A TA Game's effects on Math Understanding, Attitude & Self-Efficacy

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The Squares Family is a game- and story based microworld 1 for understanding arithmetic concepts, without describing mathematics in terms of digits and symbols. Instead we’ve constructed a microworld of arithmetic as a world of play grounds, colored squares, square boxes, and a family with lots of children who loves to play various games with their squares and square boxes on the playground. The reason is to allow for children to easier relate to, talk about and see arithmetic objects and learn how they behave. The graphical arithmetic microworld has a direct translation to “ordinary” mathematics, that is to the language of digits and symbols, so that everything that can be done in the microworld is mathematically valid. http://rutigafamiljen.se

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A Teachable-Agent Arithmetic Game’s effects on Mathematics Understanding, Attitude and Self-Efficacy:

A Teachable-Agent Arithmetic Game’s effects on Mathematics Understanding, Attitude and Self-Efficacy Lena Pareto, Tobias Arvemo, Ylva Dahl, Magnus Haake, Agneta Gulz University West, Lund University and Schools in Sweden

Our Approach to mathematics :

Our Approach to mathematics 2 Patterns Generalize Solve problems Think strategically Discover new rules Recognize situations Create computational algorithms … What fascinates a mathematician?

Can children be fascinated just as mathematicians?:

Can children be fascinated just as mathematicians? 3 Discover how numbers and operations behave Think strategically, reflect and reason Act in the role of expert A graphical, animated microworld of arithmetic Play strategic games based on the microworld Teach an agent to play 1 2 3

The Teachable Agent Math Game:

The Teachable Agent Math Game 2–7 3+16 12 ⁄ 4 5·4 4+5-12+(-3) Graphical model Arithmetic Teachable Agents Games User User plays Agent plays User teaches agent to play

Graphical Arithmetic Microworld:

Graphical Arithmetic Microworld Graphical numbers 446 Symbolic Quantity Graphical Graphical: quantitative view

Game play: reason, anticipate result, make good choices:

Game play: reason, anticipate result, make good choices Video

Targeted mathematical knowledge:

Targeted mathematical knowledge Playing well requires arithmetic understanding (to judge cards) and causal reasoning (to make good choices) Video

Teach the agent by apprenticeship:

Teach the agent by apprenticeship The TA asks reflective questions about the child’s choice:

Teach by showing how to play:

Teach by showing how to play 9 Teachable Agent Student ”Master” ”Apprentice” 1. Master chooses card 2. Apprentice observes 3. Apprentice asks why 4. Master answers

Let the agent try to play:

Let the agent try to play 10 Teachable Agent Student ”Master” ”Apprentice” 3. Apprentice asks why 4. Master answers 1. Apprentice chooses card 2.Master decides if good choice

Agent plays on its own:

Agent plays on its own 11 Teachable Agent Student ”Master” ”Apprentice” 1. Apprentice chooses card 2.Master observes

Purpose of reflective questions:

Purpose of reflective questions Prompt to explain (justify) actions TA models a “good inquisitive learner” Questions within “proximal zone of learning” Basic understanding of model Judge card  predict effect of computation Choose best of hand d iscriminate between 4 choices Choose best considering opponent/partner hand  predict 2-step computations & d iscriminate between 4 X 4 = 16 alternative paths Purpose multiple-choice responses Provide reasonable explanations Successively scaffold more advanced reasoning skills

The study:

The study pre-post experimental design, 3 part tests: Math comprehension Attitude towards math Self-efficacy 153 students in Sweden, 3 rd and 5 th grade 9 weeks, during regular math lessons 2 conditions Game play: ~ 40 min/week No-intervention: regular math class

Part 1: Attitude questionnaire:

Part 1: Attitude questionnaire Very boring Very fun 4 general questions: How do you feel in the morning when you think about having math? Is it easy to concentrate when working with math? What do you think about learning new topics in math? Do you like explaining how you solved a math problem to someone else? One math enjoyment variable (for categorization) Do you think math is boring or fun ? Negative judgment Positive judgment

Part 2: Self-efficacy questionnaire:

Part 2: Self-efficacy questionnaire 4 task-specific questions, such as: How confident are you in deciding which of the sums 47+32 or 35+41 is the largest? Not at all confident Very confident

Part 3: Math comprehension test:

36 items in 7 problem types, adapted to grade Inspired by national standard math tests Example questions: Nature money: = 213 translating between nature-money and integers, using nature-money for computations and judging the value of nature objects (place value). Which sum is larger 857+275 or 475+639 ? Will the result of 361+439 be an even ten? Part 3: Math comprehension test

Results: pre-treatment comparison:

Results: pre-treatment comparison Mann-Whitney, within group comparison: No significant difference between conditions No significant difference math enjoyment N Pre Math Achievement (max 36) Pre Attitude (min -12, max 12) Pre Self-Efficacy (min -12, max 12) Mean SD Mean SD Mean SD Control 85 26,11 5,51 2,67 4,90 6,79 4,19 Play 68 24,86 7,02 3,97 4,25 5,50 4,39

Results: post-treatment gains:

Results: post-treatment gains N Gain Math Achievement Gain Attitude Gain Self-Efficacy Mean SD Mean SD Mean SD Control 85 ,93 4,38 1,50 3,82 -,23 3,62 Play 68 3,19 5,28 ,93 3,09 1,44 3,52 p=,01 p=,009 Mann-Whitney, between group comparison: S ignificant difference math achievement ( eff.size 0,47) S ignificant difference self-efficacy (effect size 0,47) No significant difference attitude Similar results with ANCOVA controlling for pre-test results: p=,01 and p=,03

Within play group exploratory analysis:

Within play group exploratory analysis Split the play group according to Low, medium and high attitude (enjoyment variable) Semi- and fully authentic setting

Results: indications within treatment:

Results: indications within treatment Comparison semi-authentic and fully authentic setting: Comparison low, medium and high enjoyment math:

Conclusion:

Conclusion Significant learning effect? Math comprehension Yes Attitude towards math No Self-efficacy beliefs Yes

Self-efficacy gain exciting result:

Self-efficacy gain exciting result Strong predictor of future math accomplishments Not often studied as separate issue We suggest the game design explains this by the absence of failures; choices can be better or worse but never wrong, and the TA allowing students to act the role of an expert, boosting self-esteem and confidence.

Within play group difference:

Within play group difference The low attitude group show the largest gains: an unconventional approach to math could attract these, at-risk students The semi-authentic group somewhat larger gains: Smaller groups? Instructors conviction of the game’s value? Structured sessions with explicit goals?

Future work:

Future work Study which game features contribute to learning to what extent: Game without Teachable Agents Game with TA but without explanatory questions Game with TA and explanatory questions (as now) Game with full on-task TA and social chat Study teachers roles and usage of the game

Slide 25:

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