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.

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.

“The ability of TI-Nspire CAS technology to provide multiple, dynamically linked representations of graphs, equations and
tables proved particularly useful in teaching graphing and linear functions, one of the most important concepts in the
9th grade Math A curriculum. Despite the difficulty of the exam, the average score was 80% (it is normally in the low 70 percentile), and half of the class received an A or B grade.

CSG Liudger is a state secondary school in the Netherlands. I have been using TI-Nspire handhelds and software with this group of students since September 2007 and TI-Nspire Navigator since May 2009. In this lesson I used File transfer, Screen Capture and Live Presenter features.
The students were able to use their existing knowledge of statistical variables such as the mean average and the median to confirm or refute their statistical hypotheses. They also considered how the use of different statistical graphs might support this process.

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 year-long study introduced TI-Nspire with professional development to 14 KS 3-4 teachers in seven UK 11-16 secondary schools.  The qualitative study reported many examples of how teachers used TI-Nspire with the goal of enhancing students’ mathematical understanding.
There was a strong evidence that  TI-Nspire: 
- Supports the trajectory of the teachers towards selecting and/or designing more exploratory activities to use in classrooms. Teachers evaluated the use of TI-Nspire in these lessons lesson very positively with respect to their students learning outcomes.
- Helps teachers increase opportunities for students to engage in purposeful plenary activities in which the students shared outcomes and approaches. 
- Provides immediate, non-judgemental feedback  to students
- Increases opportunities for students to follow their own lines of mathematical enquiry.
- Students accessing mathematical content that was above the teachers’ age-related expectations.

After two decades of incremental advances in the capabilities of graphing calculators, handheld
technologies have recently made a leap into a new genre of educational tool – the “microworld maker.”
One such example is the TI-Nspire handheld device that allows for the creation of dynamic documents
endowed with “hot links.” The goal of a hot link is to achieve the optimum in visual proximity,
immediacy, and transparency by providing two or more external representations linked together in such a
way that the actions performed in one representation have virtually simultaneous discernible consequences
in the others. Such hot links can provide uniquely powerful settings for exploration of connections, pattern
searching, and inductive reasoning. That is, students are presented with environments where they can
directly manipulate or take actions on mathematical objects and immediately see the mathematically
meaningful visual consequences of those actions. We offer a variety of examples of such environments
drawn from a range of mathematical areas and raise two issues of import for both teachers and developers:
mathematical fidelity (faithfulness to the mathematical representations) and cognitive fidelity (faithfulness
to the cognitive perceptions of the user).

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

A qualitative case study in France of six 10th second grade classes using TI-NspireTM 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.

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.

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.

New Jersey’s urban students traditionally don’t do well on the high stakes NJ High School Proficiency Assessment. Most current remedial mathematics curricula provide students with a plethora of problems like those traditionally found on the state test. This approach is not working. Finding better ways to teach our urban students may help close this achievement gap. This study examined whether a problem/project-based data analysis unit incorporating the document features of the TI-Nspire would help students master data analysis concepts. The study used a quasi-experimental pre/Post-test design enhanced by a qualitative component. A four-week problem/project based data analysis unit served as the curriculum for the intervention treatment. Students were assigned either the TI-84 or the TI-Nspire calculator. Twelve sections of ninth grade students were divided into four basic study groups: (Intervention (TI-84), Traditional (TI-84), Intervention (TI-Nspire), and Traditional (TI-Nspire)).
The quantitative component of the study analyzed differences between students’ pre/post- Total, Multiple-choice, Open-ended mean scores and quantified attitudinal responses. The analysis showed students in the TI-Nspire groups improved more on the Total test and Multiple-choice questions while students in the TI-84 group performed better on Open-ended questions. The Intervention Curriculum was more effective for Multiple-choice questions, Traditional Curriculum for Open-ended questions and Total scores. Student interviews revealed they didn’t like taking notes and answering questions on the TI-Nspire. Some students liked referring to the information in the calculator while others felt that accessing information was too time consuming. The merits of the TI-Nspire document feature needs further exploration. Analysis of the quantified attitudinal survey showed an increase in the positive attitudes of students using the TI-Nspire.
Both qualitative and quantitative evidence showed the Traditional TI-84 group had fewer changes in attitude and content knowledge than everyone else combined, suggesting the need to change how we teach data analysis. Problem/project-based learning, if introduced gradually, may prove to be an effective teaching/learning educational practice.
Further exploration needs to match students’ technological and data analysis proficiencies when determining readiness for student-centered learning that expects students to be calculator proficient and comfortable with basic quantitative procedures such as finding measures of central tendency and variation.

This study compares the achievement of students, enrolled in an integrated algebra course, taught with two different types of handhelds over a period of one year. One group was taught with TI-Nspire handhelds and was compared with another group taught with TI-84 graphing calculators.  The teachers of both groups received on-going professional development.  Student achievement was measured via a midyear school test, fall and spring semester grades, and New York State Regents exam scores.  Results indicated that the group taught with TI-Nspire outperformed the other group in all assessments except the Regents exam.  Further, analysis of scores indicated that girls outperformed boys in all assessments except the Regents exam, while there were no differences in achievement by race.

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,.

Based on our limited experience, the templates do seem to open avenues for student thinking and create opportunities for discussion not only about the mathematics but about strategies for using the template to reason about the mathematics. For example, some teachers made deliberate changes in what they can move and record the results; Using the number line template (Figure 3), some held the x-value constant, increased the y-value by 1 unit at a time, and recorded the output then changed the x-value by 1 and repeated the process; others looked at extremes, what happens to the difference between the expressions when x is large or when x is small. Helping students understand how to think in these ways is a fundamental part of learning to do mathematics, and it will be important for teachers to recognize this.
The next phase of the work is to formally pilot the templates and to consider the implications for research related to both the design and implementation. The potential is clearly present to make a difference in what students learn; the challenge is to make this happen in ways that can be replicated across the teaching communi

 The Math Nspired series of curriculum supplements currently include Algebra Nspired and Geometry Nspired. The supplements grew from research on the “tough to
teach/tough to learn” topics, which our item analysis of state tests showed to be common points of difficulty for many students. To determine the underlying reasons for
the difficulty, we consulted the research on the reasons why students struggle with key concepts in Algebra and Geometry.

The driving question revolves around a shaping of learning experiences for children with the aid of an advanced graphing calculator in an informal environment. This study investigates how learning is triggered by an event that deeply engages learners, offering affordances that are typically missing from inert sequences of learning in everyday classrooms.
Findings highlight three important considerations: (i) all participants showed a positive gain in knowledge, both in procedural and, more importantly, in conceptually connected knowledge; (ii) participants who had access to graphing calculators learned with understanding and appeared to be better able to draw inferences that connected inert knowledge with observed and grounded phenomena; and, (iii) low-achieving participants who had access to graphing calculators seemed to show the highest gains