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In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of lessons is important as it can help teachers better support students' self-efficacy in their everyday work. In this paper, we expanded previous studies by investigating changes in students' self-efficacy across a sequence of 3–4 lessons when students were learning a new topic in mathematics (nStudents = 170, nTime-points = 596). Nine classes of Norwegian grade 6 (n = 77) and grade 10 students (n = 93) reported their self-efficacy for easy, medium difficulty, and hard tasks. Using multilevel models for change, we found (a) change of students' self-efficacy across lesson sequences, (b) differences in the starting point and change of students' self-efficacy according to perceived task difficulty and grade, (c) more individual variation of self-efficacy starting point and change in association with harder tasks, and (d) students in classes who were taught a new topic in geometry had stronger self-efficacy at the beginning of the first lesson as compared to those who were taught a new topic in algebra (grade 10), and students in classes who were taught a new topic in fractions had steeper growth across the lesson sequence as compared to those who were taught a new topic in measurement (grade 6). Implications for both research and practice on how new mathematics topics are introduced to students are discussed. [ABSTRACT FROM AUTHOR]

In this paper we consider implications of the current world-wide inclusion of computational thinking in relation to children's development of algebraic thinking. Little is known about how newly developed visual programming environments such as Scratch could enhance early algebra learning. The study is based on examples of programming activities used by mathematics teachers in Sweden, teaching students aged 10–12 years during the first two years of implementing programming in the mathematics curriculum. Informed by Chevallard's praxeology in terms of praxis and logos, we describe, unpack, discuss and expand these activities. Core issues related to algebra found in the three activities are as follows: making implicit variables explicit; using a counter variable; and identifying parameters as a specific type of variable. Our findings show that, in addition to already identified uses of variables in early algebra, programming activities in the early years bring in new aspects and new ways of treating variables that could, potentially, enhance students' understanding of variables and generalization, provided that programming praxis is embedded in an appropriate algebra logos. [ABSTRACT FROM AUTHOR]

Algebra is a key course in the secondary mathematics curriculum. As a prerequisite for post-secondary mathematics, science and engineering courses, it is considered a gateway course. Since mathematical knowledge for teaching involves more than content knowledge algebra, teachers must be able to do more than successfully complete algebraic problems. They should understand algebra deeply and flexibly so that they are able to mediate students’ ideas, make choices about representations of content and modify curriculum materials. Yet, little is known about how certain groups view algebra and its teaching. In order to determine the beliefs held by a group of South African mathematics teachers with historically disadvantaged backgrounds teaching in schools that were previously segregated through Apartheid, this paper reports on what the group felt are the most important features of algebra. [ABSTRACT FROM PUBLISHER]

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were teaching from the same curriculum materials, the teacher with higher MKT had more complete and concise ways to describe key concepts, had multiple ways to represent ideas about linear equations, could move nimbly among different mathematical expressions of linear relationships, and gave students a larger role in articulating the mathematical ideas of the lesson. However, curriculum materials seem to have moderated what would otherwise have been larger disparities in the quality of instruction between the two teachers. The lower-MKT teacher made minor mathematical errors, stayed on topic, and defined concepts in reasonably accurate ways when he followed the curriculum materials closely. [ABSTRACT FROM AUTHOR]

The aim of this paper is to direct the attention of the international mathematics education community to the emergence of a growing network of teachers, researchers, and developers who are using and discussing an open-source software package entitled GeoGebra. Created by Markus Hohenwarter in 2001, GeoGebra represents a digital learning environment that was designed to combine geometry, algebra, and calculus in a single, dynamic user interface. The emergence of GeoGebra as an increasingly popular mathematics education resource is likely due to a number of key characteristics: open-source status, multiple language translations, versatility (i.e., algebraic and geometric representations), and an on-line wiki and user forum. The authors provide a brief history and description of the GeoGebra software, and also discuss the nascent International GeoGebra Institute (IGI) in terms of its vision and related international developments. [ABSTRACT FROM AUTHOR]

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher's professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra. [ABSTRACT FROM AUTHOR]

In this paper we describe a strand of activities for teachers of mathematics that we used with two cohorts of participants in a professional development program called Revitalizing Algebra (REAL). We first discuss our goals and describe the participants, and then we describe the construction and selection of the tasks followed by teacher responses. Finally, we reflect on different iterations of the tasks, their impact on the teachers’ thinking and practice, and the role of school and department culture in the process of change. [ABSTRACT FROM AUTHOR]