Teaching as a natural cognition and its relations to preschoolers’ developing theory of mind

Teaching is an important aspect in people’s lives and cultures. We explore it from a cognitive-developmental perspective. Teaching may be a natural cognition that, despite its complexity, is learned at an early age without any apparent instruction. We propose that theory of mind may be an important cognitive prerequisite for teaching. We briefly describe a study that tested relations between children’s developing theory of mind and actual teaching. Children at the ages of 3- and 5-years were presented new theory of mind tasks about teaching and then were observed teaching peers a game they had just learned. We found corresponding age-related differences in children’s understanding of teaching as manifested in their performance on the teaching-theory of mind tasks and in their teaching strategies. It is suggested that theory and research on theory of mind might need to be expanded to include on-line, interactive situations such as teaching.     

Assessment of the Language Preferences of Five Children with Autism from Spanish-Speaking Homes

Although the number of English Language Learner students is increasing in the US school system, little is known about the preferences of language of instruction, particularly among young students with autism. We implemented a choice assessment with five children with autism to determine preference between English and Spanish instruction using a concurrent-operant design. Participants were allowed to choose between English instruction, Spanish instruction, and a no-language control condition using BIGmack communication devices. We compared choice allocation between previously mastered skills (easy tasks) and targets in the acquisition phase of learning (difficult tasks). None of the participants indicated a preference for language of instruction during easy tasks, while four participants indicated a preference during difficult tasks. Results suggest that the concurrent-operant procedure is an effective method for assessing preference of language of instruction with students with autism.     

Group instruction with profoundly retarded persons: acquisition, generalization, and maintenance of a remunerative work skill.

We evaluated a group instruction program for teaching a vocational skill to profoundly retarded adults. The program involved designated trainer roles and both individual student-directed and total group-directed procedures. Results indicated that, following the program, participants acquired the skill of stamping addresses on envelopes, the skill generalized across an untrained type of envelope, and the skill maintained over time. The group activity was incorporated into the regular classroom without increased disruption and the participants earned a wage for their productivity. Implications for the development of a group instruction technology for severely handicapped persons are discussed.     

Addressing the struggle to link form and understanding in fractions instruction

Background. Although making explicit links between procedures and concepts during instruction in mathematics is important, it is still unclear the precise moments during instruction when such links are best made. Aims. The objective was to test the effectiveness of a 3‐week classroom intervention on the fractions knowledge of grade 5/6 students. The instruction was based on a theory that specifies three sites during the learning process where concepts and symbols can be connected ( Hiebert, 1984 ): symbol interpretation, procedural execution, and solution evaluation. Sample. Seventy students from one grade 5/6 split and two grade 6 classrooms in two public elementary schools participated. Method. The students were randomly assigned to treatment and control. The treatment (Sites group) received instruction that incorporated specific connections between fractions concepts and procedures at each of the three sites specified by the Sites theory. Before and after the intervention, the students’ knowledge of concepts and procedures was assessed, and a random subsample of 30 students from both conditions were individually interviewed to measure their ability to make specific connections between concepts and symbols at each of the three sites. Results. While all students gained procedural skill (p < .001), the students in the Sites condition acquired significantly more knowledge of concepts than the control group (p < .01) and were also better able to connect fractions symbols to conceptual referents (p < .025). Conclusions. The current study contributes to the literature because it describes when it might be important to link concepts and procedures during fractions instruction.     

Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children.

The relationship between counting knowledge and computational skills (i.e., skill at counting to solve addition problems) was assessed for groups of first-grade normal and mathematically disabled (MD) children. Twenty-four normal and 13 MD children were administered a series of counting tasks and solved 40 computer-administered addition problems. For the addition task, problem-solving strategies were recorded on a trial-by-trial basis. Performance on the counting tasks suggested that the MD children were developmentally delayed in the understanding of essential and unessential features of counting and were relatively unskilled in the detection of certain forms of counting error. On the addition task, the MD children committed many more computational errors and tended to use developmentally immature counting procedures. The immature counting knowledge of the MD children, combined with their relatively poor skills at detecting counting errors, appeared to underlie their poor computational skills on the addition task. Suggestions for future research are presented.     

TRIADIC INSTRUCTION OF CHAINED FOOD PREPARATION RESPONSES: ACQUISITION AND OBSERVATIONAL LEARNING

This research examined whether constant time delay would be effective in teaching students with moderate mental retardation in triads to perform chained tasks and whether observational learning would occur. Three chained snack preparation tasks were identified, and each student was directly taught one task. The other 2 students observed the instruction. The instructed student told the observers to watch and to turn pages of a pictorial recipe book. The teacher provided frequent praise to the instructed student based on performance and to the observers for watching the instruction and turning pages. A multiple probe design across students and tasks was used to evaluate the instruction. The results indicated that each student learned the skill he or she was taught directly, and the observers learned nearly all of the steps of the chains they observed. The implications for classroom instruction and future research in observational learning are discussed.     

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.     

Explicit Instruction With or Without High-<Emphasis Type="Italic">p</Emphasis> Sequences: Which is More Effective to Teach Multiplication Facts?

Basic fact acquisition is an important component for developing higher-order math skills. However, getting students with a history of academic noncompliance to engage in activities related to skills acquisition can be difficult. Prior research demonstrates that engagement increases when nonpreferred activities are preceded by a series of brief activities with a high probability of completion. This technique, called high-p task/request sequences, was not fully explored within the context of skill acquisition. The purpose of this study was to examine the effects of adding high-p sequences to explicit instruction on the math fact acquisition of three elementary-age students in a learning support classroom. Results showed no differences in fact acquisition between explicit instruction and explicit instruction with an added high-p component. However, the high-p sessions took nearly twice as long to complete when compared to explicit instruction alone. Implications for instructional efficiency and limitations of the high-p procedures for acquisition tasks are discussed.     

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.     

Using an Embedding Strategy to Teach Preschoolers with Significant Disabilities

The purpose of this study was two-fold. First, this study analyzed the effects of using response prompting procedures within an embedded skill approach on skill acquisition by 4 preschoolers with significant disabilities. Two target skills were identified from each student's IEP and taught during three preschool activities. A multiple probe across subjects design assessed the effects of the intervention. All students made progress above baseline performance. More importantly, there was consistency in performance of the target skills across at least two of the three activities for all children. Second, the reliability with which paraprofessionals in the preschool setting implemented response prompting procedures was evaluated. Data indicated that the paraprofessionals implemented the procedures with a high degree of accuracy. The impact of embedded skill instruction is addressed, as well as the impact of using non-degreed personnel to teach students with significant disabilities within inclusive preschool programs.     

Understanding and Integrating Multiple Science Texts: Summary Tasks are Sometimes Better Than Argument Tasks

One of the major challenges of a knowledge society is that students as well as other citizens must learn to understand and integrate information from multiple textual sources. Still, task and reader characteristics that may facilitate or constrain such intertextual processes are not well understood by researchers. In this study, we compare the effects of summary and argument essay tasks when undergraduates read seven different texts on a particular scientific topic, finding that an instruction to write summaries may lead to better understanding and integration than an instruction to write argument essays. We discuss several possible explanations for this result. We also found that beliefs about the certainty of knowledge in some instances can moderate the effect of task on comprehension performance.     

Concurrent Relations Between Perspective-Taking Skills,Desire Understanding,and Internal-State Vocabulary

Recent studies suggest that there appears to be a similar developmental sequence in the understanding of mental states in both internal-state language and in standard theory-of-mind tasks. These findings suggest possible developmental relations between children's ability to talk and think about the mind. Two experiments investigated the concurrent relations between internal-state vocabulary and theory-of-mind abilities in 30-month-old toddlers. In Experiment 1, children's internal-state language vocabulary was significantly and specifically related to their concurrent understanding of others' visual and emotional perspectives and was less strongly related to desire understanding. Experiment 2 replicated and extended these findings by examining the link between internal-state vocabulary and visual perspective-taking and comprehension of own versus other's desire, controlling for general verbal skills. Children with a more developed internal-state vocabulary performed better on perspective-taking tasks. These findings suggest that labeling and reasoning about mental states are related abilities at the early stages of theory-of-mind development.     

EVALUATION OF THE GENERALIZED EFFECTS OF A PEER-TRAINING PROCEDURE WITH MODERATELY RETARDED ADOLESCENTS

The use of peer-training procedures by moderately mentally retarded adolescents was evaluated in two experiments. In Experiment 1, 2 students received instruction on peer-training skills to teach a vocational task to 7 classmates. Following instruction, both peer trainers were successful in teaching their classmates to perform the target task and a second untrained (generalization) task. In Experiment 2, 1 peer trainer taught 3 peers to use picture prompts to complete one or two complex vocational tasks. Following instruction by the peer trainer, the trainees independently used novel pictures on novel tasks. The results of both experiments indicate that peer training with moderately handicapped students can be an effective instructional procedure, with generalization occurring for both the trainers (Experiment 1) and the trainees (Experiment 2).     

Stigma building blocks: how instruction and experience teach children about rejection by outgroups

Gaining an understanding of intergroup relations and outgroup rejection is an important childhood development. Children learn about rejection by outgroups via their own experiences and external instruction. A comparison of the impact of experience and instruction on first-, third-, and fifth-grade children's evaluations of rejection by outgroups in a minimal-groups paradigm suggests that the relative impact of experience and instruction differs as children age. In Study 1, younger children were more influenced by instruction, and older children were more influenced by what they experienced for themselves. In Study 2, younger children were more influenced by instruction, even when that instruction conflicted with what they experienced; older children were more influenced by their own experiences, even when those experiences contradicted what they were told to expect. These findings suggest that children begin learning about outgroup rejection through instruction but start to rely more on their own experiences as they age.     

Learning Mathematics From Examples and by Doing

This article demonstrates the feasibility and effectiveness of teaching several mathematical skills by presenting students with carefully chosen sequences of worked-out examples and problems - without lectures or other direct instruction. Thinking-aloud protocols of 20 students learning factorization by this method are analyzed to determine the kinds and depth of understanding students attained. Students did not simply memorize procedures but were able to recognize when the procedures were applicable and to apply them. Most students were also able to use their understanding of the concept of factorization to help learn the procedures and to check their results. The method of learning from examples has now been tested successfully with a class covering the entire 3-year curriculum in algebra and geometry in a Chinese middle school.     

The Influence of Reasoning with Emergent Quantities on Students' Generalizations

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize.     

Children's Criteria for Representational Adequacy in the Perception of Simple Sonic Stimuli

This article describes how children build increasingly abstract knowledge of linear measurement, emphasizing ways they relate space and number. Assessments indicate children struggle to understand measurement, especially concepts related to complex paths as in perimeter tasks. This article draws on developmental accounts of children's knowledge of measurement to describe the coordination of cognitive processes as a progression through increasingly abstract layers of strategy (Clements, 2003; Lehrer, 2003) within a constructivist perspective (Steffe &; Cobb, 1988; Steffe &; Thompson, 2000). This article reports 4 case studies from a 6-month teaching experiment with Grade 4 students to examine ways of promoting their strategy development. Attending to children's understanding of length along straight objects alone proved inadequate in predicting and validating models of children's developing strategies and concepts for perimeter. Setting perimeter tasks that emphasized integral relations among unit of length, sides of polygons and perimeter, and prompting children to integrate partitive, iterative, and counting schemes appeared to promote increasingly abstract length measurement strategies. The researchers came to distinguish between a naïve use of units to find length (Level 2a) and a more abstract strategy for unitizing and iterating (Level 2b), extending an earlier framework (Clements, Battista, Sarama, Swaminathan, &; McMillen, 1997). Finally, implications for instruction are drawn from the development of tasks and questioning sequences.     

Intermodal matching of vision and audition in infancy: A proposal for a new taxonomy

The aim of this review paper is first to devise a common framework for the various procedures used in experimental investigations of intermodal auditory – visual matching by human infants, and second to propose a new taxonomy of intermodal tasks in order to gain a better understanding of the perceptual-cognitive processing underlying these tasks and their relationships to other cognitive achievements such as the development of language. Based on an examination of the tasks used in the developmental literature, we suggest analysing them in terms of (a) their mode of presentation (simultaneous or sequential) for accessing the information in the two modalities (auditory and visual) and (b) the type of relation (amodal or arbitrary) between these two stimulus sources. A review of the literature in the light of this classification shows that most experimental studies employ parallel intermodal presentation (PIP) using both amodal and arbitrary relations between stimuli. Very few investigations have used sequential intermodal presentation (SIP) with amodal relations, and none have used SIP procedures with arbitrary relations. It is claimed here that this last approach might be the most appropriate one for furthering our understanding of (a) the categorical and semantic processing involved in intermodal matching and (b) how the developing infant learns to process words.     

The importance of job autonomy, cognitive ability, and job-related skill for predicting role breadth and job performance

Role theory suggests and empirical research has found that there is considerable variation in how broadly individuals define their jobs. We investigated the theoretically meaningful yet infrequently studied relationships between incumbent job autonomy, cognitive ability, job-related skill, role breadth, and job performance. Using multiple data sources and multiple measurement occasions in a field setting, we found that job autonomy, cognitive ability, and job-related skill were positively related to role breadth, accounting for 23% of the variance in role breadth. In addition, role breadth was positively related to job performance and was found to mediate the relationship between job autonomy, cognitive ability, job-related skill, and job performance. These results add to our understanding of the factors that predict role breadth, as well as having implications for how job aspects and individual characteristics are translated into performance outcomes and the treatment of variability in incumbent reports of job tasks.     

Stimulus equivalence instruction of fraction-decimal relations

Stimulus control technology was applied to the instruction of fraction ratio (e.g., (1/5)) and decimal (e.g., 0.20) relations, with 7 students who demonstrated difficulty in fraction and decimal tasks. The students were trained to match pictorial representations of fractions (B comparison stimuli) to printed counterpart fraction ratios (A sample stimuli), and to match printed decimals (C comparison stimuli) to pictorial representations of counterpart quantities (B sample stimuli). Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures. Limited generalization of fraction-decimal relations was observed.