were the Casio Classpad
330 and the Texas Instruments TI’Nspire CAS.
The main results are that the CAS-calculator itself is easy to learn and
that the students are satisfyed with their experience with the calculator when
solving exercises in mathematics.

The main issue of the paper concerns the way new technologies (TI-Nspire and TI-Navigator) influence the different students’ multimodal production, in terms of words, gestures, inscriptions, and actions on the artefacts. Specifically, it investigates how they can modify students’ processes of mathematics learning, what descriptors are the most suitable for grasping such changes, and what are the new opportunities for the teacher in designing and managing mathematical activities within such environments. Three different lenses (instrumentation, humans-with-media, multimodality) are used to analyse some classroom activities, where students employ such new technologies. It is also shown how the multi-representations present in the two technological environments can support the students’ multimodal production, interaction, and communication, when they are engaged in constructing mathematical meanings. In particular, the article underlines new features of the new technologies , such as handheld environments, compared with the older ones.

The history of efforts to improve the teaching of science, technology, engineering and math (STEM) curricula has included a number of change initiatives over the past 50 years at every level of education from elementary through post-secondary.  Recently, the National Academy of Sciences (NAS) has published a framework for development of common core standards for science (Standards, 2011).  Of particular importance for this discussion are five of the eight practices of science identified in the framework: planning and carrying out investigations (in particular, data collection); analyzing and interpreting data; developing and using models; using mathematics, information and computer technology, and computational thinking; engaging in argument from evidence. 
These five practices frame this paper.  Specifically, this report examines how features of TI’s Nspired Learning system (including TI-Nspire and TI-Navigator, align with the need to build the practice of science into the curriculum, through the combination of hardware, software and research-based practices for learning and instruction.

The purpose of the study was to examine the effectiveness of using a hand-held Computer Algebra System (CAS) to create rich mathematical explorations for middle grades students. Participants were 20 undergraduate students. They used a CAS in a mathematics education content course designed to make connections to the middle grades for such topics as number theory, trigonometry, and calculus. The results of the study demonstrated that the prospective teachers were able to design a rich mathematical activity using CAS. The prospective teachers' teaching philosophy for using CAS with middle grades students was changed.

Prior to the project, 93% of teachers indicated that they never used supplemental materials in algebra or
geometry in the classrooms. Since purchasing the TI-Nspire calculators for all students, daily classroom
usage of the equipment increased to 77%. Sixty percent of teachers said their students use the calculators
for in-class inquiry-based explorations using the calculator’s scientific functions. Additionally, math
benchmark test data show that the classes furthest along in implementation (utilizing the technology most
consistently) demonstrate the greatest score gains.

Longitudinal analysis was conducted of a grade 9-10, and a grade 12-13 Italian classroom in one school, using TI-Nspire CAS, using a descriptive observation and video analysis methodology.  Major conclusions of the study were:
1. New praxeologies are introduced in the classroom because of fresh specific instrumented actions supported by TI-Nspire. Some of them have a positive consequence on learning processes of the students and on their attitudes towards mathematics.
2. The major new entries in the instrumental actions supported by TI-Nspire concern the specificity of the transition to the theoretical side of mathematics, to its modeling and to a meaningful introduction to the use of symbols.
3. TI-Nspire seems to modify the tempos of some multimodal behaviours of students; this makes TI-Nspire possibly similar to some new Representational Infrastructures used in nowadays technological society, e.g. the increasing habit of simultaneously surfing of youngest people through different technological devices for shorter period of times –the multitasking attitude compared with the old way of operating in sequence for longer periods of time.

Research on teachers’ use of TI-Nspire technology in mathematics and science classrooms shows that the unique capabilities of this new generation of handheld device help teachers engage learners in exploration, focus on conceptual understanding, and deepen learners’ work with mathematical and scientific models. In addition, research suggests that forthcoming integration of the TI-Nspire Navigator System will further enhance classroom collaboration and formative assessment.

Improving mathematics teaching and learning through and beyond Algebra is one of the most important challenges facing educators worldwide. The powerful capabilities of technology to engage students, support their cognitive effort, represent mathematics insightfully, and better connect teachers and students are important to addressing the Algebra challenge. To leverage technology effectively, teachers need an appropriate pedagogical model.
We propose a pedagogical model based on the concept of interactivity. By interactivity, we mean increasing the quality and frequency of back-and-forth interplay among the
teacher, her students, and the mathematical content at hand. Technology can enhance many forms of interactivity, especially when:
• students and teachers use technology to explore mathematical models, not just as a calculation tool,
and when:
• teachers use a shared display and instant feedback to increase students’ cognitive engagement, not only to demonstrate or assess.
Across these forms of interactivity, the most important goal is to increase student engagement centered on the doing and making sense of mathematics. Application of this principle leads to highly interactive mathematics classrooms, in which teachers:
1. engage their students in mathematically meaningful activities;
2. focus on mathematics with connections;
3. track what mathematics their students know and adapt accordingly;
4. make mathematics learning a shared responsibility of teachers and students.
Implementing a highly interactive mathematics classroom takes more than technology, it requires support for professional development and time for teachers to learn and adapt. For example, the new capability to instantly capture and display students’ screens can provide cognitive contrasts that drive learning, but only when the teacher uses classroom
discussions to probe the meaning of contrasting screens. We propose an implementation model that proceeds in stages, based on research data that shows what teachers typically
accomplish immediately, with experience and, eventually, as masters of the technology-rich classroom. By thinking in terms of not just technology but also a pedagogical model and
implementation in stages, schools can realize deepening benefits over time. Within the first year, schools can experience increased student achievement and more positive
student attitudes. Teachers see immediate benefits from knowing more about their students. Over time, with continued technological support and sustained professional development, schools can make progress in closing achievement gaps and introducing higher-order skills, such as mathematical problem solving, collaboration, and argumentation. Over many years, schools will develop master teachers who can lead further improvement in their regions, aimed at developing students’ passion to pursue and succeed in university level mathematics and on toward challenging STEM careers.

This case study documents the struggles and successes encountered
by a pre-calculus teacher while using classroom
connectivity technology (CCT) daily in her community college
mathematics course. CCT refers to a wireless communication
system that connects a teacher’s computer with an
individual student’s handheld calculator and has been associated
with positive academic outcomes (Pape et al., 2011).
CCT allows the instructor to send documents, collect student
responses, and project student work for classroom discussion.
Due to the increased complexity of teaching using CCT, however,
teachers often struggle with initial implementation. For
example, the instructor struggled with a lack of time to plan
and execute activities using CCT. She also had to develop
an understanding of how to use CCT effectively and how to
resolve technical issues that arose during the lesson. The instructor
also experienced numerous successes. CCT was used
for formative assessment, to promote involvement among students,
and to exhibit and connect multiple representations of
a mathematical concept. This case study provides mathematics
educators seeking to understand the costs and benefits of
implementing CCT with valuable insight into issues of early
implementation.

In 80% of the 66 lesson evaluations received, The teachers concluded that the use of multiple representation with TI-Nspire enhances students’ relational understanding of the mathematics involved and they were willing to provide
extensive evidence to support their argument. Only 3% contained a negative response.

Do teachers find that the use of dynamically linked multiple representations enhances their students’ relational understanding of the mathematics involved in their lessons and what evidence do they provide to support their findings? Throughout session 2008–2009, this empirical research project involved six Scottish secondary schools, two mathematics teachers from each school and students from different ages and stages. Teachers used TI-Nspire PC software and students the TI-Nspire handheld technology. This technology is specifically designed to allow dynamically linked multiple representations of mathematical concepts such that pupils can observe links between cause and effect in different representations such as dynamic geometry, graphs, lists and spreadsheets. The teachers were convinced that the use of multiple representations of mathematical concepts enhanced their students’ relational understanding of these concepts, provided evidence to support their argument and described changes in their classroom pedagogy.

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.

This study compares the respective achievements of students in an integrated algebra course taught with two different types of handhelds over a period of one year. The experimental group was taught with TI-Nspire handhelds and was compared to the control group taught with TI-84 graphing calculators.  The teachers of each groups received on-going professional development in the same format.  Student achievement was measured via a midyear department test; Fall and Spring semester grades; and New York State Regents exam scores and passing rates.  Results indicated that the group taught with the TI-Nspire outperformed the other group in all assessments, including passing rates on Regents but not on the Regents exam scores. Further analysis indicated that girls outperformed boys in an identical pattern.  No significant differences in achievement by race were observed.

A qualitative study in one algebra geometry III classroom of students using TI-Nspire CAS showed TI-Nspire CAS  had a positive effect on students’ understanding of solving equations, using parentheses, and understanding equivalent operations.

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.

Among the results of this research:
• The extension of the work done in the computer room (with the software) by activities in class or at home with the handheld is a fundamental element which favors the dual-technology solution;
• Both versions of TI-Nspire technology inherently include a documentation aspect (organizing resources, exchanging, transforming, creating) that have impacts on the work of teachers and students;
• TI-Nspire technology is easy to access, though at the very beginning, teacher training is  necessary;
• The introduction of the TI-Nspire technology is a factor favoring the transformation of teacher practices but the technology is not the sole cause of the transformation;
• The presence of professional development can optimize the time to getting started with technology. This training can be internal (between the teachers in the same school) or external (by experts);
• The resources used by teachers are built on their previous experiences. The way in which the form of resources used by a teacher change is related to their professional habits and is gradually and continually developed.
Conclusions
We noted the need to support teachers, particularly for resource design and their use in specific scenarios in the classroom to show how to integrate the technology in maths lessons.
The technology is a lever for change in teaching practices, but must be accompanied by training.
This research could be extended by a thorough study of the technology used by teachers and students, linked to resource design and effective learning,.