Shaaron AINSWORTH & Nicolas VAN LABEKE University of Nottingham

1. Using a Multi-representational Design Framework to Develop and Evaluate a Dynamic Simulation Environment Shaaron AINSWORTH & Nicolas VAN LABEKE University of Nottingham {sea,nvl}@psychology.nottingham.ac.uk

2. Many multi-representational systems (e.g. FunctionProbe, StatPlay, spreadsheets, www, multi-media). Tabachneck, et al (1994) found that students who used more than one rep were twice as successful at algebra. Ainsworth et al (1998) found that presenting children with a place value and a table improved maths performance. Mayer & Anderson (1991) paired animations with narrations and text to improve performance. Yerushalmy (1991) taught 14 yr olds functions. Only 12% of students’ answers involved both visual and numerical reps. Resnick & Omanson (1987) taught children to subtract using Dienes blocks and conventional symbols. It did not help eradicate bugs. Van Somerman & Tabbers (1998) found that qualitative reps did not help learners solve quantitative physic problems. Gruber et al (1995) found that adding multiple perspectives to an economics simulation was harmed learners’ performance. Why do we need a framework?

3. The DeFT Framework • DeFT (Design, Functions, Tasks): Provides a conceptual framework for describing the issues unique to learning with more than one ER. • Three aspects of learning with MER • Cognitive tasks • Functions of MERs • Design Parameters • Aims • To describe systems • To explain conflicting results • To guide experimentation • To design systems • To develop design principles

4. DeFT - Tasks When learning with presentedgiven ERs • the properties of the ER • the relation between the ERs and the domain When learning with a choice ERs • how to select appropriate ERs When learning with self-constructed ERs • 1 & 2 & (3) + • how construct an appropriate ER • When learning with multiple ERs • 1 & 2 & (3) & (4) • how to translate between ERs

5. FUNCTIONS Strategies Tasks Individual Differences Complementary Roles Constrain Interpretation Construct Deeper Understanding Different Processes Different Information Constrain by Familiarity Constrain by Inherent Properties Abstraction Relation Extension DeFT - Functions

6. DeFT – Design Parameters: Information and Form • Information. Information can be distributed in different ways between the ERs which influences the complexity of the ER and the redundancy of the system. • Many studies have shown its not wise to unnecessarily split information across MERs (e.g. split attention studies) but sometimes a single ER can become very complex or contain information which is best expressed in different ways. • Form: A multi-representational system can contain representations of different computational properties (e.g. heterogeneous systems, multi-modality systems, multi-dimensional systems). • Particular benefits may accrue from different approaches (e.g. Barwise & Etchemendy 1992; Schnotz, 2001, Mayer, 1997) but also particular problems (e.g. Ainsworth et al, 2002; Moher et al, 1999)

7. DeFT – Design Parameters: Information and Form: Translation and Number • Translation: The degree of support provided for mapping between two representations, ranging from no support through to highlighting and on to full dyna-linking where behaviour on one representation is reflected onto another. • Some people recommend dyna-linking (e.g. Kaput, 1992). • Ploetzner, Bodemer, & Feuerlein (2001) proposed an approach based on structure mapping where learners are encouraged to map familiar aspects of an ER onto an unfamiliar ER. • Van-Labeke & Ainsworth (2001) base their approach on scaffolding theory (contingent translation) which fades the degree of system support as the learner experiences grows (supported by Seufert, 15 minutes time). • Number: By definition, a multi-representational environment uses at least two ERs, but many systems use more than that. A related issue is how many ERs to use simultaneously?

8. DeFT – Design Parameters: Sequence • Sequence: Many systems present only a subset of their ERs at a time; consequently further decisions must be made. • The order in which the ERs should be presented. • e.g. teach integration before differentiation and so velocity-time before position-time). • e.g. qualitative representations to guide subsequent interpretation of quantitative (Plötzner, Fehse, Kneser, & Spada (1999) • e.g. concrete -> abstract or Verdi, Johnson, Stock, Kulhavy, & Ahern, (1997) graphical before textual • When to add a new ER • Before knowledge has become proceduralised (Resnick & Omanson, 1997) but not so early that learners become overwhelmed • When to switch between the ERs • e.g. when a learner understands the relations between ERs • e.g. judicious switching not thrashing (Cox, 1996, Anzai, Tabachneck et al, 1994).

9. DEMIST • DEMIST is a simulation learning environment in the area of population dynamics • It provides full flexibility for manipulating the design parameters of DeFT • DEMIST supports additional activities • Hypothesis on future values, action on the current values

11. Pilot Study • Experiment on 3 models of population dynamics • Participants • 18 University UGs – no biologists or mathematicians • Multiple-choice Pre-test and Post-test • Conceptual • Single Representation • Multi Representations • Procedure • One hour to explore the 3 models

12. Example (Concept – SSUG) One of the following types of population will double in a fixed amount of time. Is it APrey in the predator-prey model BPredators in the predator-prey model CA single species showing unlimited growth DA single species showing limited growth

13. Example (Single – SSLG) Given this graph of population growth rate against population density (dN/dT v N), on which point is population growing fastest ?

14. Example (MERs – TSP) Three of these graphs were generated from the same predator and prey model and one was not. Which one is it? A B C D

15. Design Decisions

16. Pre-test / Post-Test Results • Average pre-test score above chance (p<0.001) but MERs below chance (p=.024) • Significant performance increase (p<0.008)

17. Categories of ERs in DEMIST

18. Unit 1 – 08:34 00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 Controller Value: N Chart: N Graph: N v Time Table: N New Terms Dynamic Equations Graph: Ln(N) V T Graph: N V T (Log) Graph: N v (dN/dT) Controller Map Relation Action & Hypothesis Experimental Set Users’ Traces

19. Which Representations are used? • Large exploration of the representational space (73 out of 80 ERs available) but unequal use of ERs • Striking correlation between our provision of ERs and the learners’ preferred ones (p < 0.02)

20. Acting on Representations • Representations are used for display to request translation or predict a value at some future point • Hypothesis only from the X-Time Graph • 59 Translation requests, more than expected from XY, Log and Table

21. Relationship between ER use & performance • No significant relationship between use of representations (number seen, number co-present, time spent with a particular representation) and; • Pre-test scores • Post-test scores • Prior experience with maths/biology • Stated preference as to visualiser/verbaliser

22. DEMIST One:Conclusions and next steps • Need for fine-grained protocols to gain insight into the processes involved in learning with multiple representations. • In particular, how do learners’ goals, decisions and strategies influence their use of representation. • E.g. Does spending a long time working with an ER indicate knowledge or ignorance • Systematic variation of some of the design parameters (e.g. 5 co-present ERs v 1 ER of the 5 at a time) • Keep on reading all of your papers to see if your results support my hypotheses! (describe your system according to DeFT at http://www.psychology.nottingham.ac.uk/research/credit/projects/multiple_representations/deft_systems/)