Cognition and Instruction

Published by Taylor & Francis (Routledge)
Online ISSN: 1532-690X
Print ISSN: 0737-0008
Publications
Developmental changes in how children talk about reading preferences.  
In a 3-year longitudinal, mixed-method study, 67 children in two schools were observed during literacy activities in Grades 1–3. Children and their teachers were interviewed each year about the children's motivation to read and write. Taking a grounded theory approach, content analysis of the child interview protocols identified the motivations that were salient to children at each grade level in each domain, looking for patterns by grade and school. Analysis of field notes, teacher interviews, and child interviews suggests that children's motivation for literacy is best understood in terms of development in specific contexts. Development in literacy skill and teachers' methods of instruction and raising motivation provided affordances and constraints for literate activity and its accompanying motivations. In particular, there was support for both the developmental hypotheses of Renninger and her colleagues (Hidi & Renninger, 200621. Hidi , S. and Renninger , K. 2006. The four-phase model of interest development.. Educational Psychologist, 41(2): 111–127. [Taylor & Francis Online], [Web of Science ®]View all references) and of Pressick-Kilborne and Walker (2002)46. Pressick-Kilborn , K. and Walker , R. 2002. “The social construction of interest in a learning community.”. In Sociocultural influences on motivation and learning, Edited by: McInerney , D. and Van Etten , S. 153–182. Greenwich, CT: Information Age Publishing. View all references. The positions of poor readers and the strategies they used were negotiated and developed in response to the social meanings of reading, writing, and relative literacy skill co-constructed by students and teachers in each classroom. The relationship of these findings to theories of motivation is discussed.
 
This ethnographic study explores kindergarten children's emergent motivation to read and write, its relation to their developing concepts of reading and writing (Guice & Johnston, 1994; Johnston, 1997; Turner, 1995), and to their teachers instructional goals and classroom norms. Teachers and students together constructed legitimate literate activity in their classrooms, and this construction framed the motivation of students who were at risk for developing learning disabilities in reading and writing. Specifically, the kinds of reading and writing activity that were sanctioned in each class and the role of student-student collaboration colored students' views of the purposes of literacy and their own ability to learn. Findings extend our understanding of how young children's literacy motivation influences, and is influenced by, their classroom literacy culture. Implications for early literacy instruction for children with learning disabilities, and for their continuing motivation to read and write, are discussed.
 
A study was conducted to test the hypothesis that instruction with graphically integrated representations of whole and sectional neuroanatomy is especially effective for learning to recognize neural structures in sectional imagery (such as MRI images). Neuroanatomy was taught to two groups of participants using computer graphical models of the human brain. Both groups learned whole anatomy first with a three-dimensional model of the brain. One group then learned sectional anatomy using two-dimensional sectional representations, with the expectation that there would be transfer of learning from whole to sectional anatomy. The second group learned sectional anatomy by moving a virtual cutting plane through the three-dimensional model. In tests of long-term retention of sectional neuroanatomy, the group with graphically integrated representation recognized more neural structures that were known to be challenging to learn. This study demonstrates the use of graphical representation to facilitate a more elaborated (deeper) understanding of complex spatial relations.
 
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for sensemaking or as an assignment to fill out a worksheet. The student's understanding of the nature of the activity affects what she notices, what knowledge she accesses, and how she thinks to act. Previous analyses have found evidence of framing primarily in linguistic markers associated with speech acts. In this paper, we show that there is useful evidence of framing in easily observed features of students' behavior. We apply this observational methodology to explore dynamics among behavior, framing, and the conceptual substance of student reasoning in the context of collaborative active-learning activities in an introductory university physics course.
 
Two experiments, theoretically motivated by the construction-integration model of text comprehension (Kintseh, 1988), investigated the role of text coherence in the comprehension of science texts. In Experiment 1, junior-high students' comprehension of one of three versions of a biology text was examined via free recall, written questions, and a keyword sorting task. This study demonstrates advantages for globally coherent text and for more explanato text. In Experiment 2, interactions between local and global text coherence, readers background knowledge, and levels of understanding were examined. Using the same methods as in Experiment 1, we examined students' comprehension of one of four versions of a text, orthogonally varying local and global coherence. We found that readers who know little about the domain of the text benefit from a coherent text, whereas high-knowledge readers benefit from a minimally coherent text. We argue that the poorly written text forces the knowledgeable readers to engage in compensatory processing to infer unstated relationships in the text. These findings, however, depended on the level of understanding, textbase or simational, being measured by the three comprehension tasks. Whereas the free-recall naeastne and text-based questions primarily tapped readers' superficial understanding of the text, the inference questions, problem solving questions, and sorting task relied on a situational understanding of the text. This study provides evidence that the rewards to be gained from active processing are primarily at the level of the situation model, rather than at the superficial level of textbase understanding. Interactions of text coherence, background knowledge, People learn a great deal from texts -- story books, textbooks, newspapers, or...
 
This is the first issue of Cognition and Instruction that is made up of articles accepted by the new team of executive editors. As such, it is a good time for a note from the editor. For the most part, the aims and range of the journal will remain the same under the new regime. Cognition and Instruction will not lower standards to gain theory. As with dialectical approaches, whether this emphasis will succeed depends on the state of the art, and on both readers and contributors. This dialectical genre is tricky to nurture. Editors in charge may be the best people to think about possible contributions, but rarely will they be the best people to make the contribution. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
 
The present study explored how students' mental representations of an expository text and the inferences they generate vary as a function of text difficulty and of differences in the task. Ninety-six students from Grades 4, 10, and College were asked to write summaries of an expository text and then to answer orally several probe questions about the content. Reading difficulty was systematically manipulated at the microstructure and macrostructure processing levels. The results supported the prediction of qualitative changes in the way the meaning is represented by different age groups in different text conditions.
 
Studied under a variety of names (e.g., self-explanation, self-directed and generative summarization), it is now a well-accepted finding that the process of learner articulation contributes to new learning. While prior research has focused on measuring the effects of various forms of articulation on learning outcomes, this report focuses on how such articulation maybe accomplished, moment to moment and turn by turn. Specifically, it documents some of the ways in which participants use their bodies and, in particular, their hands while displaying what they know. It presents fine-grained analyses of three videotaped fragments of naturally occurring interaction among medical teachers and students participating in tutorial meetings in a Problem-Based Learning curriculum. Within these three exhibits, we find evidence of recipient design with regard to gesture production and recipient response with reference to its performance. We also find evidence of gesture re-use as a mechanism for cohesion across turns at talk and as a display of mutual understanding. This paper represents a preliminary step toward a more general program of research focusing on sense making practices in learning settings. Extending our understanding of how such practices are accomplished interactionally is a crucial step toward eventually being able to give an adequate account of what makes any exemplary form of instruction effective.
 
This article outlines a research strategy for investigating, in a laboratory setting, the acquisition and the "limits" of a cognitive skill. Expert digit memory is used as an illustration. Two participants with initial average digit- and word-span memory were trained to memorize and reproduce strings of 80 to 90 digits presented at 10- to 1-sec rates. The instruction and training program, based on a theory of skilled memory, focused on three components: (a) acquisition of a mnemonic system (i.e., recoding digits into historical dates or concrete nouns), (b) use of a long-term memory retrieval structure (i.e., instruction in the Method of Loci), and (c) improvement in processing speed. After 86 experimental sessions, one participant recalled 90 random digits presented at a 1-sec rate. The digits were, however, constrained to be compatible with the participant's historical knowledge. The second participant recalled 80 random digits presented at a 5-sec rate after 70 sessions. Speed of encoding and retrieval processing was the only component that required extensive practice for skilled digit-memory acquisition.
 
The examination of alternative hypotheses can initiate students into scientific practices and equip them with scientific literacy skills that will help them participate in ongoing debates involving complex socio-scientific problems. Hypothesis testing, in which the examination of alternative hypotheses is situated, has received much attention in the literature. However, the topic of alternative hypotheses has not been examined as extensively in scaffolded data-rich instructional interventions. This article contributes to that body of knowledge by reporting on middle-school students' inquiry practices as they relate to considering alternative hypotheses of their data. Specifically, the article reports a multiple-case study examining six pairs' reasoning as they try to solve a data-rich, scientific problem, scaffolded by the software investigation, the task setup, and the teacher. The students' generation and testing of alternative hypotheses was examined through students' discourse, actions, inquiry products, and interactions with their teacher and peers. Pre-post assessment analyses showed statistically significant learning gains while the analyses of the students' inquiry discourse and actions indicated that the scaffolding contributed to students' inquiry. However, several epistemological problems surfaced relating to students' perception of the usefulness of examining and communicating alternative explanations. These findings indicate the importance of epistemologically targeted discourse alongside guided inquiry experiences, and underline the need for further examination of appropriate scaffolding to support students' scientific reasoning processes.
 
Looking away from an interlocutor’s face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such “gaze aversion” (GA) is used far less by 5-year old school children, its use increases dramatically during the first years of primary education, reaching adult levels by 8-years of age (Doherty-Sneddon, Bruce, Bonner, Longbotham, & Doyle, 2002). Furthermore GA increases with increasing mental demands, with high levels signalling that an individual finds material being discussed challenging but remains engaged with it (Doherty-Sneddon et al., 2002; Doherty-Sneddon & Phelps, 2006). In the current study we investigate whether patterns of gaze and gaze aversion during children’s explanations can predict when they are in states of transient knowledge (Karmiloff-Smith 1992; Goldin-Meadow, Kim, & Singer, 1999). In Study 1, fifty-nine 6-year-olds took part and completed a “Time Task” along with periodic teaching intervention to improve their comprehension of telling the time. Some children improved immediately, whereas others did so more gradually. The gradual improvers showed the highest levels of GA, particularly when they were at an intermediate level of performance. In Study 2, thirty-three 6-year-old children completed a balance beam task (Pine & Messer, 2000). Children who improved the representational level of their explanations (Karmiloff-Smith, 1992) of this task with training used more GA than those who did not. Practical implications for teaching and for recognizing transient knowledge states are discussed.
 
Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of advanced addition strategies. A third model suggests that children may invent labor-saving addition strategies without appreciating the commutativity principle. A study tested these three models by evaluating 36 kindergarteners' responses on two types of commutativity tasks. Both tasks involved predicting whether commuted and noncommuted pairs of problems would produce the same or different answers. Over two sessions, children's addition strategies were also assessed. Strategies noted were spontaneous counting-all with concrete supports; counting-all mentally, starting with the first addend; counting-all mentally, starting with the larger addend; counting-on mentally from the first addend; and counting-on mentally from the larger addend. (Counting-all strategies begin at the number 1; counting-on strategies begin at the value of the first addend selected by the child.) Findings indicated that, as proposed by the second model, commutativity was not naturally assumed by children, but appeared to be discovered. Contrary to the first model and consistent with the third, an understanding of commutativity was not evident in all subjects who invented labor-saving addition strategies. (Author/RH)
 
Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.
 
Cognitive load theory suggests that effective instructional material facilitates learning by directing cognitive resources toward activities that are relevant to learning rather than toward preliminaries to learning. One example of ineffective instruction occurs if learners unnecessarily are required to mentally integrate disparate sources of mutually referring information such as separate text and diagrams. Such split-source infonnation may generate a heavy cognitive load, because material must be mentally integrated before learning can commence. This article reports findings from six experiments testing the consequences of split-source and integrated information using electrical engineering and biology instructional materials. Experiment 1 was designed to compare conventional instructions with integrated instructions over a period of several months in an industrial training setting. The materials chosen were unintelligible without mental integration. Results favored integrated instructions throughout the 3-month study. Experiment 2 was designed to investigate the possible differences between conventional and integrated instructions in areas in which it was not essential for sources of information to be integrated to be understood. The results suggest that integrated instructions were no better than split-source infonnation in such areas. Experiments 3, 4, and 5 indicate that the introduction of seemingly useful but nonessential explanatory material (e.g., a commentary on a diagram) could have deleterious effects even when presented in integrated format. Experiment 6 found that the need for physical integration was restored if the material was organized in such a manner that individual units could not be understood alone. In light of these results and previous findings, suggestions are made for cognitively guided instructional packages.
 
Dixon (1991) and Goldman (1991) have provided thoughtful commentaries on Chandler and Sweller (1991). The general issue they raise concerns the scientific procedures we should use when conducting research in cognition and instruction. It is an issue of great importance, and we welcome the opportunity provided by their criticisms to discuss the techniques we use. To clarify the findings based on cognitive load theory, we begin by indicating the essential characteristics of a theory concerned with cognition and instruction, followed by a brief history of cognitive load theory to make clear that it has these characteristics. These statements will then be used to address specific comments made by Goldman and Dixon.
 
In the predominant symbolic approach of AI in the 1970s and early 80s, a description—such as an expert system rule, frame, script, or natural language grammar—was often called a "knowledge representation." Knowledge was viewed as something that could be inventoried. Human memory was modeled as a repository of knowledge representations. Arguments that "there are no knowledge representations in the brain," were then misinterpreted in this community as "throwing the baby out with the bathwater."
 
People often justify history's place in the curriculum by its relationship to citizenship, yet there is little research to help educators picture how people use historical knowledge for civic purposes. This expert–novice study used the think-aloud method to examine how eight political scientists and eight high school students employed historical knowledge to reason about a political issue. Findings indicated that detailed historical narrative played an important role for experts’ reasoning, and the experts used narrative to frame the issue, support their positions, and evaluate historical claims. Participating students used narrative as well, but their narratives were lacking in detail. They never used history to frame the problem, contextualize documents, or to support their positions, and they rarely used narrative to evaluate claims. These differences in how experts and novices use history to make sense of the present have implications for history instruction and research in history and civic education.
 
In this article, we report on a design experiment conducted in an 8th grade classroom that focused on students' analyhsis of bivariate data. Our immediate goal is to document both the actual learning trajectory of the classroom community and the diversity in the students' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. On a broader level, we also focus on the learning of the research team by documenting the conjectures about the stuydents' statistical learning and the means of supporting it that the research team generated, tested, and revised on-line while the experiment was in progress. In the final part of the article, we synthesize the results of this learning by proposing a revised learning trajectory that can inform design and instruction in other classrooms. In doing so, we make a contribution to the cumulative development of a domain-specific instructional theory for statistical data analysis.
 
The experiments reported in this article flow from the following assumptions concerning our cognitive processes: (a) Schema acquisition and automation are major learning mechanisms when dealing with higher cognitive activities and are designed to circumvent our limited working memories and emphasize our highly effective long-term memories. (b) A limited working memory makes it difficult to assimilate multiple elements of information simultaneously. (c) Under conditions where multiple elements of information interact, they must be assimilated simultaneously. (d) As a consequence, a heavy cognitive load is imposed when dealing with material that has a high level of element interactivity. (e) High levels of element interactivity and their associated cognitive loads may be caused both by intrinsic nature of the material being learned and by the method of presentation. (f) If the intrinsic element interactivity and consequent cognitive load are low, the extraneous cognitive load is critical when dealing with intrinsically high element interactivity materials. These assumptions are the basic points of cognitive load theory. They were used to suggest that, when learning to use equipment such as computer applications, learning might be facilitated by not having the equipment present, if the material that needed to be learned had an intrinsically high degree of element interactivity. A series of four experiments supported this hypothesis. It was concluded that an analysis of both intrinsic and extraneous cognitive load can lead to instructional designs generating spectacular gains in learning efficiency.
 
We report two studies involving an intelligent tutoring system for Lisp (the Camegie Mellon University Lisp Tutor). In Experiment 1, we developed a model, based on production system theories of transfer and analogical problem solving, that accounts for effects of instructional examples, the transfer of cognitive skills across programming problems, and practice effects. In Experiment 2, we analyzed protocols collected from subjects as they processed instructional texts and examples before working with the Lisp Tutor and protocols collected after subjects solved each programming problem. The results suggest that the acquisition of cognitive skills is facilitated by high degrees of metacognition, which includes higher degrees of monitoring states of knowledge, more self-generated explanation goals and strategies, and greater attention to the instructional structure. Improvement in skill acquisition is also strongly related to the generation of explanations connecting the example material to the abstract terms introduced in the text, the generation of explanations that focus on the novel concepts, and spending more time in planning diminishing returns. Finally, reflection on problem solutions that focus on understanding the abstractions underlying programs or that focus on understanding how programs work seems to be related to improved learning.
 
Observation task for participants in the weak-model condition.  
Orchestration of cognitive activities per condition. CO = control condition; WM = weak-model condition; and GM = good-model condition.  
Orchestration of transcribing per individual writer. " ooo " line = individual writers in control condition; solid line = individual writers in the weak-model condition; dotted line = individual writers in the good-model condition.  
Random Parameters for the Relation Between the Writing Processes Goal Orientation and Analysis and Text Quality (SE in Parentheses)
In this study, we examined why observational learning positively affects learning outcomes of new writing tasks. In this study, we focused on the effects of observational learning on the temporal organization (i.e., orchestration) of writing processes and on the subsequent influence on text quality. An experiment was set up in which participants (N = 52; 8th-grade students) were assigned to 1 of 2 observational-learning conditions or a control (CO) condition. In the observational-learning conditions, participants learned by observing peer models' writing processes and in the CO condition by performing writing tasks. To measure the orchestration of writing processes, the participants performed posttest-writing tasks under think-aloud conditions. Results show that observational learning affected writing processes differently than the CO condition. Writers who learned by observation performed more high-level processes like planning. Furthermore, for some activities, these writers showed a changing pattern of execution over time, whereas writers in the CO condition performed these activities at a constant rate during the writing process (i.e., a monotonous process). Finally, we show that the orchestration performed by the students who learned by observation was positively related to the quality of the writing product.
 
The purpose of this study was to investigate the relations between cognitive activities and text quality: Are qualitatively different texts preceded by different distributions of cognitive activities? The main assumption was that the same cognitive activity might have a different impact, depending on the moment it is engaged in during the writing process. The research material consisted of 40 compositions on two themes, written by 20 ninth-grade students. Thinking-aloud protocols were recorded to assess the writing processes underlying the production of these texts. Data were analyzed by means of multilevel analyses of variance. It appeared that frequency of cognitive activities was not distributed at random over text production. Some cognitive activities appeared to be relatively restricted to the first part of the writing process, whereas others dominated at later stages. The relations between text quality and cognitive activities seemed to depend on the stage in the writing process at which a cognitive activity was employed; the same cognitive activity that showed a positive effect on text quality during one episode showed either a negative effect during another phase or no effect at all. Including time as a variable proved to make results clearer and more specific; the effect of activities having different signs, depending on the episode, would have been absent if the time variable had not been included in the analysis.
 
When reading multiple texts about controversial scientific issues, learners must construct a coherent mental representation of the issue based on conflicting information that can be more or less belief-consistent. The present experiment investigated the effects of text–belief consistency on the situation model and memory for text. Students read four texts about a scientific controversy. Learners' situation model was biased towards their beliefs when belief-consistent and belief-inconsistent texts were presented block-by-block. When the texts were presented alternatingly, situation models for belief-consistent and belief-inconsistent texts were equally strong. Moreover, the text base was better for belief-inconsistent texts. These results support the idea that prior beliefs influence the processing of conflicting information in multiple texts differently on the level of the situation model and on the propositional text base. A more balanced situation model of scientific controversies can be promoted by presenting belief-consistent and belief-inconsistent texts in an alternating sequence.
 
This study investigated how varying the lexical encodings of technical terms in multiple texts influences learners' dyadic processing of scientific-related information. Fifty-seven pairs of college students read journalistic texts on depression. Each partner in a dyad received one text; for half of the dyads the partner's text contained different lexical encodings of the same concepts; for the other half the lexical encodings and texts were identical. They then read a case report on first signs of depression. Communicating via a chat room, each dyad had to write a causal diagnosis and suggest a treatment. Results showed that dyads in the different-encoding condition explicitly elaborated the meaning of technical terms more often, produced more differentiated answers, and acquired more knowledge. It is concluded that deliberately switching different words for the same underlying content, and engaging students in discussion of that content, influences learners' discourse and promotes scientific/conceptual understanding.
 
Figure . Collaborative lesson and activity design cycle. The process involves teachers and researchers working together to design, implement, evaluate, and revise/adapt lessons and activities based on an identified area of focus or student need. This process is based on a model of teacher professional development known as Japanese Lesson Study (for details, see Lewis et al., ). The white boxes (stages ,,,) refer to the widely recognized four-stage model, while the grey boxes refer to the four additional adaptations.  Building the intervention: Combining research, practice, and theory 
Figure . Display of group by time interactions across all seven measures. Error bars represent standard error of the mean. * p < .. 
This study describes the implementation and effects of a 32-week teacher-led spatial reasoning intervention in K–2 classrooms. The intervention targeted spatial visualization skills as an integrated feature of regular mathematics instruction. Compared to an active control group, children in the spatial intervention demonstrated gains in spatial language, visual-spatial reasoning, 2D mental rotation, and symbolic number comparison. Overall, the findings highlight the potential significance of attending to and developing young children's spatial thinking as part of early mathematics instruction.
 
Mastery goal structures, which communicate value for developing deeper understanding, are an important classroom support for student motivation and engagement, especially in the context of science learning aligned with the Next Generation Science Standards. Prior research has identified key dimensions of goal structures, but a more nuanced examination of the variability of teacher-enacted and student-perceived goal structures within and across classrooms is needed. Using a concurrent mixed-methods approach, we developed case studies of how three 7th-grade science teachers enacted different goal structures while teaching the same chemistry unit and how their students perceived these goal structures. Student perceptions were largely consistent with our observational analysis and suggested that a positive social climate and autonomy support are important elements of mastery goal structure. However, balancing socio-emotional support with sufficient academic rigor may be especially important for students with high levels of mastery goal orientation and self-efficacy in science. Implications for research include the need for further research linking classroom stimuli to variability in perceived goal structure, especially across students with different motivational characteristics. Implications for practice include strategies for science teachers to promote perceptions of a mastery goal focus in students, particularly through feedback and recognition practices.
 
In this article, we provide a novel view of mathematics learning disability (MLD) by studying a student with an MLD (Dylan) who had compensated so effectively that she was able to major in statistics. We push back on the dominant deficit model used in studies of MLD, and consider issues of access and compensation from a Vygotskian theoretical frame. Through 8 videotaped interview sessions, we identified that Dylan’s primary difficulties were with mathematical notation and number sense, which resulted in issues accessing standard mathematical forms. Analysis revealed 8 compensatory strategies that Dylan used to address these issues of access. We frame our approach as emancipatory research. Dylan was involved in all phases of the study’s design, implementation, analysis, and dissemination, and is the second author. This work acknowledges that individuals with disabilities have research agendas of their own and have critical insight to share about the lived experience of their disability.
 
This study examines the development of secondary preservice science teachers’ (PSTs’) sociopolitical understandings in the context of a yearlong, masters-level, justice-oriented teacher education program. It articulates a theoretical perspective regarding teachers’ conceptions of the work-of-teaching in terms of pedagogical and disciplinary commitments. These conceptions are ideological links between classroom practices and teachers’ understanding of the sociopolitical context of their work. Teachers’ conceptions include how they view their and their students’ agency to gain access to enabling structures or dissent against oppressive structures that contribute to inequity in science education. The embedded case study design with 10 PSTs draws on various data sources from three time periods, and several types of experiences, in the teacher education program. A focus on four cases illustrates how PSTs rearticulated ideological committments in ways that have direct implications for the development of their practice and also connections to the content areas they teach. One case reinforces that teachers may begin to reject deficit views and embrace their agency by learning about the ways in which racism structures society. Another case shows how PSTs’ political clarity may be pushed in the direction of understanding multiple forms of oppression as structural. Together, the four cases illuminate an ideological component to content area teaching, or content area considerations in teachers’ ideological committments. Science teachers may develop sophisticated views of their work by analyzing their disciplines and curriculum as structures that are subject to the same critiques levied against other social structures. While PSTs did not feel that justice-centered pedagogies were within their full reach at the end of the program, they moved from aiming to demonstrate to students the utility, value, and importance of content areas toward exploring the relevance of the content areas with students.
 
The present study is motivated by a significant body of research documenting teachers’ perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of multiplication and of fractions and by coordinating symbolic representations with math drawings. The dataset spans 1 semester of Nina’s in-class work during a content course—explicitly designed to foster coherence within the multiplicative conceptual field—as well as her written assignments for the course and her moment-to-moment reasoning during three interviews conducted near the beginning, middle, and end of the semester. A main result is that constructs from coordination class theory, a strand of theory within the knowledge-in-pieces epistemological perspective, were particularly useful for tracking and explaining Nina’s piecemeal progress. The broad contribution of the article is two-fold—(a) a shift in focus from research on reasoning about one or two topics toward reasoning across a wider range of topics related to multiplication and (b) highlighting refinement and coordination of knowledge resources as basic processes by which future teachers can progress toward coherent understandings of critical school mathematics content.
 
Mathematics and science education researchers focused on teacher education emphasize attention and responsiveness to student thinking as central to effective classroom practice. Being responsive to student thinking involves attending to the substance of students’ ideas—the meaning students are making—and pursuing that thinking, adjusting the flow of instruction as needed. Yet, attention and responsiveness to student thinking is irregular and generally rare among novice teachers. In this theoretical paper, we argue that the irregularity of attention and responsiveness to student thinking, including variability within individual teachers’ practice, can be explained by a framework grounded in teachers’ localized framings of their classroom activity—their sense of “what is it that’s going on here.” Using analyses of classroom episodes across contexts and timescales to illustrate our claims, we demonstrate how a framing-anchored framework can coordinate and improve upon three common explanations for the irregularity of novice teachers’ attention and responsiveness to student thinking: underdeveloped skills and/or knowledge for attending and responding, “transmissionist” beliefs about learning, and institutional constraints (and teachers’ perceptions thereof). Building on this argument, we suggest that teacher educators can work with novice teachers’ framings of their classroom activities as a generative anchor for supporting attention and responsiveness to student thinking in classroom settings.
 
Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students’ generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support more productive generalizations. In response, we report on results from 146 interviews with 93 participants in middle school through college in the domains of algebra, advanced algebra, trigonometry/pre-calculus, and combinatorics while solving complex problems. Our findings yielded the Relating-Forming-Extending (RFE) Framework, which distinguishes multiple related forms and types of generalizing. We also present two aspects of mental activity that promote generative generalizations: operative activity, and building and refining activity.
 
Gesture is recognized as part of and integral to cognition. The value of gesture for learning is contingent on how it gathers meaning against the ground of other relevant resources in the setting—in short, how the body is laminated onto the surrounding environment. With a focus on lamination, this paper formulates an integrated theory of viewpoint and spatial reasoning; develops an embodied approach to documenting and understanding the live construction of students’ spatial models; and offers new implications for the teaching of spatially complex concepts. We start with a study of how undergraduate students playfully gesture the first-person movements of components of an engineering system, step out to depict how the system appears from the outside, and all the while track how the components of the system spatially interact in the open canvas of empty space around the body. Students who manage all three—switching from character viewpoints to observer viewpoints while maintaining a coherent organization of space—better learn the engineering concept. We then examine this process in the unscripted discourse of a classroom of 1st and 2nd graders pretend-playing as bees. This second study extends the analysis of interactions between spatial reasoning and viewpoint into unplanned teacher-student discourse (including adjustments in talk and action over time) and a materially rich setting. In all, the paper formulates an embodied learning framework that integrates viewpoint and spatial reasoning with implications for learning design.
 
This article reports on students’ problem-solving approaches across three representations—number lines, coordinate planes, and function graphs—the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a hierarchical representational narrative (HRN), a discursive narrative around a set of representations that model conventional mathematics in structurally consistent ways. A paper-and-pencil assessment was administered to students in grades 5 and 8 along with videotaped interviews with a subset of students. Results revealed students’ application of particular meta-rules, which reflect their attempts to find and make use of recurring patterns in mathematics discourse. One such meta-rule, consistent with the HRN, was characterized by students’ coordination of geometric and numeric properties of an axis, whereas alternate meta-rules reflected coordinations inconsistent with conventional mathematics. Detailed analyses of problem-solving strategies are reported, and implications for theory, curriculum, and instruction are discussed.
 
This commentary summarizes the argument Charles Goodwin presents in Co-Operative Action (Co-A, 2018 Goodwin, C. (2018). Co-operative action. New York, NY: Cambridge University Press. [Google Scholar]), his most recent book. Through exploration of the breadth of conceptual and methodological tools that he has built over the course of his career and represents in this book, we suggest paths forward for Learning Sciences towards engaging in more equitable and relational research.
 
This essay examines the role of public education in the process of place-remaking that relies on a false separation between teaching and issues of race, politics, and power. I construct a historical case study of my hometown that presents a counter narrative, presented by students, of race and legacy in the context of a public school and the surrounding community. Building upon a walk-as-method approach, I illustrate the confluence of historical, racialized narratives that are discoverable at the scale of the city but invisible within the walls of the school. I conclude with an in-progress professional code of ethical teaching and research practice for the learning sciences. These commitments are intended to support and protect students (and all young people in our communities) from bearing sole responsibility for critical stances based on their identities and histories-in-place.
 
Connection-making among multiple representations is a crucial but difficult competence in STEM learning. Prior research has focused on one type of learning process involved in connection-making: sense-making processes leading to conceptual understanding of connections. Yet, other research suggests that a second type of learning process is important: inductive learning processes leading to perceptual intuitions about connections. We investigate whether combining instructional activities designed to support sense-making processes for understanding of connections (understanding activities) and instructional activities that support inductive processes for perceptual intuitions about connections (perception activities) enhances students’ learning of chemistry knowledge. A laboratory-based experiment with 117 undergraduate students compared students in (a) a control condition that received only conventional activities that did not require connection-making; (b) a condition that received conventional and understanding-activities; (c) a condition that received conventional and perception-activities; and (d) a combined condition that received conventional, understanding-activities, and perception-activities. Results show that only the combined condition outperformed the control condition on a test of chemistry knowledge. Eye-gaze data and verbal reports show that understanding-activities and perception-activities have complementary effects on how students integrate information from multiple representations during the learning phase. Finally, we found that students’ spatial skills moderate their benefit from understanding-activities and perception-activities.
 
This article presents findings from TechTales, a participatory design research (PDR) project where learning scientists, public library staff members, informal science educators, and staff members from Native-American-serving organizations collaborated to design a family-based robotics workshop that was grounded in storytelling. We approach this by engaging Indigenous ways of knowing and being from a sociocultural learning theory perspective. Through analyzing families-in-interaction as they constructed dioramas with robotics that told their family stories, we explore how cultivating consequential learning environments in STEM is intimately intertwined with historicity, knowledge systems, and the agentic positioning of learners to design new technologies. We find that using storywork as the design focus of building dioramas created learning environments where computer programing and robotics became dynamic tools toward family-making, collaboration, and the active presencing of Indigenous knowledge systems and cultural practices. Living and interrelating with story and its knowledge systems through making were enactments of Indigenous resurgence in everyday ways. From a structure of social practices perspective, this opens up learning spaces for engagement in STEM-Art practices and in relation to other social practices of consequence, such as cultural flourishing and affiliation, collaboration and family-making, and societal repositioning.
 
Theoretical Framework -The intertwining of Indigenous Knowledge Systems and Materiality and Engagement towards Indigenous resurgence.
Coding Scheme and the Operationalization of Theoretical Framework.
This article presents findings from TechTales, a participatory design research (PDR) project where learning scientists, public library staff members, informal science educators, and staff members from Native-American-serving organizations collaborated to design a family-based robotics workshop that was grounded in storytelling. We approach this by engaging Indigenous ways of knowing and being from a sociocultural learning theory perspective. Through analyzing families-in-interaction as they constructed dioramas with robotics that told their family stories, we explore how cultivating consequential learning environments in STEM is intimately intertwined with historicity, knowledge systems, and the agentic positioning of learners to design new technologies. We find that using storywork as the design focus of building dioramas created learning environments where computer programing and robotics became dynamic tools toward family-making, collaboration, and the active presencing of Indigenous knowledge systems and cultural practices. Living and interrelating with story and its knowledge systems through making were enactments of Indigenous resurgence in everyday ways. From a structure of social practices perspective, this opens up learning spaces for engagement in STEM-Art practices and in relation to other social practices of consequence, such as cultural flourishing and affiliation, collaboration and family-making, and societal repositioning.
 
An important element of adaptive expertise involves stepping away from a routine to retool one's knowledge or environment. The current study investigated two forms of this adaptive pattern: fault-driven adaptations, which are reactions to a difficulty, and prospective adaptations, which are proactive reformulations. Graduate and undergraduate students with no medical training engaged in a medical diagnosis task that involved complex information management. The graduate students, who were relative experts in information management and data analysis, uniformly made prospective adaptations by taking the time to create external representations of the available information before they diagnosed a single patient. In contrast, the undergraduate students only made representations reactively, when experimental manipulations made their default behaviors impractical. Graduate students tolerated the time lost creating representations in favor of future benefits—well-structured representations led to more optimal diagnostic choices. Overall, the results indicate that long-term educational experiences are correlated with prospective adaptation, even in a novel task domain that is not explicitly a part of those educational experiences. This research provides new metrics for evaluating educational interventions designed to move students along a trajectory toward adaptive expertise.
 
An emerging pattern of relationship between additive strategies and mDC reasoning (Rasch measure).
Auxiliary item to assess the child's recognition of towers/cubes pictorials.
Rasch measure (mDC, 0-100) as a variable dependent on a child's additive strategy.
Adel's progressive summation of grouped 1 s.
We examine a hypothesis implied by Steffe’s constructivist model of children’s numerical reasoning: a child’s spontaneous additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders’ responses during clinical, task-based interviews. All participants spontaneously used one of three additive strategies—counting-on, doubling, or break-apart-make-ten (BAMT)—to correctly solve an addition word problem (8 + 7). We found between-group differences, with asymmetric association of those ordinal variables. We found counting-on to be mainly related to premultiplicative reasoning and BAMT to mDC reasoning. We discuss the theoretical significance and implications of this corroboration of Steffe’s model.
 
Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.
 
Teacher solidarity co-design is a special case of participatory design research that emphasizes the unique power dynamics of partnering with teachers who are multiply positioned in schooling, educational policy and research, and society. Through contrastive case analysis of four instrumental cases, five principles that characterize teacher solidarity co-design emerged. Collectively, the cases traverse the professional life-course of teachers in a variety of contexts but foreground co-learning and relationality between teachers and researchers in their efforts to create transformational change in schools. Additionally, the analysis of the cases centers our own experiences and insights as former teachers who are currently educational researchers. The principles account for the complex and nested systems of power that teachers occupy within efforts that seek to transform schools into more equitable and just spaces.
 
As scientific models of student thinking, learning progressions (LPs) have been evaluated in terms of one important, but limited, criterion: fit to empirical data. We argue that LPs are not empirically adequate, largely because they rely on problematic assumptions of theory-like coherence in students’ thinking. Through an empirical investigation of physics teachers’ interactions with an LP-based score report, we investigate 2 other criteria of good models: utility and generativity. When interacting with LP-based materials, teachers often adopted finer-grained perspectives (in contrast to the levels-based perspective of the LP itself) and used these finer-grained perspectives to formulate more specific, actionable instructional ideas than when they reasoned in terms of LP levels. However, although teachers did not use the LP-based materials in ways envisioned by LP researchers, the teachers’ interactions with the score reports embodied how philosophers envision the fruitful use of good models of dynamic, complex systems. In particular, teachers took a skeptical, inquiring stance toward the LP, using it as an oversimplified starting place for generating and testing hypotheses about student thinking and using concepts from the model in ways that moved beyond the knowledge available in the LP. Thus, despite—and perhaps even because of—their empirical inadequacy, LPs have the potential to serve teachers as productive models in ways not envisioned by LP researchers: as tools for knowledge generation.
 
A visual representation of the processing chains created in Rachel's and Andy's 20-minute reading strategy use for open website searching and focused website learning. Twenty-minute timed course reading from the beginning of each session was divided into approximately 5-minute intervals. Magnitudes of all color-coded cells are identical to one another, so each cell represents one time of occurrence for the corresponding strategy but not the duration of each strategy. TL = text location. SM = self-monitoring. IE = information evaluation. MM = meaning-making.
A Snapshot of Encoded Protocols of Verbal Reports and Screen Moves, With Examples of Labeling and Coding of Cells of Strategic Action
The Coding Scheme Emerging From the Course of Data Analysis Guided by the Framework of Constructively Responsive Reading 
An Overview of Reading Strategies Identified From Seven Participants' Internet Reading (Continued)
Cross Tabulation of Strategy Type and Internet Reading Session Strategy Type 
The purpose of this study was to investigate the type, pattern, and complexity of Internet reading strategies used by seven accomplished high school readers. Individual participants performed an academic Internet reading task with the goal of developing critical questions about their chosen controversial topic. Strategies for Internet reading were analyzed from the perspective of constructively responsive reading, both qualitatively and quantitatively, using participant-generated verbal reports complemented by recordings of their computer screens. The data described the nature and sequence of reading strategies that participants used to construct meaning, and the interplay of those multiple strategies in Internet settings. The results demonstrated that the participants’ Internet reading involved the iteration and modification of traditional print-based reading strategies (e.g., meaning-making, self-monitoring, information evaluation) and also the use of strategies characteristic of Internet settings (e.g., text location). Implications of the study's findings on Internet reading strategy use for theory and research are discussed.
 
This paper argues that the terms through which we interpret and work to develop expansive pedagogical practices are overly constrained by the binary of adult-centered versus child-centered education. Analyzing ethnographic data developed over three years in a making/tinkering afterschool program serving Black, Latinx, and Asian American students (K-5), we explicate and imagine beyond this binary by (1) analyzing key forms of pedagogical talk, listening, and embodied assistance that supported generative forms of learning and relationality and defied categorization as either adult- or child-centered; and (2) theorizing joint activity as a pedagogical practice by historicizing and unmooring the work of critical education from the perpetual negation of Western, adult-centered models, thereby creating distinct grounds for specifying the role of direct assistance and its salience for questions of educational dignity and justice. Taken together, we argue for a more complex view of when and how direct teaching can support meaningful learning, and further delineate the relationships between such teaching and a broader ethos of joint, intergenerational activity.
 
Engle and Conant’s productive disciplinary engagement (PDE) framework has significantly advanced the study of learning in mathematics and science. This artilce revisits PDE through the lens of critical education research. Our analysis synthesizes two themes of power: epistemic diversity, and historicity and identity. We argue that these themes, when integrated into PDE, strengthen it as a tool for design and analysis of disciplinary learning in relation to power and personhood, and describe the broadened framework of connective and productive disciplinary engagement (CPDE). By comparing and contrasting the use of PDE and CPDE in relation to two cases of classroom learning—for science, Warren et al.’s metamorphosis and for mathematics, Godfrey and O’Connor’s measurement—we demonstrate how CPDE surfaces issues of history, power, and culture that may otherwise be overlooked by PDE alone. In particular, we analyze how CPDE makes visible unseen identities and generative resources of disciplinary knowing and doing among minoritized students. We discuss how the revised framework redresses epistemic injustice experienced by minoritized learners held to the narrow rubric of western epistemologies and compels close attention to the diversity of human activity in mathematics and science. Further, we elaborate how it provides a structure for teachers, teacher educators, and researchers to design and analyze learning environments as safeguarding the rightful presence of minoritized learners in STEM classrooms and beyond.
 
While issues of (in)justice in K12 STEM learning have garnered increasing attention, limited research has attended to learning as social-spatial transformation. We draw upon a justice-oriented framework of equitably consequential learning to call attention to how learning and engagement in K12 STEM is rooted in the history and geographies of young people’s lives. Without attention to the ways in which learning is an historicized and sociopolitical activity, efforts to address seemingly intractable equity challenges in K12 STEM education across the intersections of racial and class inequality will remain elusive. Using data from middle school classroom studies focused on engineering for sustainable communities, where community ethnography is central to engineering design, we investigate the social-spatial relationalities that minoritized youth bring to engineering design, and how relationalities may support youth in transforming oppressive knowledge and power structures toward equitably consequential learning. Findings reveal that organizing learning engineering design around youths’ rich everyday experiences and community wisdom through community ethnography, addressed hyperlocal, sociopolitical community challenges. As a result, the social-spatial terrain upon which subject-object relations are enacted shifted, expanding the discourses, practices and outcomes of middle school engineering design that were legitimized. Making present this power-mediated terrain makes visible the often hidden, but ever present, unjust school-based relationalities, enabling them to be re-mediated in justice-oriented ways. Paying attention to social-spatial relationalities reveal (1) the multiple scales of activity, (2) inter-scalar mobilities and interactions, and (3) possible resultant impacts of such interactions that further affect activity at each scale. We discuss implications for how theories of equitably consequential learning can be advanced through the frame of social-spatial justice.
 
This study explored whether a month-long instructional intervention in affective evaluation can help struggling high school readers to engage in literary interpretation in ways similar to expert readers’ practices. We compared pre- and post-intervention think-aloud protocols from five high school students as they read a literary short story with the protocols from five experienced English teachers for the same story. After the intervention, student readers attended more frequently to story details that expert readers also found salient to interpretation. Students also made interpretive moves similar to those made by experts, such as inferences about character goals, interpretation of potential symbols, and attention to patterns and juxtapositions in the text. Further, students’ focus on interpretively salient details influenced their thematic inferences. These findings suggest that the recruitment of everyday, affect-based practices can help novice readers develop more “expert-like” literary schemata and construct more meaningful interpretations of a literary text.
 
We study the case of Marya, a freshman engineering major who showed and spoke of a drastic shift in her feelings and approach to learning physics during an introductory course. For the first several weeks, she was anxiously manipulating equations without considering physical meaning, and she was terribly worried about being correct. By the end of the semester, however, she was sense-making and taking pleasure in it, showing and expressing an enjoyment of challenges and uncertainty. In this paper, we illustrate Marya’s transformation using data from her interview and coursework, and we propose it as an example of meta-affective learning. We argue that meta-affective learning was an important part of Marya’s physics learning and that it was deeply entangled with her developing epistemology.
 
Top-cited authors
Annemarie Palincsar
  • University of Michigan
Andrea A. Disessa
  • University of California, Berkeley
Graham Cooper
  • Southern Cross University
Randi A Engle
  • University of California, Berkeley
Susan Nolen
  • University of Washington Seattle