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Section 1

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Berkowitz et al 2015

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Math

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Mar 1, 2020

Cards (14)

Section 1

(14 cards)

Berkowitz et al 2015

Front

- First grade children demonstrated a significant improvement in maths ability after completing mathematics problems as part of their bedtime routine - Children either read math passages (reading group) or completed questions (math groups) - Using tablet to access adapted version of 'Bedtime Math' app - Children who used app to complete problems at least 2x per week significantly improved ability - Children who read maths passages did not improve - Benefits especially strong for children of high maths anxious parents

Back

Key points in Emerging Minds: process of change in children's thinking

Front

- Staircase learning = Piaget, distinct and different between ages 1. Piagetian stage model = sensorimotor, pre-operational ... 2. Case's Neo-Piagetian stages = sensorimotor, relational, dimensional ... - overlapping waves learning 1. Wellman's theory of mind = desire theory > belief-desire theory 2. Carey's theory of biology = psychological > biological 3. Ashcraft's single-digit addition model = sum, min, retrieval 4. Seigler's number conservation = length, counting, transformation - min method = counting from larger addend - decomposition = dividing problem into two simpler ones

Back

Variability contributes to cognitive growth

Front

- Seigler argues "variability is not just an incidental feature of thinking; it appears to play a critical role in promoting cognitive change." - Evidence: 1. On trial before new discovery, children show particularly variable performance 2. Children show gesture speech mismatches in conversation tasks benefit more from explicit instruction

Back

Seigler and Jenkins 1989

Front

- How do children learn the min strategy ? (counting up from larger of two numbers) - Followed eight 4-5 year older for 11 weeks - All started with simple addition proficiency - 7 problems in each 3 sessions - Measured speed and accuracy - Asked kids to report strategies - 75-100% correlt - Multiple strategies: fingers, retrieval, min - Variables 1. Percent of each strategy that was used across sessions 2. Kids used different strategies on ⅓ of trails to the same problem

Back

Numerical understanding (5p)

Front

- Ratio 1:2 for 6th month old to recognise - Most basic understanding is numerical equality (= the realisation that all sets of N objects have something in common) - 5 month olds have sense of numerical equality (at least with sets of 1-3 objects) - Infants possess an approximate sense of larger numbers - Only after 3-4 years do children show precise representation of sets slightly larger 3

Back

Infant's understanding of arithmetic (5p)

Front

- In certain experiments infants show surprise when objects are added or subtracted behind a screen - Findings not always replicated - Infants' competence is limited to small sets of objects - Some researchers conclude infants' competence reflects perceptual rather than arithmetic processes - Rely on subtising (= process by which look at objects and immediately know how many objects)

Back

Overlapping waves theory (3p)

Front

- At any one age, children use multiple strategies - With experience, they rely increasingly on more advanced strategies - Development involves changes in the use of existing strategies as well as the discovery of new approaches

Back

Wynn 1992 (2p)

Front

- Infants under 6 months look longer at the seemingly impossible event - Suggests they are surprised at seeing 1 doll rather 2

Back

Dupont-Biome and Thevenot 2017

Front

- Counting on fingers smart strategy - 84 6 year old Swiss children observed completing maths problems, 52 counted on fingers - Finger counting significantly correlated with better performance and with working memory ability - Discovering finger counting and the min strategy seems to require good working memory - The authors recommend explicitly encouraging finger counting to help less gifted

Back

Using board games to teach numerical understanding (8p)

Front

- The greater the number square, the greater the distance moves/more moves made etc - Geetha Ramani and Robert Siegler conducted similar studies - Preschool children - Adults play with children 1 on 1 - Play 20 games over 2-3 weeks, each around 3 mins long - Children struggle with idea that numbers are linear - Seigler and Ramani 2008 (no improvement for colour game group, ,significant improvement for number game group, understanding mostly preserved 9 weeks later) - Seigler and Ramani 2009 (little improvement for control and circular group but significant for linear)

Back

Variability and selection (2p)

Front

- In challenging situations, children generate variety of problem solving strategies - With repeated experience, strategies that work best 'survive' = Hebbian learning

Back

Sullivan and Brown 2015

Front

- British cohort study followed same people born in one week in 1970 - Kids who read at least once week at age 10 better mathematics scores at age 16 (10% advantage) - Reading for pleasure impact nearly four times greater than effect of parental education - Reading helps children learn to understand and absorb new information and concepts which likely helps with learning mathematics too

Back

Most preschoolers seem to understand basic principles: (5p)

Front

- 1-2 correspondence = one object per number word - Stable order = always recite in same order - Cardinality = N = number - Order irrelevance = left to right = right to left - Abstraction = any set can be counted

Back

Development of counting

Front

By age 3 most can count to 10

Back