Counting and reading in the early years of schooling

Gary Davis, University of Southampton, UK

Catherine Pearn, La Trobe University, Australia

Geraldine Price, University of Southampton UK

Keith Smith, University of Southampton, UK

Paper presented to SEMT 97, International Symposium on Elementary Mathematics Teaching. The Evaluation of Elementary School Mathematics. August 24-29, 1997 Prague, The Czech Republic

Results from interviews used to identify children needing to participate in a Mathematics Intervention program have highlighted a link between children needing to be included in both Mathematics Intervention and Reading Recovery. This perceived reading/mathematics link has implications for the type of intervention programs currently being offered to children "at risk". We report on a study in Australia and the United Kingdom in which young children were tested for counting and reading abilities, and suggest that unitizing plays a major role in both counting and reading.

In the learning disabilities literature, many authors have observed a between children's reading difficulties and their arithmetic problems (Ackermann et al, 1986; Geary, 1994; Kulak, 1993; Light and De Fries, 1995; Pearn, 1994). In the earliest years of schooling, children's counting strategies are a clear indicator of their development in arithmetic (Steffe et al, 1983, 1988; Wright, 1991). In particular, a child's ability to recognise and flexibly operate with composite units is recognised to be of critical importance in their arithmetic development (Steffe et al, 1983). On the other hand, readiness for reading is strongly linked to a child's phonemic awareness (Adams, 1995; Underwood and Batt, 1996).

We tested 29 students age 5 - 6 years at South Wonston primary school in Hampshire, U.K. to ascertain their counting abilities, their level of phonemic awareness, and their working memory (attention). Tests were administered independently.

TESTS

1. Clinical interviews

Children were interviewed, using the Initial Clinical Assessment Procedure-Mathematics-Level AA, an instrument designed by three teachers (Pearn, Merrifield, Mihalic, & Hunting, 1994). This instrument utilises tasks based on stages of the construction of the number sequence and their relationship to specific counting types. These 5 stages were developed in theoretical work by Steffe, Cobb, von Glaserfeld and Richards (1983) and documented by Wright (1991).

2. Reading tests

These were based an a phonological assessment battery (details on request). There were essentially two types. The first ascertained speed in naming pictures and speed in naming digits. The second was a phonological test, designed to ascertain phonemic awareness, which included alliteration, rhyme, and spoonerisms tests.

There are at least three ways of breaking up a word into its constituent sounds, and thus at least three possible forms of phonological awareness:

(Goswami & Bryant 1990)

The first way is to break up the word into its syllables and there is evidence to suggest that this poses little difficulty for most children (Liberman et al 1974). However, the majority of words children encounter when they first learn to read are monosyllabic and so awareness of syllables cannot be relevant to the constituent sounds of these words. In this case what is needed are smaller units than the syllable.

The second way to break up the word involves smaller phonological segments referred to as phonemes. A phoneme is the smallest unit of sound that can change the meaning of a word. Alphabetic letters typically represent phonemes and thus a string of alphabetic letters represents a sequence of phonemes. In order to see that a sequence of letters adds up to a meaningful word, the child has to understand that a word is in effect a collection of phonemes.

However, there is a third and intermediate kind of phonological awareness. Words can also be divided up into units that are larger than the single phoneme - units which themselves consist of two or more phonemes - but smaller than the syllable. It is usually possible to divide a syllable into two parts, an opening and an end section. The word "string", for example, has a clear beginning in its first three consonants, "str", and an equally distinct end section which contains the vowel and the last two consonants, "ing". This monosyllabic word, therefore, can be broken up into two phonological units, each made up of more than one phoneme. Units of this sort lie somewhere between a phoneme and a syllable, with the opening unit often referred to as "the onset" and the end unit "the rime".

3. Star Counting

The Star Counting Test was designed "to measure a person's ability to activate and inhibit processes in working memory" (de Jong and Das-Smaal, 1995, p.81). Each item in the Star Counting Test consists of a pattern of stars with arrows in between. The child starts counting the stars from the given number. The upward and downward arrows indicate the direction (forward or backward, respectively) in which the stars should be counted.

RESULTS

There was a high correlation between the variable "arithmetic" and the sum of variables "phonology+attention: r²= 0.73, p = 0.0001. This says that about 3/4 (precisely, 73%) of the variation in students' arithmetic performance on the modified Initial Clinical Assessment Procedure -Mathematics-Level AA test can be accounted for by the average variation in phonological awareness and attention. "Attention" alone correlates 50% with "arithmetic" (i.e., r2 = 0.50), whilst the correlation between "attention" and "phonology" is only 18% (r2 = 0.18). This lends support to the following point of view: there is a common unitizing feature of the brain that deals with arithmetic units and phonological units. Arithmetic development, unlike phonological awareness, is also significantly connected to attention.

The ability to operate flexibly with phonemes can be viewed as a problem with knowing the roles of the constituent parts of a syllable: the onset and the rhyme (Adams, 1995; Underwood and Batt, 1996). There are numerous constraints on the formation of onsets and rhymes in any language, but apparently almost no constraints on how these sub-units can be put together (Adams, 1995). It appears therefore that phonemic awareness is linked to the understanding of syllables as composite units of an onset and a rhyme. A child's readiness for reading appears to be a function of the child's ability to be aware of these sub-units and to operate flexibly with them. On the other hand children's difficulties in counting are also strongly linked to their developing ability to operate flexibly with composite numerical units. We hypothesise that a common feature in the observed connection between reading and arithmetic difficulties that many young children have may be a in a common "unitizing" feature of the brain. Moreover, this hypothesised unitizing feature, in the case of arithmetic, seems to have some connection with attentional aspects of the brain's functioning.

REFERNCES

Ackerman, P.T., Anhalt, J.M. and Dykman, R.A. (1986), Arithmetic automation failure in children with attention and reading disorders: Associations and sequela. Journal of Learning Disabilities, 19(4), 222-232.

Adams, M.J. (1995), Beginning to read. Thinking and Learning About Print. Cambridge, Mass.: MIT Press.

de Jong, P. F. & Das-Smaal, E. A. (1995), Attention and intelligence: The validity of the Star Counting Test. Journal of Educational Psychology. 87(1), 80-92

Geary, D. C. (1994), Children's mathematical development: research and practical applications. 2nd ed. Washington, DC: American Psychological Association.

Goswami, U. & Bryant, P. (1990), Phonological skills and learning to read. Hove: Lawrence Erlbaum Associates.

Kulak, A.G. (1993), Parallels between math and reading disabilities: Common issues and approaches. Journal of Learning Disabilities, 26(10), 666-673.

Liberman, I.Y., Shankweiler, D., Fischer, F.W. & Carter, B. (1974), Explicit syllable and phoneme segmentation in the young child. Journal of Experimental Child Psychology. Vol 18, p 201-212

Light, J. G. and DeFries, J. C. (1995), Co-morbidity of reading and mathematics disabilities: Genetic and environmental etiologies. Journal of Learning Disabilities, 28(2), 96-106.

Pearn, C. A. (1994), A connection between mathematics and language development in early mathematics. In G. Bell, R. Wright, N. Leeson & J. Geake (Eds.), Challenges in Mathematics Education: Constraints on Construction, Vol 2, pp. 463-470. Lismore, NSW: Southern Cross University.

Pearn, C. A., Merrifield, M., Mihalic, H., & Hunting, R. P. (1994), Initial clinical assessment procedure, Mathematics - Level A A (Years 1 & 2). Bundoora: The Clinical Mathematics Laboratory, La Trobe University.

Steffe, L. P. , Von Glasersfeld, E., Richards, J. & Cobb, P. (1983), Children's Counting Types: Philosophy, Theory, and Application. New York: Praeger.

Steffe, L. P., Cobb, P. & Von Glasersfeld, E. (1988), Construction of arithmetical meanings and strategies. New York: Springer-Verlag.

Underwood, G. & Batt, V. (1996), Reading and Understanding. Oxford: Blackwell.

Wright, R. J. (1991), The role of counting in children's numerical development, The Australian Journal of Early Childhood, 16(2), 43-48.

Back to CRME Home Page