Developing Interactive Geometry Applets for Use in Research: Some Methodological Issues

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Developing Interactive Geometry Applets for Use
in Research Some Methodological Issues

• Margaret Sinclair,
• York University
• Toronto, Ontario, Canada

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Design research

• Task design - central yet usually part of
  development rather than the focus of research.
• Research on task design needed
• to clarify what is arbitrary and what is
  essential about tasks
• to allow replication of task-based research
  results, and to inform the development of systems
  of tasks.
• (Sierpinska, 2004)

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Research methods

• Observations, interviews, surveys, tests
• For Design research
• Iterative process of design, test and refine in
  light of
• pedagogical design principles
• Content and process
• interface design principles
• user feedback.

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Design and the user

• For any design to be successful, in terms of
  developing usable and understandable products,
  then that design must be based on the needs and
  interests of the users and be informed by an
  understanding of their limitations and
  capabilities.
• Norman, D. (1998). The psychology of everyday
  things. New York, NY Basic Books

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Research methodology

• Includes consideration of
• the researchers beliefs, attitudes and values,
• the research questions being explored,
• the answers being sought,
• and crucially,
• the nature of the key informants together with
  their social and cultural environments.
• (Goodchild, S., English, L. (Eds.). (2002).
  Researching mathematics classrooms A critical
  examination of methodology. Westport, CT
  Greenwood Publishing p. xii)

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The study

• 2 classes of grade 7 students
• Students worked in pairs in a lab
• Math content transformations
• Task materials JavaSketches and worksheets
• Task reviewers the 2 teachers and 3 math
  education students.

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The two reflection tasks

• Reflection concepts
• Wheres the mirror?

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Reviewer feedback

• Comments mostly favourable
• Numerous small errors reported
• Specific problems size of screen, use of
  prime notation, use of conjecture
• After modifications and corrections reviewers
  confident students would not have problems with
  content/terminology/use of applets.

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Observations

• Students were enthusiastic participants, actively
  involved in working with the sketches, discussing
  what they noticed and writing responses to
  questions
• but .

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Findings design problems

• Some students -
• didnt notice buttons, segments, or angles, or
  missed particular questions and prompts
• in, Reflection Concepts, had difficulty figuring
  out which segment or angle was being controlled
• didnt interpret questions as expected problem
  vague wording.

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Other findings

• Students tentative needed encouragement and
  help
• Difficulty with
• Math terms - parallel, perpendicular
• Terms with double meanings coincide, always
• Naming angles and segments
• Line of symmetry vs mirror no transfer of
  properties
• Poor explanations.

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Examining the difficulties

• Some could only be discovered by having students
  engage with the tasks
• technical glitches
• the extent of students tentative behaviour
• difficulty with always.
• Many could have been predicted
• line of symmetry rather than mirror
• difficulty with naming objects
• insufficient prior content knowledge
• lack of experience giving written explanations
  and/or doing investigations.

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What did we know about the students?

• Had covered background topics in previous grades
• Average to above average ability
• Used computers frequently but not for math.
• According to reviewers Students should have no
  trouble with content/terms/use of applets.

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What did we know about the reviewers?

• Relative newcomers to technology in mathematics
• Teachers
• not math specialists, but did teach math
• had taught these students since Sept. (Study was
  in March)
• Other reviewers math specialists at end of
  teacher training for grades 6-10.

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Questions

• Did the tasks appear deceptively straightforward?
  
• Did reviewers lack sufficient background/experienc
  e to critically examine the tasks?

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Questions

• Were reviewers reluctant to critique finished
  objects?
• Is there added difficulty in predicting student
  behaviour in a technological environment?

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Methodology revisited

• In design research we need to gather information
  about the tasks in relation to the users.
• During the testing the students are key
  informants.
• Before the testing the reviewers are key
  informants.

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Conclusion

• A designer requires first-hand knowledge of
  reviewers and testers attitudes, approaches to
  mathematics, prior content knowledge, and level
  of technological skill, in order to make informed
  decisions.