Using GeoGebra To Teach Maths in Ireland David Hobson   davidhobson@loretothegreen.ie

Some Background State Exams are held at the end of third year and sixth year   Fourth year is optional Exams are "High stakes" Maths is offered at three levels Syllabus heavy emphasis on algebra and euclidian geometry Exams test "Reproduction", a small amount of "Connections" and no "Reflection" http://www.erc.ie/documents/pisa_maths_teachers_guide.pdf   PISA (Programme for International Student Assessment OECD) PISA identifies eight types of cognitive processes involved in mathematisation – reasoning; argumentation; communication; modelling; problem-posing and -solving; representation; using symbolic, formal and technical language and operations; and use of aids and tools. A mathematical task may involve one or more of these processes at various levels of complexity. In PISA, these processes are represented at different levels of complexity in three broad competency clusters: Reproduction, Connections, and Reflection.

Project Maths New syllabus to be phased in from 2010 Emphasis on    Emphasis on "Realistic Mathematics" Problem Solving Statistics and probability Changing teaching methodologies The national curriculum body commissioned research "International Trends in Post-Primary Mathematics Education: Perspectives on Learning, Teaching and Assessment" Paul F. Conway and Finbarr C. Sloane  http://www.ncca.ie/uploadedfiles/Publications/MathsResearch.pdf   The work of Hans Freudenthal on Realistic Mathematics Education is frequently referred to in this book . The new syllabus is being piloted in 20 schools - information is available at http://www.projectmaths.ie/  Reference to GeoGebra is here - near the end of the page!  In teaching Geometry reference is made to the Van Hiele Model http://www.projectmaths.ie/junior_cycle_strands/geometry_trigonometry#van_hiele

Subtracting negative numbers Some examples Subtracting negative numbers  

Examples from website http://www.loretothegreen.scoilnet.ie/GreenMaths/index.html   Applets are used in class and students are encouraged to try them at home Reaction from students has been positive

Using Applets in teaching and learning - an example from Physics In assessing the usefulness of different applets to teach the same topic the authors found that the details of each applet had little or no effect on learning outcomes.   However "minimal instructor scaffolding substantially influenced student use and value perceptions of the simulation" Converging lens simulation design and image predictions J A Bryan and S W Slough PhysicsEducation Vol 44 No. 3 May 2009 Converging lens simulation design and image predictions J A Bryan and S W Slough PhysicsEducation Vol 44 No. 3 May 2009   Abstract. While computer technology continues to enhance the teaching and learning of all science disciplines, computer simulations, in particular, have become exceptionally beneficial in physics education. In addition to the manner in which physics instructors integrate computer simulations into their instructional practices, the design of a simulation may also determine its potential for influencing a student's conceptual development and understanding. This paper examines the effects of four differently designed simulations on students' predictions and subsequent understanding of how images are formed by converging lenses, specifically in relation to outcomes when portions of the lens or object are covered. Results indicated that differing numbers of rays depicted in the lens simulations had little effect on student predictions, but the origination point(s) of the rays did influence student predictions. Also reported is how minimal instructor scaffolding substantially influenced student use and value perceptions of the simulation.

 Links to some references can be found in the speaker notes. Thank you