Registration
Please register for the event via this link: https://uni-koeln.zoom.us/meeting/register/tJ0tdeCsqT8rGNTjNJdJoE3h8OI_ARin8Fpj
This informal Symposium is organized as an online meeting via Zoom. For more information about zoom take a look at:
If you have any problems to register, please write an email to: lukas.baumanns (at) uni-koeln.de
This informal Symposium is organized as an online meeting via Zoom. For more information about zoom take a look at:
- https://rrzk.uni-koeln.de/en/support-information/information-on-collaboration-tools-for-working
- https://rrzk.uni-koeln.de/en/support-information/information-on-collaboration-tools-for-working/zoom-faq
If you have any problems to register, please write an email to: lukas.baumanns (at) uni-koeln.de
Speaker:
- Konrad Engel (Rostock)
- Torsten Fritzlar (Halle)
- Klaus Henning (Hamburg)
- Boris Koichu (Weizmann Institute of Science)
- Igor' Kontorovich (Auckland)
- Uwe Leck (Flensburg)
- Roza Leikin (Haifa)
- Terese Marianne Olga Nielsen (Science Talenter)
- Marianne Nolte (Hamburg)
Shedule
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Friday, January 22.
15:40 – 16:00 16:00 – 18:00 18:00 – 18:30 18:30 – 19:10 19:20 – 20:00 20:00 – 21:00 Saturday, January 23. 16:00 – 18:00 18:00 – 18:30 18:30 – 19:10 19:20 – 20:00 20:00 – 21:00 |
All Times UTC+1 (Berlin-time zone)
Opening: Incl. greetings by the President of the MCG: Marianne Nolte Panel on the Mathematics Olympiad: Konrad Engel (Rostock), Klaus Henning (Hamburg), Uwe Leck (Flensburg), Break Boris Koichu (Weizmann Institute of Science): Problem posing in the context of teaching for advanced problem solving Terese Marianne Olga Nielsen (Science Talenter) School mathematics vs competition mathematics. A comparison of problems with comments from the kids Dinner + Open Discussion Panel: How to work with students in times of corona – Impression of some experiences at primary grade and lower secondary level Torsten Fritzlar (Halle) & Marianne Nolte (Hamburg) Break Roza Leikin (Haifa) Differences and similarities between Open-start and Open-end mathematical tasks. Igor' Kontorovich (Auckland) Where mathematics competition problems come from? Dinner + Discussion of future activities |
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Videos / Slides
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Torsten Fritzlar (Halle) & Marianne Nolte (Hamburg)
How to work with students in times of corona – Impression of some experiences at primary grade and lower secondary level |
Part of the panel on the Mathematics Olympiad | ||||||
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Boris Koichu (Weizmann Institute of Science):
Problem posing in the context of teaching for advanced problem solving |
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Terese Marianne Olga Nielsen (Science Talenter)
School mathematics vs competition mathematics. A comparison of problems with comments from the kids | ||
Abstracts:
Problem posing for the Mathematical Olympiads - a well established team work
By Konrad Engel (Rostock)
Abstract: Each year the problem committee of the German Mathematical Olympiad produces about 150 problems for school students from grades 3
to 13. We present the organisation of this work which is based on a close cooperation of all members in a friendly atmosphere.
We discuss some general principals and reflect our experiences, e.g. concerning the covering of different levels of difficulty and a balanced mix of areas like elementary number theory, graph theory, combinatorics, algebra and elementary geometry.
How to work with students in times of corona
Torsten Fritzlar (Halle) & Marianne Nolte (Hamburg)
– Impression of some experiences at primary grade and lower secondary level
Where mathematics competition problems come from?
By Igor' Kontorovich (Auckland)
Instigated by Kilpatrick’s (1987) “Where do good problems come from?”, I will report on a study that tapped into problem posing of experienced problem posers for mathematics competitions.
The study was conducted with 26 problem posers residing in nine countries, and who had experience in creating problems for national, regional, and international competitions.
The central finding pertains to the construct of a trigger as a key driver of a process, one of the outcomes of which is a freshly posed problem. The educational implications of this study will be discussed.
Problems for the 5th and 6th grade - dealing with the transition from heuristic work to proof
By Klaus Henning (Hamburg)
Abstract: Posing problems for this age group faces particular difficulties; the kids lack any experience in mathematical reasoning and also in many fields of potential problems. Therefore, problems for this age group should aim at three goals: the use of heuristic strategies, the introduction of a more formal reasoning - and the possibility to expand the range of the particular problem into a wider mathematical context.
This will be shown be means of a couple of examples.
The German Mathematical Olympiads and the International Team Competition "Baltic Way" - a Brief Survey
By Uwe Leck (Flensburg)
Abstract: The German mathematical olympiads are a national competition for school students from grades 3 to 13. Directed by the association "Mathematik-Olympiaden e.V.", four rounds (school, regional, state, national) are carried out annually. We will give an overview of the rich history of the olympiads and provide some more detailed information about the different rounds. This is also meant to be a preparation for later talks in this panel which focus on the development of problems for the different age groups and rounds. In addition, we will give a brief introduction to the international team competition "Baltic Way" and discuss a few aspects of problem posing in this context.
School mathematics vs competition mathematics. A comparison of problems with comments from the kids
By Terese Marianne Olga Nielsen (Science Talenter)
Abstract: Twentyfour gifted pupils from grade 8 and 9 were presented with a set of problems from the mathematics examination and a set of problems from the Georg Mohr competition (https://www.georgmohr.dk/mc/mc17pben.pdf ). We discussed similarities, differences and level of hardness. Interestingly, the kids think about competition mathematics as if it was a subdiscipline of mathematics on a par with geometry, algebra or possibility theory, pointing to mathematical style being more important to them than subject matter.
By Konrad Engel (Rostock)
Abstract: Each year the problem committee of the German Mathematical Olympiad produces about 150 problems for school students from grades 3
to 13. We present the organisation of this work which is based on a close cooperation of all members in a friendly atmosphere.
We discuss some general principals and reflect our experiences, e.g. concerning the covering of different levels of difficulty and a balanced mix of areas like elementary number theory, graph theory, combinatorics, algebra and elementary geometry.
How to work with students in times of corona
Torsten Fritzlar (Halle) & Marianne Nolte (Hamburg)
– Impression of some experiences at primary grade and lower secondary level
- What kind of theoretical approach in general do we have for fostering students?
- How can we make this happen in times of corona pandemic?
- Theoretical foundation of our talent search process (primary grade level)
- Example of realization in times of corona pandemic
Where mathematics competition problems come from?
By Igor' Kontorovich (Auckland)
Instigated by Kilpatrick’s (1987) “Where do good problems come from?”, I will report on a study that tapped into problem posing of experienced problem posers for mathematics competitions.
The study was conducted with 26 problem posers residing in nine countries, and who had experience in creating problems for national, regional, and international competitions.
The central finding pertains to the construct of a trigger as a key driver of a process, one of the outcomes of which is a freshly posed problem. The educational implications of this study will be discussed.
Problems for the 5th and 6th grade - dealing with the transition from heuristic work to proof
By Klaus Henning (Hamburg)
Abstract: Posing problems for this age group faces particular difficulties; the kids lack any experience in mathematical reasoning and also in many fields of potential problems. Therefore, problems for this age group should aim at three goals: the use of heuristic strategies, the introduction of a more formal reasoning - and the possibility to expand the range of the particular problem into a wider mathematical context.
This will be shown be means of a couple of examples.
The German Mathematical Olympiads and the International Team Competition "Baltic Way" - a Brief Survey
By Uwe Leck (Flensburg)
Abstract: The German mathematical olympiads are a national competition for school students from grades 3 to 13. Directed by the association "Mathematik-Olympiaden e.V.", four rounds (school, regional, state, national) are carried out annually. We will give an overview of the rich history of the olympiads and provide some more detailed information about the different rounds. This is also meant to be a preparation for later talks in this panel which focus on the development of problems for the different age groups and rounds. In addition, we will give a brief introduction to the international team competition "Baltic Way" and discuss a few aspects of problem posing in this context.
School mathematics vs competition mathematics. A comparison of problems with comments from the kids
By Terese Marianne Olga Nielsen (Science Talenter)
Abstract: Twentyfour gifted pupils from grade 8 and 9 were presented with a set of problems from the mathematics examination and a set of problems from the Georg Mohr competition (https://www.georgmohr.dk/mc/mc17pben.pdf ). We discussed similarities, differences and level of hardness. Interestingly, the kids think about competition mathematics as if it was a subdiscipline of mathematics on a par with geometry, algebra or possibility theory, pointing to mathematical style being more important to them than subject matter.
GOAL
The main aim is to achieve some networking among the many diverse activities around the world and facilitate future cooperation. Beside this we would like to have a short discussion on topics we find crucial for enrichment projects. If we all see that the meeting is productive and the participants find this attractive, we would organise future meetings and try to edit a book with contributors among the participants.
Possible topics may include:
(1) Best practices: What are key-lessons learned from your problem-posing experiences,
(2) How to find / evaluate "good" problem fields,
(3) what are guidelines for moderations / tutors working in problem fields,
(4) how to analyse / evaluate the participants' output.
Mathematical problem posing refers to the the generation of new and reformulation of given tasks (Silver, 1994). It has been emphasized as an important mathematical activity by mathematicians (Cantor, 1867; Halmos, 1980) as well as mathematics educators (Kilpatrick, 1987; Brown & Walter, 2005). As an important companion of problem solving (Pólya, 1945), it can encourage flexible thinking, improve problem-solving skills, and sharpen learners’ understanding of mathematical contents (English, 1997). Therefore, this activity, which is a central skill of mathematicians, is often associated with mathematical creativity and giftedness.
Possible topics may include:
(1) Best practices: What are key-lessons learned from your problem-posing experiences,
(2) How to find / evaluate "good" problem fields,
(3) what are guidelines for moderations / tutors working in problem fields,
(4) how to analyse / evaluate the participants' output.
Mathematical problem posing refers to the the generation of new and reformulation of given tasks (Silver, 1994). It has been emphasized as an important mathematical activity by mathematicians (Cantor, 1867; Halmos, 1980) as well as mathematics educators (Kilpatrick, 1987; Brown & Walter, 2005). As an important companion of problem solving (Pólya, 1945), it can encourage flexible thinking, improve problem-solving skills, and sharpen learners’ understanding of mathematical contents (English, 1997). Therefore, this activity, which is a central skill of mathematicians, is often associated with mathematical creativity and giftedness.
Organized by
Supported by
We are very thankful for the ideal support by the International Group for Mathematical Creativity and Giftedness:
