What is the foundational knowledge that children rely on to provide meaning as they construct an exact symbolic number system? People and animals can quickly and accurately distinguish small exact quantities (i.e., 1 to 3). One possibility is that children’s ability to map small quantities to spoken number words supports their developing exact number system. To test this hypothesis, it is important to have valid and reliable measures of the efficiency of quantity-number word mapping. In the present study, we explored the reliability and validity of a measure for assessing the efficiency of mapping between small quantities and number words – speeded naming of quantity. Study 1 (N = 128) with 5- and 6-year-old children and Study 2 (N = 182) with 3- and 4-year-old children show that the speeded naming of quantities is a simple and reliable measure that is correlated with individual differences in children’s developing numeracy knowledge. This measure could provide a useful tool for testing comprehensive theories of how children develop their symbolic number representations.
Humans acquire a complex symbolic system for representing number. The symbolic number system has a visual code (i.e., Arabic digits) that is shared universally among the majority of numerate cultures, and spoken and written codes (i.e., number words) that vary across languages. The symbolic number system allows the representation, manipulation, and communication of exact quantities. Children’s learning of the symbolic number system is a central component of education: Knowledge of the symbolic number system forms the foundation of all STEM disciplines (i.e., Science, Technology, Engineering, and Mathematics) and is used extensively in everyday life. The question of how nonsymbolic quantity knowledge supports the development of the symbolic system is central to theories of numerical cognition (
Humans are sensitive to various features of objects that may also help to determine quantity, including spatial contour and continuous magnitude ( The approximate magnitude system has often been referred to as the approximate
Performance on tasks that tap the approximate magnitude system (e.g., which of two sets of dots has more?) is correlated with various mathematical outcomes (
In support of an early link between visual attentional processes and quantities, infants show evidence of representing exact quantities of 1, 2, and 3 (reviewed by
In this paper, we propose that the exact magnitude system helps children to connect non-symbolic quantities to their developing representation of the symbolic number system (
Many longitudinal studies have shown that verbal counting (i.e., recitation of the counting string), measured in kindergarten, predicts children’s acquisition of other numerical skills (e.g.,
Some work with children who have specific cognitive disabilities supports the link between the EMS and early numeracy development. For example, children and adults with Williams syndrome, a chromosomal disorder related to spatial processing, show worse performance than typically-developing children on mathematical measures that implicate quantity representations or mapping between quantities and symbols (
Children who have specific numerical deficits, for example, developmental dyscalculia, may also have difficulty with mapping symbols to the EMS.
Very few researchers have explored the relations between subitizing performance and mathematical tasks for typically-developing children. Researchers who have studied children’s counting, for example, have often not distinguished between quantities in the subitizing (i.e., 1 to 3) versus counting range (i.e., 4 to 9;
One limitation of existing research on non-symbolic exact number skills has been the lack of a reliable and valid measure of the EMS that can be used in a variety of situations, specifically, with different age groups, with different populations of children, and in both cross-sectional and longitudinal projects. Research on the AMS has benefitted, in contrast, from the availability of online measures (e.g., PanaMath;
Accordingly, we used a brief speeded naming task for small quantities, specifically 1, 2, and 3, termed speeded naming of quantities (i.e., SN-Quantity). We focused on quantities of 1, 2, and 3 because there is evidence that subitizing of 4 develops later (
In two studies with adults, the SN-Quantity task predicted unique variance in a measure of calculation fluency, even after controlling for speeded naming of letters and factors such as location of educational experience (Asia vs. Canada), gender, math anxiety, and age (
In Study 1, we hypothesized that speeded naming of quantities (SN-Quantities) would predict early mathematical skills for 5- and 6-year-old children, whereas speeded letter naming (SN-Letters) would predict early literacy skills. There is a large literature on the relation between speeded letter naming and early reading skill (
Two hypotheses were tested in Study 1: (a) speeded processing of non-symbolic quantities (dots) would predict early numeracy, but not early literacy performance, whereas (b) speeded processing of letters would predict early literacy, but not early numeracy performance (
Participants were 128 kindergarten children (70 boys; 58 girls) with a mean age of 5:10 years: months. They were recruited through contacts with child care centres and other early childhood learning facilities in a large Canadian city. At recruitment, parents provided information about home numeracy and literacy activities (see
Category / Name of Task | Study |
---|---|
Speeded Naming | |
SN-Quantities | 1, 2 |
SN-Letters | 1, 2a |
SN-Colors | 2b |
Nonverbal Cognitive skills | |
Spatial span | 1, 2 |
Nonverbal reasoning | 1 |
Verbal Cognitive skills | |
Phonological awareness | 1 |
Receptive vocabulary | 1, 2 |
Performance Measures | |
Word reading | 1 |
Nonsymbolic arithmetic | 1, 2 |
KeyMath Numeration | 1, 2 |
Object counting | 2 |
Verbal (rote) counting | 2 |
aCanadian children only at pre-test. bTurkish children at pre-test; all children at post-test.
Children were shown two pages of stimuli for each of the SN-Quantities and SN-Letters tasks. The SN-Quantities task included dots in groups of 1, 2, or 3, each presented 8 times per page in four rows of six. Speeded naming of pictures, letters, colors, and digits have been used in many versions of these tasks (e.g., in the CTOPP;
Cognitive tasks included both nonverbal and verbal measures.
Children completed two early numeracy measures (numeration and nonsymbolic arithmetic) and one early literacy measure (word reading). The KeyMath numeration test (
The nonsymbolic arithmetic task is a variant of the test used by
To measure word reading, children were given the Letter-Word Identification subtest of the Woodcock-Johnson Reading Mastery Test (
As shown in One child made 18 and 16 errors on the letter naming pages; this child’s data were excluded from further analyses.
Page | Time (s) |
Naming Errors |
||||||||
---|---|---|---|---|---|---|---|---|---|---|
Study 1: Quantity Naming | ||||||||||
1 | 126 | 22.8 | 6.6 | 12.2 | 52.5 | 123 | 0.16 | 0.56 | 0 | 4 |
2 | 127 | 23.1 | 7.8 | 8.6 | 76.4 | 124 | 0.34 | 0.99 | 0 | 8 |
Study 1: Letter Naming | ||||||||||
1 | 125 | 20.9 | 6.9 | 9.7 | 49.8 | 123 | 0.49 | 1.7 | 0 | 18 |
2 | 125 | 20.7 | 7.7 | 10.2 | 64.5 | 123 | 0.46 | 1.6 | 0 | 16 |
Study 2: Canadian Quantity Naming | ||||||||||
1 | 59 | 50.2 | 24.5 | 23 | 172 | 65 | 3.32 | 4.33 | 0 | 23 |
2 | 59 | 45.7 | 18.1 | 21 | 115 | 64 | 3.50 | 5.26 | 0 | 24 |
Study 2: Canadian Letter Naming | ||||||||||
1 | 57 | 39.7 | 15.9 | 18 | 79 | 66 | 3.39 | 4.95 | 0 | 24 |
2 | 55 | 38.6 | 16.2 | 19 | 112 | 62 | 2.84 | 4.96 | 0 | 24 |
Study 2: Turkish Quantity Naming | ||||||||||
1 | 78 | 60.6 | 26.5 | 29 | 168 | 86 | 2.93 | 4.18 | 0 | 19 |
2 | 76 | 55.1 | 21.6 | 27 | 129 | 84 | 2.89 | 4.58 | 0 | 22 |
Study 2: Turkish Colour Naming | ||||||||||
1 | 76 | 48.8 | 15.9 | 19 | 100 | 82 | 2.89 | 4.45 | 0 | 17 |
2 | 75 | 48.6 | 18.0 | 21 | 137 | 82 | 2.90 | 4.47 | 0 | 17 |
Performance was consistent across pages. The correlations for efficiency scores between Pages 1 and 2 were:
Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1. Age (months) | ||||||||||||
2. Income (Cdn$) | -.132 | |||||||||||
3. Gender | -.111 | .111 | ||||||||||
4. Vocabulary | .206* | .401** | -.089 | |||||||||
5. Sound Match | .203* | .288** | .180* | .465** | ||||||||
6. NV Reasoning | .266** | .010 | -.177* | .186* | .273** | |||||||
7. Spatial Span | .123 | -.013 | .014 | .050 | .285** | .337** | ||||||
8. Letter Word | .136 | .175 | .030 | .521** | .570** | .268** | .073 | |||||
9. Numeration | .221* | .199* | -.243** | .407** | .409** | .427** | .210* | .517** | ||||
10. NS Arithmetic | .196* | .296** | -.084 | .425** | .445** | .312** | .305** | .490** | .534** | |||
11. SN-Quantity | .142 | .117 | .006 | .361** | .551** | .370** | .188* | .650** | .654** | .574** | ||
12. SN-Letters | .153 | .049 | .040 | .331** | .552** | .335** | .157 | .742** | .524** | .427** | .790** | |
70.2 | 70260 | a | 92.27 | 11.22 | 4.30 | 3.85 | 17.99 | 6.20 | 6.49 | 1.11 | 1.25 | |
3.4 | 20715 | 12.16 | 5.44 | 2.37 | 1.74 | 6.54 | 1.90 | 3.07 | 0.28 | 0.39 | ||
126 | 124 | 126 | 128 | 124 | 128 | 128 | 128 | 124 | 127 | 125 | 124 |
a70 boys; 58 girls.
*
The correlations among the nine variables are shown in
The two speeded-naming tasks were correlated with most of the cognitive and academic measures. As expected, however, the two numerical measures were more highly correlated with speeded naming of quantities than with speeded naming of letters (for numeration, Comparisons between correlations were done using the online cocor calculator (
Each of the three performance measures (i.e., numeration, nonsymbolic arithmetic, and word reading) was used as the dependent measure in a hierarchical linear regression. The three control measures (i.e., age, parental income, and gender) were included in the first block of predictors. Domain-general predictors that are relevant for each domain were added in the second block, followed by the speeded naming task that was not specific to that domain (i.e., quantities for reading; letters for numeracy tasks) in the third block. The domain-specific speeded naming task was added in the final block. As shown in
Predictors | Hierarchical |
Final Model |
||
---|---|---|---|---|
β (step) | β | |||
Block 1: Control variables | ||||
Income | .128 | .169 | -.053 | .413 |
Age | .164 | .080 | -.045 | .470 |
Gendera | .033 | .724 | .015 | .808 |
Block 2: Domain-Specific | ||||
Vocabulary | .384*** | < .001 | .274*** | < .001 |
Sound Matching | .415*** | < .001 | .107 | .166 |
Block 3 | ||||
Speeded Naming - Quantities | .426*** | < .001 | .026 | .792 |
Block 4 | ||||
Speeded Naming - Letters | .582** | < .001 | .582*** | < .001 |
aCoded 1 = boys; 2 = girls.
*
Variable | Numeration ( |
Nonsymbolic Arithmetic ( |
||||||
---|---|---|---|---|---|---|---|---|
β (block) | β (final) | β (block) | β (final) | |||||
Block 1: Control variables | ||||||||
Income | .210* | .018 | .147* | .028 | .297** | .001 | .250** | .001 |
Age | .221* | .013 | .097 | .163 | .199* | .028 | .097 | .216 |
Gender1 | -.253*** | .004 | -.250*** | < .001 | -.077 | .390 | -.081 | .287 |
Spatial reasoning | .343*** | < .001 | .133 | .087 | .238** | .010 | .064 | .467 |
Spatial span | .111 | .191 | .071 | .308 | .235** | .008 | .189* | .017 |
Block 3: Speeded Naming – Letters | .428*** | < .001 | .036 | .740 | .324*** | < .001 | -.017 | .890 |
Block 4: Speeded Naming – Quantities | .523*** | < .001 | .523*** | < .001 | .461*** | < .001 | .461*** | < .001 |
aCoded 1 = boys; 2 = girls.
*
Variables included in the second block of the regressions were those that were expected to predict specific outcome measures. Thus, as shown in
Regression analyses for the two early numeracy measures are shown in
The results of Study 1 showed that the speeded naming of quantities task is a reliable and valid measure for 5- and 6-year-old children. Speeded naming of quantities predicted numeracy outcomes whereas speeded naming of letters predicted early reading. This dissociation between the two speeded naming tasks is especially impressive given the high correlation between them. Despite considerable shared measurement similarity, the core cognitive factors that influence speeded naming in each task appear to be distinct.
In Study 2, we used the speeded naming of quantities task with 3- and 4-year-old children. The goals were to determine whether younger children would be able to complete the task, whether it was reliable with the younger age group, and to establish construct validity for the measure for younger children. All of the children in this study were participants in a large project that involved training of verbal counting skills. The results of the intervention were reported in two papers (
Data for the early numeracy measures were completed at twice, first at the pre-test before a training session began, and second, at a post-test session six weeks later, after the intervention. Children met with an experimenter each week and counted as high as possible, then either (a) played one of two number games, (b) played a colour game, or (c) returned to the classroom. Performance on all the early numeracy measures improved over the six-week intervention, however, differential improvement in the number game conditions only occurred for verbal counting.
A total of 182 children participated in the larger study, 94 (46 boys; 48 girls) in Canada and 88 (48 boys; 39 girls; one not specified) in Turkey. The Canadian children were recruited from four child care centres and ranged in age from 34 to 62 months (
Parents who completed the consent form were asked to specify the level of education of both mother and father. Parents’ highest level of education was coded from 0 to 4, with 0 = less than high school, 1 = high school, 2 = community college degree, 3 = university degree, and 4 = postgraduate degree. The level of education of mothers and fathers was strongly related, χ2(16,
The stimuli used in the speeded naming tasks were exactly the same as in Study 1 for the quantity and letter naming versions. The speeded naming of colors (i.e., red, blue, and black) version of the task was also used in the current study, because pilot testing showed that the Turkish children were not familiar with letters. The other difference from Study 1 was that the procedure used to administer the measures was modified because the children were so much younger than in the first study. Specifically, the experimenter pointed to each stimulus and the child was asked to name them. If the child hesitated for more than (approximately) two seconds, the experimenter moved on to the next item and recorded an error for that item. As in Study 1, children were shown practice items before attempting the test. If they were unable to name the practice stimuli, then the testing was discontinued. Further details are given in
Children were asked to count as high as possible, ostensibly to help a puppet count. When the child stopped counting, they were prompted with the preceding number (e.g., if they stopped at 12, then the experimenter asked if they could count higher and said “12 and …” with a rising intonation. Highest count, allowing for one error, was used as the index of performance. For example, if children counted 1, 2, 3, 4, 5, 7, 8, they were credited with a highest count of 8. If, however, they counted 1, 2, 3, 4, 6, 8, 9, they were credited with a highest count of 6 (i.e., allowing for one error on 5).
Children were given a group of small animal figures and asked to place a certain number on a place mat in front of them. First, children were asked to show a set of small numbers, that is, 3, 4, 5, and 6 (small set); next they were asked for larger quantities, that is 7, 8, 9, and 10 (medium set). If children were successful on the previous two trials, they were asked for 14, 15, 16, and 17 (large set). Testing was always terminated after children made two unsuccessful attempts or if they said “I don’t know” for two trials in a row. Within each set size, a fixed random order was used, starting with 4 for the initial trial. The number of successful trials was used as the index of performance (i.e., 0 to 12), however, the majority of children were stopped before they reached the large set size.
Children were administered the tasks in two 15- to 20-min sessions which constituted the pre-test assessment for the intervention study and in one or two sessions at post-test, six weeks later (
Although all of the children who attempted the two pages of the task could name the stimuli, nevertheless, the speeded tasks were more challenging for 3- and 4-year-olds than for the older children in Study 1. The experimenters noted that it was sometimes difficult to ensure that children followed the instructions and occasionally response times were not valid if children did not understand the requirement to continue from horizontally from one item to the next. Average data for each page of each test is shown in
Variable | Canadian |
Turkish |
Comparison |
||||||
---|---|---|---|---|---|---|---|---|---|
Pre-test Scores | |||||||||
SN-Letters (items-per-s) | 56 | .68 | .25 | ||||||
SN-Colours (items-per-s) | 73 | .55 | .20 | ||||||
SN-Quantity (items-per-s) | 55 | .59 | .21 | 82 | .46 | .19 | 13.07 | 113.76 | < .001 |
Vocabulary (number correct) | 71 | 41.14 | 12.41 | 87 | 51.95 | 9.78 | |||
Spatial Span (sequences) | 55 | 2.29 | 2.02 | 82 | 2.18 | 1.49 | .13 | 124.51 | .719 |
Verbal Counting | 55 | 18.71 | 17.51 | 82 | 15.67 | 9.89 | 1.68 | 114.17 | .198 |
Nonsymbolic Arithmetic | 55 | 2.76 | 2.53 | 82 | 2.85 | 1.69 | .06 | 153.16 | .803 |
Numeration (number correct) | 55 | 3.22 | 1.64 | 82 | 2.12 | 1.73 | 13.76 | 124.19 | < .001 |
Object Counting | 55 | 4.49 | 3.58 | 82 | 2.48 | 2.89 | 13.17 | 138.86 | < .001 |
Post-test Scores | |||||||||
SN-Quantity (items-per-s) | 48 | .71 | .22 | 38 | .47 | .21 | 25.08 | 84 | < .001 |
SN-Colours (items-per-s) | 48 | .71 | .19 | 38 | .55 | .21 | 14.81 | 84 | < .001 |
Verbal Counting | 48 | 21.15 | 10.01 | 38 | 16.58 | 8.10 | 5.20 | 84 | .025 |
Nonsymbolic Arithmetic | 48 | 3.60 | 2.29 | 38 | 3.45 | 2.23 | .10 | 84 | .751 |
Object Counting | 48 | 6.21 | 3.13 | 38 | 2.50 | 2.50 | 35.43 | 84 | < .001 |
Numeration | 48 | 3.54 | 1.50 | 38 | 2.68 | 1.40 | 7.35 | 84 | .008 |
Mean performance on the early numeracy and cognitive tasks are shown in
Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|
1. Parent Edu | -.076 | .281* | -.425** | .099 | .239* | .162 | .285** | .036 | .075 | .183 | |
2. Age (months) | -.210* | .464** | -.005 | .440** | .424** | .265* | .327** | .392** | .404** | .360** | |
3. Vocabulary | .162 | .395** | -.225* | .357** | .493** | .304** | .384** | .417** | .407** | .419** | |
4. Country | -.468** | .150 | -.092 | -.104 | -.510** | -.238* | -.524** | .002 | -.462** | -.437** | |
5. Spatial Span | -.021 | .482** | .319** | .039 | .328** | .190 | .332** | .260* | .397** | .180 | |
6. Numeration | .137 | .448** | .490** | -.298** | .394** | .366** | .602** | .514** | .458** | .316** | |
7. Verbal Count | .079 | .357** | .363** | -.071 | .391** | .549** | .595** | .337** | .431** | .274** | |
8. Object Count | .161 | .412** | .454** | -.251** | .443** | .682** | .551** | .417** | .571** | .397** | |
9. NS Arithmetic | -.134 | .435** | .371** | .111 | .474** | .404** | .435** | .486** | .282* | .209 | |
10. SN-Quantitya | -.007 | .518** | .451** | -.220* | .503** | .579** | .414** | .591** | .414** | .583** | |
11. SN-Control | .007 | .395** | .447** | .075 | .501** | .379** | .361** | .441** | .342** | .579** |
aAt pretest, the correlation for the Canadian children between SN-Quantities and SN-Letters was
*
Test-retest reliabilities for efficiency scores were calculated for those subsets of children who did both versions of a measure at pre- and post-test. For quantities, the test-retest correlation was
As in Study 1, we used multiple regression to assess whether speeded naming of quantities was uniquely related to the numeracy outcomes, after controlling for individual differences in visual-spatial attention (i.e., spatial span), linguistic skills (i.e., vocabulary), and demographic (i.e., age and group) factors. Because the control speeded naming task was different for the two groups at pre-test, we calculated the
As shown in Three students whose verbal counting scores were outliers (i.e., much higher than expected) were excluded from the analysis at pretest because they had very large residuals and thus influenced the results.
Variable | Verbal Counting |
Object Counting |
Numeration |
Nonsymbolic Arithmetic |
||||
---|---|---|---|---|---|---|---|---|
β | β | β | β | |||||
Model 1 | ||||||||
Parent Education | -.019 | .846 | .057 | .515 | .005 | .954 | -.110 | .242 |
Age | .142 | .180 | .221 | .019 | .293 | .002 | .160 | .112 |
Countrya | -.100 | .301 | -.263 | .002 | -.330 | < .001 | .042 | .645 |
Vocabulary | .270 | .008 | .192 | .038 | .131 | .145 | .312 | .002 |
Spatial Span | .092 | .379 | .186 | .038 | .252 | .004 | .220 | .023 |
SN-Control | .162 | .127 | .193 | .037 | .110 | .223 | .021 | .831 |
Model 2 | ||||||||
Parent Education | .026 | .794 | .094 | .274 | .038 | .654 | -.089 | .347 |
Age | .053 | .622 | .141 | .139 | .223 | .019 | .116 | .272 |
Country | .022 | .836 | -.163 | .072 | -.242 | .007 | .098 | .327 |
Vocabulary | .230 | .022 | .145 | .112 | .089 | .317 | .286 | .005 |
Spatial Span | .021 | .843 | .152 | .084 | .222 | .011 | .201 | .039 |
SN-Control | .049 | .656 | .088 | .370 | .017 | .860 | -.038 | .727 |
SN-Quantity | .334 | .009 | .290 | .009 | .255 | .018 | .162 | .180 |
aCountry coded 1 = Canada, 2 = Turkey.
Variable | Verbal Counting |
Object Counting |
Numeration |
Nonsymbolic Arithmetic |
||||
---|---|---|---|---|---|---|---|---|
β | β | β | β | |||||
Model 1 | ||||||||
Age | .108 | .419 | .180 | .094 | .257 | .037 | .270 | .037 |
Countrya | -.203 | .088 | -.475 | < .001 | -.221 | .041 | .026 | .817 |
Vocabulary | .176 | .166 | .131 | .194 | .224 | .053 | .274 | .025 |
Spatial Span | .018 | .880 | .162 | .097 | .092 | .405 | .018 | .878 |
SN-Control | -.009 | .943 | .038 | .716 | -.019 | .875 | -.010 | .934 |
Model 2 | ||||||||
Age | .050 | .706 | .132 | .213 | .185 | .114 | .242 | .064 |
Country | -.098 | .427 | -.389 | < .001 | -.092 | .395 | .077 | .524 |
Vocabulary | .156 | .208 | .115 | .243 | .199 | .069 | .264 | .030 |
Spatial Span | -.044 | .715 | .110 | .254 | .015 | .888 | -.013 | .914 |
SN-Control | -.107 | .427 | -.042 | .692 | -.139 | .243 | -.057 | .661 |
SN-Quantity | .334 | .021 | .275 | .017 | .409 | .002 | .159 | .256 |
aCountry coded 1 = Canada, 2 = Turkey.
In this study, between 85% and 92% of the 3- and 4-year-old children were successful on the speeded naming tasks (depending on which version) and their performance was consistent across pages. Multiple regression analyses (controlling for age, gender, parents’ education, country, and spatial span) indicated that speeded naming of quantities was a significant predictor of children’s performance on object counting, verbal counting, and numeration, both at pre-test and after a six-week intervention. All of these measures involve children’s knowledge of the number words, with the object counting and numeration measures requiring mapping between number words and quantities. In contrast, speeded naming of quantities did not predict nonsymbolic arithmetic. This measure involves memory and one-to-one matching processes, but does not require children to use number names (
The goal of the present research was to determine whether a measure of children’s efficiency on speeded naming of small quantities was a reliable and valid measure for 3- to 6-year-old children. We used a speeded naming task that is assumed to index the efficiency with which children access the identity of small exact quantities. In adults, the efficiency of access to small quantities via naming is referred to as subitizing (
In support of the domain-specific nature of speeded naming, in Study 1, speeded naming of letters predicted word reading whereas speeded naming of quantities predicted numeracy measures. A large literature links word reading ability to speeded naming of letter names (i.e., RAN or rapid automatized naming;
Developmentally, the SN-Quantity task was easier for older than for younger children. Speeded naming of quantities improved with age, as did the various numeracy measures. Longitudinal studies which measure both speeded naming of quantities and other numeracy measures across time are needed to better understand whether any causal links exist among these indices, or whether shared variance can be attributed to improvements in more general cognitive abilities (
The present results are consistent with the results of
For somewhat older children, a similar measure of speeded naming of the quantities 1, 2, and 3 predicted more advanced symbolic number knowledge, specifically number comparison (i.e., which is larger 4 or 7?;
Although the present results show that the SN-Quantity task is reliable and valid for 3- to 6-year-old children, modifications were needed to help the younger children successfully perform the task. Simpler versions, for example, providing a smaller set of items per page, would reduce the task demands further. Researchers have used less complex mapping tasks, for example, choosing between two quantities to match a spoken word or digit to evaluate the earliest levels of symbol-quantity mapping abilities in young children (
Further research should be undertaken to explore the limits of speeded quantity naming as a predictor of mathematical skills. In Study 1, speeded naming of quantities was a predictor of nonsymbolic arithmetic. In Study 2, speeded naming of quantities did not uniquely predict nonsymbolic arithmetic (although the simple correlation was significant), instead, speeded quantity naming predicted unique variance in tasks which required symbolic number knowledge. Older children, as in Study 1, are more likely to use counting in nonsymbolic arithmetic tasks (
In the present paper, we focused on a very simple index of the mapping between the earliest symbolic number codes (i.e., verbal number words) and nonsymbolic quantities. The results show that individual differences in the efficiency of naming small exact quantities predicts children’s developing number skills from ages three to seven (
The primary focus of the research project for which the data for Study 2 were collected was a number game intervention that was intended to support children’s verbal counting skills (
Group | Pre-test |
Post-test |
||||
---|---|---|---|---|---|---|
Canadian | Turkish | Total | Canadian | Turkish | Total | |
94 | 88 | 182 | 78 | 45 | 123 | |
Quantities | ||||||
Administered | 66 | 86 | 152 | 65 | 42 | 107 |
Completed | 58 | 78 | 136 | 57 | 42 | 99 |
Valid Score | 58 | 82 | 140 | 53 | 41 | 94 |
Letters/Coloursa | ||||||
Administered | 66 | 87 | 153 | 70 | 43 | 113 |
Completed | 58 | 76 | 134 | 62 | 43 | 105 |
Valid Score | 56 | 73 | 129 | 61 | 42 | 103 |
aAt pre-test, Canadian children did letter naming and Turkish children did colour naming. Both groups did colour naming at post-test.
Corrected scores for each page were calculated as [24 – errors]/response times. Pages with more than 12 errors (
As shown in
Data collection for Study 1 was supported by a grant from Healthy Child Manitoba to S.-L. Skwarchuk and J.-A. LeFevre, by research funding from the University of Winnipeg to S.-L. Skwarchuk, and by the Social Sciences and Humanities Research Council of Canada (SSHRC) through scholarships to C. Sowinski and a grant to J.-A. LeFevre, J. Bisanz, D. Kamawar, S.-L. Skwarchuk, and B. L. Smith-Chant. Data collection for Study 2, and the writing of the manuscript, was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) to J.-A. LeFevre.
All the speeded naming tasks are provided in the supplementary materials, along with the instructions and practice pages (for access see
The authors have declared that no competing interests exist.
The authors have no additional (i.e., non-financial) support to report.