Mathematical notebook, and commonplace book, circa 1689-1769

Manuscript notebook, possibly kept by Harvard students, containing 17th century English transcriptions of arithmetic and geometry texts, one of which is dated 1689-1690; 18th century transcriptions from John Ward’s “The Young Mathematician’s Guide”; and notes on physics lectures delivered by John Winthrop, the Hollis Professor of Mathematics and Natural Philosophy at Harvard from 1738 to 1779. The notebook also contains 18th century reading notes on Henry VIII, Tudor succession, and English history from Daniel Neal’s “The History of the Puritans” and David Hume’s “History of England,” and notes on Ancient history, taken mainly from Charles Rollin’s “The Ancient History of the Egyptians, Carthaginians, Assyrians, Babylonians, Medes and Persians, Macedonians and Grecians.” Additionally included are an excerpt from Plutarch’s “Lives” and transcriptions of three articles from “The Gentleman’s Magazine, and Historical Chronicle,” published in 1769: “A Critique on the Works of Ovid”; a book review of “A New Voyage to the West-Indies”; and “Genuine Anecdotes of Celebrated Writers, &.” The flyleaf contains the inscription “Semper boni aliquid operis facito ut diabolus te semper inveniat occupatum,” a variation on a quote of Saint Jerome that translates approximately as “Always good to do some work so that the devil may always find you occupied.” In the seventeenth and eighteenth centuries, Harvard College undergraduates often copied academic texts and lecture notes into personal notebooks in place of printed textbooks. Winthrop used Ward’s textbook in his class, while the books of Hume, Neal, and Rollin were used in history courses taught at Harvard in the 18th century.

Codeship: Financing growth: Case study and Teaching note

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

A Virtual Mathematics Learning Environment for Engineering Students

Teachers of the course Introduction to Mathematics for Engineers at the UOC, an online distance-learning university, have designed and produced online study material which includes basic pre-university mathematics, instructions for correct follow-up of this content and recommendations for finding appropiate support and complementary materials.

Una visión actualizada de la didáctica de la matemática en educación infantil = An up-to-date vision of pre-school mathematics teaching

This article aims to investigate pre-school mathematics teaching from an uptodate perspective. To pursue this contemporary vision we focus on four key questions: what kind of maths is being worked on, who is doing it, how it is being done, and why it is being done

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

The impact of integrated programming on student attitude and achievement in grade 9 academic mathematics and science

This research studioo the effect of integrated instruction in mathematics and~ science on student achievement in and attitude towards both mathematics and science. A group of grade 9 academic students received instruction in both science and mathematics in an integrated program specifically developed for the purposes of the research. This group was compared to a control group that had received science and mathematics instruction in a traditional, nonintegrated program. The findings showed that in all measures of attitude, there was no significant difference between the students who participated in the integrated science and mathematics program and those who participated in a traditional science and mathematics program. The findings also revealed that integration did improve achievement on some of the measures used. The performance on mathematics open-ended problem-solving tasks improved after participation in the integrated program, suggesting that the integrated students were better able to apply their understanding of mathematics in a real-life context. The performance on the final science exam was also improved for the integrated group. Improvement was not noted on the other measures, which included EQAO scores and laboratory practical tasks. These results raise the issue of the suitability of the instruments used to gauge both achievement and attitude. The accuracy and suitability of traditional measures of achievement are considered. It is argued that they should not necessarily be used as the measure of the value of integrated instruction in a science and mathematics classroom.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Commonplace book of Benjamin Penhallow, 1721-1724

This leather-bound volume contains excerpts copied by Benjamin Penhallow from books he read while he was a student at Harvard in the 1720s. The volume contains extracts from two texts: Johanis Henrici Alstedii's (John Henry Alsted / Johann Heinrich Alsted) Geometria Domini, and the anonymous text "The Legacy of a dying Father; bequeath'd to his Beloved Children, or Sundry Directions in Order unto a well Regulated Conversation," from 1724 (originally published in 1693-4). The last page of text in the volume contains the hymn "The Sacred Content of Praise" first published in 1734, and added after Penhallow's death.

Treatise on mathematics and astronomy: written about the year 1680, in Boston

Bound volume containing a late 17th century handwritten mathematical and astronomical text in one hand. The text is separated into mathematical and astronomical sections with rules, instructions for performing calculations, tables, and drawings. The subjects include arithmetic, geometry, astronomy, and trigonometry, and segments have titles such as "Subtraction," "A decimal table of English coince," "Logarithes & their use," and "To find the true place of the sun." The text is undated and unattributed but references Briggs, Oughtred, Ramus, and Apollonius. Certain tables are calculated from latitudinal and longitudinal numbers associated with Boston, and many of the examples use dates in the 1670s and 1680. The manuscript pages are mounted onto unruled pages, and some of the manuscript pages are fragments.

Good practice guide in learning and teaching

Once again this publication is produced to celebrate and promote good teaching and learning support and to offer encouragement to those imaginative and innovative staff who continue to wish to challenge students to learn to maximum effect. It is hoped that others will pick up some good ideas from the articles contained in this volume. We have again changed our approach for this 2007/08 edition (our fifth) of the Aston Business School Good Practice Guide. As before, some contributions were selected from those identifying interesting best practice on their Annual Module Reflection Forms in 2006/2007. Brookes? contribution this year is directly from her annual reflection. Other contributors received HELM (Research Centre in Higher Education Learning and Management) small research grants in 2006/2007. Part of the conditions were for them to write an article for this publication. We have also been less tight on the length of the articles this year. Some contributions are, therefore, on the way to being journal articles. HELM will be working with these authors to help develop these for publication. Looking back over the last five years it is brilliant to see how many different people have contributed over the years and, therefore, how much innovative learning and teaching work has been taking place in ABS over this time. In the first edition we were just pleased for people to write a few pages on their teaching. Now things have changed dramatically. The majority of the articles are grounded in empirical research (some funded by HELM small research grants) and Palmer?s article was produced as part of the University?s Postgraduate Certificate in Learning and Teaching. Most encouraging of all, four of this year?s articles have since been developed further and submitted to refereed journals. We await news of publication as we go to press. It is not surprising that how to manage large groups still remains a central theme of the articles, ABS has a large and still growing student body. Essex and Simpson have looked at trying to encourage students to attend taught sessions, on the basis that there is a strong correlation between attendance and higher performance. Their findings are forming the platform of a further study currently being carried out in the Undergraduate Programme. A number of the other articles concentrate on trying to encourage students to engage with study in an innovative way. This is particularly obvious in Shaw?s work. Everyone who has been around campus lately has had evidence that the students on Duncan?s modules have clearly been inspired. I found myself, for example, playing golf in the student dining room as part of this initiative! The articles by Jarzabkowski & Guilietti and Ho involved much larger surveys. This is another first for the Good Practice Guide and marks the first step on what will clearly be larger research efforts for these authors in this area. We look forward to the journal publications which will result from this work. The last articles are the result of HELM?s hosting of the national conference of the Higher Education Academy?s Business, Management, Accounting and Finance (BMAF) Subject Centre Conference in May 2007. Belal and Foster have written about their impressions of the Conference and Andrews has included the paper she gave. The papers on employability and widening participation are the centre of HELM?s current work. In the second volume we mentioned the launch of the School?s Research Centre in Higher Education Learning and Management (HELM). Since then HELM has stimulated a lot of activity across the School (and University) particularly linking research and teaching. A list of the HELM seminars for 2007/2008 is listed as Appendix 1 of this publication. Further details can be obtained from Catherine Foster (c.s.foster@aston.ac.uk), who coordinates the HELM seminars. We have also been working on a list of target journals to guide ABS staff who wish to publish in this area. These are included as Appendix 2 of this publication. May I thank the contributors for taking time out of their busy schedules to write the articles and to Julie Green, the Quality Manager, for putting the varying diverse approaches into a coherent and publishable form and for agreeing to fund the printing of this volume.

A virtual mathematics learning environment for engineering students

Teachers of the course Introduction to Mathematics for Engineers at the UOC, an online distance-learning university, have designed,developed and tested an online studymaterial. It includes basic pre-university mathematics, indications for correct follow-up of this content and recommendations for finding appropriate support and complementarymaterials. Many different resources are used,depending on the characteristics of thecontents: Flash sequences, interactive applets, WIRIS calculators and PDF files.During the last semester, the new study material has been tested with 119 students. The academic results and student satisfaction have allowed us to outline and prioritise future lines of action.