This study aims to analyse the advance organizers included in the course book "Secondary School Mathematics Course Book 5"--which was prepared in accordance with 2017 secondary school mathematics curriculum and which was accepted as an educational material by Turkish Education Board of Ministry of National Education for use in 2017-2018…

Through post-observation and general discussions our preservice teachers thought they were asking good questions by asking "why?". While these questions are important, "why?" questions are not always effective, especially when a student responds with "I don't know". Such questioning techniques must be explicitly…

Through their work on the Fractions Project, Steffe and Olive (2010) identified a progression of fraction schemes that describes students' development toward more and more sophisticated ways of operating with fractions. Although several quantitative studies have affirmed this progression, the question has remained open as to whether it is specific…

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space R[superscript m x n] in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

Researchers from different fields have developed different observational instruments to capture instructional quality with a focus on generic versus content-specific dimensions or a combination of both. As this work is fast accumulating, the need to explore synergies and complementarities among existing work on instruction and its quality becomes…

This paper provides an overview of the teaching for robust understanding (TRU) Framework, its origins, and its evolving use. The core assertion underlying the TRU Framework is that there are five dimensions of activities along which a classroom must do well, if students are to emerge from that classroom being knowledgeable and resourceful…

The Instructional Quality Assessment (IQA) identifies the nature and quality of classroom instruction by considering students' opportunities to engage in cognitively demanding mathematical work and discussions. The IQA assesses ambitious mathematics instruction based on the following dimensions: potential of the task, task implementation, rigor of…

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS--indexed as the most difficult ratio of two numbers that children can reliably discriminate--is well known to improve with development: whereas infants require relatively large ratios to…

The goal of this article is to raise questions that will promote discussions among secondary mathematics teachers about the concept of inverse functions and how to motivate a more conceptual understanding of them in their classrooms. The authors share data to answer the following questions: (1) What meanings of inverse functions do high school…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

The purpose of this study was to investigate the effectiveness of the ORIGO Stepping Stones program in a large suburban school district in the Midwestern U.S.. The sample included 11 elementary schools that implemented the program during the 2013-2016 school years. Findings are presented from teacher surveys, classroom observations, and analysis…

The structures of secondary mathematics teacher preparation (SMTP) programs in the United States are not well documented. This study sought to identify baseline data for SMTP programs. Survey data was collected from 86 different institutions regarding their SMTP programs. Results indicated that most SMTP programs are housed in mathematics…

With the publication of Bold Beginnings, Reception teachers and educationists felt their principles and practices were under attack. The main focus of the debate that ensued targeted the formality of learning, and especially teaching writing sitting at desks. The comments about the mathematics practices of the good schools incorporating Year 1…