To see or not to see: analyzing difficulties in geometry from the perspective of visual perception

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual organization: Gestalt principles, (2) recognition: bottom-up and top-down processing; and (3) representation of perception-based knowledge: verbal vs. pictorial representation, mental images and hierarchical structure of images. Examples given in the paper were mostly taken from Gal's study (2005) which aimed at identifying and analyzing Problematic Learning Situations (after Gal & Linchevski, 2000) in junior high school geometry classes. Gal's study (2005) suggests that while this theoretical perspective became part of teachers' pedagogic content knowledge, the teachers were aware of their students' thinking processes and their ability to analyze and cope with their students’ difficulties in geometry was improved.     

How Does the Degree of Guidance Support Students’ Metacognitive and Problem Solving Skills in Educational Robotics?

Educational robotics (ER) is an innovative learning tool that offers students opportunities to develop higher-order thinking skills. This study investigates the development of students’ metacognitive (MC) and problem-solving (PS) skills in the context of ER activities, implementing different modes of guidance in two student groups (11–12 years old, N1 = 30, and 15-16 years old, N2 = 22). The students of each age group were involved in an 18-h group-based activity after being randomly distributed in two conditions: “minimal” (with minimal MC and PS guidance) and “strong” (with strong MC and PS guidance). Evaluations were based on the Metacognitive Awareness Inventory measuring students’ metacognitive awareness and on a think-aloud protocol asking students to describe the process they would follow to solve a certain robot-programming task. The results suggest that (a) strong guidance in solving problems can have a positive impact on students’ MC and PS skills and (b) students reach eventually the same level of MC and PS skills development independently of their age and gender.     

Exploring alternative approaches to methodology in educational research

The objective of this study is to provide in-service teachers an opportunity to become familiar with the controversial nature of progress in science (growth of knowledge) and its implications for research methodology in education. The study is based on 41 participants who had registered for a nine-week course on Methodology of Investigation in Education, as part of their Master’s degree program. The course is based on 20 readings drawing upon a history and philosophy of science perspective (positivism, constructivism, Popper, Kuhn, Lakatos) and its implications for educational research. Course activities included written reports, class room discussions based on participants’ presentations, and written exams. Based on the results obtained it was concluded that: (a) participants were able to understand the basic ideas of constructivist philosophy and its pedagogical implications; (b) the role of behavioural objectives in actual educational practice was questioned; (c) integration of qualitative and quantitative research methods was considered to be an alternative to the current debate about the replacement of one method by the other; (d) participants considered the dilemma of evaluating students based on what they have learned or what they should have learned, within the social constructivist framework and generally favoured the former; and (e) most of the participants were reluctant to accept constructivism as a form of positivism, a controversial thesis that is gaining support in the research literature. Given the importance of alternative approaches to growth and meaning of knowledge, it is important that teachers be aware of conflicting situations in the classroom that refer to: objectivity, scientific method, qualitative-quantitative methods, relationship between method and problem, evaluation, and a critical appreciation of constructivism.