Quantitative reasoning is critical to developing understandings of function that are important for sustained success in mathematics. Unfortunately, preservice teachers often do not receive sufficient quantitative reasoning experiences during their schooling. In this paper, we illustrate consequences of underdeveloped quantitative reasoning abilities against the backdrop of central function concepts. We also illustrate tasks that can perturb preservice teachers' thinking in ways that produce opportunities for quantitative reasoning. By implementing strategically designed tasks, teacher educators can support preservice teachers–and students in general–in advancing their quantitative reasoning abilities and their understanding of secondary mathematics content.
Purpose
Founded in sociocultural theories of learning, the authors argue that engaging learners in collaborative knowledge building is critical. When responding to others’ ideas, research shows that learners in online settings more frequently focus on surface-level aspects of colleagues’ contributions – sharing, comparing and praising – rather than engaging in knowledge building. Collaborative, knowledge-building discourse includes generative interactional practices that feature disagreeing, negotiating meaning, testing and reflecting on co-constructed ideas, summarizing conversations and making metacognitive contributions to discussions. The purpose of this paper is to review studies that show evidence of key design features and pedagogical practices that support collaborative knowledge building by promoting generative interactional practices and particular patterns in interaction.
Design/methodology/approach
This conceptual paper presents pragmatic design and instructional guidelines for online course discussions. The purpose is to synthesize existing research and share a detailed framework for supporting generative discussion in asynchronous online work.
Findings
The authors review studies that show evidence of key design features and pedagogical practices that support collaborative knowledge building. Design features to promote generative discourse include using the asynchronous nature of online settings to have students work privately, share their work, discuss their work with the class and then revise; providing instructions/discussion criteria that scaffold knowledge building; and using appropriate digital tools that mediate interaction around content. The pedagogical practices that affect patterns of interaction include modeling generative discourse, promoting increased interactions by and between participants and using opportunistic grouping strategies.
Originality/value
The authors include examples from one of their existing online courses that include these design features and pedagogical practices and discuss results from their ongoing work regarding the generativity of learner interactions in this course.
Our goal is to use the context of image processing to stimulate interest and, ultimately, develop students' understandings of the math and science concepts in the K-12 classroom. The paper will present ideas to the signal processing community on how image processing can connect directly to standard curricular concepts. Since many teachers are confined to set-curricula, this can limit the scope of illustrating more advanced DSP concepts in the high school classroom. Ultimately, the goal is for students to conduct their own inquiry and to understand the principles behind artistic tools while learning math and science. This paper presents the development of image processing tools that will be tested throughout the 2008-2009 school year.
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