Student Preference for Explicit Timing and Interspersal Procedures as a Function of Math Problem Completion Rates: Testing the Discrete Task Completion Hypothesis

A within-subjects design was used to compare explicit timing and interspersal with college students. Students were given 3 minutes to complete problems on the explicit timing assignment (25 problems, 3 digits –3 digits) and the interspersal assignment (25 similar problems and 10 problems, 1 digit –1 digit). Results indicated that: (a) students completed more total problems during interspersal for both trials, (b) students completed more target problems during explicit timing for the second trial, and (c) students only preferred interspersal for the first trial. The data from trial one fit the discrete task completion hypothesis and matching law, yet the data from trial two do not match as closely (Skinner, 2002). Discussion focuses on continued need for more research on academic interventions, comparing academic interventions, the discrete task completion hypothesis, and the matching law.     

An Experimental Analysis of Mathematics Instructional Components: Examining the Effects of Student-Selected Versus Empirically-Selected Interventions

Within the context of an experimental analysis, the current study examined the effects of student- and empirically-selected interventions on the mathematics computational fluency of three elementary-aged students. For all of the participants, the empirically-selected intervention resulted in higher levels of computational fluency then the student-selected intervention. These results suggest that empirically-selected interventions may enhance the mathematics computational fluency of students experiencing mathematics problems. However, individual responsiveness to empirically-selected interventions suggests the importance of conducting brief experimental analyses to determine the most efficacious intervention. The implication of these results for intervention selection and incorporating choice-making opportunities into academic interventions are discussed.     

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students’ strategies were classified into four categories. A data set resulted with two types of repeated observations within students: the nominal strategies and the dichotomous achievement scores (correct/incorrect) on the items administered.It is argued that latent variable modeling methodology is appropriate to analyze these data. First, latent class analyses with year of assessment as a covariate were carried out on the multivariate nominal strategy variables. Results showed a shift from application of the traditional long division algorithm in 1997, to the less accurate strategy of stating an answer without writing down any notes or calculations in 2004, especially for boys. Second, explanatory IRT analyses showed that the three main strategies were significantly less accurate in 2004 than they were in 1997.     

初中生数学自我效能问卷的编制

根据国内外关于数学自我效能研究的文献,结合我国初中生数学学习的内容特点与实际背景情况,编制数学自我效能问卷。研究以初一与初二学生为对象,采用开放式问卷对188名学生和53名数学教师进行调查,首先编制出44个项目的初测问卷;采用封闭式问卷对479名学生的初测结果进行验证性因素分析与项目分析,形成了包含日常生活中数学任务的效能、数学相关课程的效能与数学学业问题解决效能三个维度的26个项目的正式问卷;最后对350名学生施测正式问卷。分析研究结果表明,该数学自我效能问卷的因素结构清晰,具有合理的信度和效度。     

流畅体验、内/外动机、数学焦虑及数学成绩的路径分析

目的：研究旨在考察数学学习中的流畅体验,探讨流畅体验、内/外动机、数学焦虑及数学成绩的关系。方法：招募296名高中生,在数学月考后完成自编考试流畅体验量表、学习动机量表、数学焦虑量表。结果：路径分析表明,存在四条显著路径,即内部动机→流畅状态→数学成绩;数学焦虑→流畅状态→数学成绩;外部动机→流畅状态→数学成绩;外部动机→数学成绩。结论：只有通过考试过程中的流畅体验,内部动机和数学焦虑才能影响考试成绩。     

Self-recording and goal-setting: Effects on on-task and math productivity of low-achieving Korean elementary school students

Using an alternating treatments design, we investigated the effects of self-recording and goal-setting on the on-task behavior and the mathematics productivity of five low-achieving elementary school students in a group of eleven students in Korea. We also examined which intervention students preferred after they experienced self-recording and goal-setting. Visual analyses of the data showed (a) increases in students' on-task and mathematics productivity levels contingent upon the implementation of both self-recording and goal-setting, (b) no differential effects of the two interventions, and (c) students' general preference of goal-setting to self recording. We interpreted these results as indicating that both self-recording and goal-setting are effective self-management strategies, but practitioners must consider the features of the interventions before selecting one from them, and future researchers must examine the effect of combining the two procedures.     

Can Constructive Mathematics be Applied in Physics?

The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.     

Do examples of failure effectively prepare students for learning from subsequent instruction?

Studies on the productive failure (PF) approach have demonstrated that attempting to solve a problem prepares students more effectively for later instruction compared to observing failed problem-solving attempts prior to instruction. However, the examples of failure used in these studies did not display the problem-solving-and-failing process, which may have limited the preparatory effects. In this quasi-experiment, we investigated whether observing someone else engaging in problem solving can prepare students for instruction, and whether examples that show the problem-solving-and -failing process are more effective than those that only show the outcome of this process. We also explored whether the perceived model–observer similarity had an impact on the effectiveness of observing examples of failure. The results showed that observing examples effectively prepares students for learning from instruction. However, observing the model's problem-solving-and-failing process did not prepare students more effectively than merely looking at the outcome. Studying examples were more effective if model–observer similarity was high.