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Patterning, as a component of early mathematic knowledge, is a common activity carried out at elementary levels in which children are not equally successful. This study aimed to measure different variables affecting performance on patterning tasks in early childhood. For this purpose, the success of Pre-K (N = 33), K (N = 31) and first-grade (N = 33) children when solving 14 repeating-pattern tasks, which varied in complexity, was analysed. The results revealed no significant differences between core-2 and core-4 length patterns, and greater success with patterns involving size. The study also introduces distractors, as a novel factor, in the patterning activities related to the presence of contradictory or surplus data. The impact of each factor and the relations between complexity and difficulty on the patterning tasks are discussed in order to contribute to the design of teaching itineraries. [ABSTRACT FROM AUTHOR]

Statistical literacy is key in this heavily polarized information age for an informed and critical citizenry to make sense of arguments in the media and society. The responsibility of developing statistical literacy is often left to the K-12 mathematics curriculum. In this article, we discuss our investigation of K-8 students' current opportunities to learn statistics created by state mathematics standards. We analyze the standards for alignment to the Guidelines for the Assessment and Instruction in Statistics Education (GAISE II) PreK-12 report and summarize the conceptual themes that emerged. We found that while states provide K-8 students opportunities to analyze and interpret data, they do not offer many opportunities for students to engage in formulating questions and collecting/considering data. We discuss the implications of the findings for policy makers and researchers and provide recommendations for policy makers and standards writers. [ABSTRACT FROM AUTHOR]

The alignment between the geometric and metric content evaluated in the Tests of Knowledge (Grade 5) and the suggestions of the Curriculum Guidelines and Standards have been studied. The data are considered qualitatively and inductively; the data was analysed by categories: thoughts and knowledge associated with the study of geometry and measurement. The research evidence, Among several aspects, that the test tends to evaluate the ideas spatially and metric separately, to ignore its link with other thoughts and to privilege, in some occasions, the disjointed competencies of specific content. In conclusion, the alignment studied is not adequate, therefore, making decisions to prepare students for the application of the test should carefully consider their results and the questions discussed in it. If not, we seek reflections that go against the suggestions of the official documents that determine the curriculum in Colombia. [ABSTRACT FROM AUTHOR]

Behavioral fluency refers to the relationship between the achievement of performance standards, or frequency ranges of behavior, and critical learning outcomes. Over the past 20 years, Precision Teaching and related research have contributed a number of studies examining behavioral fluency. The subsequent review investigates the empirical evidence from mathematics intervention research. Several studies suggest numerical markers that best support behavioral fluency. Results indicate that fluency interventions set to performance standards increased behavioral fluency and associated critical learning outcomes; however, more research is warranted to operationalize and standardize each outcome to the principles of behavior and numerical markers that constitute behavioral fluency. [ABSTRACT FROM AUTHOR]

The authors review the influence of state, national and international large-scale assessments (LSAs) on education policy and research. They distinguish between two main uses of LSAs: as a means for conducting research that informs educational reform and LSAs as a tool for implementing standards and enforcing accountability. The authors discuss the influence of the international TIMSS study on US mathematics standards and the development of the Common Core as an example of LSA’s potential for research-based reform. They also examine how the controversy over using assessments to evaluate teacher performance suggests some of the problems with using LSAs as a lever for policy. They conclude by suggesting that the ‘assessment to inform policy’ model may be more promising (and yield greater long-term fruits) than an ‘assessment as policy’ model. [ABSTRACT FROM AUTHOR]

Patterns are a pervasive and important, but understudied, component of early mathematics knowledge. In a series of three studies, we explored (a) growth in children's pattern knowledge over the pre-K year ( N = 65), (b) the frequency of pattern activities reported by parents ( n = 20) and teachers ( n = 5) relative to other mathematical activities, and (c) changes in 4-year-old children's pattern knowledge after brief experience generating or receiving explanations on patterns ( N = 124). Together, these studies illustrate the types of experiences preschool children are receiving with patterns and how their pattern knowledge changes over time and in response to explanation. Young children are able to succeed on a more sophisticated pattern activity than they are frequently encouraged to do at home or at school. [ABSTRACT FROM AUTHOR]

Principles and Standards for School Mathematics outlines essential features crucial to teaching mathematics so that all students have opportunities to learn mathematics content with conceptual understanding. Although the document outlines extensive goals for the teaching and learning of mathematics, the majority of classrooms fall short in its implementation, especially high-poverty middle schools. Therefore, the authors investigated the mathematics pedagogical and instructional skills of sixty-four in-service teachers who teach in high-poverty middle schools (grades six through eight). The results indicated that although the subjects are implementing a variety of practices, lecture, drill and practice, and teacher-directed instruction continue to dominate many high-poverty classrooms. [ABSTRACT FROM AUTHOR]