High school teachers often encounter incorrect solutions from students, especially when teaching combinatorics. This study investigates the ability of prospective mathematics teachers to assess the correctness of solutions to combinatorial problems and to falsify incorrect ones. 39 second-year prospective teachers participated in the experiment,…

This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

The effects of fluency-based instruction and accuracy-based instruction on contingency adduction were assessed using an alternating treatments design. Stimulus equivalence tasks were used to measure contingency adduction. Stimulus classes were composed of arbitrary visual forms. One treatment condition consisted of teaching fast, fluent responding…

Background: With the development of computational literacy, there has been a surge in both research and practice application of text-based and block-based modalities within the field of computer programming education. Despite this trend, little work has actually examined how learners engaging in programming process when utilizing these two major…

Learner corpora have been used extensively in corpus research to identify gaps and errors within learner writing but have rarely been directly used in corpus-informed instruction (CII). Importantly, scholars in CII have pointed out that "it is as important to see what learners can do as well as what they can't" when using learner corpora…

Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of…

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

Undergraduate biochemistry students frequently find the quantitative treatment of weak acids and bases troublesome. Given the p"K"[subscript a] of a weak acid "HA," for instance, many students struggle to calculate the pH of a solution of the conjugate base A[superscript -] at concentration "C," pH(A[superscript -],…

The present study examined whether a defense rebuttal expert can effectively educate jurors on the risk that the prosecution's fingerprint expert made an error. Using a sample of 1716 jury-eligible adults, we examined the impact of three types of rebuttal testimony in a mock trial: (a) a methodological rebuttal explaining the general risk of error…

This study contributes to discussions on facilitating students' sense-making in science by analyzing the utterances of high-achieving students in dialogues during practical work and identifying characteristics of their language use and learning processes. The context of the study is a general science course at an upper secondary school in Norway.…

One of the critiques of proficiency as defined by scales, such as that of ACTFL, is its lack of grounding in linguistic realities. Measures of complexity, accuracy, and fluency provide a route in which proficiency can be quantitatively measured by identifying linguistic correlates (see Brown et al., 2017; Long et al., 2012). This project aimed to…

In the present study, researchers used problem-posing instruction to examine elementary students' understanding of multiplication. Students in fourth and fifth grade classrooms (n = 24) from a rural school district participated in a semester-long study. The focus of this study was examining student solutions to two specific lessons with problems…

We evaluated two procedures to teach auditory-visual conditional discriminations (receptive labeling) to children with autism. The procedures evaluated a modified Structured Mix (SM) procedure and a modified Counterbalanced Random Rotation (RR) procedure. The modified SM procedure was based on the logic of simplifying the task by breaking it down…

Whether or not to teach grammar explicitly is an issue that has long been debated in the field of SLA. There seems to be a growing consensus among many researchers now in support of embedding some element of explicit instruction within a communicative curriculum. The main arguments in support of explicit instruction are threefold: two widely cited…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…