Supporting early mathematical development through a ‘pattern and structure’ intervention program

Mulligan, Joanne; Oslington, Gabrielle; English, Lyn D.

doi:10.1007/s11858-020-01147-9

Cited by 46 publications

(36 citation statements)

References 26 publications

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“…Thirteen of the research examined variables impacting algebraic reasoning. Some studies (Afonso & Mc Auliffe, 2019;Blanton et al, 2015;Mulligan et al, 2020;Papadopoulos & Patsiala, 2019) have been conducted to determine the efficacy of applied programs, curricula, games and activities on algebraic thinking. Additionally, it was explored if the students' cognitive characteristics had an influence on their algebraic thinking (Chimoni & Pitta-Pantazi, 2017;Somasundram, 2021).…”

Section: Resultsmentioning

confidence: 99%

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A Systematic Review on Algebraic Thinking in Education

Sibgatullin

Korzhuev

Khairullina

et al. 2022

EURASIA J Math Sci Tech Ed

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Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school students, must be aware of how kids think and reason algebraically. A detailed literature review provides an overview of research on algebraic thinking. The goal of this study was to compile a list of full-text papers that presented empirical research on algebraic thinking. The "algebraic thinking" search phrase was used to search the ERIC and Scopus databases. A total of 36 studies were included in the review. The educational levels, participants, nations, research methodologies, study objectives, data collecting tools, and analytic approaches have all been considered in studies on algebraic thinking. The number of studies published has risen over time. 2019 was the year with the most studies. The majority of the research was carried out in the United States of America. The majority of the participants in the study were elementary and secondary school pupils. Teachers' knowledge, elements impacting algebraic thinking, relations, and comprehension, as well as measuring categories, were determined when the study was grouped according to the study's topic. The algebraic thinking exam was the most popular data gathering instrument. The qualitative technique was used in the study of algebraic thinking. The most common method was found to be qualitative analysis. While inferential statistics are preferred in quantitative techniques, latent class analysis, cluster analysis, and test development analysis are used depending on the study design. According to the results, it was stated that in-service or pre-service teacher training is needed for the development of algebraic thinking and non-routine activities such as games should be used in the classroom. In addition, it has been determined that teaching strategies such as geometry representation, multiple representation strategies, mental computational activity also improve algebraic thinking.

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Section: Resultsmentioning

confidence: 99%

“…Seven of them are college or university. There are two studies (Mulligan et al, 2020;Rittle-Johnson et al, 2013) at the kindergarten level. Four study is undertaken at the high school level.…”

Section: Resultsmentioning

confidence: 99%

A Systematic Review on Algebraic Thinking in Education

Sibgatullin

Korzhuev

Khairullina

et al. 2022

EURASIA J Math Sci Tech Ed

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“…The visuospatial representations made by children as they explore mathematical relationships are diverse, creative, and sometimes unexpected (Deliyianni et al, 2009;Worthington & Carruthers, 2003), compared to those for whom the material has become familiar and routine. Learners representing their mathematical thinking in not-yet-routinized ways can be a particularly valuable source of data for researchers, analysis of which can provide a window into early mathematical understanding and reasoning, in particular the awareness of patterns and structures which is fundamental to mathematical development (Mulligan et al, 2020).…”

Section: Representation and Arithmeticmentioning

confidence: 99%

“…Where there exists a perception of what 'typical' development or progression looks like, a contrasting group is thus implicitly created of all learners with 'atypical' development (often interpreted as those who have failed to progress as expected according to local norms). Some studies-particularly those using quantitative methods-have contrasted the strategies of participant groups predefined on such bases, e.g., 'normal'/'mathematically disabled' in Ostad (1997), 'high'/'low achievers' (Gray et al, 2000;Karsenty et al, 2007), 'highly-' or 'less-able' (Mulligan et al, 2020), and 'typically achieving students'/'poor performance'/'arithmetic learning disabilities' (Gonzalez & Espinel, 2002). While this is sometimes done with good intentions-such as better understanding difficulties in order better to support learning-there is a danger of considerable oversimplification in dividing up student populations in this way, and problematizing those who do not or cannot comply with narrow culture-and context-dependent expectations.…”

Section: Diversity Of Learners' Representational Strategiesmentioning

confidence: 99%

Beyond categories: dynamic qualitative analysis of visuospatial representation in arithmetic

Finesilver

2022

Educ Stud Math

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Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad categorizations of representations and argues the benefits of dynamic qualitative analysis of arithmetical-representational strategy across multiple semi-independent aspects of display, calculation, and interaction. It proposes an alternative methodological approach combining the structured organization of classification with the detailed nuance of description and describes a systematic but flexible framework for analysing nonstandard visuospatial representations of early arithmetic. This approach is intended for use by researchers or practitioners, for interpretation of multimodal and nonstandard visuospatial representations, and for identification of small differences in learners’ developing arithmetical-representational strategies, including changes over time. Application is illustrated using selected data from a microanalytic study of struggling students’ multiplication and division in scenario tasks.

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“…Building Blocks; ) and patterning abilities in particular (cf. Pattern and Structure Mathematics Awareness Program [PASMAP]; Mulligan et al 2020).…”

Section: Ecuadorian Young Children's Repeating Pattering Abilities and Errorsmentioning

confidence: 99%

Ecuadorian children’s repeating patterning abilities and its association with early mathematical abilities

et al. 2020

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Young children's early repeating patterning abilities are important foundations for their later mathematical development. Prior studies on young children's repeating patterning abilities have been conducted exclusively in developed countries differing in economic, societal, and educational characteristics from developing countries. In this study, we analyzed the performance and the errors of 4-to 5-year-olds on three repeating patterning tasks, and we investigated the association between children's repeating patterning abilities and their early mathematical abilities in a developing country, Ecuador. A total of 60 preschoolers and 56 kindergartners completed a repeating patterning test and an early mathematics test at the end of the school year. Results first indicated rather low repeating patterning performances of both preschoolers and kindergartens, with large inter-individual differences in these performances. Kindergartners had significantly better patterning abilities than preschoolers. Second, error analyses indicated that children made different types of errors when solving the patterning tasks. The majority of errors were pattern-related errors, with preschoolers making more errors that were not pattern related than kindergarteners. Third, children's patterning abilities were positively associated with early mathematical abilities in both grades. These results complement current theoretical models of young children's mathematical development and inform educational policy and practices in this domain for developing countries.

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Supporting early mathematical development through a ‘pattern and structure’ intervention program

Cited by 46 publications

References 26 publications

A Systematic Review on Algebraic Thinking in Education

A Systematic Review on Algebraic Thinking in Education

Beyond categories: dynamic qualitative analysis of visuospatial representation in arithmetic

Ecuadorian children’s repeating patterning abilities and its association with early mathematical abilities

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