Math and Technology Designing tasks that use DGS to support
students high-level thinking
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Technology Tasks How do we, as teachers, select or design tasks
that will use technology in support of high-level thinking?
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Sinclair (2003) Design Principles When a question aims to focus
student attention, the sketch must provide the visual stimulus. It
must draw attention through color, motion, and markings. When a
statement prompts action, such as asking students to drag, observe
or deduce, the sketch must contain the necessary provisions. It
must provide affordances so that the student can take the required
steps. Questions that invite exploration are open-ended. In order
to explore uncharted territory, the student requires a sketch that
allows options. Thus, when a question invites exploration, the
sketch must provide alternate paths. A question can surprise which
may lead to further exploration; how- ever, the teacher is not
necessarily there to correct any misinterpretation. Thus, the
sketch must support experimentation to unmask the confusion. It
must be flexible enough to help students examine cases, yet
constrained enough to prevent frustration.
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Amplifier/Reorganizer Amplifier: makes a task more accurate or
efficient, but could be accomplished without it Reorganizer: makes
use of affordances of technology to accomplish a goal that would be
practically impossible without it
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Draw Attention GoalQuestionAmplifierReorganizer Foster
connections across representations How does the sketch support
connections between representations? Visual stimulus (e.g., color,
motion, markings) used exclusively for aesthetic purposes. Visual
stimulus linked with mathematical concepts to develop mathematical
meaning, representations, and/or relationships.
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Draw Attention: Amplifier
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Draw Attention: Reorganizer
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Provide Affordances GoalQuestionAmplifierReorganizer Make
mathematically meaningful observations; look for invariant
relationships. Do the sketch and prompts use DGS in a way that
would be difficult to replicate without it? Students use dragging
to create multiple static examples, and reason from those static
examples. The sketch allows for continuous dragging, and students
are guided to examine measurements or relationships
dynamically.
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Provide Affordances: Amplifier
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Provide Affordances: Reorganizer
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Provide Alternative Paths GoalQuestionAmplifierReorganizer
Mathematical exploration; use appropriate tools strategically. How
open-ended is the task? Sketch and prompts guide students to
investigate the same examples to explore mathematical connections
or invariances. Students are prompted to explore based on
individual observations within the sketch. Prompts are open- ended
or the sketch provides alternate paths.
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Provide Alternative Paths: Amplifier
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Provide Alternative Paths: Reorganizer
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Support Experimentation GoalQuestionAmplifierReorganizer Foster
curiosity and modify thinking; make and test conjectures Does the
sketch provide feedback? Do the prompts encourage students to use
feedback? Sketch does not provide feedback to allow students to
explore their own conjectures; or prompts do not explicitly guide
students to test conjectures. Sketch provides feedback and prompts
encourage students to test and refine conjectures.
Slide 15
Support Experimentation: Amplifier
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Support Experimentation: Reorganizer
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Notes on this framework Goals are essential Foster connections
across representations Make mathematically meaningful observations;
look for invariant relationships. Mathematical exploration; use
appropriate tools strategically. Foster curiosity and modify
thinking; make and test conjectures Applies to tasks utilizing any
dynamic software (e.g., GSP, GeoGebra, Tinkerplots, Fathom, etc.)
Not meant to be only evaluative Can provide insight into how a
sketch or prompts can be revised to better support students
thinking