This article aims to share five practical approaches for how teachers can identify, adapt, and create their own writing prompts they assign to students: (1) Promote Students' Solution Paths; (2) Go beyond Asking Students to Simply "Explain"; (3) Prompt Students to Share Their Reasoning; (4) Have Students Consider the Validity of a Given…

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. This resource describes the progressions of learning within each course and provides content support, which includes broad ideas about effective instruction as well as practical instructional strategies. Math…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

Mathematical thinking beliefs are a significant element in supporting teachers' practices of learning and teaching school mathematics. Most prior researches on mathematics beliefs have focused on teachers' beliefs about learning and teaching mathematics in general. This research aimed to validate a Mathematical Thinking Belief instruments (MTB).…

Current international curriculum frameworks and research advocate for K-12 mathematics to emphasize proof and argumentation. This review synthesizes literature related to conceptions, content, and supportive actions for proof and argumentation across four grade-level bands: K-2, 3-5, 6-8, and 9-12. Our systematic search and subsequent screening…

The purpose of this study is to explore elementary educators' perceptions regarding what it means to conceptually understand mathematics, the emphasis teachers place on utilizing evidence-based teaching processes, as identified as effective by National Council of Teachers of Mathematics (NCTM), and how these perceptions influence their…

This manuscript reports the results of two pilot studies that investigated the views of international cohorts of teacher educators regarding the efficacy of the flipped classroom paradigm in K-12 schools. A void in the literature addressed by each pilot study was the relevance of flipped classrooms to student subgroups requiring specialized…

Based on findings from a large meta-data-based literature survey, this article is intended to provide a comprehensive synthesis of key features of China's music education system as seen through the lens of n = 116 major research studies, drawn from a total of N = 3,257 high-impact Chinese journal articles published during 2007 to 2019. The…

In this study, we analyzed and compared reasoning and proving opportunities in geometry lessons from American standard-based textbooks and Korean textbooks to understand how these textbooks provide student opportunities to engage in reasoning and proving activities. Overall, around 40% of exercise problems in Core Plus Mathematics Project (CPMP)…

Root cause analysis is a powerful method schools use to analyze data to solve problems; it aims to identify and correct the root causes of problems or events, rather than simply addressing their symptoms. In this webinar, veteran practitioner, Roni Silverstein, talked about the value of this process and practical ways to use it in your school or…

This report describes the implementation of professional development (PD) reforms and efforts to use teacher effectiveness (TE) data to inform PD through the third year of the initiative for all seven sites: Hillsborough County Public Schools (HCPS), Shelby County Schools (SCS, formerly Memphis City Schools), Pittsburgh Public Schools (PPS), and…

School personnel make a variety of decisions within multitiered problem-solving frameworks, including the decision to assign a student to group-based support, to design an individualized support plan, or classify a student as eligible for special education. Each decision is founded upon a judgment regarding whether the student has responded to…

This article reviews some key ideas about the nature of proof, kinds of proofs, and the way of reasoning called proving. This provides background for a discussion of the teaching of proof, in which some important aspects of teaching that support students' proving are described, and the ideas of a tool-box of accepted premises and local…

This article presents a review of the Comprehensive Test of Nonverbal Intelligence-Second Edition (CTONI-2), a nonverbal intelligence test created to assess reasoning and problem solving of children and adults. The goal of the CTONI-2 is to minimize the influence of language ability on intelligence test scores. Oral or pantomime instructions can…

The contributors to this special issue have helped everyone consider the next steps in building a research and practice agenda regarding the use of treatment integrity. Such an agenda must converge with the big ideas that link treatment integrity to the effectiveness of evidence-based practices (EBPs), and ultimately that of the profession. In…