Constructive habituation as an educational approach to process-object reification in mathematics

Sfard and Thompson (1994) state that what matters most is that educators develop ways of thinking, teaching, and learning mathematics. This study introduced constructive habituation, a new strategy developed to aid both students and teachers in the thinking, teaching, and learning of mathematics. Constructive habituation attempts to unite constructivist teaching methods aimed at supporting students’ conceptual understanding of content and habituationist teaching method aimed at establishing routine responses to routine tasks. This study is exploratory in nature, designed to investigate if constructive habituation is a more effective means than a traditional teaching method in helping students reach process-object reification as evidenced by higher levels of student achievement. The study primarily addressed introductory function concepts and symmetry and transformations of functions. The subjects were university students enrolled in a precalculus I course. The results indicated that constructive habituation was not a more effective means in helping students reach process-object reification than a traditional teaching method. No significant differences were found for any of the variables examined. However, some promising practical results were revealed. The students taught using the experimental method averaged more than nine points higher than the students taught using a more traditional teaching method on an examination that evaluated their understandings of the relationship between changes made to the graph of a function and changes made to its formula. Explanations on why constructive habituation may not have reached its intended goal are given. A discussion is presented of the developmental stage at which constructive habituation may become an effective pedagogical method. Study also includes a brief history of the major pedagogical movements over the last half century and the psychological perspectives that influenced each

A content analysis of the two state-approved kindergarten and first grade reading programs in California

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Communication Patterns and Strategies in Software Development Communities of Practice

Some of the greatest challenges in the relatively new field of software development lie in the decidedly old technology of communication between humans. Software projects require sophisticated and varied communication skills because software developers work in a world of incomplete, imperfect information where teams evolve rapidly in response to evolving requirements and changing collaborators. While prescriptive models for software process such as Agile suggest ways of doing, in reality these codified practices must adapt to the complexities of a real workplace. Patterns, rather than rules of behavior within software process are more suitable to the varied and mutable nature of software development. Software development communities are also learning communities, attempting to sustain themselves through internal ambiguity and external changes. We study different types of software development communities to fulfill our goal of understanding how these communities implement and evolve different communication strategies to sustain themselves through change. We observe student software development projects, open source software development, and a professional, rigorously Agile software development community. We employ Wenger\u27s concept of Community of Practice to frame our understanding, especially focusing on the notions of identity, participation, reification, negotiation of meaning and trajectory of the participants of the software development communities. From these different sources, we identify the emergent themes of mentoring and knowledge management as critical for sustainable communities. Through our long running, immersive, participant observer, ethnographic study of the Agile software development community, we contribute both a quantitative and qualitative analysis of the their communication practices and depict the evolving nature of their onboarding and mentoring strategies. We share our experience of implementing such an immersive industry ethnographic study. We employ a pattern language approach to capturing, analyzing and representing our results, thereby contributing and relating to the larger bodies of work in Scrum and Organizational Patterns. This work also informs our concurrent efforts to enhance our undergraduate computer science and software engineering curriculum, exposing students to the communication challenges of real software development and help them to develop skills to meet these challenges through practice in inquiry, critique and reflection

The Effects of Blended Instruction and Visual Representations on Area Problems Involving Quadratic Expressions for Secondary Students with Mathematics Difficulties

The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions. The instructional package included a blend of research-based instructional practices for secondary students with LD (i.e., concrete-representation-abstract instruction, graphic organizers, and components of explicit instruction) and the process standards recommended by the National Council of Teachers of Mathematics process standards (i.e., problem solving, reasoning and proof, communication, connections, and representations). A concurrent embedded mixed methods design was utilized with the quantitative data representing the main strand, while qualitative data provided supplemental data (Creswell & Clark, 2011). Specifically, the quantitative data were collected from a multiple-probe design across two groups replicated over five students. The participants were five high school students identified as a learning disability or difficulty in mathematics. The qualitative analysis of transcriptions from instructional sessions, field notes, and work samples was completed on one participant, who represented a critical case (Creswell, 2007). Results of the study indicated that all five participants improved their algebraic accuracy on tasks involving quadratic expressions embedded within an area context. Further, providing multiple representations allowed participants to make connections to algebraic content and enhanced their metacognition. Additionally all participants maintained their performance up to six weeks following intervention. Three participants also transferred the performance to novel and more complex tasks. The study suggests that students with MD may be successful with higher-level algebra content when provided blended instruction and visual representations

INSTRUCTIONAL COACHING AND ITS EFFECTS ON MIDDLE SCHOOL MATHEMATICS TEACHERS’ PERCEPTIONS OF COACHING AND CONTENT KNOWLEDGE: A MIXED METHODS STUDY

Instructional coaching has been a professional learning opportunity that many school districts have employed to support teacher practice. Pairing instructional coaching with on-going workshops is a relatively new approach to professional development. Participants for this study include fourteen middle school teachers that teach either mathematics or collaborate with special needs students. This study examines the effect that pairing instructional coaching with on-going workshops (with a primary focus on proportional reasoning) has on participants’ content knowledge and their perceptions of coaching. Drawing on Wenger’s community of practice theory and post-modern theory of power, this study employs mixed-methods design. Pre- and post-tests for proportional reasoning were administered to analyze the extent to which content knowledge changed over the course of the study. Pre- and post-interviews were conducted with each participant to determine any misconceptions each had on proportional reasoning and their perceptions of coaching (before and after the study’s instructional coaching). Grounded theory and thematic analysis was employed on the pre-and post-interviews to examine the role that power played in the participants’ perceptions of effective coaching attributes. Results suggest that (a) instructional coaching coupled with on-going professional workshops can change content knowledge in participants; (b) perceptions of coaching can change as the result of experiencing a coaching relationship and (c) power dynamics in the coaching experience determine the extent to which participants see the effectiveness of coaching as a professional development activity

Late-bound code generation

Each time a function or method is invoked during the execution of a program, a stream of instructions is issued to some underlying hardware platform. But exactly what underlying hardware, and which instructions, is usually left implicit. However in certain situations it becomes important to control these decisions. For example, particular problems can only be solved in real-time when scheduled on specialised accelerators, such as graphics coprocessors or computing clusters. We introduce a novel operator for hygienically reifying the behaviour of a runtime function instance as a syntactic fragment, in a language which may in general differ from the source function definition. Translation and optimisation are performed by recursively invoked, dynamically dispatched code generators. Side-effecting operations are permitted, and their ordering is preserved. We compare our operator with other techniques for pragmatic control, observing that: the use of our operator supports lifting arbitrary mutable objects, and neither requires rewriting sections of the source program in a multi-level language, nor interferes with the interface to individual software components. Due to its lack of interference at the abstraction level at which software is composed, we believe that our approach poses a significantly lower barrier to practical adoption than current methods. The practical efficacy of our operator is demonstrated by using it to offload the user interface rendering of a smartphone application to an FPGA coprocessor, including both statically and procedurally defined user interface components. The generated pipeline is an application-specific, statically scheduled processor-per-primitive rendering pipeline, suitable for place-and-route style optimisation. To demonstrate the compatibility of our operator with existing languages, we show how it may be defined within the Python programming language. We introduce a transformation for weakening mutable to immutable named bindings, termed let-weakening, to solve the problem of propagating information pertaining to named variables between modular code generating units.Open Acces

Intelligent interaction in diagnostic expert systems

AbstractAdvisory systems help to improve quality in manufacturing. Such systems, however, both human and computerized, are less than perfect and frequently not welcome. Sharp separation between working and learning modes is the main reason for the apparent hostility of advisory systems. Intelligent interaction deploys computerized advisory capabilities by merging working and learning modes. We have developed a knowledge-based interactive graphic interface to a circuit pack diagnostic expert system. The graphic interface integrates both the domain knowledge (i.e. circuit pack) and the troubleshooting knowledge (i.e. diagnostic trees). Our interface dynamically changes the amount of detail presented to the user as well as the input choices that the user is allowed to make. These changes are made using knowledge-based models of the user and of the circuit pack troubleshooting domain. The resulting system, McR, instead of guiding the user by querying for input, monitors users actions, analyzes them and offers help when needed. McR is able both to advise “how-to-do-it” by reifying shallow knowledge from the deep knowledge, and to explain intelligently “how-does-it-work” by abstracting deep knowledge from the hallow knowledge, McR is used in conjunction with the STAREX expert sytem which is installed at AT&T factory