How do children read numbers? Explicit-knowledge acquisition versus cognitive development
Read the full dissertation (in Hebrew), or the article based on Ella’s dissertation.
Reading numbers is an important ability, both in itself and as means to improve other mathematical skills, including arithmetic. Reading numbers may sound simple and easy, nevertheless, this is a complex skill, which is anything but easy to learn. The present study examined whether number reading is difficult for children, and if so, what causes this difficulty.
We examined 100 third-grade children without reported learning disorders. They performed a task of reading aloud 2- to 5-digit numbers, tasks that examined whether they were familiar with the structure of the decimal system rules and with the rules of constructing verbal numbers, and tasks to identify the cognitive origins of number-reading errors.
The participants made many errors when reading numbers, both in absolute terms (26%) and compared to slightly older children, in 4th grade. The variance among the participants was very high: some children had a lot of errors (over 70%), whereas others read numbers almost like adults.
To identify the core of the difficulty in number reading, we analyzed the participants’ error types. They made more syntactic errors (incorrect number structure) than digit substitutions or transpositions. Moreover, there were more errors in syntactically-complex numbers than in syntactically-simpler numbers. For example, there were only a few errors in round numbers (4000), but more errors in non-round numbers with zero (4503). We concluded that the main origin of difficulty in number reading lies in the need to process the number’s syntactic structure.
When comparing the reading of numbers that have different syntactic structures, we found a double dissociation between numbers of different lengths. There were participants who had difficulty with 5-digit numbers, the longer ones, but read well the 4-digit numbers, the shorter ones. There were also participants who showed the opposite pattern: good reading of 5-digit numbers and difficulty in 4-digit numbers. Even within numbers of a given length, we observed a dissociation between numbers with regular and irregular syntactic structures: there were more errors in numbers in the range 2,000-2,999, whose verbal form in Hebrew is irregular, than in other 4-digit numbers; and more errors in numbers in the numbers 10,000-10,999, which are irregular too, than in other 5-digit numbers. We concluded that the different syntactic patterns are separate from each other and each must be acquired specifically. Irregular patterns are harder or learned later, but other than that, the syntactic patterns are not necessarily learned according to the numerical order (small to larger) – they can be learned in arbitrary order, presumably according to the specific child’s characteristics and experience.
We also tested the origin of reading errors for each participant. We examined several possible origins. First, we examined factors related to the participants’ knowledge – lack of knowledge of the decimal structure of numbers (units, decades, hundreds, …), and lack of knowledge of specific syntactic-verbal structures. Indeed, some participants had difficulty both in number reading and in these knowledge tasks. For these participants, the errors seem to originate from insufficient knowledge. Critically, however, other participants had number-reading errors although they performed well in the knowledge tasks and showed good mastery of the decimal system and verbal-syntactic structures. For these participants, the number reading errors do not originate in lack of knowledge but have a different reason.
We then examined potential cognitive origins of the number reading errors: difficulty at the visual analysis stage, responsible for parsing digit strings, and at the verbal production of the numbers. We found a large group of children (20%) with reading errors who had knowledge of the decimal structure of numbers, of verbal-syntactic structures, and had difficulty in tasks that tested the cognitive mechanisms. For these children, the origin of the number-reading errors seems to be cognitive immaturity of the syntactic mechanisms at the visual-analysis level or verbal-production level. It therefore seems that reading numbers requires a combination of syntactic knowledge about numbers and sufficient development of relevant cognitive processes.
Overall, the study shows that it is important to acquire proficiency in specific syntactic rules of number reading. It further shows that proficiency in a specific syntactic rule cannot arise merely from conceptual knowledge, e.g., mastering the decimal categories, and even not from theoretical-procedural knowledge about the syntactic structure of the verbal numbers. Moreover, proficiency in one syntactic structure/rule does not guarantee proficiency in another syntactic structure – e.g., being able to read 4-digit numbers does not guarantee good reading of 5-digit numbers. To read numbers, one must learn each type of numbers specifically. Following these conclusions, we recommend to add number reading, with specific focus on their syntactic structure, as a new, independent topic in elementary school math curriculum.