mathematics, anxiety, and gender

what are the main influences to maths development?

• reading

• exposure

• variability & selection

explain Siegler & Ramani (2008) - exposure example

• number line game (colour vs number condition)

• approx. 100 repetitions over 2-3 weeks

• children struggle with the idea that numbers are linear

• number line estimation significantly improved for number group (no change for colour group) and results were stable after 9 weeks

explain Siegler & Jenkins (1989) - variability & selection example

• microgenetic study exploring simple addition strategies - 11 weeks

• observed use of multiple strategies to solve the same problem

• with experience children begin to rely on more advanced strategies

• development involves changes in existing strategies and implementation of new approaches

key aspects of teaching maths

• procedural knowledge vs conceptual understanding

• maths resilience

• the role of working memory

what is procedural knowledge?

• knowing how to do something

what is conceptual understanding?

• knowing why something is done (in a certain way)

importance of conceptual understanding

• performance (e.g. error spotting)

• adaption (e.g. applying strategies to diff scenarios)

• development of new strategies

• motivation

explain Baroody & Dowker’s framework (for maths) (2003)

• conceptual understanding (comprehension of maths concepts, operations, and relations)

• computational fluency (skills in computing efficiently, appropriately, and flexibly; leads to automacy)

• strategic mathematical thinking (strategic competence and adaptive reasoning)

• productive disposition (inclination to see maths as sensible and useful, coupled with belief in diligence and self-efficacy)

how to promote conceptual understanding in maths?

• use of higher-order conceptually challenging questions

• use of plausible and meaningful contexts (possible need for cultural contextual differences)

• collaborative discussions of different strategies 

Newstead (1998) - collaboration and anxiety

• found that non-traditional approaches that promote discussion about strategies led to difference in social anxiety but not in problem solving anxiety

• anxiety about getting an answer right or wrong

• suggests entity theory of maths ability

what is the entity theory (of mathematical ability)?

• assumes ability is fixed, hereditary, and/or biological

what is incremental theory?

• assumes maths ability is malleable and can improve

what generates maths anxiety?

• having to perform a task rapidly that requires use of memory

• memorising formulae without understanding what they mean

• listening to a teacher explain a single isolated technique and then imitating repeatedly

motivations factors in gender differences (Stipek & Gralinski, 1991)

self-perception, attribution, and shame

• higher competence belief in boys

• higher expected performance in boys

• lower belief in value of effort for success by girls (belief they succeeded by luck)

• greater tendency to feel like hiding paper by girls

• BUT no difference in actual performance

parental expectations and gender differences

• parents have sex-based ideas about maths performance despite actual similarity (Parsons et al. 1982)

• parents beliefs even more important for shaping children’s self-perceptions than their own past performance

• Bleeker & Jacobs (2004) - mother’s predictions of child success in maths career was associated with adolescent perception of self-efficacy in STEM career 12 years later

role of gender stereotypes and maths ability

• 5-year olds have own-gender bias for who they perceive to be smart

• 6-year olds - only boys show own-gender bias; girls lose this bias

• girls beliefs are not correlated with beliefs about school achievement

• Bian, Leslie & Cimpian (2017)

explain Huguet & Raynor (2009)

• when told they were being tested on geometry girls performed worse than when they were told they were being tested on drawing ability (stereotype threat)

• but girls believed they were better at geometry (own-gender bias)

• boys had own-gender bias but showed stereotype threat result 

consequences of anxiety on performance (Ramirez et al., 2013)

• only maths anxious participants with good working memory showed worse performance on more complex tests (compromised their advantage)

• when problems start to get more complex, anxiety and stereotypes can start to affect performance

social context of conceptual change (Boaler, 2002)

• interviewed students and found they they often wanted to give up maths not because they struggled with it but because they don’t want to be perceived as received knowers

• implies that girls want to have agency in their learning (controversial - don’t boys need this too?)