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Assessment when using GeoGebra
Transcript of Assessment when using GeoGebra
no computers for mathematics The Euler method for solving a differential equation
using a calculator http://en.wikipedia.org/wiki/Euler_method Compulsory in Mathematics E IB schools
in Europe ET - Educational Technology statistical significance? Sweden number of students that use computers on a regular basis to: % finding information on the web writing essays/reports/papers doing mathematics 94 89 7 in upper secondary scools
2010 http://www.skolverket.se/publikationer?id=2373 from 5:th grade My "Evangelistic" Period difficult
situation show that technology is beneficial for education get resources to use technology GeoGebra -> workshops for
teachers swap classrooms
to gain access to
computers Swedish students Is this in the syllabus? Will this knowledge be useful on the standardized test? Two (three) syllabi Sweden 100% of the grade based on standardized test not in theory but in reality International Baccalaureate 80% of the grade based on final exam 20% of the grade based on "portfolio" tasks enough for
the students! "Our own syllabus" jointly with the Department of Mathematics, Lund University Anna-Maria Persson Mathematics profile Algebra & Geometry Problemsolving Linear Algebra we wrote the syllabus criteria for setting the grades
same as for all Swedish courses Euclidean Geometry using GeoGebra main objective:
formal mathematical proof project funded by a Wallenberg foundation stating the obvious You must assess what you teach! Euclidean Geometry "secondary" objective the students should discover everything by themselves make tools (congruence) cases http://www.malinc.se/math/geometry/toolsen.php Assessment Matrices IB Criteria the students
had no textbook A: use of notation and terminology
C: mathematical investigation: searching for patterns C: mathematical modelling: developing a model
D: mathematical investigation: generalization D: mathematical modelling: interpretation
E: use of technology
F: quality of work mathematical content presentation "Mathematical content" on standardized tests Sweden attempt...show it for a special case find a general pattern/statement/conjecture prove the general statement Euclidean Geometry using GeoGebra minimum requirement: produce a general statement full and resourceful use of a computer Setting grade Giving feedback formative assessment In an experimental environment students should collaborate
assess each other
use external sources IB external examination moderation of the portfolio teacher & judge Sweden possibly stupid questions this will have an impact on your grade this will not have an impact on your grade questions are still allowed Geometry & Calculus making the construction
helps proving the general statement Avoid unnecessary restrictions use trigonometry to... use a spreadsheet to... Instead use hints
they are needed "good" or "bad" mathematics criticism empirical approach to geometry
mathematics is reduced to spotting patterns
no real understanding Conrad Wolfram: Teaching kids real math using computers false assumptions about pupils all pupils: want to learn
want to understand
want a high grade not true in upper secondary school is it enough to "spark an interest" Presentation Is a "scientific article" the ultimate goal? Conclusion there is no recipe write your own tasks/matrices discuss with colleagues computers on regular tests get rid of the calculators!!! Open questions how do we assess collaboration can we skip formal proofs for some students Algebra 20 minutes -> 3 lessons General triangles? dynamic
task Computers on national tests First solution: Monitor the traffic airodump-ng using Linux Second solution: Run Ubuntu from a usb-stick Hope teachers in mandatory school
will lead us into the future how do we handle the increased level of "standardization" email@example.com