open-ended modeling tasks in dutch math & science education summerschool 2014 dédé de haan...

Open-ended modeling tasks in Dutch math & science education

Summerschool 2014Dédé de Haan & Monica [email protected] [email protected]

mailto:[email protected]

mailto:[email protected]

Yesterday

August 2013 Summerschool - Open ended problems 2

Today

• Experience working on an ‘inquiry based’ RME task for a length of time.


Realistic Mathematics Education (RME)

• Guided reinvention• Meaningful contexts, tools and models• Math as human activity (Freudenthal, 1991)• Intertwining learning strands• Own productions and constructions

• Question: how does this relate to inquiry based learning?


How is RME integrated in Dutch math education?• meaningful contexts, tools and models: textbooks• learning strands intertwined: textbooks• guided reinvention: textbook / teacher

More difficult to integrate into the curriculum:• Own productions and constructions, modeling,

math as human activity • Higher order thinking skills (HOTS)


Higher order thinking skills in Mathematics and Science education


Process skills Modelling Problem solving Communicating Information assessment skills

Assessing the reliability of numerical information and its relevance for the solving of a problem

Research competenciesConstructing and assessing of a model

based on given information, adjusting the model after testing it.

Dutch solution

One whole day mathematics as ‘problem solving’, as a competition for teams

•Lower secondary school:Mathematics day•Upper secondary school:Mathematics A-lympiadMathematics B-day


Assignments for today

• 3 different assignments (Mathematics day, Mathematics A-lympiad, Mathematics B-day)

• You work in teams during the day and present the process and your results on a poster at the end of the day


Schedule

9:15 – 12:15 work on assignment in small groups

12:15 – 12:30 plan posters

12.30 – 13.30 lunch

13:30 – 14:15 finish posters

14:15 – 15:15 discuss posters in small groups

15.15 – 15.30 short tea break

15:30 – 16:30 summarizing and judging the work

16:30 - 17:00 closure


Elevators

• Elevators (Math A-lympiad): design an “elevator-schedule” for the 6 elevators in an office-building with 20 floors and 1200 employees that brings everybody to his/her workplace as quickly as possible.


Security in museum

• Security is an art in itself (Mathematics Day/Mathematics A-lympiad). A museum for modern art organizes a large exhibition. The organization has to deal with problems concerning security. Your team has to figure out the best way (economically and artistically) to protect/survey the exhibition, using camera’s and removable walls.


Paper strips

• Paper folding (Math B-day):repeatedly fold two strips of paper in a prescribed manner. Sharp folds will result in interesting geometrical figures, that consists of straight parts that bend at a right angle on every folding line. The goal is to explain, and predict, the patterns.


• How to make groups en decide on the type of tasks?


Start working on the assignment!

Work in groups for about 30 minutes.

Quick round for questions.How are you doing?Problems, questions?


Check for the assignment on Elevators

How many seconds does it take the elevator to start at floor 1; stop at 3 and 4 and run to 7 and stop there?

Answer:53 seconds or 63 s (if you include the time it remains on 7)


On the poster

• Solution (partial solution is okay) • Models; Representations; etc.• Assumptions• Solution process (maybe)

Make clear to others what you worked on and how.


REFLECTION


Three aspects

• The task (40 minutes)

• The student (15 minutes)

• The teacher (20 minutes)


Round 1: the task (40 minutes)Part 1: 20 minutes

• Walk around, talk about posters, ask questions, take notes.

Aim:What are the main characteristics of these task(s)

and the solutions?• HINT: Use the Mascil diagram.


Round 1Part 2: discuss (20 minutes)

• Change groups to E!

• Compare your notes (5 minutes)

• Interactive discussion on task characteristics(15 minutes)


Task characteristics (specific)


•Accessibility•Use of mathematics•(Natural) differentiation

•Open ended problem with a structure: Start (closed) – body (analyse, use math) – end (create)

•Different skills •More than basic math•For teams•Whole day

Part 2: the student (15 minutes)

10 minutes:•In one word write on a sticky note how you felt during the activity = ‘working on the task’.

•Share in your new group (E!)

5 minutes:•Stick your note on the whiteboard


Part 3: the teacher (20 minutes)

In small groups E•How did we (Monica and Dede) act as teachers?

•What would you as a teacher need to know/do/… in order to implement this type of activities in your classroom?• Use Mascil diagram• Use results of parts 1 and 2


SHORT TEA-BREAK


How to judge the products?

Your suggestions………….

Our experiences ………..


Judging the work• General criteria with task• Teachers’ own criteria (rubrics, e.g.)


Different way of judging

• Ordering/ranking (4x)

• Combined ranks


Finals


Thank you!


http://www.fisme.science.uu.nl/alympiade/en/welcome.html(Alympiade – English sitehttp://www.fi.uu.nl/wisbdag/ (B-day – Dutch site)

http://www.fisme.science.uu.nl/publicaties/subsets/alympiad/ (tasks Alympiad in English)

http://www.fisme.science.uu.nl/publicaties/subsets/mathsbday/ (tasks B-day in English)

open-ended modeling tasks in dutch math & science education summerschool 2014 dédé de haan...

Documents

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