maths development 2 - home numeracy and quantitative skills and WM

Question 1

home numeracy environment definition

Answer 1

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

Question 2

observational studies of the home numeracy environment

Answer 2

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

Question 3

study of home numeracy environment - 2 types of activities in the home numeracy environment

Answer 3

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

Question 4

home numeracy environment questionnaire - 2 parts to it with examples

Answer 4

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

Question 5

home numeracy environment and maths achievement correlations (2)

Answer 5

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

Question 6

home numeracy environment - 4 parental factors

Answer 6

mothers vs fathers
parent education level
parent attitudes and expectations
parent maths anxiety

Question 7

home numeracy environment - parent factors - mothers vs fathers

Answer 7

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

Question 8

home numeracy environment - parent factors - parent education level

Answer 8

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

Question 9

home numeracy environment - parent factors - parents attitudes and expectations

Answer 9

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)

Question 10

home numeracy environment - parent factors - parent maths anxiety

Answer 10

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

Question 11

early numeracy skills variation in classrooms

Answer 11

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

Question 12

early maths skills as a predictor (3)

Answer 12

early maths skills predict:

• later maths skills (strong)
• later reading skills
• later academic performance (strongest predictor)

Question 13

early maths skills impact beyond school years

Answer 13

Numeracy skills are important for life outcomes:
- employment opportunities
- obtaining and retaining employment,
- promotion opportunities,
- owning a home
- income
- quality of healthcare
- mental health

Question 14

predictors of numeracy: pathways to mathematics model

Answer 14

Summarises early cognitive precursors to later numeracy skills
Three pathways:

• Quantitative
• Working Memory
• Linguistic Skills

path to concurrent and later maths achievement

Question 15

quantitative skills (5)

Answer 15

Early numeracy skills of quantifying, labeling, comparing, and manipulating sets

How have quantitative skills been measured:

• Subitising
• Non-symbolic arithmetic
• Counting
• Estimation
• Number comparison

Question 16

quantitative skills - subitising

Answer 16

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

Question 17

quantitative Skills - Non-Symbolic Arithmetic

Answer 17

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”

Question 18

Quantitative Skills - counting

Answer 18

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

Question 19

quantitative skills - estimation

Answer 19

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

Question 20

quantitative skills - number comparison

Answer 20

Common measure of quantitative skill

Numerical comparison proposed as key foundational capacity for numeracy

Two types of tasks: Non-symbolic and symbolic

Question 21

quantitative skills - number comparison - non-symbolic

Answer 21

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

Question 22

quantitative skills - number comparison - symbolic

Answer 22

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)

Question 23

is symbolic or non-symbolic number comparison a better predictor

Answer 23

symbolic number comparison demonstrates more predictive power than non-symbolic

Question 24

working memory and maths skills

Answer 24

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

Question 25

test of visuospatial working memory and maths

Answer 25

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

Question 26

verbal working memory and maths

Answer 26

task: repeat these numbers in reverse - go until failure

verbal WM = responsible for the maintenance and storage of verbal information

Question 27

visuospatial and verbal working memory together and maths skills (3)

Answer 27

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

Question 28

linguistic skills and maths

Answer 28

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

Question 29

linguistic skills tasks (2)

Answer 29

“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

Question 30

linguistic skills (receptive vocab and phonological awareness) as predictors (3)

Answer 30

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

Question 31

summary of 3 pathways to maths

Answer 31

• 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

Question 32

early intervention for maths - why intervene

Answer 32

change developmental trajectory

improve numeracy outcomes

> 60% of children identified as having maths difficulties in kindergarten continued to have difficulties in Grade 5

Question 33

early intervention for maths - related to the three pathways - (3)

Answer 33

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

Question 34

criteria for evaluating interventions (6) - and stat for meaningful intervention effect

Answer 34

1. studies must use children identified as at risk, based on low numeracy performance, and contain an explicit, quantitative criterion to define low performance
2. studies must include an at-risk comparison group
3. group assignment (intervention/control) must be determined based on random assignment
4. studies must include a pre-test, intermediate post-test, and delayed post-test
5. numeracy outcome measures must be reliable, valid, and unbiased
6. 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