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

(2011-2015)

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 in2019 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 timechanges 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, questions1. 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 2012-2013• No computers in the classroom

• Year 2013-2014• 5 computers in the classroom• Experiment lasted for whole course, 6*3, 75min• More collaboration

2012-2013

• ICE-notes• Material in blog• Idea: students use

geogebra at home• I wasn’t familiar with

the students -> …

2013-2014

• 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 learning1. Launch2. Explore3. Discuss4. Summarize

Geogebra is a dynamic geometry program

Geogebra is a dynamic geometry program

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 2013-14, 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

http://en.wikipedia.org/wiki/File:Hype-Cycle-General.png