Abstract
This paper explores how four good teachers, who do not have a special interest in technology, meet the challenge of introducing the rapidly developing mathematics analysis software (e.g. spreadsheets, function graphers, symbolic algebra manipulation and dynamic geometry) into their classrooms. These teachers’ practice is viewed through the lens of Roger’s framework for the diffusion of innovation and Pierce and Stacey’s pedagogical opportunities map. Data on teachers, views and practices were collected over 2 years. ‘Pedagogical Maps’ give a picture of the teachers’ perception and uptake of pedagogical opportunities. New practices have been added slowly to each teacher’s repertoire and their increasing fluency in practical ability to teach with the technology resulted in some changes to the classroom didactic contract. Overall, new technology seemed to have been absorbed into current practice, more than changing practice. At this stage of their development, these teachers do not identify the distinctive new mathematical capabilities as contributing to the major relative advantage of the innovation. Instead, they see the relative advantage mostly in the incremental improvements to capabilities of earlier calculators, and meeting the need for students to be up to date. One of the current challenges is that significant changes in both software and hardware design have been happening so rapidly that these early majority teachers felt almost constantly hampered by the need to learn and teach new technical skills and so continue to make limited progress in taking advantage of opportunities to approach mathematics concepts in new ways.
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Acknowledgments
We wish to thank the teachers and students who participated in this study, Roger Wander, Lynda Ball, and guest observers of the research lessons, and we acknowledge the financial support of Texas Instruments Australia.
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Appendix: P-Map teacher survey
Appendix: P-Map teacher survey
P-Map teacher survey part A: Likert items
Teachers were asked to respond to the following items using the 5-point scale below
No opportunity | Didn’t choose to do this | Tried didn’t work well | Tried went OK | Tried went well |
P-Map link* | Item no. | Item |
|---|---|---|
Let students use technology to: | ||
F T PP | A1 | Check each step of their work |
F T | A2 | Do ‘hard’ or ‘long’ arithmetic calculations (e.g. divide by 0.A323) |
F T | A3 | Do ‘hard’ or ‘long’ algebra |
F T | A4 | Sketch ‘hard’ graphs |
F T | 5 | Draw/construct accurate geometric diagrams |
Set tasks which required students to: | ||
T RD | 6 | Conduct experiments and collect real data |
F T RD | 7 | Work with ‘messy’ real-world data provided by the teacher |
T RD | 8 | Think about a real-world context but using data that have been modified to make calculations ‘simpler’ |
T PP E | 9 | Do many similar algebraic examples to spot a pattern |
T PP E | 10 | Draw many graphs to identify the features of various families of curves |
T E | 11 | Change the coefficients in an algebraic example to see what happens. (e.g. try various values of c to see effect when solving y = ax2 + bx + c for x) |
T E | 12 | Draw many graphs to identify the effect of varying a coefficient or constant |
Set tasks which required students to: | ||
T S | 13 | Use simulated data I had provided (e.g. by using random number generator) |
T S | 14 | Collect data from a statistical simulation |
T S | 15 | Collect data from a geometric simulation of a real-world problem |
T LR | 16 | Use a graph to solve an equation |
T LR | 17 | Use tables/spreadsheets to solve an equation |
T LR | 18 | Used tables/spreadsheets and statistical graphs (charts or plots) to solve a problem |
As a teacher I: | ||
S MO | 19 | Used technology to give students an overview then went back to look at details |
S IM | 20 | Used non-standard output produced by technology to deepen students’ understanding |
S IM | 21 | Deliberately set tasks which I knew would produce non-standard or unexpected output |
C DC | 22 | Encouraged students to use technology to check answers instead of asking me |
C DC | 23 | Set problems that my students could not solve without using technology |
C SD | 24 | Made use of technology when I was introducing a new topic |
C SD | 25 | Used technology via a viewscreen/data projector to illustrate a mathematical concept |
C DC | 26 | Used technology via a viewscreen/data projector to demonstrate solution strategies |
C SD | 27 | Encouraged students to use technology via a viewscreen/data projector to show their solution strategies to the rest of the class |
P-Map teacher survey part B: open response items
P-Map link* | Item No. | Item |
|---|---|---|
F T S | 1 | What use is currently made of TI-Nspire(CAS) in your class? Please give details/examples |
DC | 2 | For your Year 10 class, has the availability of TI-Nspire(CAS) prompted any change in what you expect of students during a lesson? or out of class? Please give details/examples |
DC | 3 | For your Year 10 class, has the availability of TI-Nspire(CAS) prompted any change in what students expect of you during a lesson? or out of class? Please give details/examples |
SD | 4 | In classes where considerable use of TI-Nspire(CAS) takes place when compared to a class where no technology is used: Have you observed any change in the interactions between students or between the students and teacher? Please give details/examples |
SD | 5 | TI-Nspire(CAS), like other CAS calculators, can produce unexpected results such as unexpected format, unexpected error messages, unexpected setting out, etc. How do you deal with this in class? Please give details/examples |
RB | 6 | Has the availability of TI-Nspire(CAS) had any impact on the emphasis or sequencing of topics you teach in Year 10? Or on the details within the topic? Please give details/examples |
RB | 7 | Are there any other ways in which the availability of TI-Nspire(CAS) has made you think differently about how to teach a particular topic? Please give details/examples |
8 | Anything else you think we should know about teaching with TI-Nspire(CAS)… |
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Pierce, R., Stacey, K. Teaching with new technology: four ‘early majority’ teachers. J Math Teacher Educ 16, 323–347 (2013). https://doi.org/10.1007/s10857-012-9227-y
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DOI: https://doi.org/10.1007/s10857-012-9227-y