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Technology and the Yin & Yang of Teaching and Learning Mathematics. B Kutzler, Austria. Humans are ruled by two opposite forces: hold on let go. Humans are ruled by two opposite forces: hold on (yin) let go (yang). In our context these show as hold on = connect let go = automate.
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Technology and the Yin & Yang ofTeaching and Learning Mathematics B Kutzler, Austria
Humans are ruled by two opposite forces: hold on let go
Humans are ruled by two opposite forces: hold on (yin) let go (yang)
In our context these show as hold on = connect let go = automate
Automate Automate = compensate + amplify = compensate + (solve + explore)
automate compensate explore solve
Connect Connect= = represent + document + communicate
Connect Connect = model = represent + document + communicate model
Connect Connect = model model = represent + document + communicate model human
Connect Connect = model model human = represent + document + communicate model human human
connect document communicate represent
connect automate document communicate compensate represent explore solve
connect automate document communicate compensate represent explore solve
Math-Pedagogy-Technology Space technology mathematics pedagogy
Math-Pedagogy-Technology Space technology mathematics
With a helicopter one can reach places that one cannot reach otherwise.
With a helicopter one can reach places that one cannot reach otherwise.B Waits: Tech makes some math possible
With a helicopter one can reach places that one cannot reach otherwise.B Waits: Tech makes some math possible Tech makes some math pedagogy possible
Not the tool, but the use of the tool is or is not pedagogical. (Vlasta Kokol-Voljc)
Teacher training: Step 1: technology axis Step 2: math/technology plane Step 3: math/pedagogy/technology space Introducing teachers to technology needs as much (pedagogical) care as any other teaching
(1) Represent Mathematical problem solving = the art of transforming representations (until the solution is visible)
(1) Represent Mathematical problem solving = the art of transforming representations (until the solution is visible)such as transforming 5x-6=2x+15into x=7
(1) Represent Algebraic/graphic/numeric 1+2 3 3a+4a 7a 24 2 6 24 4.89898
(1) Represent Use technology to simulate a mathematician‘s mind New pedagogy (helps more students to understand)
(2) Document = share your work with an anonymous person argue (= convince sb with certain level of knowledge) designdescribe
(2) Document Describe/understand Newspaper articles Mathematical logic27 is divisible by 3 x(3x=27) every number is greater than its predecessor x(x>x-1) Use wordproblems to practice understanding
(2) Document Argue - Examples such asExplain why one uses the first derivative to find the extreme values of a function If a curve is symmetric in both the x- and y-axes, is it then symmetric through the origin? Give a reason or find a counter-example.
(2) Document With technology: Result loses importance Choosing keys/commands is mathematical work New pedagogy (shift focus fromexecuting algorithms to documenting mathematical work)
(3) Communicate = impart or transmit idea, knowledge, information Documentation = „offline“ communication „Online“ communication
(3) Communicate Student teacher: - front teaching - teacher as advisor and assistant Student student: - alone (cf traditional exam) - teamwork New pedagogy (enables new teaching/learning styles)
