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Assessment of Early Mathematics and Working Memory

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One of the critical aspects for Children’s early academic growth is a successful acquisition and development of mathematical skills and concepts (Baroody, Lai, & Mix, 2006), and these skills are; foundations for cognitive development (Clements & Sarama, 2009), strongly predicts their later success in math (Denton, West, & Walston, 2003) and to all other subjects (Clements, 2014); more surprisingly preschool mathematics(numeracy) knowledge predicts achievement even into high school and career outcomes(Duncan et al., 2007). It also predicts later reading achievement even better than early reading skills. From researches; doing more mathematics increases oral language abilities and even when measured during the following school year. These include vocabulary, inference, independence, and grammatical complexity(Sarama, Lange, Clements, & Wolfe, 2012)

Unluckily, many children fail to achieve early success in mathematics, and these early difficulties tend to persist and become more pronounced over time (Aunola, Leskinen, Lerkkanen, &Nurmi, 2004; Baroody& Ginsburg, 1990). In recent years, the major focus of the global education community has been on getting children into school (Pritchett, Banerji & Kenny, 2013; Van Fleet, Watkins &Greubel, 2011) and that effort has been a success. For instance, in Ethiopia, the Net Enrolment Rate (NER) in 2014/2015 was 78.45% and in 2017/2018 increased to 89.19% (MOE, 2018). Yet, in many developing countries, progress in learning outcomes, especially in the area of mathematics was stagnant or even declining (Beatty & Pritchett, 2012; Kremer et al., 2013; Perlman – Robinson, 2011).

Several empirical studies support this argument. A study by UNESCO (2013) indicated that about 250 million primary school-age children in low and middle-income countries, of which 130 million spent at least four years in school, we’re unable to meet the minimum learning standards in reading and mathematics. This figure could have been much worse had it been measured more widely, but the problems in many developing countries do not measure basic reading or arithmetic in primary grades (Aga Khan Foundation, 2010).

Evidence as to the state of mathematics education in Sub Saharan Africa in terms of student achievement comes from a diverse and growing number of sources. The limited information available from international comparative assessments such as Early Grade Mathematics Assessment (EGMA), Trends in International Mathematics and Science Study which is a series of international assessments of the mathematics (TIMSS), suggests that all major countries in Sub Saharan Africa would appear towards the bottom of the international rank order (Bethell, 2016).

Early Grades Mathematics Assessment EGMA) for countries with available data, the figures are however staggering. For example, in 2011 Zambia Pupils were asked to compare single and double-digit numbers and to say which was large. In grade 2, 18% of pupils were unable to answer a single item, while in Grade 3, fewer than 12% could produce a correct response (to all items) (USAID, 2012). Similarly, EGMA 2013 in Ghana, on the missing number, addition level 2 and subtraction level 2 subtasks; there was a sharp drop-off in performance, with nearly 70% of the pupils unable to answer a single subtraction level 2 item correctly the easiest of these being: 19 – 6 = •(USAID, 2014). Similarly, Baseline Study Report in Early Grade Mathematics Assessment (EGMA) in Ethiopia, in cardinality the overall result showed that 25.4% of students were not able to correctly associate with the group of objects they count and the number value that represents the objects (NEAEA, 2014).

Children’s early mathematics skills develop cumulatively; several recent studies investigated precursors of mathematical learning in preschool children. Competencies that specifically predict mathematical abilities and which are foundational skills form a basis for the acquisition of later skills (mathematical factors) or may be considered as domain-specific precursors, such as early numeracy; however, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level which are general cognitive abilities, such as working memory that may predict performance not only in mathematics but also in other school subjects may be considered domain-general precursors (David J. Purpura& Colleen M. Ganley, 2014; Gathercole, Brown, & Pickering, 2003; Gathercole, Pickering, Knight, &Stegmann, 2004; Kroesbergen, Van Luit, Van Lieshout, Van Loosbroek, & Van de Rijt, 2009; Passolunghi&Lanfranchi, 2012; Träff, 2013).

The cumulative nature of early mathematical development later competencies building on earlier ones underscores the need for early prevention and intervention with children at risk for developing mathematics difficulties. To effectively intervene in early skills, it is particularly important to understand how these individual skills develop and what factors influence that development. A range of both mathematical and non-mathematical factors (e.g., working memory, language) affect children’s early mathematical development (Fuchs et al., 2005, 2008, 2010; Gathercole, Pickering, Knight, &Stegmann, 2004; Jarvis &Gathercole, 2003; Purpura, Hume, Sims, &Lonigan, 2011; Raghubar, Barnes, & Hecht, 2010). However, the specificity of the relation between these non-mathematical domains and early mathematics skills is not well understood.

As mathematical factors; early mathematical performance is a strong predictor of future mathematics success (Duncan et al., 2007; Fuchs et al., 2010) the reason is that mathematical skills develop as a progression of interconnected facts and concepts (Baroody, 2003; Gersten& Chard, 1999; Purpura, Baroody, &Lonigan, 2013) so-called learning trajectories (Sarama& Clements, 2009). The shortcomings that can affect students’ achievements in Mathematics are lack of mastery of the basic concepts and skills (Braza and Supapo, 2014).

Advanced mathematical knowledge is dependent on the acquisition and retention of more basic prerequisites; therefore, missing (or having an underdeveloped ability in) one or more pre-requisites limits an individual’s ability to acquire the more advanced skills. For example, at the early elementary school level, for a child to successfully (and reliably) acquire fluency in basic arithmetic, the child not only should know the process of adding or subtracting but also must (a) associate specific number word names with the appropriate Arabic numerals (e.g., know that ‘‘two’’ is equal to ‘‘2’’), (b)associate specific quantities with the appropriate number words and the appropriate Arabic symbols(e.g., know that ‘‘’’ is equal to ‘‘three’’ and ‘‘3’’), and (c) understand the meaning behind operational symbols (e.g., know that ‘‘+’’ means to add). Without developing a strong foundation of these early mathematics skills, children are likely to experience difficulties in acquiring later mathematics skills and be at a higher risk for developing mathematics difficulties than children who do develop a strong foundation of early mathematical knowledge (Baroody& Ginsburg, 1990).

Nonmathematical factors; Educators, Educational and Cognitive psychologists coming with a shared interest together into the utility of working memory (WM) as a root to understand how students think, learn and remember information by taking the construct from the psychology laboratory and theory to the practice of early childhood education (Kate Cockcroft, 2015). Researches in the domain of learning and memory highlight tremendous use of studying WM as it underpins Cognitive Development, Learning, and Education (Nelson Cowan, 2014), and also they claim that poor memory is a root cause of diverse learning problems (B. Janin et al., 2015; Nelson Cowan, 2014).

Working memory has been recognized as a crucial and foremost vital psychological feature construct interconnected with effective teaching and learning to emerge from cognitive psychology (Alloway, Doherty-Sneddon, & Forbes, 2012; Dehn, 2011). Consequently, it is unstartling that working memory is one of the foremost wide researched constructs in education and psychology (Cowan 2014). However, it remains difficult to arrive at a single cohesive definition of working memory, with continued development and debate over its meaning and function.

Working memory can be defined as; a cognitive system that underlies the capacity to store and manipulate information for brief periods of time (e.g., Alloway, 2011; Baddeley, 1986; Baddeley, 2003; Baddeley& Hitch 1974), management, manipulation, and transformation of information drawn from short- or long-term memory (Baddeley 2007; Cowan 2005; Engle and Kane 2004) as a flexible mental workspace in which we can store important information in the course of complex mental activities(Gathercole, Susan &Alloway, Tracy, 2008), as an online memory configuration in which certain information is held in awareness or span of attention for use in an ongoing information processing ( Pradeep K. and Dr. Vibha S., 2017).

Likewise, working memory tasks like attempting to multiply together two two-digit numbers, require one to hold on to one important piece of information while processing the other, in mind requires one to remember the two numbers, apply multiplication rules, store intermediate products simultaneously and proceed through next stage of the calculation. The task is possible only if we manage to meet both the storage and processing demands of the activity (Gathercole, Susan &Alloway, 2008).

Carrying out such mental activities is an effortful process. Even a minor distraction or an interruption by someone is likely to result in complete loss of the stored information, and so in a failed calculation attempt. At this stage no amount of effort will allow us to recall the lost information, the only course of action is to start the calculation afresh. Our abilities to carry out such tasks are limited by the amount of information we have to store and process working memory ability). Multiplying larger numbers (e.g., 142 and 891) “in our heads” is for most of us out of the question, even though it does not require greater mathematical knowledge than the earlier example. The reason we cannot do this is that the storage demands of the activity exceed the capacity of working memory (Gathercole, Susan &Alloway, Tracy. 2004, 2008; S. E. Gathercole and T. P. Alloway, 2007). We fail to perform such tasks because the storage demands of the tasks exceed our working memory capacity.

WM is fundamental to thinking and learning. The primary function of working memory is to facilitate and enhance the capacity of encoding, storage, and retrieval functions that are essential for learning and higher-level processing of information and allows individuals to string together thoughts and ideas currently active in memory and to link those ideas with information stored in long-term memory (LTM) (Pradeep K. and Dr. Vibha S., 2017; Swanson 2000).

The key role of both domain-specific and domain-general precursors in the development of mathematical abilities has led researchers to design studies to investigate the possibility of developing training programs to improve these abilities in children. These training programs may be crucial in the prevention of mathematical learning difficulties during preschool years (Maria Chiara Passolunghi&Hiwet Mariam Costa, 2016).

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Assessment Of Early Mathematics And Working Memory. (2021, May 31). GradesFixer. Retrieved June 17, 2021, from
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