## Counting Ability of Children and Understanding of the Counting Sequence-Structure

Part 1

Counting describes three different activities. Firstly, it involves saying numbers loudly in sequence. Secondly, it involves a child explaining relative numerosity based on quantity. Thirdly, it describes a child’s use of words to quantify amounts and explain the generative rule for the counting sequence according to place value. The counting ability of children and understanding of the counting sequence-structure reflects their overall knowledge of numbers. Children understand the meaning of numbers at the appropriate developmental age. While most adults take counting for granted, it is a complex process that involves multiple mechanisms. The literature on this mathematical concept reveals important elements that determine a young pupil’s ability to perform various mathematical functions. Here is part of our Math Literature Review.

Literature Review

Cognitive development of children, which corresponds with age, determines their counting ability. Teachers have a different expectation of children based on their age. According to Boulton-Lewis (1993), teachers expect first-grade children to count up to 20, back and forth, and by odd and even numbers. They also expect second-grade pupils to count to 20 by multiples of 1, 2, and 5, and to 99 by multiples 10. They presume that grade 3 pupils can count up to 999, both forward and backward. Similarly, math instructors required year 1 pupils to read numbers from 1 to 20 and discuss the place value of the numbers (Boulton-Lewis, 1993). Furthermore, math instructors presume that year 2 can read and write, as well as model the place value with single and sets of objects from 1 to 99. Similarly, grade 3 teachers expect their pupils to write and model numbers up to 999 with different objects, such as MAB blocks, Unifix, and sticks. Pedagogy experts have studied the factors that determine age-dependent mathematical abilities of children.

Some researchers have investigated the relationship between a child’s knowledge of the counting sequence structure and place value. Boulton-Lewis (1993) found that mastery of counting correlates with knowledge of place value and ability to explain it at the initial three grades of schooling. Moreover, the study showed that young pupils learn to explain the counting sequence after they have mastered how to count numbers. It is more cognitively demanding to explain place value than counting sequence. Therefore, older children can explain place value better than younger children. Nevertheless, how fast children learn to count and explain place values depend on other underlying factors.

Schools have different curriculums that often determine the way educators teach and pupils learn. Boulton-Lewis (1993) argued that the difference in the young children’s ability to explain counting and place value may depend on the curriculum of their school, which determines the style math teachers use to teach math concepts. Boulton-Lewis  (1993) found that teachers encourage group discussion when teaching place values than when they teach counting, as teaching the former mainly involves the use of helping materials. Therefore, schools must ensure they adapt the best curriculum to facilitate better acquisition of mathematical competences by their students.

Children acquire knowledge of the counting structure by themselves or by rote. Rote counting skills is a strong indicator of future arithmetic fluency. Nevertheless, the literature on the underlying cognitive mechanisms affecting counting competence is scanty. Koponen, Eklund, and Salmi (2018) investigated the impact of language, non-verbal skills, and WM could have on counting ability in grade 1. The researchers found that language capabilities combined with working memory and nonverbal reasoning competence accounted for 22% of the variation in counting abilities. In addition, Koponen and colleagues (2018) found that morphology, vocabulary, and verbal memory were interchangeable predictors of counting. The results are similar to past studies which supported vocabulary and morphology as the underlying cognitive factor in counting. However, they each accounted for about 8% of the skill (Koponen, Eklund, & Salmi, 2018). Similarly, Negen and Sarnecka (2012) found a strong correlation between vocabulary and number-word skills in children aged 2.5 to 5 years. However, the variance in counting skills among the population could attribute to personal variations in vocabulary acquisition. The result, therefore, challenges the conception of counting as a language-centered skill. Further, the study showed that language skills and memory, coupled with a child’s gender and commitment, explain between 34% and 46% of counting competence in children with dyslexia (Koponen, Eklund, & Salmi, 2018). Comparatively, the results show that language skills and memory in 5-year-olds have different predictive values on counting ability at the start of school. This finding suggests the involvement of other cognitive factors in determining the counting skills of young pupils.

Young pupil’s task-orientation, commitment, and parent’s or guardian’s educational level have been thought to partly determine rote counting competence in first grade pupil. In this case, Koponen et al. (2018) found that these factors accounted for 5% of the variation in rote counting. The findings suggested that significant task-avoidant predicted less and slower progress in math performance. Koponen and peers (2018) revealed that the education level of the father accounted for 10% of the counting variance of the sample. The results suggest that parents acquired knowledge during school that determines how they interact with their children at home relative to academic activities. Alternatively, their understanding of the educational system can influence home-centered academic activities and children’s competences. Moreover, Koponen et al. (2018) found that boys were better than girls in counting. However, a more recent studies has showed absence of gender variation in counting performances among young learners. Experts need to focus on the factors that directly relate to children’s cognitive capability, since these skills connect directly with the curriculum and teaching style.

Some aspects of Early Childhood Development (ECD) curricula are worthy of assessment. Milner, et al. (2019) evaluated the measurement approaches incorporated across the ECD portfolio used in many middle- and low-income countries. Particularly, the study showed certain loopholes in the ECD Monitoring and Evaluation (M&E) framework for improvement. They showed shortcomings in the measurement of ECD outcomes. The current M&E framework focuses on the short-term cross-sectional measurements of the outcome as opposed to the long term. Additionally, the research revealed challenges in measurement related to the quality of the ECD curriculum.

Many studies have highlighted the function of working memory during numerical development. Past studies have shown the importance of working memory (WM) in learning mathematical concepts. Specifically, research has shown that WM capacity improves after training. Some studies have established that it determines the academic performances of pupils. Hanore and Noel (2017) investigated the effects of training visuospatial WM on numerical competences in children aged 5 to 6 years. The results suggested that the training had a significant effect on the adaptive version on visuospatial executive abilities, but a smaller effect on the comparison of Arabic numbers. Importantly, the training did not affect counting, comparison, and addition of collection, as well as verbal working memory. Hence, teachers cannot rely on training visuospatial working memory with the intent to boost counting and adding competences in young children. Thus, they must search for proven alternatives to the visuospatial short-term memory training.

The ability to undertake an arithmetical task depends largely on the short-term memory, which influences the operation and maintenance of information in the brain. Past researches revealed that procedural strategies, such as counting, depend more on working memory than strategies of retrieving essential information. Children deploy different retrieval strategies and are more accurate and efficient in its execution. This implies that the role of short-term memory in math may change with age. Cragg, Richardson, Hubber, Keeble, and Gilmore (2017) studied the extent to which short-term memory requirements for various arithmetic techniques changed with age between 9-11 years and 12-14 age brackets. The researchers found that children and adults need working memory to solve arithmetic tasks regardless of the strategy used. Therefore, educators should attribute the challenges that children and adults encounter with mathematics to dysfunctional WM, so as to apply interventions that can facilitate it. The study emphasizes the need to incorporate short-term memory in theoretical models of arithmetic cognition.

The mechanism by which working memory determines numerical skills is elusive. Regarding this, Cragg et al. (2017) showed that working memory distracted both procedural and retrieval strategies to the same degree. The researchers showed that the problem size influenced the effect of working-memory on the accuracy of the result of the task. Besides, the load of working memory reduced the individual arithmetic performance for all the strategies. In contrast, a past study showed a greater effect of short-term memory load on procedural than retrieval methods. Cragg et al.  (2017) noted that the rationale for this difference is unclear, as both studies employed identical arithmetic problems and recruited participants from the same study population. However, the discrepancy suggests that the differential effects of load on arithmetic techniques are not as straightforward as initially perceived.

The duration of the training effects on the working memory of young learners is important to compare its benefits versus its shortcomings. Hanore et al. (2017) found that the effects of the training vanished within ten weeks. Some previous studies supports this position, as they showed that the effects of training on verbal WM were short-term but slightly longer on visuospatial WM.  In contrast, Dunning et al. (2013) found long-lasting effects on the WM of young pupils. These reveal discrepancies in the effects of training on WM. It means that the duration of training effects on WM is dependent on its quality. However, researchers have not investigated the impact of training characteristics on the duration of their effects on WM. Thus, the effect of training on WM is not conclusive, and therefore, it is not a dependable means of boosting mathematical competences of children.

Conclusion

Various factors underlie the development of arithmetic skills in children. Language skills and memory play a significant role in determining a child’s ability to tackle numerical tasks. Whereas research has yielded divergent views on the role each factor play, most research has stressed the function of working memory in facilitating children’s arithmetic performance. The size of the problem and memory load influences the accuracy of the result of an arithmetic problem. The ECD curriculum should include an effective WM training to speed the development of cognitive skills. Future, research should seek to measure the memory capacities of children at different ages, so that the findings can be used to develop better curriculum and teaching strategies.

Part 2: Reflection

Curriculum and teachers instructional approach determines the ease with which learners acquire mathematical skills. Pupils age determines how fast they learn and what types of arithmetic task they can perform at a given age. Educators should understand the effects of WM capacity on the capability of children to perform arithmetic tasks. In this case, teachers should consider the working load of young children in order to align a task to the capacity of the brains of young children. The brains of children can hold less information than older learners. Thus, ECD curriculum should be adjusted to limit the load on working memory.

The assignment has been informative. It helps a learner appreciate the importance of reviewing the literature on the relevant topic. The task can help the student develop adequate skills to undertake a literature review on a subject and apply critique past research concerning a problem at hand. In this case, the assignment can help a learner understand a mathematical concept and apply the evidence-based practice. Thus, this assignment has improved the leaner regarding teaching mathematical concepts. In particular, arithmetic teachers can learn to minimize the load of working memory on young pupils to facilitate the accuracy of the results of their arithmetic task. More research are needed to clarify the underlying factors and their mechanisms in order to improve teaching arithmetic concepts.

References

Boulton-Lewis, G. (1993). An Analysis of The Relationship between Sequence Counting and Knowledge of Place Value in the Early Years of School. Mathematics Education Research Journal, 5(2), 94-106.

Cragg, L., Richardson, S., Hubber, P., Keeble, S., & Gilmore, C. (2017). When Is Working Memory Important for Arithmetic? The Impact of Strategy and Age. PLoS ONE, 12(12), 1-18.

Hanore, N., & Noel, M. (2017). Can Working Memory Training Improve Preschoolers Numerical Abilities? Journal of Numerical Cognition, 3(2), 516-39.

Koponen, T., Eklund, K., & Salmi, P. (2018). Cognitive Predictors of Counting Skills. Journal of Numerical Cognition, 4(2), 410-28.

Milner, K., Bhopal, S., Black, M., Dua, T., Gladstone, M., Hamadani, J., . . . Lawn, J. (2019). Counting Outcomes, Coverage and Quality for Early Year Child Development Programmes. Arch Dis Child, 104, 13-21.