Cooperative learning in third graders' jigsaw groups for mathematics and science with and without questioning training

Background. There is much support for using cooperative methods, since important instructional aspects, such as elaboration of new information, can easily be realized by methods like ‘jigsaw’. However, the impact of providing students with additional help like a questioning training and potential limitations of the method concerning the (minimum) age of the students have rarely been investigated. Aims. The study investigated the effects of cooperative methods at elementary school level. Three conditions of instruction were compared: jigsaw, jigsaw with a supplementary questioning training and teacher‐guided instruction. Sample. Nine third grade classes from three schools with 208 students participated in the study. In each school, all the three instructional conditions were realized in three different classes. Method. All classes studied three units on geometry and one unit on astronomy using the assigned instructional method. Each learning unit comprised six lessons. For each unit, an achievement test was administered as pre‐test, post‐test and delayed test. Results. In the math units, no differences between the three conditions could be detected. In the astronomy unit, students benefited more from teacher‐guided instruction. Differential analyses revealed that ‘experts’ learned more than students in teacher‐guided instruction, whereas ‘novices’ were outperformed by the students in the control classes. Conclusions. Even third graders used the jigsaw method with satisfactory learning results. The modest impact of the questioning training and the low learning gains of the cooperative classes in the astronomy unit as well as high discrepancies between learning outcomes of experts and novices show that explicit instruction of explaining skills in combination with well‐structured material are key issues in using the jigsaw method with younger students.     

An investigation of high school social studies teachers' understandings of vocabulary teaching and learning

This qualitative study focused on high school social studies teachers' understandings of and perspectives about vocabulary acquisition and instruction. The research questions were the following: (1) What do high school social studies teachers understand about vocabulary instruction? and (2) How do high school social studies teachers support vocabulary learning? Face-to-face interviews were conducted with 25 high school social studies teachers. Findings indicate that external factors shaped instructional decision-making for teaching vocabulary, teachers' belief systems guided instructional choices, and the diverse needs of students called for differentiated instruction not only for English language learners but also for all students given the unique nature of the language of social studies.     

Cognitive Tutor: Applied research in mathematics education

For 25 years, we have been working to build cognitive models of mathematics, which have become a basis for middle- and high-school curricula. We discuss the theoretical background of this approach and evidence that the resulting curricula are more effective than other approaches to instruction. We also discuss how embedding a well specified theory in our instructional software allows us to dynamically evaluate the effectiveness of our instruction at a more detailed level than was previously possible. The current widespread use of the software is allowing us to test hypotheses across large numbers of students. We believe that this will lead to new approaches both to understanding mathematical cognition and to improving instruction.     

Phonological Awareness and Beginning Reading in Spanish-Speaking ESL First Graders: Research into Practice

In the first study, 30 Spanish-speaking English-as-a-second language (ESL) first graders whose families were Latino immigrants and who received all their school instruction in English completed an assessment battery with both Spanish and English measures of phonological awareness, Verbal IQ (VIQ), oral language proficiency, and single-word reading (real words and pseudowords); they also named English alphabet letters. Phonological awareness in Spanish predicted (a) phonological awareness in English and (b) English word reading; thus, phonological awareness may transfer across first and second languages and across oral and written language. English VIQ and oral language proficiency predicted both English and Spanish word reading, but Spanish VIQ and oral language proficiency did not predict English word reading. In the second study, the 4 males and the 4 females with the lowest reading achievement participated in an instructional design experiment in which empirically supported instructional components for teaching beginning reading to monlingual English speakers were included. These components were phonological awareness training (in both Spanish and English), explicit instruction in alphabetic principle (in English), and repeated reading of engaging English text with comprehension monitoring (in English). Both individual students and the group as a whole increased in real-word reading and pseudoword reading beyond the level expected on the basis of their Spanish or English VIQ or oral proficiency. Implications of this research for school psychology practice are discussed, especially the importance of early reading intervention and progress monitoring for Spanish-speaking ESL first graders.     

The knowledge-learning-instruction framework: bridging the science-practice chasm to enhance robust student learning

Despite the accumulation of substantial cognitive science research relevant to education, there remains confusion and controversy in the application of research to educational practice. In support of a more systematic approach, we describe the Knowledge-Learning-Instruction (KLI) framework. KLI promotes the emergence of instructional principles of high potential for generality, while explicitly identifying constraints of and opportunities for detailed analysis of the knowledge students may acquire in courses. Drawing on research across domains of science, math, and language learning, we illustrate the analyses of knowledge, learning, and instructional events that the KLI framework affords. We present a set of three coordinated taxonomies of knowledge, learning, and instruction. For example, we identify three broad classes of learning events (LEs): (a) memory and fluency processes, (b) induction and refinement processes, and (c) understanding and sense-making processes, and we show how these can lead to different knowledge changes and constraints on optimal instructional choices.     

Instruction,Understanding, and Skill in Multidigit Addition and Subtraction

We traced the emerging relations between children's understanding of multidigit numbers and their computational skill and investigated how instruction influenced these relations. We followed about 70 children over the first 3 years of school while they were learning about place value and multidigit addition and subtraction in 2 different instructional environments. By interviewing the students several times each year, we found that understanding and skill were closely related on tasks for which students had not yet received instruction as well as on more difficult tasks even after instruction. Students appeared to apply specific understandings to invent new procedures and modify old ones. The alternative instruction, which encouraged students to develop their own procedures and to make sense of procedures presented by others, appeared to facilitate higher levels of understanding and closer connections between understanding and skill.     

Overcoming Instructor‐Originated Math Anxiety in Philosophy Students: A Consideration of Proven Techniques for Students Taking Formal Logic

Every university student has his or her nemesis. Biology and social science students anticipate with great apprehension their required statistics course, while many philosophy students live in fear of formal logic. Math anxiety is the common thread uniting all of them. This article argues that since formal logic is an algebra requiring similar kinds of symbol‐manipulation skills needed to succeed in a basic mathematics course, then if logic students have math anxiety, this can impede their progress. Further, it argues that math anxiety is primarily caused by and exacerbated by poor instruction. Formal logic instructors who employ effective instructional techniques for reducing it can help their students overcome math anxiety to foster learning. Methods of instruction leading to anxiety reduction and evidence supporting their efficacy are discussed, including co‐operative learning, the mastery goal approach, and self‐paced learning. None of these methods holds back more advanced students.     

The Instructional Characteristics of Inclusive Classes for Elementary Students with Severe Disabilities: An Exploratory Study

This exploratory study examined several instructional characteristics of elementary classrooms serving students with severe disabilities including the individuals who provided instruction to students, the instructional behaviors of these teachers, and grouping structures. The analysis focused on the impact of these variables on the academic responding of students and the extent to which they were the exclusive target of instruction by the various teachers. Observation data were collected on six students with severe disabilities participating in general elementary classrooms for reading or math, and at least one other subject area. The academic responding of students was similar across general education teachers, special education teachers, paraprofessionals, and peers; and the instructional behaviors of each of these groups of instructors was similar. Students had higher rates of academic responding during one-on-one and small group instruction, but they also were engaged in instructional tasks during whole class instruction. Finally, academic responding was positively associated with instruction focused on the student, one-on-one instruction, and instructional interactions with teachers. Academic responding was negatively correlated with whole class instruction and instructional behaviors that were not directed at the student.     

The transition form theory to therapy: Test of two instructional methods

This study compared college students' understanding of the role of three language learning theories (operant, sociolinguistic, cognitive) in language theory through two instructional methods: video-based anchored instruction and traditional classroom instruction. Results indi-cated no significant difference between the performance of students in the two instructional groups on the post-test while students who received anchored instruction scored significantly higher on two transfer tests than students who received the traditional instruction. Video-based anchored instruction was found to be a valuable instructional tool which increased students' understanding of theoretical principles; through observations they experienced abstract theoretical principles as the foundation for clinicians' actions and interactions with language-impaired children.     

EFFECTS OF PARENTAL INVOLVEMENT IN DEVELOPING COMPETENT READERS IN FIRST GRADE

Software that teaches users to sing in tune and in rhythm while providing real-time pitch tracking was used in a study of struggling middle school readers. The software, Carry-a-Tune (CAT) was originally developed to improve singing; however, since it involves a repeated reading format, we used it to determine its effect on comprehension and reading achievement. Twenty-four students in grades 7 and 8 utilized the software program for 30 minutes, three times a week for 9 weeks. A matched control group of 24 students had a different reading experience during the same time period. The mean pretest instructional reading level for both groups was fourth grade. The mean instructional level scores for the treatment group improved significantly (7 months during the 9-week study). The matched control group students did not experience gains. Sustainability data from assessment 4 months after the study's conclusion indicated treatment students gained another 6 months. This placed them solidly in mid-fifth grade for instructional reading level. The control students, again, evidenced no significant gains.     

Self‐regulated learning of basic arithmetic skills: A longitudinal study

Background. Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students’ strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other important aspects in self‐regulated learning. Aim. The main purpose of this study was to examine relations between young primary school children's basic mathematical skills and their use of math strategies, their metacognitive competence and motivational beliefs, and to investigate how students with basic mathematics skills at various levels differ in respect to the different self‐regulation components. Sample. The participants were comprised of 27 Year 2 students, all from the same class. Method. The data were collected in three stages (autumn Year 2, spring Year 2, and autumn Year 3). The children's arithmetic skills were measured by age relevant tests, while strategy use, metacognitive competence, and motivational beliefs were assessed through individual interviews. The participants were divided into three performance groups; very good students, good students, and not‐so‐good students. Results. Analyses revealed that young primary school children at different levels of basic mathematics skill may differ in several important aspects of self‐regulated learning. Analyses revealed that a good performance in addition and subtraction was related not only to the children's use of advanced mathematics strategies, but also to domain‐specific metacognitive competence, ability attribution for success, effort attribution for failure, and high perceived self‐efficacy when using specific strategies. Conclusions. The results indicate that instructional efforts to facilitate self‐regulated learning of basic arithmetic skills should address cognitive, metacognitive, and motivational aspects of self‐regulation. This is particularly important for low‐performing students.     

The Efficacy of a Dialogic Learning Environment in Fostering Literacy

This comparative study examines the role of contextual features embedded in a dialogic environment in fostering literacy. The study, implemented by language arts teachers in a middle school setting, investigates the effectiveness of an instructional program designed to create a collaborative dialogic learning environment that imparts literacy. The program is compared to a traditional learning environment in which reading and writing are imparted through direct teacher instruction. Results indicate that embedding literacy instruction in communities of discourse is superior to traditional methods in fostering reading comprehension and writing competence. Findings suggest that a dialogic environment creates the context within which students develop cognitive tools to achieve literacy.     

Developing elementary science skills: Instructional effectiveness and path independence

We explore the immediate and longer term consequences of different types of instruction about a central topic in middle school science: the “Control of Variables Strategy” (CVS). CVS represents the procedural and conceptual basis for designing simple, unconfounded experiments, such that unambiguous causal inferences can be made. CVS appears to be what has been called a “developmentally-secondary” process, because even though infants and pre-schoolers can make simple causal inferences from data, middle school children do poorly at CVS unless they receive instruction on this important topic in the science curriculum. In this study, 72 third, fourth, and fifth-grade students were taught CVS via two instructional methods located at extreme points on the direct-to-discovery spectrum with respect to the amount of guidance, information, support, teacher control, and feedback provided during training. Our design included near- and far-transfer measures (at 1 week, 3 months and 3 years). There were two primary outcomes, both of which replicated and partially extended earlier work by Klahr and Nigam (2004) [Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction: Effects of direct instruction and discovery learning. Psychological Science, 15, 661–667] First, at each of the three grade levels, many more children learned CVS in the explicit condition than in the exploration condition. Second, but equally important, what students learned was a better predictor of far transfer than the way that they learned.     

Effects of Curriculum-Based Monitoring on Classroom Instruction and Math Achievement

In recent years, concerns about the math achievement of U.S. students have been highlighted in the popular press, journal articles, major conference presentations, and official U.S. Department of Education (1998) reports. School personnel have responded to the issue of low math achievement by a) writing or rewriting standards, b) “ratcheting up” current standards, c) building accountability systems that include all students, d) developing programmatic interventions, e) extending the school year, and f) implementing effective instructional management systems. Research on teaching has linked instructional environment and achievement. Thus, this study was designed to determine whether the implementation of an instructional management system served to improve student math achievement and the classroom instructional environment. In addition, the study examined the extent to which adding a curriculum-based monitoring system to an ongoing math curriculum would result in positive changes in the classroom instructional environment and in achievement.     

Performance of Fourth-Grade Students with Learning Disabilities on Multiplication Facts Comparing Teacher-Mediated and Technology-Mediated Interventions: A Preliminary Investigation

Instructional applications (apps) are educational software programs that can be accessed via mobile technologies (e.g., iPad, smartphone) and used to help students acquire various academic skills, including mathematics. Although research suggests that app-based instruction (AI) can be effective, there is a paucity of research comparing AI, to teacher-directed instruction (TDI) or to a combination of instructional approaches (CI) involving both AI and TDI in tandem. In an alternating treatments design, we compared AI, TDI, and CI conditions during instruction targeting multiplication facts with six students with learning disabilities. Results were inconsistent across students, and no condition emerged as consistently better than the others. Students completed social validity rating scales, and all approaches were favored by at least one student. Our results support findings from previous research involving similar comparisons between these instructional formats in which no (or minimal) differences across conditions were detected. We conclude that there may not be a meaningful difference between the outcomes achieved using AI, TDI, or CI for many students. Results are discussed in terms of directions for the future research.     

A cognitive perspective on Singaporean primary school pupils' use of reading strategies in learning to read in English

Background . This study is conducted in Singapore, where learning to read in English is regarded as essential because it is offered as a First Language (L1) subject in the curriculum and is stipulated as the medium of instruction in the education system, and the mother tongues are offered as Second Language (L2) subjects, although the majority still learn English as an L2. Aims . The paper reports on the reading strategies used by Singaporean primary school pupils from a cognitive perspective, which is part of a larger study that aims to investigate these pupils' language learning strategies. Sample . The participants were 18 pupils from three neighbourhood primary schools, in grades Primary 4, 5 and 6. Method . The data were collected from high‐ and low‐proficiency pupils at each of the three grades in each school, who read two texts at each level. Grounded in an information‐processing theory and based on successful experiences of scholars using think‐aloud for data collection, we asked the pupils to read and report what they were thinking about while reading. The think‐aloud protocols were recorded, transcribed verbatim, coded and analysed. Results . The results suggest that participants' flexible and appropriate use of reading strategies varies according to language proficiency and grade level, with the high‐proficiency group outperforming its lower‐proficiency counterpart and the high‐graders outnumbering the lower‐graders in terms of the number of strategies that they used. These differences were also exemplified with qualitative findings from case studies. Conclusions . The use of reading strategies differs according to proficiency levels, and the quality of pupils' strategy‐use patterns has more significant implications for understanding efficient reading among primary school pupils.     

Linking Teacher Instruction and Student Achievement in Mathematics: The Role of Teacher Language

Although high-quality early educational environments are thought to be related to the growth of children’s skills in mathematics, relatively little is known about specific aspects of classroom instruction that may promote these abilities. Data from a longitudinal investigation were used to investigate associations between teachers’ language while teaching mathematics and their students’ growth in mathematical skill during the 2nd grade. Specifically, the extent to which mathematics lessons included cognitive-processing language (CPL)—instruction that is rich in references to cognitive processes, metacognition, and requests for remembering—was related to changes in students’ math achievement. Demonstrating the role of the language of instruction, the findings indicated that children whose 2nd-grade teachers included greater amounts of CPL during instruction evidenced greater growth in math fluency and calculation than did their peers whose teachers employed lower levels of CPL.     

Enhancing Multiplication Performance in Students with Moderate Intellectual Disabilities Using Pegword Mnemonics Paired with a Picture Fading Technique

The present study examined the effectiveness of an instructional package that included an adapted version of pegword mnemonics paired with a picture fading technique in teaching two students with moderate intellectual disabilities to recall 28 single-digit multiplication facts between 2 and 9. The instructional package was assessed using a multiple baseline design across students. Results indicated that instruction produced substantial and immediate effects in that both students increased their accuracy at recalling basic multiplication facts, maintained the newly acquired skill, and were able to generalize it across material, format, and another trainer. These results have implications for teaching students with intellectual disabilities basic math facts that are considered important for gaining access to the general curriculum.     

The expertise reversal effect: cognitive load and motivational explanations

The expertise reversal effect occurs when a learner's expertise moderates design principles such as the redundancy principle (i.e., redundant information should be excluded rather than included) derived from the cognitive load theory. Although this effect is supported by numerous experiments, indicating an overall large effect size, a variety of explanations have been proposed. The present experiment tested a cognitive load and a motivational explanation with 104 students, who reported a lack of experience in the presented instructional contents. They spent about 30 min with the instructional material to learn fundamental concepts about the gradient descent (a mathematical optimization algorithm), and with a retention and transfer test used as dependent measures. Each learner was randomly assigned to one cell of a 2 (either novices or experts introduced to through the instructional design presented previously) × 2 (either with or without additional text explaining the animations) between-subjects factorial design. The expertise reversal effect concerning the redundancy principle was replicated. Novices receiving additional text scored higher on retention and transfer than did novices without additional text, while this result was reversed for experts. Results suggest that this effect can be explained by the learner's cognitive load differences rather than overall motivation differences. Furthermore, a partial overlap was found between the motivational subdimension, "probability of success," and a cognitive load measure. On the practical side, instructional designers should consider the learner's level of expertise and their cognitive load when applying design principles. Further implications for adaptive learning environments are discussed.     

Instructional ecology and academic responding time for students at three levels of teacher-perceived behavioral competence

Thirty third and fourth grade students, ages 8-10 years, were observed systematically over two entire school days to examine the nature of instruction and academic responding time for students at varying levels of teacher-perceived behavioral competence. Data were recorded on six categories in 10-sec intervals. While the amount of time spent in active academic responses (about 45 min in a typical school day) did not differ significantly between groups, it was found that students perceived to be lower in behavioral competence spent more time engaged in certain inappropriate behaviors and received more teacher disapproval. Yet, students grouped on the basis of teachers' perceptions of their behavioral competence did not differ on the majority of instructional or student responding variables. Findings related to the relationship between responding times and achievement also are presented. Implications of findings for understanding the classroom ecology for students exhibiting behavior problems are discussed.