Development of mathematical concepts as basis for an elaborated mathematical understanding

Fritz, Annemarie; Ehlert, Antje; Balzer, Lars

doi:10.4102/sajce.v3i1.31

Cited by 21 publications

(20 citation statements)

References 52 publications

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“…In this task, children were requested to generate subsets of a particular number from a larger set of objects that is placed in front of them (e.g., "Give me three marbles"). Fritz et al (2013) published a model that aims to map the development of early numeracy, with a particular focus on conceptual understanding. This model of conceptual numerical development has been empirically validated in cross-sectional as well as longitudinal studies (Fritz et al, 2018) and builds the theoretical foundation of the LPA introduced in this study.…”

Section: Learning Progressions In Early Numeracymentioning

confidence: 99%

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

2020

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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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Section: Learning Progressions In Early Numeracymentioning

confidence: 99%

“…Table 1 shows the central numerical concept for each level and a short description of the associated skills. For a detailed description of the model, see Fritz et al (2013).…”

Section: Learning Progressions In Early Numeracymentioning

confidence: 99%

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

2020

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“…Mentor B explained how she used the Fritz et al (2013) model for the development of numerical concepts from the ages of four to eight years to aid in the development of student teachers' understanding of number sense. There is thus some evidence of conceptual development being underpinned by a theoretical framework and the implementation of development opportunities provided by the university.…”

Section: Teaching Strategiesmentioning

confidence: 99%

“…We agree with the view that mentor teachers shape students' mathematics teaching practice in particular ways (Hudson & Hudson, 2011) and thus play a significant role in influencing the type of mathematics teachers students will become (Rhoad, Radu & Weber, 2011). We were keen to investigate how the mentoring practices of teachers in the setting of a teaching or laboratory school in which they are appointed and trained as mentors for student teachers of mathematics, using a specific model for the development of numerical concepts was realised (Fritz, Ehlert & Balzer, 2013). In our view, the teaching school is an ideal environment for the creation of cognitive apprenticeships (Collins, Brown & Hollum, 1991) as the mentors and student teachers are being apprenticed, the teachers into mentors of student teachers and the student teachers into teachers.…”

Section: Introductionmentioning

confidence: 99%

Mentoring and preparing primary school mathematics teachers

Msimango

Fonseca

Petersen

2020

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This article reports on the mentoring of foundation phase teachers and their development of disciplinary-specific knowledge, particularly how the practicum provides a space for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) for student teachers, given the generalist knowledge base of many primary school teacher mentors. Data were collected through semi-structured interviews with two Grade 2 mentors and focus group interviews with 12 third-year student teachers in an urban university setting. A two-step process of analysis comprising open-ended coding, followed by a form of deductive coding, within a framework derived from literature on the development of MCK and MPCK, led to two main findings. Firstly, mentors might have hindered student teachers' development of MCK and MPCK, thus affecting the building of comprehensive conceptual models of good mathematics teaching practice. Secondly, the efficacy of the university-led training for mentors did not seem to have been successful for preparing them to work effectively with student teachers. We therefore recommend that greater emphasis be placed on the development of subject-specific mentoring practices, especially in scarce-skills areas such as mathematics and argue for a set of standards for mathematicsspecific mentoring practices in South African primary school teacher education.

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“…Knowledge about the development of early numeracy skills and their relevance for later mathematics learning has been increasing rapidly during last 10 years (Aunio & Räsänen 2015;Fritz, Ehlert & Balzer 2013;Krajewski & Schneider 2009). In general, authors agree that numeracy performance in the early childhood years adequately predicts later mathematics performance (Jordan, Glutting & Ramineni 2010).…”

Section: Early Numeracy Skills Relevant For Later Mathematics Learningmentioning

confidence: 99%

Early numeracy performance of South African school beginners

Aunio

Mononen²,

Ragpot

et al. 2016

SAJCE

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Early numeracy skills are highly relevant for children’s mathematics learning at school, especially in the initial years when much mathematics learning relies on early numeracy competence. The aim of this study was to investigate the level of early numeracy skills in a sample of South African children in the first months of formal schooling. In this cross- sectional study, there were 443 first graders (206 girls and 237 boys) from Gauteng Province schools. The mean age of the children was 81.61 months (6 years 10 months) (SD 5.40 months). Their early numeracy skills were measured with the ThinkMath Scale. The main finding of this study was that there were statistically significant differences in early numeracy skills between the children when they started first grade. The differences were related to the home language of the first graders in the English medium schools, as well as the type of school (public vs. private). This article concludes that the numeracy competence of the children from the sample was notably varied in the beginning of their formal schooling, which has implications for teaching in the vastly different classroom populations that are all served by one national curriculum.

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Development of mathematical concepts as basis for an elaborated mathematical understanding

Cited by 21 publications

References 52 publications

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

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

Mentoring and preparing primary school mathematics teachers

Early numeracy performance of South African school beginners

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