An examination of grade three mathematics textbooks for problem solving strategies

Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.

Instructor support for self-directed learning in higher education

This study addressed the problem of instructor support for self-directed learning, specifically, learner-directed program planning, within a classroom setting in higher education. A combination of survey, interview, document analysis, and observation was used to assess and evaluate the attitudes and practices of a sample of full-time faculty at an Ontario university. Eighty-seven percent of the study sample reported instructional beliefs, values, and expectations that were not supportive of self-directed learning, especially in terms of student participation in program planning. Planning was seen as the responsibility of the instructor. Instructors were least open to student participation in the planning of the evaluation of learning. However, there was considerable stated support for other of the basic principles of adult education. The remaining 13% of the study sample reported instructional beliefs, values, and expectations that were fully supportive of self-directed learning. Instructional practices were analyzed in relation to the instructors' stated beliefs. Although practices reflected, in many instances, instructors' statements of support, there were some significant discrepancies between apparent support for the concept of self-directed learning and actual classroom practice. Both beliefs and practice were compared to a research model of self-directed learning. Most instructors did not have a concept of self-directed learning as comprehensive as that described in the research model. Instructor support for self-directed learning was profoundly influenced by the university setting. It was concluded that more strenuous attempts to research, enhance, and promote instructional and institutional support for self-directed learning in higher education are warranted.

Accommodating College ESL Learner Communication Needs: Perceptions, Policies, and Practices

The purpose of this qualitative inquiry was to determine how the Practical Nursing and Pharmacy Technician programs in one southern Ontario community college could more effectively accommodate ESL learners' communication needs. The literature review examined (a) linguistic issues, such as language testing and second-language learning theories, (b) organizational matters, such as ESL curriculum and teacher training, and (c) affective issues, such as motivation for second-language learning, learning styles, and the student-teacher relationship. I gathered perceptual data from the programs' administrators, faculty members, and ESL learners. Eleven participants took part in individual interviews or a focus group session. The results suggest that ESL learners need assistance with discipline-specific vocabulary and cultural nuances. College ESL learners' weak communicative competence, together with misleading acceptance standards for ESL learners and limited support available to faculty members and to students, decrease opportunities for successful completion of the programs. The results point to re-assessment of the college's admission policies and procedures, program evaluation practices that consider the needs of ESL learners, discipline-specific language support, and strategies to enhance the ESL student-teacher relationship. The study highlights theory relating to ESL learners' self-perception and engagement, as well as the importance of including the voice of college ESL learners in educational research. The results suggest that despite ESL learners' perseverance in completing their studies, power imbalances remain. The college has yet to implement organizational strategies such as discipline-specific communications and ESL courses and extended language support that could meet the communication needs of ESL learners in the two programs.

Experience in introduction of English terminology in engineering lessons: methodology and evaluation

This communication explains a experience for the introduction of English terminology in a technical degree of higher education. We present the methodology and assessment procedures used to evaluate the way the students perceived the introduction of terminology in English in two different subjects from 3rd and 5th year courses of a Computer Science degree in which English was not the vehicular language. We propose a strategy based on two main pillars, namely: 1) The design of materials, explanations, and exams, paying particular attention to the way in which the specific terminology was exposed to the students, and 2) The assessment of the impact in the students by means of the analysis of the feedback trough a set of enquiries. Our experience showed that the students responded very positively to the introduction of English terminology, and presented an affirmative feedback about the impact that an improvement of their linguistic abilities would have in their future work. Further, we present statistics regarding the use of English as the vehicular language for technical reports, which is envisaged as very useful by the students. Finally, we propose a set of questions for further debate which are centered in the role that English terminology should pay in technical degrees, and about the way in which universities should deploy resources in English languages within the different Syllabus

La Ambientalización curricular de la educación matemática

Uno de los retos más importantes que ante sí tiene la universidad en el s.XXI es el de formar profesionales críticos con el desarrollo actual de la sociedad y capaces de actuar en pro del desarrollo sostenible. La educación para la sostenibilidad es un área de estudio compleja por el hecho de que en ella intervienen muchos saberes y técnicas entre los cuales deberán estar las matemáticas y la educación matemática. Nuestro trabajo está centrado en el estudio de la relación establecida entre la educación matemática y la educación para la sostenibilidad en el marco de la formación inicial de maestros

Narrativas sobre a prática de ensino de matemática de professores dos anos iniciais do ensino fundamental

Pós-graduação em Educação Matemática - IGCE

Um retrato de uma licenciatura em matemática a distância sob a ótica de seus alunos iniciantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Os limites e as possibilidades de uma sequência didática: o conceito de proporcionalidade e a aprendizagem de alunos do 5º ano do Ensino Fundamental

This study aimed to analyze the limits and possibilities of a didactic sequence, addressing the concept of proportionality in the learning of students in 5th year of elementary school. From the results of the Diagnostic Assessment Initial applied to students in a class of 5th grade of elementary school, we selected eight (8) students who participated in the constituent activities of that instructional sequence. For the development of this sequence were used theoretical elements of Genetic Epistemology (Piaget, 1990), the theory of fields of Conceptual Vergnaud (1996) and the definition of instructional sequence proposed by Zabala (1998). Finally, after 20 days of application of these activities, we applied the Diagnostic Assessment Final aimed at investigating which concepts related to proportionality were built by the participating students. By analyzing the collected data, it can be concluded the following about the possibilities of teaching sequence: 1) students who, in Diagnostica Home Assessment used the multiplication algorithm, but also did not indicate the comparison between quantities are now performing; 2) students who, in the Diagnostic Assessment Initial, used the addition algorithm, now gradually are using the multiplication algorithm; 3)students who, in the Diagnostic Assessment Initial, could not solve problems involving the idea of proportionality, are now resolving, however, still use, in large part, the addition operation as a strategy for this proportional thinking. Now, in relation to the limits of the sequence noted: 1)time sufficient to propose a higher number of problem conditions to be carried by students who may have been a trigger of construction have not through the proportional multiplication;2)the distant proposition situations of assimilation schemes (interpretation) of the students, which may have caused certain imbalance in them, preventing them from thinking about the problem situation;3)the rapid passage of...

Mathematics notebook : manuscript, 1782

With sections on numeration, surveying, trigonometry and other topics, accompanied by diagrams and hand-colored illustrations.

The summary of a course of experimental lectures in natural philosophy by Dr. John Winthrop (manuscript copy), 1772-1774

Notebook with a handwritten copy of lecture summaries for a physics course given by Harvard Professor John Winthrop. The notes were made by Timothy Foster in 1772 and 1773. The volume contains twenty-five lectures with some diagrams.

Mathematics notebook : manuscript, 1785-1789

Sections on numeration, interest, square root, geometry and surveying with accompanying diagrams.

Steps to success : family-friendly guide for fourth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fourth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.