Insights Into First Grade Students' Development of Conceptual Numerical Understanding as Drawn From Progression-Based Assessments

Abstract

Early numeracy has been found to be one of the strongest predictors for later success in learning. Equipping children with a sound conceptual numerical understanding should therefore be a focus of early primary school mathematics. Assessments that are aligned to empirically validated learning progressions can support teachers to understand their students learning better and target instruction accordingly. This study examines numeracy learning of 101 first grade students over the course of one school year using progression-based assessments. Findings show that the students' performance increased significantly over time and that the initial conceptual numerical understanding had a positive effect on the students' learning progress as well as their end of school year performance. Analyzing the performance data based on the levels of the underlying developmental model uncovered an increasing elaboration of conceptual numerical understanding over time, but also individual differences within this process that need to be addressed through targeted intervention.

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“…With regard to previous research on LPM instruments in the field of computation, Christ et al (2008) conclude that the use of more systematic sampling and item construction would improve the quality of LPM. To date, there has been little literature on the investigation on DGICs in the field of basic mathematical skills and for developing LPM (e.g., Balt et al, 2020;Ehlert et al, 2013). However, for the theory-based construction of test items for LPM, it is necessary to obtain valid information about which characteristics influence the difficulty of an item.…”

“…14, No. 1 (2022) little literature available on the investigation of difficulty-generating item characteristics (DGICs) in the area of basic mathematical competencies that can be used for systematic LPM item construction (e.g., Balt et al, 2020). The present study addresses this research gap by focusing on the design and evaluation of an item generation system, applying theory-based modeling of item complexity using LLTM to analyze items exemplarily for an LPM addition and subtraction test for numbers up to 100.…”

Parental Involvement in Young Children’s Learning of Numeracy

“…The importance of early numeracy experience as the foundation for mathematical learning in school is frequently reported. To demonstrate, the past studies found a significant predictive link between the verbal counting skills (Koponen, Aunola & Nurmi, 2019), subitising (Hannula-Sormunen, Lehtinen & Räsänen, 2015, basic arithmetics (Singer & Strasser, 2017;Pardo, et al, 2020), and number concepts (Balt, Fritz & Ehlert, 2020) in early years with later mathematics performance in school. Sobkow, Olszewska and Traczyk (2020) and Darriet, et al (2020) claimed that the numerical competency could further predict preferences in real-life choices.…”

Place Value Understanding Explains Individual Differences in Writing Numbers in Second and Third Graders But Goes Beyond

“…If children solved at least 75% of the items of a level, they were assigned to the corresponding level. The highest achieved level was recorded as the current conceptual level of place value understanding (for similar approaches see Lee and Sarnecka, 2009;Ricken et al, 2013;Fritz et al, 2017;Balt et al, 2020). To address lucky guesses and mistakes, children did not have to solve all items of a level to be considered having developed the concept of the level.…”