Journal Writing in Mathematics: Exploring the Connections between Math Journals and the Completion of Homework Assignments

In this action research study of sixth grade mathematics, I investigate how the use of written journals facilitates the learning of mathematics for my students. I explore furthermore whether or not these writing journals support students to complete their homework. My analysis reveals that while students do not access their journals daily, when students have the opportunity to write more about one specific problem--such as finding the relationship between the area of two different sized rectangles – they, are nevertheless, more likely to explain their thoughts in-depth and go beyond the traditional basic steps to arrive at a solution. This suggests the value of integrating journal writing in a math curriculum as it can facilitate classroom discussion from the students’ written work.

Effect of image resolution manipulation in rearfoot angle measurements obtained with photogrammetry

The aim of this study was to investigate the influence of image resolution manipulation on the photogrammetric measurement of the rearfoot static angle. The study design was that of a reliability study. We evaluated 19 healthy young adults (11 females and 8 males). The photographs were taken at 1536 pixels in the greatest dimension, resized into four different resolutions (1200, 768, 600, 384 pixels) and analyzed by three equally trained examiners on a 96-pixels per inch (ppi) screen. An experienced physiotherapist marked the anatomic landmarks of rearfoot static angles on two occasions within a 1-week interval. Three different examiners had marked angles on digital pictures. The systematic error and the smallest detectable difference were calculated from the angle values between the image resolutions and times of evaluation. Different resolutions were compared by analysis of variance. Inter- and intra-examiner reliability was calculated by intra-class correlation coefficients (ICC). The rearfoot static angles obtained by the examiners in each resolution were not different (P > 0.05); however, the higher the image resolution the better the inter-examiner reliability. The intra-examiner reliability (within a 1-week interval) was considered to be unacceptable for all image resolutions (ICC range: 0.08-0.52). The whole body image of an adult with a minimum size of 768 pixels analyzed on a 96-ppi screen can provide very good inter-examiner reliability for photogrammetric measurements of rearfoot static angles (ICC range: 0.85-0.92), although the intra-examiner reliability within each resolution was not acceptable. Therefore, this method is not a proper tool for follow-up evaluations of patients within a therapeutic protocol.

Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Crystal structure of D-amino acid oxidase: a case of active site mirror-image convergent evolution with flavocytochrome b2.

D-amino acid oxidase is the prototype of the FAD-dependent oxidases. It catalyses the oxidation of D-amino acids to the corresponding alpha-ketoacids. The reducing equivalents are transferred to molecular oxygen with production of hydrogen peroxide. We have solved the crystal structure of the complex of D-amino acid oxidase with benzoate, a competitive inhibitor of the substrate, by single isomorphous replacement and eightfold averaging. Each monomer is formed by two domains with an overall topology similar to that of p-hydroxybenzoate hydroxylase. The benzoate molecule lays parallel to the flavin ring and is held in position by a salt bridge with Arg-283. Analysis of the active site shows that no side chains are properly positioned to act as the postulated base required for the catalytic carboanion mechanism. On the contrary, the benzoate binding mode suggests a direct transfer of the substrate alpha-hydrogen to the flavin during the enzyme reductive half-reaction.The active site Of D-amino acid oxidase exhibits a striking similarity with that of flavocytochrome b2, a structurally unrelated FMN-dependent flavoenzyme. The active site groups (if these two enzymes are in fact superimposable once the mirror-image of the flavocytochrome b2 active site is generated with respect to the flavin plane. Therefore, the catalytic sites of D-amino acid oxidase and flavocytochrome b2 appear to have converged to a highly similar but enantiomeric architecture in order to catalvze similar reactions (oxidation of alpha-amino acids or alpha-hydroxy acids), although with opposite stereochemistry.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

South America, 1807 (Image 2 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 2 of 7 total images of the eight sheet map, representing the northern portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1807 (Image 3 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 3 of 7 total images of the eight sheet map, representing the eastern portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1807 (Image 4 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 4 of 7 total images of the eight sheet map, representing the northeast portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1807 (Image 5 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 5 of 7 total images of the eight sheet map, representing the southwest portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1807 (Image 6 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 6 of 7 total images of the eight sheet map, representing the western portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1807 (Image 7 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 7 of 7 total images of the eight sheet map, representing the southern portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1825 (Image 1 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: General-Charte von Süd-America = Carte générale de L'Amerique Méridionale : en deux grandes feuilles. d'après les observations et les cartes spéciales, rapportées du Voyage dans l'intérieur du Brèsil, pendant les années 1817-1820..., par les Docteurs de Spix et de Martius, Chevaliers de L'Ordre civil de la Couronne de Bavière, membres de L'Académie Royale de Munich ; gestochen von Joh. Bapt. Seitz, Kupferstecher im topographischen Bureau des Kön. baier. General-Quartiermeister Stab. It was published by [M. Lindauer] in 1825. Scale [ca. 1:7,000,000]. This layer is image 1 of 2 total images of the two sheet source map, representing the southern portion of the map. Map in German and French. The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, roads, shoreline features, and more. Relief shown by hachures.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

South America, 1825 (Image 2 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: General-Charte von Süd-America = Carte générale de L'Amerique Méridionale : en deux grandes feuilles. d'après les observations et les cartes spéciales, rapportées du Voyage dans l'intérieur du Brèsil, pendant les années 1817-1820..., par les Docteurs de Spix et de Martius, Chevaliers de L'Ordre civil de la Couronne de Bavière, membres de L'Académie Royale de Munich ; gestochen von Joh. Bapt. Seitz, Kupferstecher im topographischen Bureau des Kön. baier. General-Quartiermeister Stab. It was published by [M. Lindauer] in 1825. Scale [ca. 1:7,000,000]. This layer is image 2 of 2 total images of the two sheet source map, representing the northern portion of the map. Map in German and French.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, roads, shoreline features, and more. Relief shown by hachures.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Jamaica, 1763 (Image 1 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: This map of the island of Jamaica; laid down from the papers and under the direction of Henry Moore, Esqr.; His Majesty's Lieutenant Governor and Commander in Chief of that island, in the years 1756, 57, 58, 59, 60 & 61; & from a great number of actual surveys performed by the publishers is humbly inscribed by his lordship's most obedient & most humble servants, Thos. Craskell, engineer, Jas. Simpson, surveyor. It was published by D. Fournier in 1763. Scale [ca 1:200,000]. This layer is image 1 of 4 total images of the four sheet map, representing the southwest portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the Jamaica Grid projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as towns, villages, and other human settlements, roads, drainage, selected buildings, ground cover, shoreline features, and more. Relief shown pictorially. Includes also illustrations.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.