Assessing symbol sense in a digital tool

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Assessing symbol sense in a digital tool

• CADGME, Hagenberg
• July 2009
• Christian Bokhove
• FISME, St. Michaël College

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Context

• Christian Bokhove
• 11 yr Teacher maths/ict secondary school
• St. Michaël College, Zaandam, the Netherlands,
  tradition math/ict projects
• Phd research. (www.dudocprogramma.nl) aimed at
  math curriculum.
• Freudenthal Institute of Science and Mathematics
  Education, Utrecht University, the Netherlands
• Supervisors Paul Drijvers and Jan van Maanen
• Educational research

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Problem statement

• Transition secondary ? higher education
• Lack of Algebraic expertise
• Entry exams
• Use of ICT
• Use to learn vs. Learn to use
• Position statement NCTM (2008) ICT can be a
  valuable asset

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In what way can the use of ICT support acquiring,
practicing and assessing relevant mathematical
skills
Assessment- Formative (for) v Summative (of)-
Feedback (Black Wiliam, 1998)
ICT tool use- Instrumentation- Task,
technology, theory (Lagrange, 1999)
Algebraic expertise- Basic skills- Symbol Sense
(Arcavi, 1994)
Christian Bokhove
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Criteria for tools

• Evaluation instrument
• Externally validated
• First formulate want we want, then see what there
  is
• A selection
• Assesses both basic skills and symbol sense
• Provides an open environment and feedback to
  facilitate formative assessment
• Stores both answers and the solution process of
  the student
• Steps
• Freedom to choose own strategy
• Authoring tool for own questions
• Intuitive interface (use to learn vs. learn to
  use)
• Close to paper-and-pencil notation

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Digital prototype

• www.fi.uu.nl/dwo/voho (enter as guest, at the
  moment in dutch)Digital Mathematics Environment
  (DME)
• www.fi.uu.nl/dwo/en for English version
• 30 items basic skills symbol sense
• Designer Peter Boon, always in close
  collaboration with teachers field.
• Store results inenvironment
• SCORM, so everymodule can be usedin VLEs
  includingMoodle

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Case studies / 1-to-1s
6 multihour think-aloud1-to-1 sessions with
17/18 year oldsI want to know whats going on
in their minds
Qual. analysis (video, camtasia, atlas TI)
Symbol Sense
Quality of tool(no focus)
Feedback
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Symbol Sense

• Four example exercises
• 1. Equations with common factorsSolve
• 2. Wenger, 1987 Rewrite as v

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Four examples (continued)

• 3. Does the student recognize the quadratic
  terms?
• 4. Recognize common factors when rewriting

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First example students work
More examples
Video clips
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Feedback

• Feedback is part of formative assessment. Types
  of Feedback (Hattie Timperley, Uni. Waterloo)
• Corrective
• Procedural
• Syntactical
• Meer..
• From the 1-to-1s we distilled modifications for
  our protoype (Matrix items vs. Feedback)
• Content
• Tool itself
• Feedback to be added
• Logging feature (for research)
• Second cycle with large group

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DEMO module

• http//www.fi.uu.nl/dwo/en/
• Random vars. I forget one solution, and get the
  above
• Custom feedback.
• Just divide by quadratic term.
• Work towards form x3
• Added random variablesbut fixed
• Random variables
• Note this adds complications.The author has to
  think about the implications.
• Feedback rules
• Featuresapplets
• This feedback can be authored

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Improving the tool

• Latest developments
• Mathematica connection. Enables(Note secondary
  school algebra in the Netherlands only needs a
  small amount of traditional CAS)
• Notation d/dx (Chain Rule)
• Limits (left, right, infinite)
• Substitutions (e.g. Chain Rule)
• Integrals (also C)
• More sophistication in feedback
• Feedback rules (webservice connection with
  research Jeuring, Open University)
• Integration of tools like Geogebra, graphing
  tool, rotating cubes
• (All benefits of a close collaboration with the
  designer)

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New developments integrals
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New developments rule feedback
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New developments GeoGebra integration
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Closing statement

• Educational researchCAS serves education and
  not the other way round
• More info
• http//www.fi.uu.nl/christianb
• http//www.fi.uu.nl/dwo/en

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Second example students work
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Third example students work
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Fourth example students work
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Student work clips

• First exampleMartin tries to solve the first
  exerciseMovie clip
• Second example
• Barbara tries the Wenger exercise.Movie clip