Cognitive Profiles Associated With Responsiveness to Fraction Intervention

This study examined differences in cognitive processing between 4th‐grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number‐line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or inadequate responders, using as the cut‐point the control‐group mean on pre‐to‐post improvement on the relevant measure. Between‐group differences identified reasoning, concept formation, and listening comprehension related to all 3 fraction outcomes. On the number‐line outcome, within‐group profile analysis indicated that inadequate responders experienced low reasoning ability relative to their other forms of cognitive processing.     

Using Calculators and Computers to Enhance the Middle Grades Mathematics Curriculum

No abstract available for this article.     

Assessing Intervention Responsiveness: Conceptual and Technical Issues

Implementing an intervention responsiveness approach to the identification of learning disabilities (LD) requires specification of procedures for the assessment process. In this article, the author uses examples in the literature to explore conceptual and technical issues associated with options for specifying three assessment components: the timing of the measurement of student response to intervention; the criterion for demarcating learning as inadequate (below which students are identified as LD); and the nature of the intervention. Then, the author summarizes research contrasting alternative assessment methods within an intervention responsiveness approach to LD identification. Conclusions are drawn, and future related work is described.     

Responsiveness to General Education Instruction as the First Gate to Learning Disabilities Identification

Most definitions of learning disabilities (LD) include a qualification that adequate general education instruction was received and the child with LD did not benefit. Rarely is this tenet assessed in either practice or research before a diagnosis is made. We review three studies that investigated children's responsiveness to general education reading instruction as an indicator of need for more intensive interventions. Adequacy of instruction was quantified by children's level and rate of progress, compared to classmates, as measured by curriculum‐based measures of oral reading fluency. We found that the response‐to‐instruction model tested was valid in that (1) children who differ from their peers on level and slope of performance (dual discrepancy) have more severe academic and behavioral problems than children who have IQ‐achievement discrepancies or low achievement; (2) children who demonstrate persistent nonresponsiveness over three years differ from other at‐risk children on reading, reading‐related, and behavioral measures; and (3) at‐risk children who participated in specially designed general education interventions had better outcomes than at‐risk children who did not participate. We conducted additional analyses to assess low achievement definitional variations and found that they lack sensitivity and coverage compared to a dual discrepancy definition.     

Early Responsiveness to Intensive Behavioural Intervention Predicts Outcomes Among Preschool Children with Autism

Archival data from a private day‐school offering early intensive behavioural intervention based on the principles of applied behaviour analysis to preschoolers with autism (N = 29) were analysed longitudinally. Teacher reports on the Assessment of Basic Language and Learning Skills (ABLLS) were available up to 4 times and on the Vineland Adaptive Behavior Scales—Classroom Edition (VABS‐CE), at 2 time points. Parent reports on the Autism Treatment Evaluation Checklist (ATEC) were available at 2 time points. All assessments occurred approximately at 6‐month intervals. Children showed statistically significant progress across all skill domains on the ABLLS and on selected subscales and the composite scales of the VABS‐CE and ATEC. Gains were substantial for some children and minor for others. When divided into performance‐based groups, both higher‐performing and lower‐performing groups showed improvement over time, with greater improvement for the higher‐performing group. Nine of 16 children who had been discharged from the programme entered inclusive kindergarten or first‐grade classrooms with an aide. Seven discharged children entered special education classrooms. No child progressed to the point that special education services were not needed. Findings are discussed relevant to the extant literature on early intensive behavioural intervention outcomes among young children with autism.     

What We Need to Know About Responsiveness To Intervention (and Shouldn't Be Afraid to Ask)

During the past several years, one of the most frequently addressed topics at conferences and in professional journals is responsiveness to intervention (RTI). This is because it is viewed by many as a new way to think about both early intervention and disability identification. Despite its relative newness, a subset of RTI proponents contend researchers and practitioners know everything they need to know to implement it effectively. We disagree and argue that the smartest and most responsible way to move forward with RTI implementation is to recognize what all of us collectively do know and do not know. In this article, we identify unresolved issues—general and specific—important to RTI implementation, teacher effectiveness, and student achievement.     

Responsiveness and Affective Processes in the Interactive Construction of Understanding in Mathematics

This paper reports on important learning processes emerging during adult mathematics classes that used a teaching approach compatible with a social constructivist theory of knowing. A cyclical teaching model encouraged much discussion about the mathematical problems presented to paired groups. Whole-class student-led sharing sessions allowed students to continue their interactive constitution of meaning and solutions.Comparisons of pre- and post-course scores on attitude and belief questionnaires indicated significant increases in positive attitudes and beliefs about mathematics and about themselves doing mathematics.The overall positive changes in scores on questionnaires are explained in terms of recurrent patterns in thinking inferred from data obtained by observation, interview, and reflective comments. Changes are explained in terms of the interactive effects of affective and heuristic processing during problem solving. Affective processes precipitated students' responsiveness, modifying the immediate learning context which, in turn, influenced the students' thinking, creating a snowballing effect on learning and affect. Changes were clearly facilitated by the interaction between students and by their shared understandings.     

The Long-Term Effects of Small Classes in Early Grades: Lasting Benefits in Mathematics Achievement at Grade 9

Reducing class size to increase academic achievement is a policy option currently of great interest. Although the results of small-scale randomized experiments and some interpretations of large-scale econometric studies point to positive short-term effects of small classes, some scholars view the evidence as ambiguous. Project STAR in Tennessee-a 4-year, large-scale randomized experiment on the effects of class size—provided persuasive evidence that small classes have immediate positive effects on academic achievement. Unlike most other early education interventions, these effects persisted for several years after the children returned to regular-sized classes. The authors of the present article report analyses of a 6-year follow-up of the students in that experiment. Class-size effects persisted for at least 6 years and remained large enough to be important for educational policy. The results suggest that small classes in early grades have lasting benefits and that those benefits are greater for minority students than for White students.     

A Longitudinal Study of the Relationship of High School Foreign Language and Mathematics Study to Freshman Grades

Abstract

The purpose of this study was to examine the prevalence and effect of answer-changing on objective test performance. 5s were 77 college students of both sexes. All types of response changes were recorded and analysed by sex and by caliber of student. Results showed that when a response was changed there was a three-to-one chance that the new response would Improve rather than lower the final score. Females were more Inclined to make changes than were males, and their overall test performance was superior to that of males. The brightest 5s of both sexes made the greatest mean number of answer changes. It was concluded that the fear frequently expressed by students that answer changes will reduce test performance was unfounded In this instance.     

Bringing Inquiry to the First Two Years of College Mathematics

Abstract

In this editorial, we provide an introduction to the special issue on Inquiry-Based Learning in First and Second Year Courses. We also discuss the essential features of inquiry-based learning and provide a brief overview of the literature and evidence for its effectiveness.     

Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections among mathematical ideas and applying them in ways that may not have been taught directly. A challenge in characterizing mathematical competency is to capture not only the variety of skills and concepts, but also their connections. Designing assessments based on learning progressions may be one way to respond to this challenge. We discuss our experience developing a learning progression and an associated task model for mathetical functions.     

Examining the Alignment of Mathematics Instructional Practices and Mathematics Vocabulary between Core and Intervention Materials

Within a multitiered system of support (MTSS), students who struggle to learn mathematics often receive core instruction and supplemental intervention in different settings, with different teachers and different sets of curriculum materials, all of which can result in poor alignment. This curriculum crosswalk describes how three sets of materials commonly used to provide core instruction and intervention differ with regard to mathematics practices and vocabulary. The results indicate that there is little overlap among all three programs for the majority (n = 6) of the mathematics practices, and very little overlap in mathematics vocabulary (ranging from 6.3 to 24 percent). We also provide a set of research-based instructional recommendations intended to help teachers address gaps and improve alignment of core instruction and intervention.     

Principles for the Prevention and Intervention of Mathematics Difficulties

Three levels of prevention and intervention in the area of mathematics are addressed: (a) primary prevention focusing on universal design, (b) secondary prevention focusing on adaptations, and (c) tertiary prevention focusing on intensive and explicit contextualization of skills‐based instruction. The purpose of this paper is to identify and discuss principles of prevention and intervention in the area of mathematics. First, we identify research‐based principles associated with primary prevention. Second, we turn our attention to secondary prevention, with a focus on prereferral intervention. We identify principles that serve to differentiate primary and secondary prevention and specify instructional variables that are promising for use within a secondary prevention mode. Finally, we discuss intervention. We identify principles of effective intervention, which include individually referenced decision making, instructional intensity, and deliberate contextualization of skills‐based instruction.     

A Math Intervention for Third Grade Latino English Language Learners at Risk for Math Disabilities

Word problems for English language learners (ELLs) at risk for math disabilities are challenging in terms of the constant need to develop precise math language and comprehension knowledge. As a result of this, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a word problem–solving strategy called Estratégica Dinámica de Matemáticas (EDM). This strategy was designed to provide math support in the native language based on students' math comprehension levels. A changing criterion multiple baseline design was used to instruct six second-grade Latino ELLs at risk for math disability. As compared with the baseline phase, EDM increased word problem solving for all participants. All students' level of performance were maintained and generalized during follow-up sessions. This study has implications for a native language intervention that focuses on strategy training to facilitate word problem–solving performance.     

1～3代树枝状聚醚的合成与表征

以3,5-二羟基苯甲醇或3,5-二羟基苯甲酸甲酯、苄卤化物、K2C03为原料,以18-冠-6为催化剂,采用一步法和两步法（氢化铝锂为还原剂）制备得到了1—3代以CH2OH为核的树枝状聚醚,采用红外光谱进行结构表征,并将产物进一步卤代进行结构验证。研究结果表明,采用一步法和两步法均可得到目标产物,但一步法得到的目标产物产率明显高于两步法。     

关于上好高等数学第一堂课的探讨

首应效应存在于课堂教学的师生交往互动中,上好高等数学第一堂课,让学生对高等数学及任课教师留下良好的第一印象,对以后教学的有效开展极其重要。文章主要探讨高等数学的第一堂课的目标定位以及具体教学建议。     

第三届国际数学及科学研究结果对华人地区数学课程改革的启示

第三届国际数学及科学研究是一项由国际教育成就评价协会主办,有四十多个国家和地区参加的长期追踪研究,这项研究由纸笔测试和录像研究两部分组成.这项研究对华人地区课程改革的启示有:虽然华人地区数学教育遭受各种批评,但从研究结果看,华人地区的数学教育并不差;我们应该仔细讨论TIMSS测试本身,分析它是否符合我们的数学教育目标;虽然华人学生相对负面的数学学习态度似乎没有影响学生的数学成绩,但是负面态度本身应该引起我们的关注.     

Inductive Reasoning in Third Grade: Intervention Promises and Constraints

The results of two evaluation studies with respect to a programme for enhancing inductive reasoning ability of third grade students are presented. The programme is a classroom version of the German programme ‘Denktraining für Kinder 1’ (Cognitive training for children; Klauer, 1989). In the first formative evaluation study, two experimental groups with 30 students in total and one control group with 9 students were involved. Observations during the lessons, and teachers' reports showed that teachers were able to implement the programme. Both experimental groups significantly outperformed the control group on a posttest immediately after the programme and on a follow-up test 3 1/2 months later. Further analyses of the data revealed tentative evidence of the superiority of a direct teaching method. In the second summative evaluation study, the same programme was applied to a larger sample (experimental groups: n = 99 in total; and control groups: n = 232 in total) of third grade students. On the basis of Study 1, the programme instructions were slightly changed. The experimental groups scored significantly higher on a posttest three months after completion of the programme.