To measure the procedural and conceptual knowledge of functions and to clarify the relationship between them in the context of mathematics education in Morocco, a structural equation modeling (SEM) analysis was used. In addition, correlation tests between students’ grades at their Mathematical Analysis Assessments and their procedural and conceptual knowledge of functions scores were established to investigate whether students' grades mainly reflect their performance on procedural knowledge or conceptual knowledge. The sample consisted of 337 high school Moroccan students. The study findings indicated that a large group of participants scored high in procedural tasks but low in conceptual tasks. Besides, the participants’ grades in their exams correlate much more strongly with the estimated procedural knowledge scores than the estimated conceptual knowledge scores. On the other hand, the confirmatory factor analysis of the SEM confirmed the reliability, validity, and fitness of the measurement model, whereas the path analysis of the SEM supports the genetic view causal relationship that procedural knowledge of functions is necessary but not sufficient condition for conceptual knowledge. These results provide a theoretical foundation for improving mathematics education by working on the content of the assessments, the teachers’ teaching approaches, and the students’ learning strategies.

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The Development of Thought: Equilibration of Cognitive Structures

Evaluation of procedural and conceptual knowledge of mathematical functions: A case study from Morocco

Mathematical Education Technology Based on the Theory of Cognitive Constructivism and Concept Map

This case study examines six U.S. pre-service teachers’ participation in an international field experience in Costa Rica. It analyzes participants’ willingness and ability to demonstrate relationship building with students culturally and linguistically different from them, and describes and interprets the circumstances that either encourage or discourage such interaction. Results indicate that in certain contexts, program participants were both motivated and successful in establishing rapport with such learners. This implies that an international field experience may help to develop pre-service teachers’ confidence and willingness to build relationships with diverse students back home. 
Because of cultural and linguistic mismatches between teachers and their students, teachers often lack the capacity to build relationships with students from diverse ethnic and racial groups and/or resist working in diverse classrooms due to their current attitudes and beliefs. This study employs the concept of “cultural responsiveness” as an analytic lens through which to examine the extent to which participants in the program were able to remedy such deficiencies and build such relationships.
Goals of this study were (a) to describe the attitudes, beliefs, and actions of participants toward serving diverse learners, (b) to understand how they enacted cultural responsiveness, and (c) to assess how cultural responsiveness is developed through an international field experience. The study employed (a) surveys of program participants before and after their overseas experience, (b) field observations over the course of four days of instruction in Costa Rica, and (c) student journal entries and post-trip reflection essays. Data were analyzed using thematic analysis, in which recurring themes and patterns of association and contrast were identified. Research questions were continuously refined over a two and a half year period of reflection and analysis. 
	Using cultural responsiveness as a concept to frame a discussion on developing relationship building, the significance of this study lies in its applications for: (a) schools of education as a tool to use to develop their students’ understanding of diversity and (b) youth-serving nonprofits to strengthen the bridge between the educators with whom they partner and the diverse youth they serve.

Pre-Service Teachers in Costa Rica: Developing Relationships with Diverse Learners and Building Cultural Responsiveness Through an International Field Experience

/pdf/semiotics-and-symbiosis-gap-closing-how-signs-symbols-and-2sykaxdlo7.pdf

Semiotics and Symbiosis – “Gap-Closing”: How Signs, Symbols, and Structure Impact the Teaching and Learning of Mathematics for Middle School African American Students

Microteaching was first introduced by Dwight W. Allen in the sixties and since then it has become a pivotal aspect of teacher training, particularly within medical education. As a form of teacher training, it enables teachers to reflect upon effective practice by implementing a deliberate cyclical reflection process. The importance of such reflective practice within medical education is well established. However, rarely is it regularly or successfully undertaken and the traditional ‘see one, do one teach one’ approach to teaching and training is widely disputed and in need of revival so that it may better reflect the shifting cultural, social and political restrictions and expectations placed on medical professionals. A plan, do, reflect, re-plan, re-do and re-reflect schema as adapted from the practice of microteaching provides a clear framework on how best to reflect on one’s own practice and therefore acts as a positive initial step towards improving self-reflection within medical education. 


The Development of Thought: Equilibration of Cognitive Structures

Citations

Evaluation of procedural and conceptual knowledge of mathematical functions: A case study from Morocco

Mathematical Education Technology Based on the Theory of Cognitive Constructivism and Concept Map

Pre-Service Teachers in Costa Rica: Developing Relationships with Diverse Learners and Building Cultural Responsiveness Through an International Field Experience

Semiotics and Symbiosis – “Gap-Closing”: How Signs, Symbols, and Structure Impact the Teaching and Learning of Mathematics for Middle School African American Students

Can microteaching inform reflective practice?

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