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Contextualisation, collaboration, constructivism andsmartphones for teaching mathematics

Brendan Tangney, Patricia O’Hanlon, Stefan Weber, Elizabeth OldhamCentre for Research in IT in Education, School of Education and School of Computer Science & Statistics, Trinity CollegeDublin, Ireland

David Knowles, Jennifer Munnelly, Ronan WatsonNational Digital Research Centre, Crane St, The Digital Hub, Dublin 8, Ireland

/www.slideshare.net/tangneytangney@tcd.ie

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Issues in Math Education

An over emphasis on didacticteaching

A behaviourist approach to learning Overemphasis on procedure Emphasis on content over literacy Decontextualisation Focus on assessment Teaching by non specialist teachers

(Conway & Sloane, 2005; Lyons, Lynch, Close, Sheerin, & Boland, 2003; Papert, 1993; Blumenfield,Marx, Patrick, Krajcik, & Soloway, 1997)

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How Many People On Grafton St?

Contextualised

Constructivist

Collaborative (Patten et al, 2006)

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Irish Context

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Traditional Math Tools

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Mobimath Toolkit

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Research Agenda To develop and validate the

efficacy of an integratedsmartphone based toolkit forthe teaching of mathematicswhich follows a contextualised,constructivist, collaborative,philosophy.

Align the learning activities andsupporting instructionalmaterial with the formalcurriculum 1st Year of the Irish

Secondary School system (~12-13 years old).

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Modes of Use

1/2?

1/4?

1/8? 1/4!

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Probability Tools

Teacher Console - Sample screenshot of class collaboration

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Geometry Tools

Measure distance – outside (GPS)Measure distance – inside

(accelerometer)Measure angle of elevation

(accelerometer)Measure angle of rotation

(accelerometer) Visual mapping tool (camera)

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Technical Architecture

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User View

Common Functionality (voting, note taking etc) +Teacher console

Geometry Number &Operation

Algebra

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In School Trial

20 students, 5 activities, 2 hours per activity

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Geometry Activities

Measure the area of large irregular shapes on playingfield

Height of structures The music festival camping problem – how many tents

can be pitched on the sports field How many hockey balls could fit into the (irregularly

enclosed) hockey field. Investigate the Golden Mean in buildings and people’s

faces.

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Sample Learning Activity

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Data Collection Instruments Usability

SUS (Brooke 1996) MPUQ (Ryu 2006)

Attitude – Mathematical and Technology Attitude Scale (Pierce2007)

Teacher observation Whole class discussions Student workbooks Interviews with students (Delayed tests for content retention)

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Sample Comments “You are involved in the question, you are actually doing something, you are more

engaged” “If you were working from the textbook, you get into a rhythm of doing the same sums

every time, but out there you have to think about it more.” ‘It’s weird the question was a trig problem. Like one minute I was using sin, cos, tan and

the next minute I was working out the average distance reading on my calculator-that’s nottrig. It was good to see how different types of maths links together!’

“This is the way to do maths I felt I could calculate the height of anything”

“We weren’t working from a book with pretend numbers; we were outside actually findingthe numbers to solve the problem-it was more realistic this way”.

“When you are doing it you can see it more clearly what it’s for rather than just workingwith triangles in the textbook.”

“3 (problems tackled) outside (the classroom) was better than 10 in the book, because(with the book) you just repeat what you did rather than think about what you are doing.”

“The hardest part was working out the way you had to do it....”

”It was funner but it wasn’t necessarily easier!”

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Emerging Themes

Exercising mathematical problem solving skills; ‘Real world’ mathematics awareness; Improved attitudes to mathematics; Smartphone affordances; Benefit of collaborative learning.

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Two Issues

The degree to which theteacher (is allowed to)embrace the pedagogicalapproach.

Device ownership.

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Selected Bibliography Brooke, J. (1996). "SUS: a "quick and dirty" usability scale". In P. W. Jordan, B. Thomas, B. A. Weerdmeester, & A. L. McClelland. Usability Evaluation in Industry.

London: Taylor and Francis. http://www.usabilitynet.org/trump/documents/Suschapt.doc. Cobb, P., Yackel, E., & Wood, T. (1992). Constructivist Alternative To The Representational View Of Mind In Mathematics Education. Research in Mathematics

Education, 23(1), 2-33. Conway, P. F., & Sloane, F. C. (2005). International Trends in Post-Primary Mathematics Education. Retrieved. from

http://www.ncca.ie/uploadedfiles/mathsreview/intpaperoct.pdf Cuoco, A. (2001). Mathematics for Teaching. Notices of the American Mathematical Society, 48(2), 168-174. Daher, W. (2009). Students’ Perceptions of Learning Mathematics with Cellular Phones and Applets International Journal of Emerging Technologies in Learning,

4(1). Ferrini-Mundy, J., & Schmidt, W. H. (2003). International Comparative Studies in Mathematics Education: Opportunities for Collaboration and Challenges for

Researchers. Journal for Research in Mathematics Education, 36(3), 164-174. Goos, M. (2004). Learning Mathematics in a Classroom Community of Inquiry. Journal for Research in Mathematics Education, 35, 258-291. Lyons, M., Lynch, K., Close, S., Sheerin, E., & Boland, P. (2003). Inside classrooms : the teaching and learning of mathematics in social context. Dublin: Institute of

Public Administration. Donald Norman, (1998) The Psychology of Everyday Things. Monaghan, J., & Sheryn, L. (2006). How do Secondary Teachers make Mathematics More Applicable. Journal of Mathematics in School(September 2006). Patten, B., Arnedillo Sánchez, I., N., Tangney, B. Designing collaborative, constructionist and contextual applications for handheld devices. Computers & Education,

Volume 46, Issue 3, pages 294-308, April 2006. Pierce Robyn, Stacey Kaye, and Barkatsas Anastasios, A scale for monitoring students' attitudes to learning mathematics with technology. Computers & Education,

2007, 48(2): p. 285-300. Papert, S. (1993). Mindstorms Children ,Computers and Powerful Ideas (2nd ed.). New York: Basic Books. Ryu, Y. S., and Smith-Jackon, T. L. 2006. Reliability and Validity of the Mobile Phone Usability Questionnaire (MPUQ). Journal of Usability Studies, 2, 1, 39--53. Tangney B., et al., MobiMaths: An approach to utilising smartphones in teaching mathematics, in Mlearn2010 - 9th world conference on mobile and contextual

learning. 2010: Malta. p. 9-15. Voogt, J., & Pelgrum, H. (2005). ICT and curriculum change. Human Technology; an Interdisciplinary Journal on Humans in ICT Environments, 1(2), 157–175. Wijers, M., Jonker, V., Kerstens, K. (2008), MobileMath: the Phone, the Game and the Math 2nd European Conference on Game Based Learning, pp

507-516.