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![Page 1: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/1.jpg)
Geogebra in the derivate course
Hannu Mäkiö
![Page 2: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/2.jpg)
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)
![Page 3: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/3.jpg)
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
![Page 4: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/4.jpg)
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
![Page 5: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/5.jpg)
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
![Page 6: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/6.jpg)
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)
![Page 7: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/7.jpg)
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?
![Page 8: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/8.jpg)
• 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
![Page 9: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/9.jpg)
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
![Page 10: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/10.jpg)
Ways to use geogebra• Ready made applications• New concepts, easy to use, scaffolding
• CAS• Students solve ordinary problems using
Geogebra• ( open problems, modelling & Geogebra )
![Page 11: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/11.jpg)
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
![Page 15: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/15.jpg)
Measurements• Students answer to google forms • On screen video + talk, what am I doing• Answers to paper & save geogebra file• End questionary• Lesson notes
![Page 16: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/16.jpg)
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.
![Page 17: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/17.jpg)
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
![Page 18: Geogebra in the derivate course Hannu Mäkiö. Background Math teacher, lincenciate degree in applied mathematics I have used Geogebra about 10 years Problems.](https://reader036.fdocuments.in/reader036/viewer/2022081506/5697bfd71a28abf838cae8aa/html5/thumbnails/18.jpg)
(just another) Hype-cycle
http://en.wikipedia.org/wiki/File:Hype-Cycle-General.png