L21 - Thinking during play

Question 1

Why is play important?

Answer 1

• Wenner (2009)
  
  • Evidence that play reduces stress and anxiety
    
    • Anxious kids much less anxious after imaginative play
  • Improves social skills
    
    • After free play, kids given social conflicts to reason about, offer better solutions
    • Improves creativity
      
      • After playing with tools, kids generate more creative uses for them
    • Increases self-regulation & lowers impulsivity

Question 2

How was play in decline?

Answer 2

• Parents putting children into organised events such as music lessons rather than play
• Evidence that nowadays kids are less creative on the whole than they were (Gray et al., 2023)

Question 3

What is play like?

Answer 3

• Sensorimotor play
  
  • learning and repeating action sequences
  • 50% of play up to 2 years of age
• Symbolic/pretend play: multiple kinds
• Constructive play
  
  • Building/making stuff
  • 50% of play of 4 – 6 year olds
• Dramatic play
  
  • Imaginary situations and role playing in such situations
  • 2-3 years old often engage in parallel play (playing in individual scenarios alongside one another)
  • 3 – 5 more group play
• Games with rules
  
  • Can be culturally pre-existing games with established rules, or kids can make up their own rules. More structured than dramatic play
  • Grows dramatically from 4 -7

Question 4

What is thinking in play?

Answer 4

• Teachers/parents say that there is little sophisticated reasoning in play
• Deny they can think mathematically, logically and scientifically
  
  • Preoperational child
• Recent research has showed just how sophisticated thinking actually us

Question 5

What is scientific thinking in play?

Answer 5

• Science is about finding out the causes of natural phenomena
• Children also appear very concerned with what causes things
• They generate causal explanations and explore the world to test
  their hypotheses
• e.g. in video example kid is hypothetically testing out things
• Children are very open about things, more than adults, about how things work

Question 6

What did Schultz & Bonawitz (2007) find about what happens in play?

Answer 6

• Play is about discovering causal structure
  
  • Motivated to find out about what they’re playing with
    
    • Jack-in-the-box type toy with 2 levers, 2 toys pop out (e.g., a
      donkey and a tiger)
      
      • One lever causes one toy, the other the other.
    • Adult and pre-school child each pull a lever
    • Confounded (i.e. ambiguous) condition: adult & child pull both levers at the same time and both toys pop up.
    • Unconfounded (i.e. clear) condition condition: adult & child pull levers sequentially and each toy pops up in corresponding sequence
    • Then child given option to play with this toy or a new toy
    • They choose new toy in unconfounded, old when confounded
    • Confounded condition needs more play to figure out how it
      works
    • Want to continue playing with toy until they figure out what they are playing with

Question 7

What did Gopnik say about causal reasoning in play?

Answer 7

• Causal reasoning in play is abstract
• Gopnik
  
  • Children are mini scientists - collecting evidence etc.
  • Promoting a position wherein children reason abstractly from quite early on, specifically when in engaging in causal reasoning

Question 8

Is scientific instruction important in play?

Answer 8

• Despite foundations of scientific thinking, school-aged children and non-scientist adults need instruction to control for variables when testing hypotheses.

o David Klahr’s work.

• Lennart Schalk and colleagues in Switzerland show that “inquiry- based” primary school physics education improves both COV strategies and physics concepts understanding
• So basically no one figures stuff out on their own
• Kids will try all sorts of stuff, not systematically control for variables when many are involved.
• Don’t have abstract representation for control-for- variables strategy
• In addition, Domain-knowledge is critical: what are the relevant variables to control for?
  
  • Think about how different theories tell you which variables are important.
  • When professional scientists don’t control for a variable, it’s not because they don’t have this understanding

Question 9

What is pretend play?

Answer 9

• Pretend play - About establishing hypothetical situations and reasoning from the premises of these hypothetical situations
  
  • Deductive reasoning
• If we are in a world like X, therefore Y follows, but if it were like A then B followers”
  
  • Counterfactual reasoning

Question 10

What did Harris (2001) find about logical thinking in play?

Answer 10

• Can children think logically about hypotheticals that contradict their experience?
  
  • “All cats bark. Rex is a cat, does Rex bark?”
  • Ask 4 – 6 year olds.
    
    • They say no. Rex is a cat, cats don’t bark. Refuse to reason from the false premise. Concrete thinking?
    • But simply prompt the question with “Imagine a world where cats bark…”
      
      • Or even “think about how things would be if…” - so elaborating prompt
      • Then 4 – 6 year olds could do it no problem.
      • Potentially contradicts classic work by collaborators of Vygotsky that abstract logical reasoning was only supported by cultural institutions like schools (investigated people in Siberia on their logical and education skills)

Question 11

What did Buchsbaum et al. (2012) find about pretense and counterfactual reasoning?

Answer 11

• 3 & 4 year old children are shown a toy that lights up and sings “happy birthday”
• Shown two objects,a zando and no zando. Zandos make the box play and non-zandos don’t
• Children are asked “what if the non-zando was a zando, then would the box play?” and vice-versa (counter-factuals)
• Then another experimenter comes in and takes the box and he toys.
• It’s a stuffed monkeys birthday, but now they don’t have the birthday singing toy. So, the experimenter takes out just some other objects and tells the kid to pretend it’s a birthday singing box and that there is a zando and a non-zando.
• Kid is then supposed to reason that the pretend zando can make the pretend toy sing “happy birthday” while the non- zando would not.
• Ability to reason correctly about the pretend zando was correlated with the ability to reason counterfactually earlier

Question 12

What did both Buchsbaum and Harris ultimately show about play?

Answer 12

Show how children can go beyond their perceptual experience, inhibit the most obvious response and about known objects and reason logically

Question 13

What kind of mathematical play is used in real life?

Answer 13

• Many teachers do not attempt to teach children under 6-7 math beyond simple counting games and using a clock because they don’t think kids can think mathematically.
  
  • And they often hate maths themselves
• Many pre-school teachers (perhaps over-reacting to need for play research) say that teaching is bad for young kids and they just need to play freely to develop properly
• Seo & Ginsburg (2004) catalogue mathematical thinking during play in 4 year-olds to show how much more children are capable of - you can build mathematical acitivties into play

Question 14

How do Seo & Ginsburg (2004) show how play should be used with mathematics?

Answer 14

• Classification
  
  • This category includes grouping, sorting, or categorizing by attributes. A child cleaned up the blocks on the rug, for example, by taking one block at a time and placing it in a box that contained the same size and shape of blocks. Also a girl took all the plastic bugs out of the container and sorted them by type of bug and then by colour. They were classifying
• Pattern and shape
  
  • This category includes identifying or creating patterns or shapes or exploring geometric properties. In one example, a child made a bead necklace, creating a yellow-red colour pattern. In another, a boy put a double-unit block on the rug, two unit blocks on the double-unit block, and triangular blocks in the middle, building a symmetrical structure. These children were playing with pattern and shape
• Also gives example of magnitude, enumeration, dynamics, spatial relations

Question 15

What are the failures in mathematical thinking?

Answer 15

• People are bad at maths on the whole
  
  • McDonalds - People thought 1/3 was smaller than a quarter-pounder
  • 4 years carefully used symmetry in their block building, but then fail to understand it formally in maths class years later
• Huge socio-economic class disparities
  
  • High rates of numerical illiteracy in US lower classes. Can’t have a job that requires the use of a cash register
  • Already major differences in formal maths reasoning by the start of primary school between SES groups, and numerical competence during childhood predicts longitudinal outcomes.
• Why the early difference?
  
  • No difference between classes in mathematical play
  • Large disparities in verbal mathematical reasoning
  • But large disparities in quantity and quality of language input/conversation in high vs. low SES groups.
  • Low SES kids have less opportunity to reflect on their play and make concepts explicit

Question 16

How can we improve mathematical thinking?

Answer 16

• Needs to be intentional instruction encouraging reflection, explicit thought, and systematic application of mathematical ideas to novel situations
• Not recommending to take time away from play to then give 4 year-olds a lecture
• Clements and Sarama say: Educators need to understand what children’s thinking is like, and build curricula building on what the children can already do and then formally mathematicize their implicit knowledge
• Siegler has a slightly different angle: what is critical to understand what are the key representations, and design games to target those.
  
  • Rather than gamifying the entire curriculum, you can be more targeted

Question 17

What is Siegler’s “The Great Race” game as a method to improve mathematical thinking?

Answer 17

• Game is a number line where rabbit and bear race down it
• Number line representations are critical
• Improves numeracy for low SES children, some evidence that complete closes the preschool SES numeracy gap
• Across papers, different control conditions- counting activities, circular version of the game, or a linear game with just the colours, not numbers
• Pre-test and post-test measures:
  
  • number line estimation, 1-10
  • Magnitude comparison “what is more, six cookies or one cookie?”
  • Single digit arithmetic. At post-test, corrective feedback and opportunities to learn more.
• Four 15 minute sessions over two weeks (for linear number game and the controls) and a post-test session later
  
  • Post-tests: between one week and nine weeks later
• Game play is simply, spin a spinner that lands on a number, move ahead that number of places. First to the end wins
• Median place on the number line for a condition. At pre-test, median for every number is where 5 should go.
  
  • Only linear number condition significantly improves. Median
    becomes accurate. Other controls look like circular game.
  • Magnitude comparison and arithmetic improves for linear game.
  • Little or no improvement on any measure for other conditions
  • Can completely make up the gap with SES kids by 2 weeks of this exercise

Question 18

What did Gentner et al., 2016 find out learning geometric/physical principles in play?

Answer 18

• Principles of stable construction
  
  • Goal Teach children a key principle of stable construction: That diagonal braces confer stability
    
    • Basic principle: The triangle is a stable polygon
    • Children often fail in free construction tasks

Question 19

How do you improve formal thinking more generally?

Answer 19

• If there is no well-designed learning game, you can at least support reflective thinking about their play
• Generally, (outside of maths as well), help children practice reflective reasoning, ask children “why did that happen? Why do you think that? How do you know?”