physiological recording (from interviewer in addition to interviewee) . As far as could be determined, interaction studies of this kind (with electromyographic and other indicators) had not been previously described in the literature ; and the present experiments thus represented a pioneering venture. Longrange aims were to gain deeper understanding of transference and related mechanisms of interaction. The immediate purpose of the pilot studies was methodological, of course. Nevertheless, reported were some

Development and learning in animals and man

 Differentiated instruction is a philosophy of teaching that asks the instructor to reach all learners on a personal level.  Differentiated instruction takes many things into consideration for each student: prior knowledge, level of readiness, learning style, age and environment.  Differentiated instruction has four main components: o Individual learner: instructors must know their individual students on a personal level o Brain cognition: knowledge of how the brain works at each stage of development o Curriculum: derived from state and district standards o Content: instructors must be knowledgeable on the subjects they teach  Differentiated instruction can be accomplished in three ways: o Process: the path a student takes to understanding the objective o Product: how a student demonstrates understanding of the objective o Content: not more work, but more readiness-appropriate work to reach the objective

/pdf/gaebyeolhwa-sueob-differentiated-instruction-yi-bonjile-2jz8a1p9z2.pdf

개별화 수업(Differentiated Instruction)의 본질에 관한 탐구

This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

Mathematics of Language

Psychogenesis and the History of Science

This article reports on a study which used the APOS (action-process-object-schema) theoretical framework to investigate university students’ understanding of derivatives and their applica-tions. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for finding derivatives and their applications were taught to under-graduate science students. This paper reports on the analysis of students’ responses to six types of questions on derivatives and their applications. The findings of this study suggest that those students had difficulty in applying the rules for derivatives and this was possibly the result of many students not having appropriate mental structures at the process, object and schema lev-els. Keywords : action, APOS, chain rule, derivatives, process, object, schema, teaching

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An APOS analysis of natural science students' understanding of derivatives

This article reports on a study which used the APOS (Action‐Process‐Object‐Schema) theory framework to investigate university students’ understanding of limits of functions. The relevant limit concepts were taught to undergraduate science students at a university in Kwazulu‐Natal in South Africa. This paper reports on the analysis of students’ responses to four types of questions on limits of functions. The findings of this study confirmed that the limit concept is one that students find difficult to understand, and suggests that this is possibly the result of many students not having appropriate mental structures at the process, object and schema levels.

/pdf/an-apos-analysis-of-students-understanding-of-the-concept-of-121xdk1tow.pdf

An APOS Analysis of Students' Understanding of the Concept of a Limit of a Function

Geometry and culture are interrelated, making school geometry closely connected to the environment as well as culture in which it is taught. With regard to this connectedness, the Zimbabwean mathematics syllabus indicates that geometry should be connected to the learners’ environment and culture. This article explores teacher-related challenges to the integration of ethnomathematics approaches into the teaching of geometry. Findings are based on feedback received from questionnaires and focus-group discussions in which 40 in-service mathematics teachers expressed their views on the challenges that affect the integration of ethnomathematics approaches into the teaching of geometry. Major challenges included lack of knowledge on ethnomathematics approaches and how to integrate these approaches into the teaching of geometry; teachers’ lack of geometry content knowledge, teachers’ views of geometry taught in schools, teachers’ competence in teaching geometry, teaching and professional experience as well as resistance to change by teachers. The study recommends that teacher training institutions need to redesign their curricula to include ethnomathematics approaches and that there is need for in-service training on ethnomathematics approaches.

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Teacher-related Challenges Affecting the Integration of Ethnomathematics Approaches into the Teaching of Geometry

The study investigated fourth–year students’ construction of the definitions of monotonicity and boundedness of sequences, at the Edgewood Campus of the University of KwaZulu –Natal in South Africa. Structured worksheets based on a guided problem solving teaching model were used to help students to construct the twodefinitions. A group of twenty three undergraduateteacher trainees participated in the project. These students specialised in the teaching of mathematics in the Further Education and Training (FET) (Grades 10 to 12) school curriculum. This paper, specifically, reports on the investigation of students’ definition constructions based on a learnig theory within the context of advanced mathematical thinking and makes a contribution to an understanding of how these students constructed the two definitions. It was found that despite the intervention of a structured design, these definitions were partially or inadequately conceptualised by some students.

/pdf/using-an-inductive-approach-for-definition-making-18ahrzrxsy.pdf

Using an inductive approach for definition making: Monotonicity and boundedness of sequences

Algebra, trigonometry and calculus concepts are dealt with in grades 10 to 12 of South African high school topics, as prescribed by the Curriculum and Assessment Policy Statement. This paper reports on a study exploring practicing teachers' subject matter knowledge of certain topics they were expected to teach. The theoretical perspectives for the design and analysis of this study were based on Shulman's conceptual framework. This study was a qualitative case study (n = 28). Practising teachers from the Pinetown district in KwaZulu-Natal participated in this mathematics' teacher intervention. Focused tasks on algebra, trigonometry and calculus were designed and administered to those teachers. The researchers analysed the data from those tests and found that certain areas of their pedagogical content knowledge required attention.

/pdf/exploring-support-strategies-for-high-school-mathematics-10vhkouivu.pdf

Aneshkumar Maharaj

Papers

An APOS analysis of natural science students' understanding of derivatives

An APOS Analysis of Students' Understanding of the Concept of a Limit of a Function

Teacher-related Challenges Affecting the Integration of Ethnomathematics Approaches into the Teaching of Geometry

Using an inductive approach for definition making: Monotonicity and boundedness of sequences

Exploring support strategies for high school mathematics teachers from underachieving schools