1. GETTING THE PICTURE The role of representational format in simulation-based inquiry learning Bas Kollöffel, Ton de Jong, & Tessa Eysink

2. LEMMA RESEARCH PROGRAMME What are the relations between external representational codes (pictorial, arithmetical, and textual), and modality (visual or auditory), learning processes, and learning outcomes?

3. INSTRUCTIONAL APPROACHES Exploration of hypertext environments IWM-KMRC, Tübingen (Ger) Learning from worked-out examples University of Freiburg (Ger) Observational learning from expert-models Open University (NL) Simulation-based inquiry learning University of Twente (NL)

4. INQUIRY LEARNING Why & how Knowledge construction Deeper knowledge Emphasis on conceptual knowledge

5. SIMULATIONS Models Focus on learner explorations How does a simulation work?

6. EXAMPLE You attend a foot race. Five runners participate in the race. You predict the outcome of the race. What is the probability that your prediction is right?

19. THEORETICAL BACKGROUND Processing (e.g. Larkin & Simon) Encoding, Storage, & Retrieval (e.g. Paivio; Mayer) Cognitive load theory (e.g. Sweller, Paas, & Van Merriënboer)

20. IMAGINE... 1.Two transversals intersect two parallel lines and intersect with each other at a point X between the two parallel lines. 2.One of the transversals bisects the segment of the other that is between the two parallel lines.

21. OR... x

22. THEORETICAL BACKGROUND Processing (e.g. Larkin & Simon) Encoding, Storage, & Retrieval (e.g. Paivio; Mayer) Cognitive load theory (e.g. Sweller, Paas, & Van Merriënboer)

23. RESEARCH QUESTION What is the relation between representational codes (pictorial, arithmetical, and textual), learning processes, and learning outcomes?

24. EXPECTATIONS Pictorial representations enhance conceptual knowledge Arithmetical representations enhance procedural knowledge Pictorial representations reduce cognitive load

25. DOMAIN Elementary Combinatorics & Probability Theory No replacement; Order important No replacement; Order unimportant Replacement; Order important Replacement; Order unimportant

26. DOMAIN Elementary Combinatorics & Probability Theory No replacement; Order important No replacement; Order unimportant Replacement; Order important Replacement; Order unimportant No replacement; Order important Example: footrace

27. DOMAIN Elementary Combinatorics & Probability Theory No replacement; Order important No replacement; Order unimportant Replacement; Order important Replacement; Order unimportant

28. DOMAIN Elementary Combinatorics & Probability Theory No replacement; Order important No replacement; Order unimportant Replacement; Order important Replacement; Order unimportant Replacement; Order important Example: PIN-code

29. DOMAIN Elementary Combinatorics & Probability Theory No replacement; Order important No replacement; Order unimportant Replacement; Order important Replacement; Order unimportant

30. PRODUCT MEASURES Conceptual knowledge (Why?) -relations between categories -relations within categories Procedural knowledge (How?) -knowledge about calculations -transfer (near & far) Situational knowledge

31. CONCEPTUAL ITEM You play a game in which you have to throw a dice twice. You win when you throw a 3 and a 4. Does it matter whether these two numbers should be thrown in this specific order?

32. CONCEPTUAL ITEM You play a game in which you have to throw a dice twice. You win when you throw a 3 and a 4. Does it matter whether these two numbers should be thrown in this specific order? ANSWER: Yes, if you have to throw the numbers in a specific order your chance is smaller than when the order doesn’t matter.

33. PROCEDURAL ITEM You are playing a board game and it is possible for you to win when you throw a certain combination with the dice. In order to win you first have to throw a 3, so that you end up in a box that says ‘throw again’ and then you have to throw a 5. What are your chances to win this game in this turn? ANSWER: 1/6 x 1/6 = 1/36

34. PROCEDURAL ITEM You are playing a board game and it is possible for you to win when you throw a certain combination with the dice. In order to win you first have to throw a 3, so that you end up in a box that says ‘throw again’ and then you have to throw a 5. What are your chances to win this game in this turn? ANSWER: 1/6 x 1/6 = 1/36

35. SITUATIONAL ITEM You throw a dice 3 times and you predict that you will throw two sixes and a 1 in random order. What is the characterization of this problem?

36. SITUATIONAL ITEM You throw a dice 3 times and you predict that you will throw two sixes and a 1 in random order. What is the characterization of this problem? ANSWER: order not important; replacement

37. PRODUCT MEASURES Conceptual knowledge -relations between categories -relations within categories Procedural knowledge -calculations -transfer Situational knowledge

38. PROCESS MEASURES Time spent in learning environment Number of experiments in simulations Cognitive Load

39. SET UP 58 participants Pretest – Posttest Design –Pre test: 12 items (open & mc) –Post test: 44 items (open & mc) 3 conditions: –Pictorial –Arithmetical –Textual

40. RESULTS (PRODUCT)

41. On the overall post-test score the textual and the arithmetical condition outperformed the pictorial condition No main effect of condition on conceptual knowledge Arithmetical condition scores better than the pictorial condition on procedural items No main effect of condition on situational knowledge Relatively low overall performance

42. RESULTS (PROCESS)

43. Time spent and number of experiments is equal in all three conditions Pictorial condition: higher cognitive load

44. CONCLUSION Arithmetical representation leads to better scores than pictorial or textual representation, especially on procedural items No differences on time and activities Arithmetical representation is found “easier” than pictorial representation

45. DISCUSSION Aren’t pictures better? -domain related? -nature and complexity of tree diagrams - procedural knowledge only Relatively low results: -unfamiliarity with inquiry learning? -insufficient guidance?

46. FUTURE DIRECTIONS Stimulating exploratory behavior Thinking aloud protocols Role of representations in expression of knowledge Role of representations in collaborative inquiry learning

47. GETTING THE PICTURE The role of representational format in simulation-based inquiry learning Bas Kollöffel, Ton de Jong, & Tessa Eysink