Os problemas clássicos da Grécia antiga

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O Ensino de Geometria por meio de atividades investigativas: uma experiência com alunos do primeiro ano do Ensino Médio

This qualitative nature of work was developed with the participation of a group of students enrolled in the first year of high school from a public school of the state of São Paulo, in the city of Taubaté. Their goal was to determine how students deal with geometry tasks in investigative classes. To guide this research was drawn up the following question: As students of the first year of high school express their knowledge of building triangles and quads in classes of investigative activities?. The choice of investigative nature of this activity occurred by enhancing student participation and thus generate a greater chance of it not be guided only by what the teacher wants, but by his own curiosity and using their own tools for this. In the data analysis process stands out the interest generated in students for this type of activity and posture maintained throughout the work, mobilizing their expertise to answer the questions posed

O Ensino de Geometria por meio de atividades investigativas: uma experiência com alunos do primeiro ano do Ensino Médio

This qualitative nature of work was developed with the participation of a group of students enrolled in the first year of high school from a public school of the state of São Paulo, in the city of Taubaté. Their goal was to determine how students deal with geometry tasks in investigative classes. To guide this research was drawn up the following question: As students of the first year of high school express their knowledge of building triangles and quads in classes of investigative activities?. The choice of investigative nature of this activity occurred by enhancing student participation and thus generate a greater chance of it not be guided only by what the teacher wants, but by his own curiosity and using their own tools for this. In the data analysis process stands out the interest generated in students for this type of activity and posture maintained throughout the work, mobilizing their expertise to answer the questions posed

Declaration signed by Harvard students to not speak in the vernacular for one year, 1712 August 23

The declaration, handwritten in Latin and signed by members of the junior and sophomore classes (Harvard Classes of 1714 and 1715), promises that the undersigned will not use the vernacular but instead "whenever, at meals, at banquets,...in our rooms, in all our gatherings, wherever and whenever" will speak in Latin, Greek, or Hebrew through the next May. Additional Latin text appears on both the front and back of the document. The original is accompanied by a typed transcription and two partial handwritten translations. Note at top of original: "Script. Leonardo Dowding, Composit. a Tho. Foxcroft."

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.

Notebook of Obadiah Ayer, 1708-1716

The leather-bound notebook contains academic texts copied by Obadiah Ayer while he was a student at Harvard, and after his graduation in 1710. There is a general index to the included texts at the end of the volume.

Student mathematical notebook of Thomas Noyes, 1793

This sewn volume contains Noyes’ mathematical exercises in geometry; trigonometry; surveying; measurement of heights and distances; plain, oblique, parallel, middle latitude, and mercator sailing; and dialing. Many of the exercises are illustrated by carefully hand-drawn diagrams, including a mariners’ compass and moon dials.

Student mathematical notebook of Ebenezer Hill, 1785

This mathematical notebook of Ebenezer Hill was kept in 1795 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by hand-drawn diagrams, including some of buildings and trees.

Student mathematical notebook of Ephraim Eliot, 1779

Handwritten mathematical notebook of Ephraim Eliot, kept in 1779 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, as well as a sketch of a mariner’s compass. The sections on navigation, mensuration of heights, and spherical geometry are titled but not completed. The ink of the later text, beginning with Trigonometry, is faded.

Greek translations by Benjamin Wadsworth, 1766

Two-page handwritten Greek translations created by Harvard sophomore Benjamin Wadsworth on folio-sized paper. The document contains Greek translations of two letters from J. Garretson's "English exercises for school-boys to translate into Latin," copied by Wadsworth in 1766. The first page contains two sections: "As it is in English. A Letter from one friend to another," containing a copy of Garretson's Epistle IV from "E.C.," and a Greek translation of the letter beginning "Kypie..." The second page contains a Greek translation of Garretson's Epistle III from "B.J," and a note by Wadsworth: "A Letter from one Brother to another. Taken out of Garetson's English Exercise. The 3rd Exercise. or 135st page. There is not room or I would write down the English out of which I translated it. September the 2d A.D. 1766. When I was a sophomore." The document is bordered with hand-drawn double lines.

Latin exercise book of James Baker, 1759-1760

Small notebook kept by James Baker in the late 1750s; the dates 1755, 1756, and 1758 were written in the book. The volume contains Latin theses, Latin translations from the Book of Genesis, and three pages of English text recording an argument about the soul. The notebook has a string binding and pages of different size. The text does not appear to follow a system of organization and includes scribbles and struck-out words.

Student notebook of James Varney, 1721-1725

The bound notebook contains academic texts copied by Harvard student James Varney in the early 1720s. The texts are written tête-bêche (where both ends of the volume are used to begin writing). The front paste-down endpaper reads 'James Varney his book 1724,' and the rear paste-down endpaper reads 'Joseph Lovett' [AB 1728].

Student mathematical notebook of William Emerson Faulkner, 1795

Leather hardcover notebook with unruled pages containing the handwritten mathematical exercises of William Emerson Faulkner, begun in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, including some of buildings and trees.

Student mathematical notebook of William Tudor, 1795

Notebook containing the handwritten mathematical exercises of William Tudor, kept in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated with hand-drawn diagrams. The Menusration of Heights and Distances section contains color drawings of buildings and trees, and some have been altered with notes in different hands and with humorous additions. For instance, a drawing of a tower was drawn into a figure titled “Egyptian Mummy.” Some of the images are identified: “A rude sketch of the Middlesex canal,” Genl Warren’s monument on Bunker Hill,” “Noddles Island,” “the fields of Elysium,” and the “Roxbury Canal.” The annotations and additional drawings are unattributed.