Geogebra in the derivate course Hannu Mäkiö

Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems in the early use: Teacher is active (producing materials etc.) Instructions to students were too strict, stepwise Early question: what is a good problem for students? Master’s degree Programme in Learning and Educational Technology ( )

Why this topic is interesting? Personal Interest in, math & computers Belief: students learn when they are active Belief: Different ways to represent the material is important General Change in national curriculum.changes in how people work? or geogebra is used in 2019 end examinations Digital barrier schools / society

Own beliefs in the begin of the study Geogebra is easy to use and learn So students can use it at home when doing their homework Students should use Geogebra as their own tool Students should make visualizations, not teacher Possibility to visualize mathematics motivates students They can make connections with different ways to represent mathematical concepts

Earlier studies How to use computers in mathematics education? From high hopes to understanding, change is not easy, but maybe possible needs long time changes in teachers/students roles

Benefits of computer use in math Different expressions provide different information Students can focus on ”bigger picture” More concrete examples To develop generalized rules To examine symbolic patterns (Heid & Edwards, 2001)

Master thesis, questions 1.How to use Geogebra in derivative course in upper secondary school? 2.Students and geogebra: how they learn to use it? how they feel about it?

Higher level math course 7 in upper secondary school About 15 students in a group/year CAS calculator was also used Year No computers in the classroom Year computers in the classroom Experiment lasted for whole course, 6*3, 75min More collaboration

ICE-notes Material in blog Idea: students use geogebra at home I wasn’t familiar with the students -> … Students use geogebra in school Inquiry based learning Extra material in onenote Geogebra also used in exams

Ways to use geogebra Ready made applications New concepts, easy to use, scaffolding CAS Students solve ordinary problems using Geogebra ( open problems, modelling & Geogebra )

Different working methods Learning new concept Learning a new way to use Geogebra Practising skills allready learnt Phases in inquire based learning 1.Launch 2.Explore 3.Discuss 4.Summarize

Geogebra is a dynamic geometry program

Measurements Students answer to google forms On screen video + talk, what am I doing Answers to paper & save geogebra file End questionary Lesson notes

Results: The use of computers means a lot of work for the teacher Teacher/ students roles change, needs time Most students were not ready to invest on learning how to use Geogebra Most of the students felt Geogebra was usefull in exams What is mathematics? How it should be studied? CAS-era meets 80’s material.

Results: Even symbols +, -, /, *, ^, := must be taught CAS brings a new way of doing math Work written in paper vs. Solution in a tool Year , students did learn to use Geogebra and were active in inquire based learning Only 2 students refered to graph, when solving problem in CAS Geogebra is a good tool for derivative course

(just another) Hype-cycle