Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

Pincheira, Nataly; Pastells, Ángel Alsina i

doi:10.3390/math9202590

Cited by 20 publications

(21 citation statements)

References 56 publications

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“…The teacher's mathematical knowledge is a key factor in ensuring adequate student learning in elementary education [58]. Among the different mathematical contents, one interesting element is the study of fractions due to, among other reasons, their importance in the learning of several science areas.…”

Section: Discussionmentioning

confidence: 99%

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

López‐Martín¹,

Aguayo-Arriagada²,

López³

2022

Mathematics

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The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge.

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Section: Discussionmentioning

confidence: 99%

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

López‐Martín¹,

Aguayo-Arriagada²,

López³

2022

Mathematics

View full text Add to dashboard Cite

show abstract

“…According to Pincheira and Alsina (2021), teachers in early childhood and primary school demonstrate a lack of mathematical expertise necessary to teach early algebra. This result confirms the necessity of teacher training.…”

Section: Discussionmentioning

confidence: 99%

“…There are no systematic literature reviews that specifically focus on algebraic reasoning. In contrast, systematic literature reviews tend to focus on the use of ICT and instructors' knowledge for algebraic thinking (Pincheira & Alsina, 2021) and using ICT to develop algebraic thinking (Goulding & Kyriacou, 2008). A systematic literature review is aimed to provide an overview for research-based studies on algebraic thinking.…”

Section: Introductionmentioning

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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“…This task allowed us to identify the strengths and weaknesses of PTs regarding probability and its didactics. The use of the MKT model to analyse PTs' mathematical knowledge for teaching has allowed us to determine where we should focus our teacher training, helping us to identify the challenges we need to address in future training programmes and allowing us to improve our own instruction, as also indicated in [59]. Studies such as [60] show that probability continues to be taught in a decontextualised way, becoming arithmetically based and dominated by the direct application of formulas, so we consider it necessary to continue working in this direction in order to improve prospective teacher training.…”

Section: Discussionmentioning

confidence: 99%

What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

et al. 2021

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The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.

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Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

Cited by 20 publications

References 56 publications

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

A Systematic Review on Algebraic Thinking in Education

What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

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