Development and use of a Numeracy Questionnaire for parents

3.1 Introduction

Researchers studying children and adults with WS frequently encounter problems in

collecting data from sufficiently large samples, because obtaining large sets o f data

involves either inviting individuals with WS and their parents or carers to travel very long distances to the research laboratory or the experimenter travelling to the homes of the

individuals with WS. Both means of data acquisition are time-consuming and costly. Furthermore, because individuals with WS have difficulties in concentrating for long

periods of time, it is not possible to run a large battery of tests examining different aspects of a given domain of cognitive functioning within a single session. Hence,

multiple testing sessions are often necessary in order to complete a given research project. The above limitations often compromise statistical power and multiple measures

of the same or similar constructs. This complication arises because only a limited number o f children or adults with WS can be tested for any one project and the investigators must

limit the number of tests on the protocol in order to be left with a meaningful data set that is not unduly affected by participant’s lack o f concentration or fatigue.

One way o f collecting large sets of data is by using a postal approach to ask parents to fill in a questionnaire about their child. Gaining insight into children’s development through

parent report has been successfully used to assess and study infants’ and young children’s

language and communicative development by means o f the now famous MacArthur

Communicative Development Inventories (GDI). This standardized parent report measure

has been widely used to assess both typical and atypical trajectories o f language and communicative development (Charman, Drew, Baird, & Baird, 2003; Feldman et al.,

measures of expressive vocabulary filled out by parents on the GDI correlate well with direct measures of vocabulary obtained through controlled experimental testing in the

laboratory, demonstrating the predictive validity o f the GDI (Ring & Fenson, 2000).

Another commonly used parent report o f cognitive function is the ‘Children’s Behaviour

Questionnaire’ which measures the development of temperament between the ages o f 3 and 7 (Rothbart, Ahadi, Hershey, & Fisher, 2001). Moreover, the ‘Child Development

Inventory’ (originally referred to as the ‘Minnesota Child Development Inventory’) is

another popular parent report measure. This inventory asks parents to answer questions about a number of different aspects of their child’s development, such as social, motor,

language, reading and number development (Ireton & Thwing, 1997).

Certainly, parent report measures cannot replace experimental measures of children’s

development, as they are only indirect, but they can complement them. Shortcomings of questionnaires include possible response biases, where parents might either over- or under-estimate their child’s ability in a given domain. Further problems can arise when

there is no significant agreement between the two parents or between a parent and a

caregiver close to the child.

Notwithstanding these problems, the use o f parent report measures is a cost-effective means o f collecting data from a large sample o f children, to supplement experimental

data on necessarily smaller groups. Might it be possible to construct a parent report measure o f children’s number development? In the context of the current thesis, such a

measure would allow for the exploration o f number abilities and their development in a

large group o f children with WS. These measurements could then be compared to those

obtained from parents o f typically developing children. Given the sparse information on the number abilities o f children and adults with WS, the completion o f such a

questionnaire by a large number o f parents with children with WS would provide a better

description o f the number abilities of children with WS. A detailed survey of the

questionnaire had yet been designed, used or published, with the exception of the ‘Child

Development Inventory’ (Ireton & Thwing, 1997) which only contains a few items relevant to number development. A Numeracy Questionnaire for parents was therefore

constructed and piloted for the explicit purposes of this thesis. The construction of this

questionnaire is discussed in the following section. A copy o f the questionnaire can be

found in Appendix A.

3.2 The construction of the Numeracy Questionnaire

Having established that the use of a parent report measure of children’s numerical skills

would help to describe further the level o f numerical competence among children with

WS and how their number development may diverge or converge with development in typically developing (TD) children, it was necessary to decide on the constructs of

number development that should be tapped by such a questionnaire, especially since there were no pre-existing questionnaires on this topic.

A decision was made to focus the study on four main areas: 1. Counting Skills; 2.

Understanding o f the Cardinality Principle; 3. Addition and subtraction and 4. Everyday number. Counting and understanding o f the cardinality principle were included as both

the ability to count and the ability to understand the meaning of counting (cardinality principle) are essential for numerical proficiency. Addition and subtraction were chosen

as these are typically the first arithmetic operations that children learn. Success in these

basic arithmetic skills is therefore crucial in children’s development o f number skills (Bryant, 1995).

In comparison with the above, the definition of the fourth construct (Everyday number)

was of necessity rather more loosely defined. Here, the aim was to ask parents about their child’s competence at handling everyday situations that entail a quantitative dimension.

addition to questions about knowledge of prices, differences between people’s ages and

their child’s comprehension of physical distance.

In addition to these four main constructs, a number o f additional questions were included, requesting parents to indicate whether their child was better at reading or number and

whether s/he preferred reading or number. These questions were included in order to

establish the extent to which number is a particularly vulnerable domain of cognitive

functioning in WS and whether children with WS encounter more problems with number than they do with reading. Given their children’s relative proficiency in language (see

Chapter 1) it could be hypothesized that more parents of children with WS will indicate that their child is better at reading than number than the reverse.

The answer formats of the questions were varied in an effort to avoid the possibility that respondent parents would answer all questions in a similar way (a phenomenon

commonly referred to as ‘response set’). Although varying the type of answer formats has the advantage o f controlling for the occurrence o f a ‘response set’, it has the disadvantage

of making answers to different questions tapping the same construct more difficult to compare with one another. Some answer formats allowed for the scoring of ordinal data,

where parents were asked to choose a number on a scale of 1-10. Other answer required parents make categorical judgments. These two types of answer formats are difficult to

compare, since one yields ordinal data while the other provides categorical data.

3.3 Questions and Hypotheses

Several questions and hypotheses motivated the design o f the Numeracy Questionnaire

for parents. The primary interest in the context of this thesis was the use o f this

measurement tool with parents of children with WS. In addition, this chapter represents the first attempt to develop a parent report measure o f children’s number development.

and discussed in the context of how the questionnaire might be altered and improved for future use and eventual standardisation.

Against the background of the evidence from the standardized tests reported in Chapter 2

it was predicted that:

1. The parents of children with WS will give their children lower scores than the parents o f typically developing children.

Related to this prediction is the following question: How substantial is the developmental

delay in numeracy skills among children with WS?

2. Parents of children with WS will indicate that their children show particular difficulties

with cardinality, addition and subtraction, while being relatively proficient at counting (since rote counting does not require an understanding of number itself).

3. Parents of children with WS will judge their children to be better at reading than

number.

Experiment 2

3.4 Methods

3.4.1 Data collection

The questionnaire was mailed to over 100 parents of children with WS. A letter

explaining the purpose o f the questionnaire was enclosed as well as a stamped addressed

envelope to enable parents to return the questionnaire to the experimenter with relative

ease. The addresses of the parents were obtained through the Williams Syndrome

all addresses were o f parents with children who had tested positive for WS by means of

the FISH genetic test. Parents of typically developing children were contacted through an institution-wide electronic mail appeal for help with the study at the Institute of Child

Health, London. All staff at the Institute o f Child Health received a brief e-mail

describing the purpose o f the study and asking whether any parents of 3-7 year old

children were interested in helping by completing the Numeracy Questionnaire. Such

interested parents were encouraged to either e-mail or telephone the investigator in order

to receive a copy of the questionnaire. This Institute-wide electronic e-mail also helped to recruit additional parents from outside the Institute o f Child Health, since various

employees kindly contacted their friends or family to recruit additional, interested

parents.