We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

This corpus-based study investigates lexical richness in English writing by Chinese senior high school students. Lexical uses in 303 compositions were compared across three grades in terms of lexical sophistication, variation, density and errors. Timed compositions were sampled from Writing Corpus of English Learners, and the sample sizes of three…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

In two experiments we examined the extent to which musicians identify discrepancies between their intentions and their playing during individual practice. In the first experiment, 60 musicians representing four levels of skill development practiced a familiar piece from their own repertoire for 5 min while being audio recorded. They then listened…

This article describes a carefully structured exploration of formative assessment, conducted in the form of a classroom research experiment. The authors are an instructor and a student in a graduate course that assigned teachers to research formative assessment strategies, implement one or more strategies for several weeks, collect data from…

Peer grading is widely used in MOOCs and in standard university settings. The quality of grades obtained via peer grading is essential for the educational process. In this work, we study the factors that influence errors in peer grading. We analyze 288 assignments with 25,633 submissions and 113,169 reviews conducted with CrowdGrader, a web based…

Writing in L2 is considered a very challenging task by both teachers and students. Language teachers play a critical role in facilitating students' L2 writing development. Therefore, it is important to explore their beliefs about writing instruction as their beliefs exert influence on classroom practices. This study draws on the Repertory Grid…

The purpose of the study was to examine the quality of open test questions directed to high school and college students. One thousand five hundred examination questions from various fields of study were examined using criteria based on the writing centers directions and guidelines. The 273 questions that did not fulfill the criteria were analyzed…

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student…

Focusing on high school grade-point average (HSGPA) in college admissions may foster ethnic diversity and communicate the importance of high school performance. It has further been claimed that HSGPA is the best single predictor of college grades and that it is more equitable than test scores because of a smaller association with socioeconomic…

An inquiry-based laboratory exercise is described in which introductory chemistry students measure the density of water five times using either a beaker, a graduated cylinder, or a volumetric pipet. Students are also assigned to use one of two analytical balances, one of which is purposefully miscalibrated by 5%. Each group collects data using…

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…