It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…

In this article, we respond to Wolery's critique of the What Works Clearinghouse (WWC) pilot "Standards," which were developed by the current authors. We do so to provide additional information and clarify some points previously summarized in this journal. We also respond to several concerns raised by Maggin, Briesch, and Chafouleas…

This article reviews the intended uses of these college- and career-readiness assessments with the goal of articulating an appropriate validity argument to support such uses. These assessments differ fundamentally from today's state assessments employed for state accountability. Current assessments are used to determine if students have…

This article addresses validity and fairness in the testing of English language learners (ELLs)--students in the United States who are developing English as a second language. It discusses limitations of current approaches to examining the linguistic features of items and their effect on the performance of ELL students. The article submits that…

Recently, 57 undergraduate students at the University of Michigan were assigned the task of solving a crystal structure, given only the electron density map of a 1.3 Å crystal structure from the electron density server, and the position of the N-terminal amino acid. To test their knowledge of amino acid chemistry, the students were not given the…

As more states begin to adopt teacher evaluation systems based on value-added measures, legal challenges have been filed both seeking to limit the use of value-added measures ("Cook v. Stewart") and others seeking to require more robust evaluation systems ("Vergara v. California"). This study reviews existing teacher evaluation…

The European inventory on validation of non-formal and informal learning provides an unrivaled source of information detailing how validation of prior learning is developing across Europe. It shows that validation strategies and legislation, despite complexity of the task before them, have been developing slowly but steadily. However, there is…

Background: Conceptual understanding is a prerequisite for engineering competence. Concept maps may be effective tools for assessing conceptual knowledge, yet further work is needed to examine scoring methods. Purpose: Our purpose was to evaluate the efficacy of three concept map scoring methods. Traditional scoring requires judges to count…

Schools are social organizations where children came together from different cultures. Creating sense of community is important for schools for the formation of social culture. In schools where sense of community is formed, it is observed that students treat each other with respect, are caring and sharing and have high academic success, and rates…

The present study investigated the concurrent validity of the Classroom Strategies Scale-Teacher Form (CSS-T), a multidimensional teacher formative assessment of instructional and behavioral management practices. The CSS-T is compared with the Classroom Assessment Scoring System (CLASS), a well-known teacher assessment of overall classroom…

It has been revealed that over the years, the number of the aged in the world has been on a steady increase. This rising number has great implications for government, researchers, families, youth and the society at large. There is therefore, the proper need for the understanding of the nature problems and challenges as well as the management…

Student attitudes toward mathematics play an important role in the teaching and learning processes of mathematics as positive attitudes correlate with higher student achievement. This paper aims to develop and explore the validity of a Chinese version of the short attitudes toward mathematics inventory (short ATMI) for Taiwanese undergraduates,…

The purpose of this study is to describe the procedure and examples of visual proofs (VP-or proof without words) developed by gifted mathematics secondary school students after their experiences. The participants of this study are three male 9th grade students enrolled in a private science high school. In the first stage of the research a briefing…

Artificial language learning (ALL) experiments have become an important tool in exploring principles of language and language learning. A persistent question in all of this work, however, is whether ALL engages the linguistic system and whether ALL studies are ecologically valid assessments of natural language ability. In the present study, we…

As an alternative to rubric scoring, comparative judgment generates essay scores by aggregating decisions about the relative quality of the essays. Comparative judgment eliminates certain scorer biases and potentially reduces training requirements, thereby allowing a large number of judges, including teachers, to participate in essay evaluation.…