This paper resulted from an unfolding of an ongoing doctoral research that deals with the characterization of a specific type of arithmetic in times of Brazilian industrial education, that is, between 1942 and 1968. The objective is to analyze knowledge produced by Roberto Mange for training, aiming not only to recognize them as such, but also to…

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned…

To support productive struggle, prospective secondary mathematics teachers (PTs) need to elicit and respond to students' mathematical ideas in ways that focus on those ideas and that position students to build on those ideas. Using the Teacher Response Coding framework (Van Zoest et al., 2021) we analyzed PTs' responses in three rehearsals of…

The purpose of this paper is to present a framework that illustrates teachers' and students' ways of noticing mathematical engagement. This framework offers clarity about the complexity of engagement, and it includes three elements: evaluations of the presence of engagement, descriptions of the nature of engagement, and features of the classroom…

Number talks, a popular mathematics teaching routine in the United States, may offer supports for beginning teachers (BTs) to engage in ambitious instruction. BTs' enactments of number talks, however, are varied, and there are few empirical studies that explore how BTs' enactment of number talks could be more (or less) ambitious. This paper draws…

In this paper, we present the spontaneous and reasoned approaches by a Physicist (B.C.) and a Mathematician (T.B.). Section 1 is by B.C and section 2 is by T.B.

This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. "Figuring Out Fluency in Mathematics Teaching and Learning" offers educators the inspiration to develop a deeper understanding of procedural fluency, along with…

Ascertaining young children's attitudes towards mathematics has its challenges. Methodologically, limitations exist regarding the type of research techniques that can be employed. The use of children's drawings as a data source has both methodological affordances and issues. The study was conducted with 106 children in Years 2 and 3 from three…

The practice assignments in a mathematics textbook or course can be arranged so that most of the problems relating to any particular concept are massed together in a single assignment, or these related problems can be distributed across many assignments -- a format known as spaced practice. Here we report the results of two classroom experiments…

Mathematics anxiety can be a debilitating experience, and research shows that elementary-level preservice teachers experience high levels of mathematics anxiety. Current shifts in mathematics education from a procedural focus to a conceptual focus may exacerbate these high anxiety levels. The research reported in this study explored how preservice…

Effective early mathematics instruction is critical to support long-term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors…

Effective early mathematics instruction is critical to support long-term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors…

This ex post facto correlational study assessed the effectiveness of an ILS, i-Ready Instruction, on student growth in the elementary school setting. The existing limited independent research has not supported the claims that the creators of i-Ready Instruction have made regarding increasing student achievement or growth. Based on the results from…

African Americans have suffered many negative consequences as a result of racism. African Americans are currently underperforming their White counterparts in the field of Mathematics. Several examples have indicated that the appropriate use of resources can significantly affect this gap in performance. The concepts of deep study and spaced…