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In this section we have highlighted research evidence of new technology that supports multiple representations of mathematical concepts and a document model.
TI-Nspire was increasingly used to stimulate students to think mathematically and, in many cases, to engage and motivate strongly with mathematical structures and concepts in way that is normally not possible with traditional paper and pencil approaches.
In a qualitative study of how teachers incorporated TI-Nspire into Scotland’s Curriculum for Excellence, lessons observed by the researcher found that attention was focused on the use of dynamically linked multiple representations and the associated issues of classroom practice, teaching methodology and student engagement.
In 80% of the 66 lesson evaluations received, the teachers concluded that the use of multiple representation with TI-Nspire enhances students’ relational understanding of the mathematics involved and they were willing to provide extensive evidence to support their argument. Only 3% contained a negative response.
The main points which arose were: |
| • | emphasis on linking representations and the impact of change in one of these
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| • | use of investigative approaches
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| • | work being tackled significantly earlier than would normally be expected
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| • | high level of questioning and teacher-student and student-student discussion
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| • | high level of enthusiasm, enjoyment and interest displayed by students
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| • | variety of approaches to help students gain mastery of the handhelds such as ‘lock-step’ teaching, use of worksheet, use of animated PowerPoint slides
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| • | issues relating to management of the technology
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| • | new approaches to the teaching of statistics |
 Reference: (Duncan 2010)
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TI-Nspire was increasingly used to stimulate students to think mathematically and, in many cases, to engage and motivate strongly with mathematical structures and concepts in way that is normally not possible with traditional paper and pencil approaches.
In addition technology helped to:
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| • | Increase autonomy, particularly where the learners had developed sufficient confidence with TI-Nspire, to enable them to determine their own pathway through a task. |
| • | Increase opportunities for assessing mathematical understanding, promoted by the use of the technology. |
| • | Motivate learners by promoting their natural interest and intrigue in the mathematics itself. |
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| A year-long study introduced TI-Nspire with professional development to 14 KS 3-4 teachers in seven UK 11-16 secondary schools. The qualitative study reported many examples of how teachers used TI-Nspire with the goal of enhancing students’ mathematical understanding.
There was a strong evidence that TI-Nspire:
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| • | Supports the trajectory of the teachers towards selecting and/or designing more exploratory activities to use in classrooms. Teachers evaluated the use of TI-Nspire in these lessons lesson very positively with respect to their pupils learning outcomes. |
| • | Helps teachers increase opportunities for learners to engage in purposeful plenary activities in which the learners shared outcomes and approaches. |
| • | Provides immediate, non-judgemental feedback to learners |
| • | Increases opportunities for learners to follow their own lines of mathematical enquiry. |
| • | Learners accessing mathematical content that was above the teachers’ age-related expectations. |
| Reference: (Clark-Wilson, Alison, 2008)
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Pupils with access to the TI-Nspire handheld device learned with understanding and appeared to be better able to draw inferences that connected inert knowledge with observed and grounded phenomena. The effect was largest for low achievers.
In a small-scale controlled experiment with random assignment, researchers found:
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| • | all participants showed a positive gain in knowledge, both in procedural and, more importantly, in conceptually connected knowledge; |
| • | participants who had access to the TI-Nspire graphing calculator learned with understanding and appeared to be better able to draw inferences that connected inert knowledge with observed and grounded phenomena; and, |
| • | low-achieving participants who had access to TI-Nspire graphing calculators seemed to show the highest gains. |
| • | researchers also observed that students easily and quickly learned to use TI-Nspire in data modeling, and showed evidence of high engagement and collaborative learning. |
| Reference: (O’Mahony, Baer et al. 2008)
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In pre-service teacher professional development, use of TI-Nspire can stimulate pedagogical reflection and willingness to learn among new teachers. A case study introducing TI-Nspire to 35 pre-service maths teachers in two cohorts found that:
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| • | the new technology served as a tool or stimulator in fostering pedagogical reflection among the participants. |
| • | the new technology stimulated among the participants a willingness to learn on their own and with their learners. |
| • | participants’ beliefs and prior experience played an important role in their justification of their proposed ways of teaching and assessment. |
| • | participants experienced tension between traditional curricular materials (e.g., the textbook) and the need to recreate their lessons. |
| • | the new technology can at times lead to conflicts between participants’ traditional view of mathematics teaching and their awareness of innovative alternatives. |
| Reference: (Spector, Jakubowski et al. 2008)
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Appropriate use of TI-Nspire can facilitate:
- Use of shared resources for collaborative learning
- High learner engagement
- A novel, integrated format for instructional units
- Beliefs that the calculator is an aid to learning mathematics (not just an efficiency device)
A qualitative case study in France of six year 10 classes using TI-Nspire with Computer Algebra System (CAS) found that:
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| • | Teachers in the project developed an effective model for pedagogical resource in the TI-Nspire environment, including a .TNS file in combination with a unit-based pupil worksheet, a teacher sheet and a scenario for use, explaining the possible use of ICT. |
| • | The document structure served as a local temporary record of the activities being performed in class, thus supporting teaching, assessment and research |
| • | Collaboration was essential to develop learning progressions and learning activities, by adapting the shared resources. |
| • | Collaboration is supported by an online shared workspace for teachers. |
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| Using one such learning activity in geometry:
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| • | 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 |
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Student opinion surveys showed:
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| • | Over 96% of pupils had a computer at home and 75% used it daily. Amongst the small portion of pupils knowing dynamic geometry, most had experience with Cabri but they still cited as advantageous the extreme portability and dynamic applications of TI-Nspire. |
| • | Regular in-class use of TI-Nspire facilitated ease in mastering the tool and difficulties of use were rapidly overcome. |
| • | As the year progressed, the handheld device was seen more as a tool available in the class |
| • | As the year progressed, pupil emphasis was far more on the possibilities for symbolic calculation and new potentials for problem solving, rather than the features of the device. |
| Reference: (Aldon, Artigue et al. 2008) IREM, INRP and University of Lyon
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Teaching with TI-Nspire CAS may improve motivation to use algebraic representations, confidence, and diversity of tasks selected by students.
Preliminary qualitative analysis of lessons in beginning Algebra taught with TI-Nspire CAS concluded that: |
| • | Pupils who have CAS are more motivated to use algebraic representations, especially when working with applied problems;
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| • | Tasks which are related to the use of CAS differ from paper and pencil tasks, and the work becomes more diversified;
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| • | Motivation to develop syntactical skills is supported by the use of CAS;
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| • | Pupils of the CAS group more often had the confidence to build long expressions and equations related to applied problems;
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| • | Pupils by themselves often use their favorite representation mode if it is meaningful for a mathematical task. Thus it is important for pupils to be familiar with the many representation modes available in TI-Nspire CAS |
| Reference: (Zeller, Barzel et al. 2009)
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