Cognitive predictors at kindergarten of first grade math achievement

Passolunghi, Maria Chiara, and Silvia Lanfranchi. "Domain‐specific and domain‐general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade." British Journal of Educational Psychology82.1 (2012): 42-63.‏

A wide scale research looking into the links between different cognitive abilities assessed at kindergarten and math achievement at the end of first grade.  Seventy children participated in this study.

 At the beginning of the last year of kindergarten (children aged 5.2 years) the children were  administered a battery of cognitive tests (Vocabulary and Block Design from the Wechsler , and tests assessing working memory, verbal and visuo-spatial short-term memory, phonological ability, verbal counting ability, and processing speed).   

At the end of the last year of kindergarten (children aged 5.8 years)    numerical competence was assessed (by tests assessing concepts of comparison, classification, one-to-one correspondence, seriation, the use of number words, counting and general understanding of numbers).

At the end of the first year of primary school (children aged 6.6 years)    mathematical achievement was assessed (by tests assessing spatio-temporal analysis, seriation, and classification (i.e., the ability to order spatio-temporal sequence and to order objects from smallest to largest), acquisition of the concept of natural numbers (i.e., to be able to position numbers on the ‘number line’), understanding of basic arithmetic operations (+, −), and the capacity to locate objects in space).

The paper adds some background on the assessed cognitive abilities:

Phonological awareness and mathematics  - one study found a significant relationship between phonological awareness (rhyme detection and initial consonant detection) assessed at 4 and 5 years of age and mathematical competencies as judged by teachers at the beginning of first grade.  Another study found that phonological awareness scores (rhyme tasks) assessed at 5 years of age predicted reading as well as arithmetic abilities 1 year later. Yet another study reported that phonological processing (measured by rapid digit naming, first sound matching, and last sound matching) was a unique determinant of fact fluency but did not predict other aspects of math performance (e.g., story problems).  There are also studies showing that phonological awareness does not predict mathematics ability and is only a predictor of reading ability.

Counting ability  - A verbal counting task (e.g., repeating as fast and accurately as possible a sequence of numbers) is a mixed measure that requires numerical knowledge of number sequence as well as speed of articulation and, therefore, the activity of phonological loop.  Counting is linked to phonological abilities, since children learn to count at 2 years of age without employing number words to describe the quantities.

 Processing speed - A number of studies showed that children with poor mathematical abilities have poor performance in processing speed.    Processing speed was found to be the best predictor of arithmetic competence among 7-year olds.  One study found that  fourth grade children with arithmetic learning disability suffered from a deficit in the speed of activating both numerical and non-numerical information from long-term memory.  Speed of retrieval of information from long-term memory  is a correlate of arithmetic skills in second to fifth graders.    In a group of third grade children, processing speed was a significant predictor of arithmetic ability when assessed by visual matching and retrieval fluency tasks.

How were the cognitive abilities assessed in this research?

 Processing speed was assessed with the WJ III visual matching test.   The child was asked to locate and circle two identical symbols that appear in a row of six symbols.  In speed pattern comparison task  60 pairs of patterns were presented, and the child had to decide as quickly as possible whether the two

patterns of each pair were identical.

Verbal Memory span was assessed with a forward digit and word recall tasks.  Visuo-spatial  memory span was assessed with a task in which   the child was shown a path taken by a frog on a 3 × 3 or 4 × 4 chessboard.    The child had to   reproduce the experimenter’s moves.  Another task was the Corsi block task that requires children to watch the experimenter pointing to a series of blocks that are arranged randomly on a board, and then to point to the blocks in the same order.

Working memory was assessed with a list of two to five words of which  the child had to  remember the first word and to concurrently perform a dual task.   Digit backwards recall task was also administered.

For the word fluency task  the child was asked to generate   as many words as possible in 1 min beginning with a particular letter.  For the semantic fluency task the child was   given a minute to name as many items as possible from particular semantic categories: animals, objects, and occupations.

Phonological awareness was assessed by word and pseudo-word repetition, recognition and repetition of the first or last sound of the word or non-word said aloud by the experimenter   in words and pseudowords, phonological analysis and synthesis of words.

For the verbal counting task, the child was asked to count as fast as possible from 1 to 10 three times.

Counting speed was assessed with   a task requiring the child to count objects as fast as possible.

Results:

Numerical competence as measures at the end of kindergarten was significantly correlated s 0.45 with processing speed, 0.42 with working memory , 0.42 with phonological skills and 0.46 with verbal counting and counting speed.

Mathematical achievement as measured at the end of first grade was significantly correlated 0.35 with vocabulary, 0.34 with processing speed, 0.32 with verbal counting and counting speed, and 0.42 with numerical competence as measured at the end of kindergarten. 

Path analysis model showed that the strongest predictors of numerical competence at the end of kindergarten are processing speed and working memory.  The strongest predictors of mathematical achievement  at the end of first grade are numerical competence at the end of kindergarten, processing speed and vocabulary.

   Processing speed  may facilitate the execution of several tasks, such as counting speed, as well as recall of partial results of problem solutions, preventing the decay of the information that must be processed. Phonological awareness and counting skills were highly correlated with processing speed in this research.  This might mean that the faster a child can process stimuli, the faster he/she can access  phonological information about numbers and counting.