
  2010  This study aims to examine how teachers’ mathematical and pedagogical knowledge develop as they learn to use a multirepresentational technological tool, the TINspire handheld device and computer software. It is conducted as an enquiry into the learning trajectories of a group of secondary mathematics teachers as they begin to use the device with a focus on their interpretations of mathematical variance and invariance. The research is situated within an English secondary school setting and it seeks to reveal how teachers’ ideas shape, and are shaped by, their use of the technology through a scrutiny of the lesson artefacts, semistructured interviews and lesson observations. Analysis of the data reveals the importance of the idea of the ‘hiccup’; that is the perturbation experienced by teachers during lessons stimulated by their use of the technology, which illuminates discontinuities within teachers’ knowledge. The study concludes that the use of such a multirepresentational tool can substantially change the way in which both the teachers and their students perceive the notions of variance and invariance within dynamic mathematical environments. Furthermore, the study classifies the types of perturbations that underpin this conclusion. The study also contributes to the discourse on the design of mathematical problems and their associated instrumentation schemes in which linked multiple representations offer a new environment for developing mathematical meanings. This thesis makes an original contribution to understanding what and how teachers learn about the concept of mathematical variance and invariance within a technological environment.  Hiccup, Instrumental genesis, TINspire, UK, Secondary Mathematics, mathematics education, mathematical generalization, multiple representations, teacher development, professional development, variance and invariance    2010  This qualitative study documents case studies on use of TINspire 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?  TINspire, Scotland    2010  As many researchers have studied, calculators may not be appropriate for all educational situations or all mathematical subjects. However, Ellington (2003) reported that the improvement to problem solving skills was most significant when (a) special curriculum materials were designed for use with the calculator and (b) the type of calculator used was the graphing calculator. The purpose of the study was to identify strengths and limitations in how prospective mathematics teachers use the graphing calculator in teaching mathematics concepts and procedures. This study included both quantitative and qualitative data collection and analysis methods, providing an opportunity for presenting a greater diversity of views. , discussion thread and essay data were qualitatively analyzed in the context of the TINspire study in search of recurring themes, informed by the Technological Pedagogical Content Knowledge (TPCK) framework (Niess, 2008).  TINspire, TPACK, TPCK, Preservice teachers    2011  In this technologyoriented 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 fivestage 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 TINspire 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 fivestage developmental model, we saw that this experience helped Jane to move among different stages. This study showed that the TPACK model with the fivestage 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.  TINspire, TPACK    2008  Education processes in our classrooms too often fail to engage children's interests, and instead come across as boring or irrelevant. Both of these challenges are harvested in an educational experiment that involves the largest dam removal project in US history. 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. We studied sixteen teenagers who undertook scientific investigations in STEMrelated comprehension, in the watershed and drainage basin of the Elwha River System. This research project establishes a baseline that foreshadows a longitudinal study addressing the learning outcomes that occur (i) before, (ii) during, and (iii) after the dams come down. A mixed methods approach was used. Empirical data was collected in pre and posttests, that involved student exercises in STEM and social studies. Qualitative data were established in thick descriptive ethnographical record derived from extensive field notes and teacher and student documentation, and a network of educator roles as participant observers. 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) lowachieving participants who had access to graphing calculators seemed to show the highest gains. Directions are proposed for future research that outlines how teachers, might effectively conceptualize, frame and develop learning environments around the advanced graphing calculator family of tools that foster collaboration and cultivate a preparation for future learning  learning sciences, informal learning, advanced graphical calculator, adaptive expertise, preparation for future learning, metacognition, TINspire, Science, Geography, STEM    2012  The Phase 2 ALN research yielded the following key findings: • TINspire Navigator is an important component of the ALN resource suite that complements other TI resources (i.e. ALN and TINspire) • The research found a marginally significant increase in learning associated with TINspire Navigator, above and beyond TINspire 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 TINspire and TINspire Navigator: ▫ Were more likely to shift their pedagogy to include more highlevel 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
 TINspire, TINavigator, Algebra, Algebra Nspired, California    2009  Bavarian grade 11 students studying calculus with symbolic calculators with CAS  the students in the project classes have learned in a more individualized way, they changed their working style, e. g. working with functions and equations, and they became acquainted with some new examples.  No difference between symbolic classrrom and comparison classes was measured. This calls into question the sensitivity of the tests used.
 Graphing Calculators, TINspire, Voyage 200, CAS, 11th grade, tests    2007  Pre/postcomparisons 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.  Case Study, TINspire, Graphing Calculators, PreService Teachers, Attitudes, Beliefs, TPACK, TPCK    2007  TINspire allowed pupils to explore the problem for themselves quickly and efficiently so the focus was on the intended learning rather than issues with drawing graphs that could have occurred otherwise.  Case Study, UK, Grade 10, ALevel, TINspire, Geometry, Key Stage 3    2008  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.  Case Study, Year 8, TINspire, Factors, UK    2008  There is direct correlation between quality and frequency of use of TINspire in the classroom and teachers’ and students’ attitudes and proficiency.  Case Study, TINspire, New York, NY, Grade 9, Title I, Low Income, MultiRacial, Algebra, FRPL, african american,hispanic, white, ELL, special needs, at risk    2008  Summary Slides for Case Study #15. This is a preliminary report on this study.  Case Study, TINspire, Algebra, Title 1, Low Income, MultiRacial, africanamerican, hispanic, white, FRPL, ELL, at risk    2009  The TINspire group demonstrated significant increase in performance, which demonstrates that students crossed performance levels (for example from lower to higher achievers).  Case Study, TINspire, New York, Geometry, Grade 10, Grade 11, TINspire, TI84, white    2009  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.  Case Study, TINspire, Algebra, Developmental, PostSecondary, Community College, adult, white, hispanic    2009  I think that many students were able to make a visual connection with the graphing and the action that created the graph.  Case Study, Developmental, Algebra, Community College, TINspire    2009  Students took the state exam, the FCAT (Florida Comprehensive Assessment Test), March 2009…FCAT yeartoyear 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…,”  Case Study, TINspire, Middle School, Florida, FL, FCAT, africanamerican, hispanic, ELL    2009  By monitoring the students’ activities whilst they were answering the problems I was able to see the wide range of approaches that the students used. For example, one student chose to insert a Spreadsheet page to create a probability distribution table to help him reach a solution. Using Screen Capture in this way gave me a real insight into the way that the students went about solving the problems. It also supported the students to see a range of strategies and learn from each other.
 Case Study, Netherlands, Math D, TINspire, TINavigator, TINspire Navigator, binominal test, tests, Secondary School    2009  The students have been using their own TINspireTM handhelds since September 2008 and I started to use TINspireTM 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 TINspireTM 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 TINspireTM 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?  Case Study, Sweden, IB school, TINspire, TINavigator, TINspire Navigator, Secondary School, exponential functions, probe, File Transfer, Screen Capture, Live Presenter    2009  George Watson’s College is a mixed independent school and I have been using the TINspireTM NavigatorTM since October 2008 with most of my classes (students: 1112 year olds following the compulsory secondary mathematics curriculum). In this lesson I used the File transfer, Screen Capture and Class Analysis features. I thought that this lesson activity gave my students an opportunity to interpret mathematics by devising and describing in words the general relationships between angles. Some of the weaker students preferred to describe things in terms of the numbers shown on their diagram in its static form. However, as I was able to identify who these people were using Screen Capture, I was able to individually guide them towards trying to describe the relationship in more general terms using words, or angle labelling conventions, rather than just numbers. Using Screen Capture enabled me to effectively target individual support to those in the class who needed it most.
 Case Study, Scotland, TINspire, TINavigator, TINspire Navigator, Secondary School, angles, Screen Capture, File Transfers, Class Analysis    2009  The students have been using their own TINspire handhelds since September 2008 and I started to use TINspire Navigator with them in May 2009. I used the File transfer and Screen capture features during the lesson. The TINspire 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 TINspireTM 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.  Case Study, Sweden, TINspire, TINavigator, TINspire Navigator, Secondary School, IB school, Screen Capture, Class Analysis, circles    2009  Blue Coat School is a state secondary school for students aged 1118 years in Walsall, UK. I have been using TINspire Navigator since May 2009 and this was the first time this class had used the TINspireTM handhelds or TINspire Navigator. In this lesson I used Screen Capture and Live Presenter. This class of eight students were working at a level below their agerelated expectation. The students were very engaged throughout the lesson and, despite being some of the weakest students in their year group, they were very motivated by their individual contribution to the class task and were also keen to support each other with ideas and approaches. The students grew in their confidence to use the correct mathematical vocabulary to describe their patterns and the position of the geometric objects within it.  Case Study, UK,TINspire, TINavigator, TINspire Navigator, Secondary School, line, simmetry, Screnn Capture, Live presenter    2009  The students, who are all following a technological programme, have been using their own TINspireTM handhelds since September 2008 and I started to use TINspire 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  Case Study, Sweden, TINspire, TINavigator, TINspire Navigator, Secondary School, lines, points    2009  Blue Coat School is a state secondary school for students aged 1118 years in Walsall, UK. Some of the students in this class have been using the TINspire handhelds since 2008 and I have been using TINspireTM Navigator with these students since May 2009. In this lesson I used File transfer, Screen Capture, Live Presenter and File collection. All of the students were able to see very quickly that, when the condition for the areas being equal was true, the triangles appeared to be right angled and, having recorded this ‘rule’ in their own words, I felt that we were in a good position to try to apply this to a new problem in a subsequent lesson when we would look at more traditional problems involving Pythagoras’ theorem.  Case study, UK, TINspireTiNavigator,TINspire Navigator, Secondary School, File transfer, Screen Capture, Live Presenter, File collection    2009  Scholengemeenschap Sophianum is a state secondary school in the Netherlands. I have been using TINspire handhelds and software with my students since September 2007 and TINspire 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 TINspire 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.  Case Study, Netherlands, TINspire, TINavigator, TINspire Navigator, Secondary School, quadratic functionsFile Transfer, Screen Capture, Live presenter    2009  George Watson’s College is a mixed independent school and I have been using the TINspire Navigatorsince October 2008 with most of my classes. In this lesson I used the File transfer, Screen Capture and Quick Poll features. The students had the opportunity to explore a numerical sequence displayed to them as a graph. This forced them to look at the trends in the terms of the sequence and not just the numbers. The sharing of thoughts at the ‘halfway’ stage led in several cases of students checking some of the declarations that had been made by their peers and revising their own statements in response.  Case Study, Scotland, TINspire, TINavigator, TINspire Navigator, Secondary School, recurrence relations, File Transfer, Screen Capture, Quick Poll    2009  Davison Church of England High School for Girls is a state secondary school and I have been using the TINspire handhelds with this class periodically since July 2007. In May 2009 I began to use TINspire 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.  Case Study,Uk, TINspire, TINavigator, TINspire Navigator, Secondary School, transformations, functions, Screen Capture    2009  George Watson’s College is a mixed independent school and I have been using the TINspire Navigator since October 2008 with most of my classes. In this lesson I used the Screen Capture feature. The students own explorations led them to notice different features. Some students thought that the rule was to do with multiples, or with odd and even numbers whilst others were able to come up with their own correct versions of the condition. By collecting back the students’ TINspire files I gained an insight into their emerging thinking. The students were also beginning to become mathematically inquisitive and explore negative and decimal values for the lengths of the triangles’ sides.  Case Study, Scotland, TINspire, TINavigator, TINspire Navigator, Secondary School, triangles, Screen Capture    2010  TINspire 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 TINspire Handhelds and class web site.  TINspire, Algebra 2, Trigonometry, Low income, at risk, special needs, white    2011  Now, with the use of TINavigator, I KNOW exactly where my students are in the Navigator activity. For one example, during the 09/10 year I was using a Match My Graph activity with a small group of geometry students reviewing algebraic concepts. With the Navigator I received feedback on each problem.  TINavigator, Geometry, Mathlab, TINspire, TI84, TI SmartView, Alternative School, At Risk, Special Needs, Special Education, IEP, Case Study    2010  This Geometry educator saw gains on quizzes and a chapter test in comparison to results from teaching the same unit the previous year without TINspire technology  TINspire, Geometry, Texas, Hispanic, African American, White    2011  For the 20082009 school year, 100% of the students in Ms. Knox’s class demonstrated proficiency in the state’s EndofInstruction (EOI) test for Algebra 2 when the students’ home school permitted use of the TINspire handheld on the test. Students from the one school that did notexperienced a 75% pass rate). Compared to other similar classes in schools that allowed calculators on the state test, this represents nearly a doubling of the proficiency rate. For the 20092010 school year, 33 of her 36 students passed; exceptional circumstances account for two of the three students who were not proficient. “It’s amazing how this is all working,” Ms. Knox comments. “Everyone loves to come to class. The second they walk through the door they’re engaged.” This success in teaching mathematics has enhanced the reputation of the Tech Center, Ms. Knox reports. “The Tech Centers have been known for watering down the course to get the kids to pass. Now, even the IEP kids are passing the state test. People used to write off the Tech Center kids. Administrators from the sending districts now say the Tech Centers are no problem – it’s a new reputation. Now, we are known as the people who teach the math. In fact, we were asked to provide the summer threeweek remediation.” Ms. Knox is also gaining converts among her colleagues. She reports that one of the sending school’s Algebra 2 teachers is getting a class set of TINspire handhelds. No surprise, she’s eager to show her system to her colleagues in all math subjects. “The TINspire technology also works with geometry and calculus,” she says.  TINspire, At Risk, High School, Algebra 2, Special Needs, case study    2007  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.  Case study, TINspire CAS, PreService, Algebra, Calculus, PostSecondary    2007  Ms. Thompson sees advantages for students in the way TINspire CAS technology connects together applications, and in the way the handheld allows students to write mathematics in the same way they will see it on screen. Ms. Thompson comments, “I think students will learn TINspire CAS technology faster than they will other (graphing) calculators since it is built more like a computer.” She estimated that reaching full classroom proficiency took approximately 36 weeks.  Case study, TINspire CAS, Algebra, Texas, Secondary, white    2007  Ms. Gagnon finds TINspire 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.  Case study, TINspire CAS, Geometry, Secondary, laptop    2011  My research showed me that the calculator can be used to differentiate instruction for students of varying abilities, interests, and learning styles. To do this successfully, time needs to be built in for educators to become familiar with the calculator and the needs of their own students. The students' feedback gave me great insight into which activities were successful, those that needed to be modified, and those that needed to be abolished. What surprised me most was how much it altered the way my classes thought about geometry...students...often discovered theorums before they were presented in class...I also saw struggling students make meaning out of complex concepts. In addition, student retention seemed to be increased.  TINspire, Geometry, High School, New York, White, differentiated instruction, case study    2008  Using TINspire, 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 TINspire  Case Study, TINspire, Algebra, College prep, California, hispanic, white, ELL    2007  “The ability of TINspire 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.  Case study, TINspire CAS, Math A, New York, Title I, PreService, africanamerican, hispanic    2007  “...“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.”  Case study, TINspire CAS, Algebra, California, white, hispanic, FRPL    2009  CSG Liudger is a state secondary school in the Netherlands. I have been using TINspire handhelds and software with this group of students since September 2007 and TINspire 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.  Case Study, Netherlands, TINspire, TINavigator, TINspire Navigator, Secondary School, File Transfer, Screen Capture, Live Presenter, statistical variables    2009  Blue Coat School is a state secondary school for students aged 1118 years in Walsall, UK. This class have used the TINspireTM handhelds previously and this was the first time I had also used TINspireTM NavigatorTM with them. In this lesson I used Screen Capture. The TINspireTM 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. TINspireTM 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 handdrawn 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)  Case Study, UK, TINspire, TINavigator, TINspire Navigator, Secondary School, Screen Capture, quadratic curves    2011  Results on Learning of Algebra from the CAYEN project 1. In lessons using the blackboxapproach (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 CASgroup 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 technologyfree way. By contrast, GCpupils 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. CASpupils’ argumentation concerning algebra included more mathematical arguments and was more objective than the argumentation of the GCpupils. 6. We observed that the thoughts of pupils using CAS were on a high algebraic level and included reference to many concepts.
 TINspire, CAS, Germany, Algebra    2008  A qualitative case study in France of six 10th second grade classes using TINspire handhelds with Computer Algebra System (CAS) found that: Teachers in the project developed an effective model for pedagogical resource in the TINspire environment, including a .TNS file in combination with a unitbased 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 TINspire. Regular inclass use of TINspire 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.
 TINspire CAS, France, Secondary Math, collaboration, geometry    2009  This international study examined firstyear use of TINavigator with TINspire.  TINspire, TINavigator, Europe, UK, Netherlands, Scotland, Sweden    2009  A qualitative study of TINspire 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
 TINspire, TINavigator, TINspire Navigator Europe, Secondary School, Qualitative, Case study    2011  Incorporating technology (including TINspire CAS) into secondary math classess resulted in:  Increased frequency and speed of feedback  Perceived better quality, structure, and ease of understanding  Increased frequency of homework completion  Increased motivation  More focus on results  TINspire CAS, Norway, Secondary Math, Interactive Whiteboard, Geometry, Statistics, Functions, VLE, LMS    2012  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 TexasInstruments product, the TINspire Navigator. The TINspire 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 TINspire Navigator affects student achievement in the classroom. Specifically, this study analyzed the use of the TINspire 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 TINspire 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.  TINavigator, TINspire, New York, Algebra, Common Core Standards, CCSS, Special Education, Case Study    2010  It is generally accepted that the introduction of networked technologies to the mathematics classroom can stimulate an irreversible change within the classroom concerning: the role of the teacher; the nature of the classroom tasks; and the way in which students engage in the process of learning mathematics. This article will use the context of a classroombased study into teachers’ developing practices with the TINspire Navigatornetworked system of handhelds to explore the nature of these practices and the implications for the mathematics classroom. The emergence of a range of formative assessment practices is described and the implication of these practices on desirable learning opportunities (as described by the teachers themselves) is discussed.  TINavigator, TINspire, formative assessment, assessment for learning    2012  The purpose of this action research study was to determine whether a more frequent integration of the TINspireTM 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 TINspireTM in particular. I also wanted to determine students’ perceptions about the use of TINspireTM graphing calculators and technology in the teaching of Advanced Algebra. Pre and postsurveys of the students were used to measure the students’ comfort with, usage of, and knowledge of graphing calculators in general and specifically the TINspireTM graphing calculator. Achievement was measured by students’ ability to reach scores of 89% on quizzes and tests. Students’ perceptions about the use of TINspireTM 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 TINspireTM 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 TINspireTM graphing calculator. I was also able to determine that my students had positive perceptions regarding the TINspireTM and the use of technology in the teaching of Advanced Algebra.  TINspire, Algebra, Case Study, Action Research    2008  A yearlong study introduced TINspire with professional development to 14 KS 34 teachers in seven UK 1116 secondary schools. The qualitative study reported many examples of how teachers used TINspire with the goal of enhancing students’ mathematical understanding. There was a strong evidence that TINspire:  Supports the trajectory of the teachers towards selecting and/or designing more exploratory activities to use in classrooms. Teachers evaluated the use of TINspire 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, nonjudgemental feedback to students  Increases opportunities for students to follow their own lines of mathematical enquiry.  Students accessing mathematical content that was above the teachers’ agerelated expectations.
 TINspire, UK, England, Secondary Maths, case study    2008  Students in the TINspire group tended to use more graphical representations. This study provides preliminary evidence that technologyenhanced instruction can influence students’ use of multiple representations while solving mathematical word problems.  TINspire, graphical representations, multiple representations    2010  Graphing calculators facilitate learners’ ability to build cognitive links between mathematical representations by providing quick access to multiple representations. This exploratory study investigated the effects of technologyenhanced instruction on student achievement, perceptions of technology use during instruction, problemsolving success, and problemsolving solution strategies. Algebra II classrooms were randomly assigned to use the TINspire CAS or TI83+; students’ responses on a survey and teachercreated unit test were compared. Students’ solution strategies were associated with treatment. Students in the TINspire CAS group employed more graphical representations whereas those in the TI83+ group tended to use symbolic solution strategies. Furthermore the number of strategies used to solve the problem was related to success regardless of treatment group. Students in the two groups did not significantly differ on a unit test, problemsolving success, and number of strategies used to solve a word problem. This study provides preliminary evidence that TINspire CASenhanced instruction may influence students’ use of multiple representations when solving mathematical word problems.  TI83, TI84, TINspire CAS    2010  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.  TINspire    2010  This study examines a classroom connectivity technology (CCT) intervention on classroom interactions and draws connections between classroomlevel factors and achievement. Using discourse eventhistory analysis (Nystrand, Wu, Gamoran, Zeisler, & Long, 2003), classroom interactions of 33 Algebra I classrooms were examined to provide an update on the classroom interactions within this national sample of mathematics classrooms, to investigate differences in interactions between classrooms using CCT and those using graphing calculators only, and to explore the relationship between classroom interactional patterns and student achievement. These Algebra I classrooms are characterized by lowcognitive load questions presented in threeutterance, initiaterespondevaluate (IRE) turns that elicit brief student responses. This pattern was more prevalent in control classrooms, which provides evidence that the intervention disrupted this typical interactional pattern. Higherorder cognitive load questions, which elicit more developed responses, were associated with higher achievement.  TINspire, CCMS    2011  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.
 TINspire CAS, Germany    2008  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 TINspire 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).  TINspire, Math Nspired, Microworlds    2011  The M³ pilot project, initiated by the Bavarian State Ministry for Education and Culture, forms the context for this research study. The longterm 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 longterm handheld use in a realistic research field and what factors influence these effects?" This research question is divided into several subquestions and each has been investigated using quantitative and qualitative methods.  TINspire CAS, Germany    2011  This ZIP file contains 4 research presentations from Power Session at T^3 International, San Antonio, Feb. 27. 2011. Titles are: Introduction (Burrill) Why Multiple Respresentations  What Research Says (Duncan) What Are the Effects of Adding TINavigator to a Graphing Calculator Classroom? (Pape) CAS We Can!  But Should We? The Integration of Symbolic Calculators into Mathematics Lessons (Weigand)
 TCubed, T^3, International, CAS, TINavigator, TINspire, Multiple Representations    2011  During seven chemistry lessons students from grade 9 and 10 conducted three chemical experiments. They used the calculator TINspire 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.  TINspire, Case Studies, Case Study, Science, Chemistry, Germany, Sensors, High School    2010  The new generations of handheld calculators can be considered either as mathematical tools with opportunities for calculation and representation or as a part of the teachers’ and students’ sets of resources. Framed by the Theory of Didactical Situations and the documentational approach, we take advantage of a particular experiment on introducing complex calculators in scientific classes to investigate the position and the role of this handheld technology both for students and teachers. The results show how different functionalities can be shared among teachers and students, but also how other functionalities remain private and may even conflict with the teacher’s intentions.  TINspire    2010  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 technologyrich mathematics education. As a conclusion, extrapolation of these lessons to a future with mobile multifunctional handheld technology leads to the issues of connectivity and in and outofschool collaborative work as major issues for future research.  TINspire    2010  Quantifying Uncertainty and Analyzing Numerical Trends (QUANT) 1 is a yearlong professional development program for high school mathematics teachers that is designed to develop their statistical proficiency for teaching. The approach used to develop such proficiency is technological pedagogical content knowledge in the areas of measurement, data collection, data analysis, probability, and statistics, combined with a classroom implementation focus on selecting, setting up, and enacting cognitively demanding tasks. This paper describes the QUANT program, its aims, the role of technology in the program, and the results from a series of exploratory investigations to measure and evaluate the program’s effectiveness. These studies have involved a total of 23 practicing teachers, and they have been used to refine and shape this ongoing professional development effort.  TINspire CAS, Probability, Professional Development, High School    2011  Draft: Do not reference or quote without the expressed, written permission of the Authors. Thirtyfive teachers teaching advanced topics in high school mathematics were engaged in a yearlong 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 matchedcontrol 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.
 TI84+, TINspire, NetLogo, MKT, Mathematical content knowledge    2010  In the last years, several studies have investigated the role of technology in teaching and learning mathematics. However, the specific role of computer algebra systems (CAS) in early algebra in contrast to graphic calculators (GC) is still unclear. The CAYEN project is researching this field by comparing 13yearold pupils—one GC class and two CAS classes have been observed while acquiring elementary algebraic competences with nearly the same teaching sequence. The field of algebraic competences is split into syntactic abilities and symbol sense. The results of this explorative case study show that the development of symbol sense is influenced by the adoption of CAS in the learning process. Especially when transitioning from arithmetic to algebra, the pupils’ views of algebra as well as their conceptions of algebraic objects seem to be affected by the availability of CAS.  TINspire    2012  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’ TINspire 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.  TINspire, Algebra, Geometry, Use Cases    2010  TINspire technology, a new generation of graphing calculators, was integrated into high school integrated algebra curriculum. Four teacherparticipants were supported through a yearlong professional development emphasizing the use of technology through an inquiry based approach. The data included the teachers’ perceptions about TINspire technology, teachers’ proficiency with TINspire technology, quality of instruction determined through classroom observations, and the frequency of technology use in the classroom based on questionnaire completed by the students. Data analysis indicates that there is a significant positive correlation between quality of instructional practice, quality of use of technology, and teachers’ level of TPACK. In general, teachers with better perceptions used technology in the classroom more frequently, were more proficient with the technology, had higher quality of instructions, and higher level of TPACK. Implications on years of experience and preservice training are discussed  TINspire, Algebra, New York, TPACK    2009  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  TINspire, France, 10th Grade Math    2008  To make a preliminary investigation into the implementation of TINspire calculators with preservice middle and high school mathematics teachers. Through this focused case study an emerging model of technological pedagogical content knowledge as it relates to the use of the next generation calculator, the TINspire, was investigated.  Preservice, TINspire, middle school, high school, case study    2012  Abstract: Im Rahmen eines Unterrichtsprojekts in der zehnten Jahrgangsstufe konnten Schüler zunächst für drei Monate mit einem iPod Touch (mit MathematikApps) 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 TINspire 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.unidortmund.de/ieem/bzmu2012/  TINspire CAS, CAS, iPod Touch, secondary mathematics, Germany    2012  This case study reports on trials of TINspire 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.  TINspire, France, Lycee, Case Study    2011  Since fall 2007 Symbolic calculators (CAScalculators) 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 CAScalculators difficult to learn, for final year Science students in Upper Secondary school? A second question is: What does the students think about using CAScalculators? 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 CAScalculator easy to work with?, 2) Is the CAScalculator 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 CAScalculator, is the experience pleasing?. When collecting the material I used both observations of the 11 students, and questionnaires. The two CAScalculators that were used were the Casio Classpad 330 and the Texas Instruments TI’Nspire CAS. The main results are that the CAScalculator itself is easy to learn and that the students are satisfyed with their experience with the calculator when solving exercises in mathematics.  Casio ClassPad 330, TINspire CAS, Algebra, Multiple representations, Sweden, Gymnasium, upper secondary    2011  The Common Core State Standards in Mathematics adopted by most of the states in the United States offer a set of mathematical practice standards as part of the expectations for all students. The practice standards suggest mathematical "habits of mind" teachers should cultivate in their students about ways of thinking and doing mathematics. With the teacher as a facilitator and using the right questions, dynamic interactive technology can be an effective tool in providing opportunities for students to engage in tasks that make these practices central in reasoning and doing the mathematics.  Dynamic Geometry, Geometry, TINspire, TI84    2010  The main issue of the paper concerns the way new technologies (TINspire and TINavigator) 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, humanswithmedia, multimodality) are used to analyse some classroom activities, where students employ such new technologies. It is also shown how the multirepresentations 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.  TINspire    2008  A qualitative case study in France of six 10th second grade classes using TINspireTM handhelds with Computer Algebra System (CAS) found that: Teachers in the project developed an effective model for pedagogical resource in the TINspire environment, including a .TNS file in combination with a unitbased 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 TINspire. Regular inclass use of TINspire 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.
 TINspire, France, Secondary Mathematics    2011  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 postsecondary. 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 TINspire and TINavigator, align with the need to build the practice of science into the curriculum, through the combination of hardware, software and researchbased practices for learning and instruction.
 Science, TINspire, TINavigator, Physics, Chemistry, Biology    2008  The principal conclusion of the study is the crucial, perhaps, decisive effect that modeling of exemplary practice in the field placement has on candidate attitudes regarding the use of advanced digital technologies in their teaching.  TINspire,preservice teacher training    2010  The purpose of the study was to examine the effectiveness of using a handheld 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.  TINspire CAS, Middle Grades, PreService Teacher Education    2010  The purpose of the study was to examine the effectiveness of using a handheld 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.
 TINspire CAS, Preservice teachers, middle grades math    2012  Prior to the project, 93% of teachers indicated that they never used supplemental materials in algebra or geometry in the classrooms. Since purchasing the TINspire calculators for all students, daily classroom usage of the equipment increased to 77%. Sixty percent of teachers said their students use the calculators for inclass inquirybased 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.  MathForward, TINspire, TINavigator, STEM, DoDEA, Clover Park, Case Study, Science    2011  To assess the effectiveness of the use of GDCs though real world examples I designed a pre and post test to be given before and after a miniunit involving three real world labs. The pretest was administered after the normal discourse of the curricular unit on the applications of the derivative. However, shortly after administering the assessment, I had doubts regarding the validity of the scores. Because of the nature of the study and not wanting to penalize students unnecessarily, I did not factor the grade of this assessment into their nine weeks grade. Because of this, students did not prepare themselves as well as they would have had this test counted. Regardless, increases in scores from the pretest to the posttest should not be summarily dismissed as the increases in scores were not totally due to a lack of preparation and an increased time in studying the content. In fact, an examination of the test scores found in Table 1 shows the class average increasing 34.5 percentage points. Further, not one student decreased scores from the pretest to the posttest. 50% of the students surveyed responded that they understood little of the content assessed before the mini unit on GDCs. However, after the mini unit, 100% of those surveyed said they understood at least a good amount of the material with 38% stating they felt very comfortable with the content assessed.  TI89, TINspire CAS, AP, Advanced Placement, Calculus, Florida, Case Study    2009  Longitudinal analysis was conducted of a grade 910, and a grade 1213 Italian classroom in one school, using TINspire 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 TINspire. 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 TINspire 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. TINspire seems to modify the tempos of some multimodal behaviours of students; this makes TINspire 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.
 TINspire CAS, grade 910, grade 1112, learning processes, modeling, praxeologies,dynamic representations,    2007  Some mathematics tools can input symbolic expressions, but output only numbers or graphs. CAS technology, however, can also output symbolic mathematical expressions. Researchers recommend that teachers use CAS features to focus on concepts, personalize the curricular sequence to fit student needs, and emphasize meaningful mathematical tasks. Although we await evidence based on the strongest research designs, studies throughout the world consistently report benefits when teachers integrate CAS with a focus on learning math concepts.  Research note, Graphing Calculator, CAS, TINspire CAS, TI89    2008  Research on teachers’ use of TINspire 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 TINspire Navigator System will further enhance classroom collaboration and formative assessment.  Research note, TINspire, TINspire Navigator, TINavigator, Interactive Math Classroom, IMC    2008  TINspire™ technology extends current graphing calculator technology in ways that fit with research recommendations. Two important enhanced capabilities are (1) dynamicallylinked multiple representations and (2) save and review of student work.  TINspire, graphing calculator, dynmicallylinked, multiple representations    2009  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 backandforth 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 technologyrich 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 higherorder 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.
 TINspire Navigator, TINavigator, Nspired Learning    2007  L’obiettivo fondamentale dei Progetti Pilota raccolti in questo libretto è quello di fornire agli insegnanti che intendono utilizzare TINspireTMCAS delle attività già sperimentate in classe. Si tratta di attività che coprono sia diversi livelli delle scuole superiori (biennio e triennio) che diverse tipologie scolastiche (Liceo Scientifico, Istituto Tecnico). Le diverse sperimentazioni si possono idealmente dividere in due tipologie. • La prima riguarda un progetto di Ricerca Didattica vero e proprio che vede coinvolti i docenti Pierangela Accomazzo del Liceo Scientifico “A. Einstein” di Torino e Domingo Paola del Liceo Scientifico “A. Issel” di Finale Ligure ed è coordinato dal Prof. Ferdinando Arzarello dell’Università di Torino. • Il secondo gruppo di sperimentazioni comprende i Progetti Pilota attuati dai docenti Nicoletta Nolli del Liceo Scientifico “G. Aselli” di Cremona, Isabella Soletta del Liceo Scientifico “E. Fermi” di Alghero e Silvano Rossetto dell’Istituto Tecnico per il Turismo “G. Mazzotti” di Treviso. Ogni insegnante potrà poi adattare una (o più) di queste sperimentazioni alla propria realtà scolastica. Analoghe sperimentazioni sono state svolte in diversi paesi europei. Ogni sperimentazione si è conclusa con un questionario; i risultati dei questionari sono riportati in Appendice.  TINspire, TINspire CAS, CAS, Italy, Europe    2013  This case study documents the struggles and successes encountered by a precalculus 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.  TINspire, TINavigator, Community College, PreCalculus, Florida    2011  This report summarises the evaluation of a pilot development project, in which a curriculum material, intended for the courses Matematik A and B at the Swedish upper secondary school, has been constructed. The material is written for the use of the TINspire technology, with which it forms a dynamic system. Three teachers and three classes from different theoretical programmes replaced their textbooks with this material during the later half of the spring semester, and their experiences was investigated through lesson logs, interviews, questionnaires and lesson observations. This report describes the main findings of the study, along with the more important conclusions that could be drawn. Some suggestions for further research, such as a main study, are also given.  TINspire, Sweden, Secondary    2010  In 80% of the 66 lesson evaluations received, The teachers concluded that the use of multiple representation with TINspire 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.  TINspire, secondary maths, Scotland, Curriculum for Excellence, Qualitative    2010  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 TINspire PC software and students the TINspire 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  TINspire    2010  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 TINspire PC software and students the TINspire 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.  Mathematics, TINspire    2009  A design experiment was conducted to examine the role of the TINspire, the latest graphing calculator from Texas Instruments, in teaching and learning calculus. This paper reports details on, and preliminary results of, the design experiment involving the design and conduct of a TINspire Intervention Programme for an intact class of thirtysix secondary four students (1516 years) from a secondary school in Singapore. Use of the TINspire was integrated into teaching and learning Calculus concepts with the aid of the TI Navigator, a wireless classroom network system that enables instant and active interaction between students and teachers. Mathematics attitudes surveys and structured interviews were administered to assess the effects of the use of the TINspire on students’ attitudes towards mathematics. It was found that appropriate use of graphical, numerical and algebraic representations of Calculus concepts using the TINspire could enable the subjects to better visualize the concepts and make generalizations of relevant mathematical properties. Results of paired samples ttests and interviews with students suggest that there the use of the TINspire has a positive effect on students’ confidence in and perceived usefulness of mathematics.  Calculus, TINspire, TINavigator, Singapore,    2011  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 TINspire 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' problemsolving 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 TINspire 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 highquality 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 TINspire 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 lowperforming students, but also carries an incredibly powerful 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.  CAS, computer, digital, high school, laptop, national test, technology, TINspire, upper secondary, Case Study    2004  There are many arguments for and against the use of CAS. This book sets out to provide an argumentative case for the use of CAS. The first section outlines of the key issues surrounding the use of CAS and the related research, which supports these findings. The next section details the ideas of teachers from various countries who already use CAS in teaching, learning and assessment. It sets out their experiences in terms of lesson ideas, teaching sessions, and the adaptations which have to be made to question types and examination papers, to assess suitably. The final section of the book outlines the arguments for and against the use of CAS ("the Advocatus Diaboli"), providing what the authors believe is a convincing case for the use of CAS in the teaching and learning of Mathematics.  CAS, TI89, TINspire, Europe, Algebra    2010  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 TINspire handhelds and was compared to the control group taught with TI84 graphing calculators. The teachers of each groups received ongoing 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 TINspire 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.
 handheld technology, TINspire, TI84, Gender, Secondary Education, Algebra, Low Income, New York    2010  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/projectbased data analysis unit incorporating the document features of the TINspire would help students master data analysis concepts. The study used a quasiexperimental pre/Posttest design enhanced by a qualitative component. A fourweek problem/project based data analysis unit served as the curriculum for the intervention treatment. Students were assigned either the TI84 or the TINspire calculator. Twelve sections of ninth grade students were divided into four basic study groups: (Intervention (TI84), Traditional (TI84), Intervention (TINspire), and Traditional (TINspire)). The quantitative component of the study analyzed differences between students’ pre/post Total, Multiplechoice, Openended mean scores and quantified attitudinal responses. The analysis showed students in the TINspire groups improved more on the Total test and Multiplechoice questions while students in the TI84 group performed better on Openended questions. The Intervention Curriculum was more effective for Multiplechoice questions, Traditional Curriculum for Openended questions and Total scores. Student interviews revealed they didn’t like taking notes and answering questions on the TINspire. Some students liked referring to the information in the calculator while others felt that accessing information was too time consuming. The merits of the TINspire document feature needs further exploration. Analysis of the quantified attitudinal survey showed an increase in the positive attitudes of students using the TINspire. Both qualitative and quantitative evidence showed the Traditional TI84 group had fewer changes in attitude and content knowledge than everyone else combined, suggesting the need to change how we teach data analysis. Problem/projectbased 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 studentcentered learning that expects students to be calculator proficient and comfortable with basic quantitative procedures such as finding measures of central tendency and variation.
 TINspire, TI84, Algebra, New Jersey, HSPA, 9th Grade, Urban    2008  A qualitative study in one algebra geometry III classroom of students using TINspire CAS showed TINspire CAS had a positive effect on students’ understanding of solving equations, using parentheses, and understanding equivalent operations.  TINspire CAS, algebra, geometry, students understanding, equations,    2009  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 TINspire handhelds and was compared with another group taught with TI84 graphing calculators. The teachers of both groups received ongoing 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 TINspire 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.  handheld technology; gender differences; secondary education; quasiexperiment; algebra; student achievement; New York; TINspire; TI84    2011  The purpose of this study was to determine the effect of TINspire 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 TINspire graphing calculator versus teachers using a nongraphing 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 (ChoiKoh, 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 TINspire. The TINspire is designed to link together multiplerepresentations within a single problem, so the concept of functions is an ideal context within which to study the impact of the TINspire. This was a quasiexperimental study. The researcher gathered and analyzed pretest, posttest, and post posttest 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 TINspire graphing calculator. Teachers were then given a TINspire, TINspire emulator and access to online Atomic learning video training (Atomic Learning, 2011), to continue their exploration of the TINspire. 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 TINspire, specific training about teaching the function concept with the TINspire, 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 TINspire. 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 TINspire and one control class using a nongraphing scientific calculator, were significant on the pretest with the control group having a higher mean score than the treatment group and statistical significance on the post posttest 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 postpost 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 TINspire graphing calculators in Algebra classrooms while studying the concept of functions. This study shows that, while using the TINspire 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 TINspire graphing calculator for the concept of functions, further research is needed to continue evaluating the impact of the TINspire across additional mathematics topics.  TINspire, Algebra, 9th Grade, Kentucky    2009  While it seems clear that instruction on both procedures and concepts is important in mathematics education, the relative importance of each and the order teachers should use each to build instruction with handheld technology such as graphing calculators is still unsettled.  TINspire, handheld technology,graphing calculators,algebra,linear equations    2009  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 dualtechnology solution; • Both versions of TINspire technology inherently include a documentation aspect (organizing resources, exchanging, transforming, creating) that have impacts on the work of teachers and students; • TINspire technology is easy to access, though at the very beginning, teacher training is necessary; • The introduction of the TINspire 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,.
 TINspire, France, secondary mathematics 



