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1.
This article reports on the last of a series of iterative research studies involving students with learning disabilities in reform mathematics classrooms at the intermediate grade levels. This study reports the findings from a larger, year‐long case study that focused on ways to include students with learning disabilities and other students who are at risk for special education services in classwide discussions of problem solving. The data reported in this article detail the changes in teacher and student discourse over a nine‐week period in one classroom. Sources of data for this study included videotapes, audiotapes, and informal interviews with the teacher, a paraprofessional, and students. A quantitative analysis of the results indicates clear patterns of change in teacher and student discourse. Nonetheless, intentional efforts to include target students in the whole‐class discussions yielded instructional dilemmas that are underdescribed in the mathematics reform literature. Findings from this study have implications for special educators interested in mathematical problem solving, as well as math reformers who value the role of classroom discourse in daily instruction.  相似文献   

2.
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention.  相似文献   

3.
This longitudinal study examined the influence of prekindergarten teacher characteristics and classroom instructional processes during mathematical activities on the growth of mathematics learning scores in prekindergarten, kindergarten, and first grade. Participants attended state-funded and Head Start prekindergarten programs. Mathematical performance was measured in fall and spring in prekindergarten and spring in kindergarten and first grade using the Test of Early Mathematics Ability–3 (TEMA-3; Ginsburg & Baroody, 2003). Two dimensions of the Classroom Assessment Scoring System (CLASS; i.e., instructional learning formats and concept development; Pianta, La Paro, & Hamre, 2008) were scored based on observed classroom mathematics activities. Teachers provided information about their education and years of prekindergarten teaching experience. Research Findings: Instructional processes that included elements of the CLASS concept development dimension, such as discussions and brainstorming to encourage children’s understanding, were related to growth of mathematics scores. Neither teacher characteristics nor instructional processes of the CLASS instructional learning formats dimension, such as using different modalities and materials, and learning objectives, were related to growth of mathematics scores. Practice or Policy: The findings extend our understandings of how instructional processes impact children’s early mathematical performance. These findings may be helpful in increasing our understanding of the types of instructional processes that might be emphasized in teacher professional development specifically related mathematical activities. Professional development that focuses on the CLASS concept development dimension may be easier for teachers to remember and implement in their classrooms and, consequently, have a greater impact on mathematics learning.  相似文献   

4.
Abstract Mathematics continues to be one of the most difficult components of the school curriculum for students with learning disabilities (LD). The National Council for Teachers of Mathematics, in conjunction with current educational legislation, challenges teachers to maintain high standards for student performance in mathematics. Fortunately, over the past two decades, researchers have identified and validated a number of instructional practices that help students with LD understand and use mathematics in meaningful ways. The purpose of this article is to discuss instructional guidelines and evidence‐based practices for building conceptual, procedural, and declarative knowledge within a comprehensive mathematics curriculum. The importance of balancing these three knowledge areas across mathematics content areas is noted.  相似文献   

5.
The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics‐vocabulary understanding of fifth‐grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and general vocabulary measures, students were categorized with no learning difficulty (i.e., typical), mathematics difficulty without reading difficulty (MD‐only), reading difficulty without mathematics difficulty (RD‐only), and combined mathematics and reading difficulties (MDRD). On the mathematics‐vocabulary measure, students with MD‐only or RD‐only scored significantly lower than typical students, and students with MDRD demonstrated significantly lower performance than students with MD‐only or RD‐only.  相似文献   

6.
We review published single subject design (SSD) studies that examine the effects of interventions for English learners at‐risk or with learning disabilities. Results of our literature search yielded 10 studies, five in reading, one in reading and behavior, and four in mathematics that met our inclusion criteria. Seven studies targeted Spanish‐speaking English learners, and three studies included students who spoke other languages than English and/or English only students. Two studies in mathematics included native language instruction. Six studies included English learners in second grade and above, and one study included high school students. We were able to calculate effect sizes (Hedges g) for eight of the 10 studies. Findings indicated a significant effect of the intervention for 12 of the 18 dependent variables measured. SSD methodology has the potential to help researchers and practitioners better understand what interventions work for English learners, and under what circumstances.  相似文献   

7.
As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital‐based instructional strategy with a limited research base for students with a learning disability is video modeling. Through a single subject alternating treatments design, this study compared the use of video modeling to face‐to‐face explicit instruction for teaching geometry word problems to three secondary students with a learning disability in mathematics. Across 10 sessions of intervention, all three students demonstrated improved performance on all dependent variables with both interventions, while the explicit instruction condition produced slightly greater accuracy scores for two of the three students. The results and their implications for the field of mathematics are discussed.  相似文献   

8.
ABSTRACT

This article reports on an intervention study into the effects of a training in the use of social and cognitive strategies on the learning outcomes of students in secondary mathematics education. Special attention is given to differential effects for high‐ and low‐achieving students. The focus on differential effects is derived from studies into learning in small co‐operative groups, and from the results of meta‐analyses into the effects of training in learning strategies. From these studies it can be concluded that in general such programs contribute to learning. However, it seems that low‐achieving students are unable to benefit from interventions of the kind investigated (i.e., co‐operative learning and training in learning strategies). The main question is whether it is possible to design an instructional program from which all students benefit, and from which the low‐achieving students profit more than their counterparts in the control‐program. In the present study three instructional programs for co‐operative learning were compared: (i) an experimental program with special instruction in the use of social strategies; (ii) an experimental program with special instruction in the use of cognitive strategies; and (iii) a control program without training in either cognitive or social strategies. The programs were identical with respect to mathematical content and general instructional settings (a combination of whole‐class instruction, working in co‐operative groups and individual work). The experiment addressed the following research question: what are the general and differential effects of a training in the use of social and cognitive strategies on the results of learning in secondary mathematics? The research was conducted in two schools for secondary education in a total of 21 classes, involving a total of 511 students. The design was a pretest‐posttest control group design, using two experimental groups and one control group. The data were analysed from a multi‐level perspective. The outcomes of the investigation clearly show the effects of the intervention. Teaching cognitive and social strategies has the expected, positive effects. In addition to this main effect, a compensatory effect for the low‐achieving students was found. The low‐achieving students in the experimental conditions outperformed their counterparts in the control group.

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9.
The purpose of this study was to examine the impact of a universal program to promote positive classroom behavior on students’ approaches to learning and early academic skills. Second grade classrooms (N = 39) were randomly assigned to treatment and business‐as‐usual control conditions. Teachers in intervention classrooms implemented the Social Skills Improvement System Classwide Intervention Program (SSIS‐CIP) over a 12‐week period. Participating students’ (N = 494) engagement, motivation, and academic skills were assessed before and after treatment implementation. Results indicated that students with lower levels of engagement and motivation at pretest experienced significant improvement in these areas after exposure to the SSIS‐CIP. Although no significant differences were observed in reading, students receiving supplemental instructional services demonstrated greater gains in mathematics than did their peers in the control condition.  相似文献   

10.
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11.
Two studies were conducted to examine the effects of Tier 2 and Tier 3 mathematics interventions on students with mathematics learning difficulties. In the first study, the work of Bryant et al. was replicated and expanded upon by documenting the sustained effects of a Tier 2 mathematics intervention on mathematics performance by second graders. In the second study, the Tier 2 intervention was intensified to a Tier 3 intervention through increases in two instructional features: group size and dosage. The results of the first study showed that the Tier 2 intervention improved mathematics performance for the majority of student participated in the study, and the effect of the intervention was sustained for the majority of students who responded to the Tier 2 intervention. The results of the second study showed that intensified Tier 3 intervention that involved one‐on‐one instruction and extended time for daily lessons may benefit students who have persistent difficulties with learning mathematics.  相似文献   

12.
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13.
Colleges of Business (COBs) have experienced high growth rates in the past decade and many colleges are imposing minimum grade point average (GPA) requirements for students to enter or remain in the college. A primary reason for this requirement may be the belief that students with high GPAs are more inclined to demonstrate higher‐order cognitive skills (HOCS) than students with low GPAs. It is not clear whether the link is valid. This study hypothesizes that students with high GPAs who are taught in the same way as students with lower GPAs will have higher perceptions of improved HOCS. We conducted an experiment in which students, with varying GPAs, at three large universities primarily used multimedia instructional materials. We obtained the students' perceptions of their improved HOCS from their responses to a survey. A regression analysis of the data reveals that the relationship between GPAs and students' perceived improvement in HOCS is significant (p < .001). We conclude the study by recommending that (a) it is critical to use research methodologies to evaluate perceived and actual learning improvements, (b) COB policies to implement GPA restrictions on admission are worthwhile, and (c) case studies need to be used much more frequently in undergraduate COB classes.  相似文献   

14.
Teacher judgments have been identified as a primary source of information regarding student academic achievement. Research examining the accuracy of teachers' judgments in assessing students' academic abilities has shown relatively high accuracy. However, previous studies have relied primarily on norm‐referenced measures to obtain estimates of students' achievement in reading and mathematics. Recent developments in the assessment of students' academic skills, such as Curriculum‐Based Measurement (CBM), provide a direct estimate of students' skill levels in basic areas such as reading and mathematics. The purpose of the present study was to examine the extent to which teachers' perceptions of students' reading and mathematics skills corresponded to direct estimates of students' reading and mathematics skills. Two second‐grade teachers estimated the reading and mathematics skills of 33 second‐grade students. Results of this study indicated that teachers were not accurate in assessing their students' mathematics functioning. Teachers were more accurate in assessing the occurrence of Mastery mathematics levels in basic addition, but were very inaccurate in assessing the occurrence of Mastery, Instructional, or Frustrational mathematics levels in all other skills assessed. In reading, teachers' judgment accuracy varied as a function of grade‐level material and instructional level. Specifically, teachers experienced considerable difficulty accurately identifying students who were reading at a Mastery level in grade‐level or above‐grade‐level material. © 2006 Wiley Periodicals, Inc. Psychol Schs 43: 247–265, 2006.  相似文献   

15.
This research replicates an earlier study and extends it by shifting instructional responsibility from researchers to special education teachers, who implemented reading instruction that included multisyllabic word decoding, academic vocabulary, and three comprehension strategies (generating main ideas, comparing and contrasting people and events, and identifying cause and effect relations) with their intact eighth grade history classes, using history text as the reading material. Participants included 73 eighth grade students with disabilities (77 percent with learning disabilities, 72 percent males, and 45 percent English language learners) and four teachers. Compared to students with disabilities in typical special education history classes, students in the treatment outperformed controls on researcher‐developed measures of word‐ and text‐level reading comprehension, as well as in the history content that students in both conditions studied. Across reading strategies, implementation of “nearly all lesson components” ranged from 72 percent to 83 percent.  相似文献   

16.
ABSTRACT

In this study I explored how elementary school students are initially assigned to homeroom classrooms (criteria used and heterogeneous vs. homogeneous grouping), subsequently assigned to mathematics classes (e.g., self‐contained, regrouped, departmentalized), and grouped for mathematics instruction within classes (e.g., whole‐class, two groups, individualized). This three‐dimensional typology of school and classroom organization was used to survey 571 elementary school principals from 12 states. Results showed that students were generally assigned to heterogeneous self‐contained homeroom classes, that they remained in these same classes for mathematics, and that mathematics was usually taught to entire classes (whole class). Within‐class ability grouping, within‐grade regrouping, and departmentalized plans were used increasingly for mathematics at the intermediate grades, but across‐grade or Joplin Plan programs were infrequent.  相似文献   

17.
This article quantitatively summarizes experimental and quasi‐experimental studies on teaching students with mathematics difficulties (MD) published between 2000 and 2014, research that was available following earlier syntheses. It reports the analysis of effect sizes of 25 intervention studies on participant characteristics, intervention parameters, domains of mathematics interventions, and instructional approaches and components. Results indicate that several participant characteristics (e.g., grade level and level of mathematics difficulties) and intervention parameters (e.g., methodological soundness, intervention agent, and grouping) mediated the treatment effects. In addition, different types of instructional approaches and several instructional components contributed to the improvements in mathematics performance in students with MD.  相似文献   

18.

Few studies have examined the student learning effects of integrating science with mathematics and technology. We compared a school that integrated mathematics, science and technology in grade 9 to a school in the same district that taught the three courses separately. The distinguishing feature of the integrating school was the reorganization of instruction in the three subjects to prepare students for seven group projects (involving a total of 25 h) that required the application of knowledge and skill that were shared by the three subjects, as well as learning outcomes that were unique to each. The study detected benefits for students in the integrated setting in terms of their ability to apply shared learning outcomes, student motivation, ability to work together and attitudes to appraisal of group work. Female students in the integrated school had a better understanding of selected science learning outcomes. Attitudes toward mid‐term exams were higher in the control school.

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19.

Existing computational thinking (CT) research focuses on programming in K-12 education; however, there are challenges in introducing it into the formal disciplines. Therefore, we propose the introduction of non-programming plugged learning in mathematics to develop students’ CT. The research and teaching teams collaborated to develop an instructional design for primary school students. The participants were 112 third- and fourth-grade students (aged 9–10) who took part in three rounds of experiments. In this paper, we present an iterative problem-solving process in design-based implementation research, focusing on the implementation issues that lead to the design principles in the mathematics classroom. The computational tasks, environment, tools, and practices were iteratively improved over three rounds to incorporate CT effectively into mathematics. Results from the CT questionnaire demonstrated that the new program could significantly improve students’ CT abilities and compound thinking. The results of the post-test revealed that CT, including the sub-dimensions of decomposition, algorithmic thinking, and problem-solving improved threefold compared to the pre-test between the three rounds, indicating that strengthened CT design enhanced CT perceptions. Similarly, the students’ and teacher’ interviews confirmed their positive experiences with CT. Based on empirical research, we summarize design characteristics from computational tasks, computational environment and tools, and computational practices and propose design principles. We demonstrate the potential of non-programming plugged learning for developing primary school students’ CT in mathematics.

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20.
Two studies were conducted to investigate the effects of cooperative learning on second‐graders’ motivation and learning from text. In Study 1, students (n = 160) in cooperative learning groups were compared with their counterparts (n = 107) in traditional instruction groups. The results revealed a statistically significant difference between the two groups, with more favourable perceptions of teachers’ instructional practices and better reading comprehension in the instructional intervention groups than in the traditional instruction groups. In Study 2, 51 second‐graders participated in the instructional intervention programme. The results showed that students’ positive cooperative behaviour and attitudes were related to their motivation and reading comprehension. When students perceived that their peers were willing to help each other and were committed to the group, they tended to be more motivated and performed better in reading comprehension.  相似文献   

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