maths development 2 - home numeracy and quantitative skills and WM Flashcards
home numeracy environment definition
parents’ involvement with mathematics, including:
- mathematical experiences
- artifacts
- parent-child talk
the mathematics-related activities that parents share in the home
researchers use a range of semi-distinct, but overlapping, terminology or use alternative conceptualisations for categorizing activities (e.g. foundation vs advanced)
no consensus on the specific components that should be included to capture this parents’ involvement in home numeracy
based on home literacy environment - where research came much earlier
observational studies of the home numeracy environment
parent number talk: parent utterances of number words (e.g., one, two, three) and words related to magnitude comparison (e.g., more, less) during children’s infancy and early toddlerhood
quantify mathematical language use by counting the number of times parents make mathematics related utterances based on observations of parents and children either in the home or a more controlled laboratory setting
but hard to know whether they would normally act this way or not- doesn’t work as well as with reading studies
study of home numeracy environment - 2 types of activities in the home numeracy environment
The home numeracy environment refers to the mathematics-related activities that parents share in the home
Direct (formal) activities: Explicit instructional activities directly targeting numeracy/mathematics
Indirect (informal) activities: Everyday activities that incidentally involve numeracy/mathematics
home numeracy environment questionnaire - 2 parts to it with examples
direct (formal):
- I teach my child to count objects to indicate quantity
- I teach my child to recognize Arabic numerals
- I teach my child to sort and classify objects by colour, shape and size
indirect (informal):
- When we shop together, I discuss the price with my child
- We sing counting songs
- We play games that involve counting, adding, or subtracting
- we play board games or cards
ISSUE:
- if child has already mastered a skill, they say they don’t practice it - the fact they are already able is not captured in the study
home numeracy environment and maths achievement correlations (2)
small, positive relation between home numeracy environment and children’s maths achievement:
- associations vary widely between studies
- varies based on age
but lots of studies don’t look past the age at the start of school - this could be very confounded by different later education
type of activity matters:
- advanced home numeracy activities associated with children’s maths skills
- basic activities were NOT associated
home numeracy environment - 4 parental factors
mothers vs fathers
parent education level
parent attitudes and expectations
parent maths anxiety
home numeracy environment - parent factors - mothers vs fathers
Mothers vs Fathers (Mutaf-Yidiz et al., 2021)
most home numeracy studies only have data from mothers
when both parents participate, only mothers’ reports of formal activities linked to children’s maths skills
home numeracy environment - parent factors - parent education level
mothers’ education levels predict maths activities beyond the home maths environment
mothers with higher education levels provide advanced numeracy activities to their children more frequently
home numeracy environment - parent factors - parents attitudes and expectations
parents’ beliefs and expectations regarding children’s maths abilities and the importance of maths influence their children’s maths beliefs and performance
also cultural differences around whether it is the parents role or the schools to teach them maths
also differences in cultures around importance of maths –> including gender differences (e.g. maths is important for boys)
home numeracy environment - parent factors - parent maths anxiety
parents who are maths anxious may engage in fewer numeracy and mathematics activities at home
maths anxiety moderates relation between home numeracy environment and children’s numeracy skills
early numeracy skills variation in classrooms
Large individual differences, even as early as kindergarten
On average, 7-year span in ability within a simple primary classroom
Numerous studies have shown that children who enter kindergarten with poor numeracy skills do not catch up
early maths skills as a predictor (3)
early maths skills predict:
- later maths skills (strong)
- later reading skills
- later academic performance (strongest predictor)
early maths skills impact beyond school years
Numeracy skills are important for life outcomes:
- employment opportunities
- obtaining and retaining employment,
- promotion opportunities,
- owning a home
- income
- quality of healthcare
- mental health
predictors of numeracy: pathways to mathematics model
Summarises early cognitive precursors to later numeracy skills
Three pathways:
- Quantitative
- Working Memory
- Linguistic Skills
path to concurrent and later maths achievement
quantitative skills (5)
Early numeracy skills of quantifying, labeling, comparing, and manipulating sets
How have quantitative skills been measured:
- Subitising
- Non-symbolic arithmetic
- Counting
- Estimation
- Number comparison
quantitative skills - subitising
Quickly determining the number of items in a small set without counting
Subitising in preschool/kindergarten predicted mathematics outcomes 2 years later (LeFevre et al., 2010)
at a point you can’t get any better - most people around 5 items and then use automatic grouping strategies
quantitative Skills - Non-Symbolic Arithmetic
Adding/subtracting with manipulatives
Non-symbolic arithmetic in preschool/kindergarten predicted mathematics outcomes 2 years later (LeFevre et al., 2010)
e.g. “how many animals are in the barn now”
Quantitative Skills - counting
present children with dots; ask them to count (like with subitising but instead count rather than know how many there are without counting)
counting in kindergarten predicted arithmetic performance in Grade 1
quantitative skills - estimation
estimate the number of dots without counting
told they weren’t expected to be exactly correct and instead guess
estimation in kindergarten predicted arithmetic performance in Grade 1
quantitative skills - number comparison
Common measure of quantitative skill
Numerical comparison proposed as key foundational capacity for numeracy
Two types of tasks: Non-symbolic and symbolic
quantitative skills - number comparison - non-symbolic
compare one set of dots to another - e.g. “which has more dots”
useful when working with younger children
non-symbolic number comparison in kindergarten predicted arithmetic performance in Grade 1 and mathematical fluency in Grade 2
quantitative skills - number comparison - symbolic
compare two Arabic digits - e.g. “which is larger”
symbolic number comparison in kindergarten predicted many maths outcomes:
- in Grade 1 (i.e., mathematical achievement, arithmetic fluency, computation, word problems)
- in Grade 2 (i.e., arithmetic, word problems, mathematical fluency, mathematical reasoning)
is symbolic or non-symbolic number comparison a better predictor
symbolic number comparison demonstrates more predictive power than non-symbolic
working memory and maths skills
WM = cognitive system responsible for the active maintenance and temporary storage of task-relevant information
measure = span tasks –> determine how many items can be held in working memory
in mathematics, working memory supports:
- performance of multiple steps (counting, arithmetic, problem solving)
- ability to keep track of intermediate results
- ability to visualise problems and solutions
Two common subtypes measured:
- visuospatial working memory
- verbal working memory
test of visuospatial working memory and maths
test = copy the path the frog takes (like the simon game) - go until failure
VS WM= responsible for the maintenance and storage of visual and/or spatial information
VS WM in preschool and kindergarten predicted mathematics outcomes 2 years later (i.e., calculation, numeracy, geometry, measurement)
VS WM in kindergarten predicted arithmetic and word problem performance in Grade 1
verbal working memory and maths
task: repeat these numbers in reverse - go until failure
verbal WM = responsible for the maintenance and storage of verbal information
visuospatial and verbal working memory together and maths skills (3)
Kindergarteners’ working memory (composite of visuospatial and verbal) predicted performance and growth in maths from Grades 1-9
Visuospatial and verbal in kindergarten predicted word problems and applied problems, respectively, in Grade 1
Visuospatial and verbal working memory contribute equally to skill in mathematics
linguistic skills and maths
early linguistic skills:
- phonological awareness = knowledge of the sound structure of language
- receptive vocabulary = words the child understands
linguistic skills support:
- learning of mathematics vocabulary (e.g., number names and numerals, more than/less than/equal to)
- learning rules of the number system
linguistic skills tasks (2)
“point to the lamb” - pick the correct image out of an array = Peabody Picture Vocabulary Test
“say bold without saying /b/” = Comprehensive Test of Phonological Processing
linguistic skills (receptive vocab and phonological awareness) as predictors (3)
linguistic skills in preschool and kindergarten predicted mathematics outcomes 2 years later
kindergarten phonological awareness predicted Grade 1 word-problem performance
phonological awareness at school entry found to be strongest predictor of both mathematics grades and national mathematics test scores 2 years later
summary of 3 pathways to maths
- strong support for quantitative skills, working memory, and linguistic skills as kindergarten predictors of later numeracy
- relations between working memory and linguistic skills in kindergarten and later mathematics skill are mediated by quantitative skills
- children vary considerably in their numeracy skills
- in combination, the three pathways account for a lot of the variability in arithmetic (44-79%), word problems (53-61%), number system knowledge (48-64%), and geometry (26-84%) 1+ years later
- performance on these measures can be used to identify which children are likely to struggle to gain numeracy skills
early intervention for maths - why intervene
change developmental trajectory
improve numeracy outcomes
> 60% of children identified as having maths difficulties in kindergarten continued to have difficulties in Grade 5
early intervention for maths - related to the three pathways - (3)
only interventions to improve numeracy outcomes involved training on quantitative skills (subitising, counting, non-symbolic arithmetic, number comparison)
domain-general interventions for working memory and linguistic skills have not convincingly been shown to improve numeracy
children’s working memory and linguistic skills can help guide selection of suitable interventions
criteria for evaluating interventions (6) - and stat for meaningful intervention effect
- studies must use children identified as at risk, based on low numeracy performance, and contain an explicit, quantitative criterion to define low performance
- studies must include an at-risk comparison group
- group assignment (intervention/control) must be determined based on random assignment
- studies must include a pre-test, intermediate post-test, and delayed post-test
- numeracy outcome measures must be reliable, valid, and unbiased
- interventions must demonstrate numeracy gains, compared to an appropriate control group, that are both statistically significant and meet the Institute of Educational Sciences criterion for meaningful intervention effects (g ≥ 0.25)
–> Hedge’s g statistic is used to measure the effect size for the difference between means
