Number identification: a unique developmental pathway in mathematics?

Abstract

We make a prima facie case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the Performance Indicators in Primary Schools (PIPS) Baseline assessment at the beginning and end of their first school year. Through a Rasch analysis of real and simulated data, we show that: (1) there appears to be a single, unidimensional pathway in learning to identify number symbols with discrete difficulty stages, (2) on examination of differential item functioning, this pathway is invariant across gender, country, socioeconomic background, first language and across the first year of schooling and (3) almost all children make progress along the pathway during the year. A number identification scale may thus be a universal ruler by which all pupils could be assessed.

Measurement of Psychometric Properties Numerical Aptitude Assessment Scale for Prospective High School Students: A Rasch Model Analysis

“…Relevant research studies related to the use of the Rasch model analysis to identify the psychometric properties of the construct of talent or intelligence instrument development and also its relationship to ability assessment and implementation in the analysis process have been carried out by several researchers in several countries such as in mainland Asia [22], [23] and Europe [21], [25], [26]. Other relevant research studies have also been carried out by several researchers for assessing the talent abilities of elementary school students [28], evaluating career placement surveys [29], and identifying the development of intelligence instruments [30].…”

“…Another relevant research study was conducted by Cramman, et al [21] to evaluate learning instruments using Hindu-Arabic numeric symbols to improve students' mathematical abilities in England and Scotland. Bokander and Emanuel [13] evaluated the suitability of the subtest on the language skills assessment instrument with the theory of the language aptitude test using the Rasch model analysis approach by involving student respondents in several countries in Europe and Asia.…”

“…Bokander and Emanuel [13] evaluated the suitability of the subtest on the language skills assessment instrument with the theory of the language aptitude test using the Rasch model analysis approach by involving student respondents in several countries in Europe and Asia. Analysis with the Winsteps 3.90 program was carried out separately using learning outcome data based on the pre and post-test stages to explore the psychometric properties of learning assessment using Hindu-Arabic numeric symbols [21]. Psychometric properties include MNSQ infit and outfit statistical criteria for item suitability with the model, PCA criteria for dimensionality, separation person index, and test reliability for instrument quality.…”

“…Identification of the quality of the talent instrument with the Rasch model analysis approach has been carried out by Kara, et al [19] was used to assess the spatial aptitude of elementary school students in Turkey and for the secondary school level in Australia [20]. Cramman, et al [21] used an analytical technique based on the Rasch measurement model to evaluate learning instruments based on Hindu-Arabic numeric symbols to improve students' mathematical ability in England and Scotland. Other relevant research studies to identify the suitability of language proficiency assessment instruments with the theory of language aptitude tests involving student respondents in several countries in Europe and Asia [13].…”

Additional Evidence of Predictive Validity of SRSS-IE Scores With Elementary Students

“…We selected these subscales based on recommendations by a national expert in math assessment. Both foundational skills are indicators of early numeracy literacy which predict later math achievement (Cramman et al, 2020; Lembke & Foegen, 2009).…”