This study is an endeavor to find how English native and nonnative EFL/ESL (English as foreign language/English as second language) writers use adversative conjunctions to connect ideas together so that texts have both coherence and cohesion. Regarding the problems nonnative writers of EFL face when composing a piece of writing, we attempted a…

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…

The emergence of empirical approaches to L2 pronunciation research and teaching is a powerful "fourth wave" in the history of the field. Authored by two leading proponents of evidence-based instruction, this volume surveys both foundational and cutting-edge empirical work and pinpoints its ramifications for pedagogy. The authors begin by…

Ask any teacher what he or she needs more of, and it is a good bet that time will top the list. Anything that promises to recoup a little bit of their workday time is sure to be a best seller. One overlooked time-saver is in how they use feedback. Teachers know that feedback is important for teaching and learning. Unfortunately, most secondary…

Early in their study of one-dimensional kinematics, my students build an algebraic model that describes the effects of a rolling ball's (perpendicular) collision with a wall. The goal is for the model to predict the ball's velocity when it returns to a fixed point approximately 50-100 cm from the wall as a function of its velocity as it passes…

Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…

"Focus in Grade 2: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 2 Focal Point as presented in 'Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics". It includes representational supports for teaching and learning that can facilitate…

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

This case provides auditing students with an opportunity to perform substantive tests of inventory using realistic-looking source documents. The learning objectives are to help students understand: (1) the procedures auditors perform in order to test inventory; (2) the source documents used in auditing inventory; and (3) the types of misstatements…

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

The academic demands of classroom English require students to think about language structure in ways that they are not used to. Everybody "knows" much English grammar intuitively but the academic rules themselves can be difficult to articulate. This goes for punctuation, too: errors often reflect students' lack of explicit knowledge of grammatical…

A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical…

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He outlines powerful diagnostic methods for analyzing student work and providing timely, specific, and meaningful…

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

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…