Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

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…

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…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

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,…

Mirror visual feedback increases neural activity, enhances performance, and induces neuroplasticity; however, mixed results have been observed during the learning of motor skills. While mirrors are commonplace in Western dance education, further research is needed to determine how mirrors are used when learning dance phrases. This study measured…

Purpose: Children make spelling errors despite classroom instruction on phoneme-grapheme connections and spelling rules. We examined whether additional practice helps to decrease the number of spelling errors for a morphological spelling rule. We distinguished explicit practice in applying a spelling rule from implicit exposure to correct word…

Empirical evidence supports the view that explicit teaching can make a positive difference to learning; however, further research is needed to understand the impact on learning to spell if spelling error analysis is used to inform explicit spelling instruction. This paper presents findings of an intervention study involving 572 students in Years 3…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

It is commonly agreed that learner target language output and spoken interaction are essential to communicative language learning. This video-based classroom observation study of five lower secondary schools in Norway investigated how second language (L2) English and third language (L3) French teachers responded to their students when they spoke…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

R and Python are commonly used software languages for data analytics. Using these languages as the course software for the introductory course gives students practical skills for applying statistical concepts to data analysis. However, the reliance upon the command line is perceived by the typical nontechnical introductory student as sufficiently…

Errors in mathematics are common hurdles for teachers and students; therefore, it is important to learn what errors students make and how students treat them. This study initially identified the types of errors students made while working with algebraic expressions and documented and analyzed the process of students completing an error analysis…