Place-value computation in children with mathematics difficulties

Lambert, Katharina; Moeller, Korbinian

doi:10.1016/j.jecp.2018.09.008

Cited by 20 publications

(23 citation statements)

References 51 publications

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“…The impact of ANS on math achievement diminishes over time as the children internalize the use of the symbolic representations of numbers. Importantly, number magnitude and place-value understanding are important precursor competencies for later arithmetic skills with other basic numerical competencies (Lambert & Moeller, 2019). Moeller et al (2009) also obtained similar results in a different study.…”

Section: Discussion Conclusion and Recommendationssupporting

confidence: 53%

Number Line Estimations, Place Value Understanding and Mathematics Achievement

Sarı

Olkun

2021

Journal of Education and Future

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Current study investigated the relationships among mathematics achievement, place value understanding and number line estimations. We used a curriculum-based math achievement test (MAT, Mathematics Achievement Test), a place value test (PVT), and a mental number line estimation test (MNL) as the data collection tools. A total of 355 fourth graders participated in the study. They were recruited from schools located in middle-low socioeconomic areas of central Anatolia. Correlations were statistically significant among all these tests scores (MAT, PVT, MNL). The highest correlation was obtained between PVT and MAT scores. PVT have also stronger correlations with MNL (0-1000). The average scores of MAT and MNL tests were correlated inversely as expected. The correlations between mathematics achievement scores and MNL (0-1000) was highest. The three MNL tests alltogether have explained 40% of the variance in MAT. Similar to PVT, MNL (0-1000) alone accounted for 36% of the variance in MAT. Meanwhile, MNL (0-1000) (large numbers) contributed MAT more. PVT explained 70% of the variance in MAT. In all tests, PVT contributed more to MAT. Generally, boys did better in all MNL tests but only the result of MNL (0-1000) was significant favoring boys. We can conclude, based on these results that both approximate number acuity and place value understanding contribute to the general math achievement as well as each other. While the place value concept seems to be a representational tool that enhence the acuity of approximate numbers, the relative magnitudes of numbers support place value understanding conceptually.

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Section: Discussion Conclusion and Recommendationssupporting

confidence: 53%

Number Line Estimations, Place Value Understanding and Mathematics Achievement

Sarı

Olkun

2021

Journal of Education and Future

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“…Moreover, deficient place-value knowledge has been discussed as a predictor or source of dyscalculia and mathematical learning difficulties (e.g., Cawley et al, 2007;Chan & Ho, 2010;Haase et al, 2014). For instance, Chan and Ho (2010) assessed 8-as well as 10-year-old children with and without mathematical difficulties and demonstrated that conceptual understanding of the place-value structure differentiated reliably between children with and without mathematical difficulties (see also Lambert & Moeller, 2019). Thus, mastering the place-value structure of the Arabic number system represents an important milestone in numerical development (see also Herzog et al, 2017Herzog et al, , 2019 for a developmental model of conceptual place-value understanding).…”

Section: Processing Multi-digit Numbersmentioning

confidence: 99%

Ties of math and language: A cognitive developmental perspective

Bahnmueller¹,

Lopes-Silva²,

Haase³

et al. 2021

Diversity Dimensions in Mathematics and Language Learning

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Because numerical and mathematical competencies play an important role in our everyday life (e.g., Butterworth et al., 2011), it is crucial to understand underlying cognitive processes and factors influencing the acquisition of these numerical and mathematical competences. In particular, a better understanding at the level of cognitive processes may help to develop targeted interventions, inform, and enhance the quality of mathematics teaching, which may raise student attainment (cf. The Royal Society & The British Academy, 2018).To be able to deal with numbers and mathematical content in a competent and efficient way, a set of concepts, procedures, and (math) facts need to be acquired starting even before (formal) education in kindergarten, preschool, and (elementary) school years. Crucially, and probably more so than it is the case in many other school subjects, mathematics education is largely hierarchical in nature (e.g., Clements & Sarama, 2021). As such it is important and necessary to be able to draw on previously acquired competences and knowledge, because new numerical and mathematical content usually builds on these previously acquired competences, concepts, and procedures.Besides considerable developmental variability on the individual level, international studies evaluating scholastic abilities have consistently reported large cross-cultural differences in mathematical achievement (e.g., OECD, 2019a). In addition to differences in schooling and cultural valuation (e.g., OECD, 2019b), it has been argued that influences of domain-general factors such as language also need to be considered as a potential source of but also resource for overcoming difficulties in the acquisition of numerical and mathematical competences. In particular, language may refer to a range of different linguistic aspects and/or specific aspects of language skills, each of which might interact with specific steps in the acquisition of numerical and mathematical competences.So far, a wide range of studies investigated various language aspects critical for the acquisition of numerical and mathematical concepts. And indeed, findings of many of these studies are in line with a weak Whorfian hypothesis suggesting that different aspects of language seem to influence the way we acquire, think about, perceive, represent, and apply numerical and mathematical concepts, procedures, and (math) facts. In an attempt to classify and structure previously observed associations of language and mathematics as well as influences Open Access.

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“…The fourth principle of learning place value is the ability to compose and decompose numbers in flexible ways, which is a prerequisite for understanding regrouping with multi-digit operations. Students with LD in mathematics tend to make more regrouping errors with multi-digit operations than their typically achieving peers, which could stem from their inability to flexibly compose and decompose numbers (Lambert & Moeller, 2019). Therefore, it is important for students to practice representing numbers with a non-standard base-10 approach (e.g., representing 243 as one 100, 14 tens, and three ones) before beginning multi-digit operations.…”

Section: Composing and Decomposing In Flexible Waysmentioning

confidence: 99%

Teaching Place Value to Students With Learning Disabilities in Mathematics

Rojo

Knight

Bryant

2021

Intervention in School and Clinic

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According to National Council of Teachers of Mathematics (NCTM), students must develop a conceptual understanding of place value by second grade to understand that mathematics processes are more than a set of procedural steps. Yet, students with learning disabilities in mathematics typically struggle to understand place value in a deeper, conceptual sense, which can have a negative impact on their future performance where application of place value concepts are foundational. Therefore, early interventions targeting place value instruction are critical for building a solid foundation in mathematics for students with learning disabilities. This article provides teachers with an overview of five place-value principles, which are critical for student success; and evidence-based practices for teaching those principles.

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Place-value computation in children with mathematics difficulties

Cited by 20 publications

References 51 publications

Number Line Estimations, Place Value Understanding and Mathematics Achievement

Number Line Estimations, Place Value Understanding and Mathematics Achievement

Ties of math and language: A cognitive developmental perspective

Teaching Place Value to Students With Learning Disabilities in Mathematics

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