The Development and Initial Validation of an Assessment of Algebraic Thinking for Students in the Elementary Grades

Ralston, Nicole C.; Li, Min; Taylor, Catherine S.

doi:10.1080/10627197.2018.1483191

Cited by 17 publications

(31 citation statements)

References 39 publications

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“…The results of this study have contributed to the body of literature on early algebraic thinking. The majority of previous research on early algebraic thinking was focused only on teaching experiments which look into children's ability to think in an algebraic way and evaluation of algebraic thinking (Carpenter & Levi, 2000;McNeil;Ralston, 2013;Rittle-Johnson & Alibali, 1999). This study has provided numeric evidence on the constructs that could play a crucial role in algebraic thinking development.…”

Section: Discussionmentioning

confidence: 96%

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Year Five Pupils’ Number Sense and Algebraic Thinking: the Mediating Role of Symbol and Pattern Sense

Somasundram¹,

Sharifah²,

Eu³

2019

tner

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This study mainly focused on the relationship between number sense and algebraic thinking. Previous studies have provided evidence that number sense plays an important role in developing algebraic thinking. The role of symbol and pattern sense are yet to discover in relation to number sense and algebraic thinking. The purpose of this study was to identify the mediating effects of symbol sense and pattern sense in year five pupils' relationship between number sense and algebraic thinking. To do so, two mathematics tests were carried out among 720 year five pupils in the district of Malacca, Malaysia. The collected data were analysed using a partial least squares-structural equation modeling approach. The data collected were analysed using SPSS 22.0 and SmartPLS 3.0. Results demonstrated that symbol sense and pattern sense are good mediators between year five pupils' number sense and algebraic thinking. This result of the study supports the past studies related to the role of number sense, symbol and pattern sense in developing algebraic thinking. The presented study provides suggestions as intervention to increase students' making sense ability in numbers, symbols and patterns to develop algebraic thinking.

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Section: Discussionmentioning

confidence: 96%

“…The second instrument was algebraic thinking diagnostic assessment (ATDA). This instrument was adapted from Ralston (2013). ATDA was selected because it was the only assessment tool available in the literature to measure elementary students' algebraic thinking which encompasses all three strands of algebraic Figure 1.…”

Section: Instrument and Proceduresmentioning

confidence: 99%

Year Five Pupils’ Number Sense and Algebraic Thinking: the Mediating Role of Symbol and Pattern Sense

Somasundram¹,

Sharifah²,

Eu³

2019

tner

View full text Add to dashboard Cite

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“…Four tasks were adapted from Algebraic Thinking Diagnostic Assessment developed by Ralston (2013). This study reports the part of results from a major study carried out on algebraic thinking involving three components namely arithmetic generalisation, modelling and functions.…”

Section: Methodsmentioning

confidence: 99%

Pattern Generalisation by Year Five Pupils

Somasundram

Akmar

2019

Int Elect J Math Ed

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Pattern generalisation is one of the most important elements in developing functional thinking in elementary school which leads to build foundation to work with algebra in later years of education. Therefore, this study took an initiative to study the performance of year five pupils in pattern generalisation and its correlation with mathematics achievement. The sample of the study comprised 720 fifth grade pupils from a district of Malacca. Data were collected using four adapted tasks. Paper and pencil-based assessment conducted during the class hours. Data were analysed using descriptive and inferential statistics with help of SPSS software. The findings showed samples' ability to work with numerical patterns is better than their ability to work with figural patterns. However, the performance in far generalisation is extremely poor compared to near generalisation. While, a significant association found between performance of numerical and figural patterning tasks. Furthermore, there is no correlation between ability to work with patterns and mathematics achievement. With the increased interest in integrating functional thinking into elementary school teaching and learning, this work may be of interest to educators to identify how working with patterns could promote functional thinking and lead to a strong foundation for formal algebra learning in later years of education.

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“…This model, adapted for this particular study with primary school students, is shown in Figure 2. Simulation and generalization work are required in all three phases, but generalization work may be more common in generalized arithmetic, whereas representation may be more common in modeling studies (Ralston, 2013).…”

Section: Contribution To the Literaturementioning

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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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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The Development and Initial Validation of an Assessment of Algebraic Thinking for Students in the Elementary Grades

Cited by 17 publications

References 39 publications

Year Five Pupils’ Number Sense and Algebraic Thinking: the Mediating Role of Symbol and Pattern Sense

Year Five Pupils’ Number Sense and Algebraic Thinking: the Mediating Role of Symbol and Pattern Sense

Pattern Generalisation by Year Five Pupils

A Systematic Review on Algebraic Thinking in Education

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