We investigated whether Early Algebra lessons that explicitly aimed to elicit mathematical discussions (Shift-Problem Lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N =160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the Shift-Problem condition. The quality of the mathematical discussions in the Shift-Problem condition was better compared to that in the Conventional Textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the Shift-Problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that Shift-Problem Lessons are powerful for eliciting mathematical discussions in seventh-grade Shift-Problem Early Algebra Lessons.
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Background: The importance of clarifying goals and providing process feedback for student learning has been widely acknowledged. From a Self-Determination Theory perspective, it is suggested that motivational and learning gains will be obtained because in well-structured learning environments, when goals and process feedback are provided, students will feel more effective (need for competence), more in charge over their own learning (need for autonomy) and experience a more positive classroom atmosphere (need for relatedness). Yet, in spite of the growing theoretical interest in goal clarification and process feedback in the context of physical education (PE), little experimental research is available about this topic. Purpose: The present study quasi-experimentally investigated whether the presence of goal clarification and process feedback positively affects students’ need satisfaction and frustration. Method: Twenty classes from five schools with 492 seventh grade PE students participated in this quasi-experimental study. Within each school, four classes were randomly assigned to one of the four experimental conditions (n = 121, n = 117, n = 126 and n = 128) in a 2 × 2 factorial design, in which goal clarification (absence vs. presence) and process feedback (absence vs. presence) were experimentally manipulated. The experimental lesson consisted of a PE lesson on handstand (a relatively new skill for seventh grade students), taught by one and the same teacher who went to the school of the students to teach the lesson. Depending on the experimental condition, the teacher either started the lesson explaining the goals, or refrained from explaining the goals. Throughout the lesson the teacher either provided process feedback, or refrained from providing process feedback. All other instructions were similar across conditions, with videos of exercises of differential levels of difficulty provided to the students. All experimental lessons were observed by a research-assistant to discern whether manipulations were provided according to a condition-specific script. One week prior to participating in the experimental lesson, data on students’ need-based experiences (i.e. quantitatively) were gathered. Directly after students’ participation in the experimental lesson, data on students’ perceptions of goal clarification and process feedback, need-based experiences (i.e. quantitatively) and experiences in general (i.e. qualitatively) were gathered. Results and discussion: The questionnaire data and observations revealed that manipulations were provided according to the lesson-scripts. Rejecting our hypothesis, quantitative analyses indicated no differences in need satisfaction across conditions, as students were equally satisfied in their need for competence, autonomy and relatedness regardless of whether the teacher provided goal clarification and process feedback, only goal clarification, only process feedback or none. Similar results were found for need frustration. Qualitative analyses indicated that, in all four conditions, aspects of the experimental lesson made students feel more effective, more in charge over their own learning and experience a more positive classroom atmosphere. Our results suggest that under certain conditions, lessons can be perceived as highly need-satisfying by students, even if the teacher does not verbally and explicitly clarify the goals and/ or provides process feedback. Perhaps, students were able to self-generate goals and feedback based on the instructional videos.
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This study investigates what pupils aged 10-12 can learn from working with robots, assuming that understanding robotics is a sign of technological literacy. We conducted cognitive and conceptual analysis to develop a frame of reference for determining pupils' understanding of robotics. Four perspectives were distinguished with increasing sophistication; psychological, technological, function, and controlled system. Using Lego Mindstorms NXT robots, as an example of a Direct Manipulation Environment, we developed and conducted a lesson plan to investigate pupils' reasoning patterns. There is ample evidence that pupils have little difficulty in understanding that robots are man-made technological and functional artifacts. Pupils' understanding of the controlled system concept, more specifically the complex sense-reason-act loop that is characteristic of robotics, can be fostered by means of problem solving tasks. The results are discussed with respect to pupils' developing technological literacy and the possibilities for teaching and learning in primary education.
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