Open-ended modeling tasks in Dutch math & science education Summerschool 2014 Dédé de Haan & Monica Wijers

Yesterday August 2013Summerschool - Open ended problems2

Today Experience working on an ‘inquiry based’ RME task for a length of time. August 2013Summerschool - Open ended problems3

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? August 2013Summerschool - Open ended problems4

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) August 2013Summerschool - Open ended problems5

Higher order thinking skills in Mathematics and Science education August 2013Summerschool - Open ended problems6  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 competencies Constructing 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-lympiad Mathematics B-day Mathematics A-lympiad Mathematics B-day August 2013Summerschool - Open ended problems7

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 August 2013Summerschool - Open ended problems8

Schedule 9:15 – 12:15 work on assignment in small groups 12:15 – 12:30 plan posters – lunch 13:30 – 14:15 finish posters 14:15 – 15:15 discuss posters in small groups – short tea break 15:30 – 16:30 summarizing and judging the work 16: :00 closure August 2013Summerschool - Open ended problems9

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. August 2013Summerschool - Open ended problems10

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. August 2013Summerschool - Open ended problems11

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. August 2013Summerschool - Open ended problems12

How to make groups en decide on the type of tasks? August 2013Summerschool - Open ended problems13

Start working on the assignment! Work in groups for about 30 minutes. Quick round for questions. How are you doing? Problems, questions? August 2013Summerschool - Open ended problems14

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) August 2013Summerschool - Open ended problems15

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. August 2013Summerschool - Open ended problems16

REFLECTION August 2013Summerschool - Open ended problems17

Three aspects The task (40 minutes) The student (15 minutes) The teacher (20 minutes) August 2013Summerschool - Open ended problems18

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. August 2013Summerschool - Open ended problems19

Round 1 Part 2: discuss (20 minutes) Change groups to E! Compare your notes (5 minutes) Interactive discussion on task characteristics (15 minutes) August 2013Summerschool - Open ended problems20

Task characteristics (specific) August 2013Summerschool - Open ended problems21 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 August 2013Summerschool - Open ended problems22

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 August 2013Summerschool - Open ended problems23

SHORT TEA-BREAK August 2013Summerschool - Open ended problems24

How to judge the products? Your suggestions…………. Our experiences ……….. August 2013Summerschool - Open ended problems25

Judging the work General criteria with task Teachers’ own criteria (rubrics, e.g.) August 2013Summerschool - Open ended problems26

Different way of judging Ordering/ranking (4x) Combined ranks August 2013Summerschool - Open ended problems27

Finals August 2013Summerschool - Open ended problems28

Thank you! August 2013Summerschool - Open ended problems29 (Alympiade – English site (B-day – Dutch site) d/ d/ (tasks Alympiad in English) day/ day/ (tasks B-day in English)