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.

Steps to success : family-friendly guide for third 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 third grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for fifth 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 fifth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

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.

Um Estudo da modelagem matemática na educação matemática e seu potencial para o desenvolvimento do pensamento crítico

The implementation of mathematical modeling curricula represents a great challenge, both for teachers and students, since it escapes the traditional teaching methodology, i.e. when the teacher speaks to his/her students. This work presents, at least, one possible way of implementing mathematical modeling inside the classroom, and how this way encourage critical thinking in students. I see mathematical modeling as an opportunity to minimize student's rejection and increase their interest for mathematics, promoting their competencies to give points of scene in every day situations. The history of mathematics shows that mathematical modeling had developed since almost the beginning of human live, when men needed to solve problems that arose in the course of his life. Mathematics has become more and more abstract, but it is important to recall what was originated it. In this way, it is possible to make this subject matter more meaningful to students. I will make an introduction of mathematical modeling, presenting some important definitions. Based on this framework, I will present a classroom instruction understand on a 7 th grade classroom by myself. With this in instruction I sustain the idea that mathematical modeling has, in fact, a great potential to improve the quality of mathematics teaching. I also sustain that, the development of critical thinking, as a competence, way be achieved with it

A inserção da educação matemática crítica na escola pública: aberturas, tensões e potencialidades

Pós-graduação em Educação Matemática - IGCE

Do improviso às possibilidades de ensino: estudo de caso de uma professora de matemática no contexto da inclusão de estudantes cegos

Pós-graduação em Educação Matemática - IGCE

Student mathematical proofs by Edward Stephen (?) Wigglesworth, 1788

Sheet with two handwritten mathematical proofs signed "Wigglesworth, 1788," likely referring Harvard student Edward Stephen Wigglesworth. The first proof, titled "Problem 1st," examines a prompt beginning, "Given the distance between the Centers of the Sun and Planet, and their quantities of matter; to find a place where a body will be attracted to neither of them." The second proof, titled "Problem 2d," begins "A & B having returned from a journey, had riden [sic] so far that if the square of the number of miles..." and asks "how many miles did each of them travel?"

A plan of Cambridge Green, 1780 September 14

Small pen-and-ink and watercolor drawing of Cambridge Green created by Harvard senior John Davis, presumably as part of his undergraduate mathematical coursework. The map surveys Cambridge Commons and includes a few rough outlines of College buildings and the Episcopal church, and notes the burying ground, and the roads to Charlestown, Menotomy, the pond, Watertown, and the bridge. The original handwritten text is faded and was annotated with additional text by Davis including the note "[taken in my Senior year at H. College Septr 1780] Surveyed in concert with classmates, Atkins, Hall 1st, Howard, Payne, &c.- J. Davis." There is a note that "Atkins afterwards took the name of Tying." Davis refers to Dudley Atkins Tyng, Joseph Hall, Bezaleel Howard, and Elijah Paine, all members of the Harvard Class of 1781.