A longitudinal assessment of early acceleration of students in mathematics on growth in mathematics achievement

Early acceleration of students in mathematics (in the form of early access to formal abstract algebra) has been a controversial educational issue. The current study examined the rate of growth in mathematics achievement of accelerated gifted, honors, and regular students across the entire secondary years (Grades 7–12), in comparison to their non-accelerated counterparts. Using data from the Longitudinal Study of American Youth, hierarchical linear models showed that early acceleration had little advantage among gifted students, small advantage among honors students, but large advantage among regular students. Equity issues, especially gender, racial, and socioeconomic equities, are not a concern once regular students were accelerated, but there are serious concerns about racial gaps among honors students and both gender and racial gaps among gifted students once they were accelerated. Schools played an important role in early acceleration, with school context rather than school climate affecting accelerated students. Students, particularly regular students, having high achievement and attending schools with high average achievement were advantageous in early acceleration. Overall, early acceleration of students in mathematics benefits regular students significantly in terms of growth in mathematics achievement.     

A computer-oriented task analysis method for mathematics instruction

Components of a computer solution for fraction problems in arithmetic have an analog in a new approach to educational task analysis. The components may be called goal-setting or planning elements, in contrast to the goal-satisfying or behavioral steps emphasized in much contemporary task analysis. A hypothetical tutorial dialogue in which a student is asked to tell a tutor what step to perform next is presented as an example of the emphasis of the planning side of computation. Explicit identification of goal-setting elements of a task is illustrated by analysis of the task of converting a pair of fractions to a new pair with a common denominator. The decomposition thus produces is simulated with two computer programs: (1) a LISP program using a set of production rules consisting of conditions to be met and subsequent actions to be taken and (2) a PROLOG program stating goals and solving goals explicitly.     

Reforming mathematics instruction: The role of curriculum materials

The crisis in mathematics education is likely to grow. One of the targets for reform is the math textbook, which largely defines the math curriculum. Several aspects of math textbooks that strongly influence student learning are explained: the organization of lessons, the use of time, the rate of introducing new concepts, the quality of instructional activities, the nature of the examples, and the provision of guided and independent practice. Excerpts from math texts illustrate these factors. Research findings on an alternative to basais, represented by the Direct Instruction math curriculum, illustrate how conceptual understanding and proficiency can be developed for a full spectrum of students.     

Using equivalence-based instruction to teach piano skills to children

The purpose of the current study was to evaluate the effects of equivalence-based instruction (EBI) on learning to play individual notes and simple songs on the piano. Participants were 4 typically developing children and 4 children with a diagnosis of autism spectrum disorder (ASD). They were exposed to a series of auditory–visual matching-to-sample procedures using musical stimuli. Following training, participants were tested on the emergence of novel untrained relations and generalization in the form of playing two songs on a keyboard. Results suggest that the EBI was effective in teaching piano playing skills with both typically developing children and children with ASD. The success of this procedure is indicative of the wide-ranging applications of EBI to novel and creative domains.     

Theory of learning mathematics with computer-assisted instruction: Hierarchical and nonhierarchical options

The learning of arithmetic problems is assumed to be a Markov process involving conditioning of a set of k subskills, each consisting of one or more productions. An axiom set is provided, with the choice between two options for one axiom controlling which of two models results. Model 1, which assumes that every subskill is attempted on every occurrence of a given problem, is a nonhierarchical model. Model 2, which assumes that every subskill in the temporal sequence for a problem is attempted until one is failed, is a somewhat unconventional hierarchical model: It is hierarchical in the sense that conditioningor chance success at one level is prerequisite to performance of the next subskill (next level) in the problem. As the value of the guessing parameter, g, declines, Model 2 leads to less efficient learning than Model 1.     

Using an abbreviated assessment to identify effective error‐correction procedures for individual learners during discrete‐trial instruction

Previous research comparing the effectiveness of error‐correction procedures has involved lengthy assessments that may not be practical in applied settings. We used an abbreviated assessment to compare the effectiveness of five error‐correction procedures for four children with autism spectrum disorder or a developmental delay. During the abbreviated assessment, we sampled participants' responding with each procedure and completed the assessment before participants reached our mastery criterion. Then, we used the results of the abbreviated assessment to predict the most efficient procedure for each participant. Next, we conducted validation assessments, comparing the number of sessions, trials, and time required for participants to master targets with each procedure. Results showed correspondence between the abbreviated assessment and validation assessments for two of four participants and partial correspondence for the other two participants. Findings suggest that a brief assessment may be a useful tool for identifying the most efficient error‐correction procedure for individual learners.     

Using equivalence‐based instruction to teach piano skills to college students

The purpose of the current study was to evaluate the effects of equivalence‐based instruction (EBI) on the emergence of basic music reading and piano playing skills. Six female college students learned to identify three musical chord notations given their respective dictated names. Participants also learned to play chords on the piano following the dictated name of the chord, and to play the chords to a song on a keyboard. Results are consistent with past research, in that stimuli became substitutable for each other and acquired a common behavioral function. Data suggest that EBI was an effective and efficient procedure to teach adults to read musical notation, as well as play chords and a song on a piano keyboard.     

A preliminary study of achievement, attitudes toward success in mathematics, and mathematics anxiety with technology-based instruction in brief calculus

This study was designed to compare achievement, attitudes toward success in mathematics, and mathematics anxiety of college students taught brief calculus using a graphic calculator, with the achievement and attitudes and anxiety of students taught using the computer algebra system Maple, using a technology based text book. 50 men and 50 women, students in three classes at a large public university in the southwestern United States, participated. Students' achievement in brief calculus was measured by performance on a teacher-made achievement test given at the end of the study. Analysis of variance showed no significant difference in achievement between the groups. To measure change in attitudes and anxiety, responses to paper-and-pencil inventories indicated significant differences in favor of students using the computer.     

Using equivalence‐based instruction to teach college students to identify logical fallacies

Although there is no consensus as to the specific skills that constitute critical thinking, there is general agreement that identifying logical fallacies is an important component skill. Clearly defined logical fallacies are suited to teaching arrangements that focus on establishing conditional discriminations, as is the case with equivalence‐based instruction (EBI) methods. EBI methods have been successfully delivered using web‐based course management software and have rapidly produced socially significant learning outcomes. The purpose of the current study was to evaluate the effectiveness and efficiency of a web‐based EBI program for teaching students to recognize and identify logical fallacies by comparing the outcomes of EBI to a self‐instruction and a no‐instruction control group. EBI was more effective and more efficient when compared to both self‐instruction and no‐instruction controls. Additionally, untrained relations were evident only after EBI.     

Videodisc instruction in science and mathematics: Implications for media research and instructional design

This article summarizes research conducted over the last seven years on videodisc instruction in science and mathematics. Research findings, as well as the instructional design principles used to create programs, have direct implications for the general debate over media and its effects on learning. The array of studies conducted with the videodisc programs indicates that the medium is very cost effective. High quality instruction can be presented reliably and with much less human effort than traditional methods of instruction. By using videodiscs, developers are also able to exploit the strong graphic features of the medium, thus allowing carefully-designed visual images to play a key role in the instruction. Empirical support for non-text presentations along with examples of the graphics used in the science and mathematics programs are discussed.     

Using equivalence‐based instruction to teach the visual analysis of graphs

Previous research has demonstrated low rater agreement when visually inspecting trends in single‐subject design graphs (see Wolfe, Seaman, & Drasgow, 2016). Didactic instruction of visual analysis of practicing behavior analysts has resulted in generally poor and unreliable performances (Danov & Symons, 2008; Diller, Barry, & Gelino, 2016). Therefore, a refined instructional technology to improve the reliability among behavior analysts is warranted. Developing research has focused on the application of equivalence‐based instruction (Brodsky & Fienup, 2018; Rehfeldt, 2011) for a variety of complex human behaviors. In the current study, equivalence‐based instruction was used to train four participants to identify functional relations displayed in five different classes of graphs. Training resulted in the formation of five equivalence classes by all participants consisting of three members (graph, functional relation rule, and functional relation statement). In addition, the skills were maintained for up to 2 weeks and generalized to novel graphs.     

The equivalence of learning paths in early science instruction: effect of direct instruction and discovery learning

In a study with 112 third- and fourth-grade children, we measured the relative effectiveness of discovery learning and direct instruction at two points in the learning process: (a) during the initial acquisition of the basic cognitive objective (a procedure for designing and interpreting simple, unconfounded experiments) and (b) during the subsequent transfer and application of this basic skill to more diffuse and authentic reasoning associated with the evaluation of science-fair posters. We found not only that many more children learned from direct instruction than from discovery learning, but also that when asked to make broader, richer scientific judgments, the many children who learned about experimental design from direct instruction performed as well as those few children who discovered the method on their own. These results challenge predictions derived from the presumed superiority of discovery approaches in teaching young children basic procedures for early scientific investigations.     

Response to instruction, English language learners and disproportionate representation: the role of assessment

Response to Intervention (RtI), a cyclical process that incorporates assessment and instruction, is both an approach to prevent learning difficulties and to establish student eligibility for special education. Assessment results are used to determine students' initial knowledge and skill, their need for successively more intensive levels of instruction, and to gauge their response to the intervention provided. Although this process is preferable to the IQ/achievement discrepancy model for determining the presence of specific learning disabilities, there are still a number of unresolved issues related to the assessment procedures in use. A pressing issue is the identification of measures and procedures that identify students with the greatest precision thus reducing inappropriate identification.     

The effects of computer-assisted instruction on the mathematics performance and classroom behavior of children with ADHD

The present study examines the effects of computer-assisted instruction (CAI) on the mathematics performance and classroom behavior of three second-through fourth-grade students with ADHD. A controlled case study is used to evaluate the effects of the computer software on participants' mathematics performance and on-task behavior. Participants' mathematics achievement improve and their on-task behavior increase during the CAI sessions relative to independent seatwork conditions. In addition, students and teachers consider CAI to be an acceptable intervention for some students with ADHD who are having difficulty with mathematics. Implications of these results for practice and research are discussed.     

早期儿童数学学习与执行功能的关系

执行功能是个体对复杂的认知活动的自我调节和以明确目标为导向的活动过程, 对早期儿童的数学学习起着重要的作用。早期儿童数学学习与执行功能呈显著正相关, 执行功能是儿童数学学习的重要认知加工机制。早期儿童执行功能和数学学习之间存在着相互预测的关系, 执行功能可以预测数学成绩, 数学成绩可以预测执行功能。高质量的早期数学教育可能具有发展儿童执行功能和数学能力的双重价值。未来研究可以明确执行功能的界定和统一测量工具, 提供更可靠的证据证明早期儿童执行功能与数学能力的因果关系, 以及进一步探究语言、数学以及执行功能三者之间的关系。     

Longitudinal study of low and high achievers in early mathematics

Background. Longitudinal studies allow us to identify, which specific maths skills are weak in young children, and whether there is a continuing weakness in these areas throughout their school years. Aims. This 2‐year study investigated whether certain socio‐demographic variables affect early mathematical competency in children aged 5–7 years. Sample. A randomly selected sample of 127 students (64 female; 63 male) participated. At the start of the study, the students were approximately 5 years old (M= 5.2; SD= 0.28; range = 4.5–5.8). Method . The students were assessed using the Early Numeracy Test and then allocated to a high (n= 26), middle (n= 76), or low (n= 25) achievers group. The same children were assessed again with the Early Numeracy Test at 6 and 7 years old, respectively. Eight socio‐demographic characteristics were also evaluated: family model, education of the parent(s), job of the parent(s), number of family members, birth order, number of computers at home, frequency of teacher visits, and hours watching television. Results . Early Numeracy Test scores were more consistent for the high‐achievers group than for the low‐achievers group. Approximately 5.5% of low achievers obtained low scores throughout the study. A link between specific socio‐demographic characteristics and early achievement in mathematics was only found for number of computers at home. Conclusions . The level of mathematical ability among students aged 5–7 years remains relatively stable regardless of the initial level of achievement. However, early screening for mathematics learning disabilities could be useful in helping low‐achieving students overcome learning obstacles.