Summary This article describes the linguistic work of Felipe Arroyo de la Cuesta (1780–1840), a F... more Summary This article describes the linguistic work of Felipe Arroyo de la Cuesta (1780–1840), a Franciscan missionary from Spain who lived and worked in the missions of Alta California for some 32 years. He was the most prolific chronicler of the indigenous languages of Alta California during the mission period, writing a vocabulary and grammar of the Costanoan/Ohlone language Mutsun, taking notes on a Yokuts language he called Nopthrinthres, and compiling shorter word lists and religious texts in numerous other languages. The present work seeks to bring together and analyze what information is available about Arroyo de la Cuesta’s life and writings and place these within the broader field of missionary linguistics.
International Journal for mathematics teaching and learning, 2018
Research in second language acquisition and the learning of mathematics has matured through long,... more Research in second language acquisition and the learning of mathematics has matured through long, albeit disconnected, histories. This study examines how theories and models of second language acquisition can be applied to the learning of mathematics and, through this, develops a novel framework defining stages in the learning of mathematics. This framework considers dimensions of language (social and academic), cognitive level (undemanding and demanding), locus of activity (student and teacher), and primary mode of communication (listening, reading, speaking, and writing) and leads to the mathematical learning stages: receiving mathematics, reading and replicating mathematics, negotiating meaning; communicating mathematics; and producing mathematics. This framework has numerous implications for the learning and assessment of mathematics.
This study investigates representational code-switching (RCS) by considering three high school st... more This study investigates representational code-switching (RCS) by considering three high school students’ communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical representations, practicing language learning, and linguistic code-switching (LCS). Attention is given to assessing student mathematical understanding based on frequency and type of RCS performed. This investigation concludes that RCS demonstrates either weaker or stronger mathematical performance depending on whether the RCS evidences semantic elaboration, isomorphic and transcendent connections, and domain register knowledge.
While one branch of literature is replete with investigations of problem solving and another bran... more While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated during either problem-solving experiences or DME use and only a handful of studies consider cognitive processes associated with problem solving when working in a DME. This paper reports a novel approach to investigating, defining, and categorizing the cognitive processes used by students in mathematical problem-solving while working in a DME with examples found in student work. Using this approach, problem-solving is found to be nonlinear, iterative, and idiosyncratic. Insights gained by this analysis have both theoretical and practical applications in mathematics education.
espanolFelipe Arroyo de la Cuesta, un fraile espanol nacido en la provincia de Burgos, paso la ma... more espanolFelipe Arroyo de la Cuesta, un fraile espanol nacido en la provincia de Burgos, paso la mayoria de su vida en la Alta California, territorio espanol y luego mexicano. Un analisis cuidadoso de su vocabulario manuscrito espanol-mutsun, el Alphabeticus Rivulus Obeundus (c. 1815), demuestra que Arroyo de la Cuesta emplea una gran variedad de terminos que se consideran tipicos del espanol mexicano. Tambien utiliza en su vocabulario terminos regionales espanoles y terminos de la lengua californiana mutsun, pero en menor grado. Este analisis apoya la afirmacion de que el espanol hablado en la Alta California tenia origenes fundamentalmente mexicanos, y contradice la afirmacion de que la influencia mexicana comenzo sobre todo despues de 1830. EnglishFelipe Arroyo de la Cuesta was a Spanish priest born in the province of Burgos who spent most of his adult life in the Spanish and then Mexican territory of Alta California. Careful analysis of his manuscript Spanish-Mutsun vocabulary, th...
Indigenous languages of the Americas are spoken by millions of people 500 years after the initial... more Indigenous languages of the Americas are spoken by millions of people 500 years after the initial period of European conquest. The people who speak these languages and the customs they continue to practice form a rich cultural texture in many parts of Spanish America and can be important components of an instructor’s Standards-based teaching. This article discusses the influence of Maya and Nahuatl languages and cultures on the language, literature, and history of Mexico and Central America. Examples of this influence range from lexical and phonological traits of Mexican Spanish to the indigenous cultures and worldviews conveyed in texts as varied as the Mexican soap opera “Barrera de Amor” and the stories by Rosario Castellanos of Mexico and Miguel Angel Asturias of Gua temala. The examples given here relate to classroom teaching at multiple levels, particularly as they apply to the Standards of Communication and Cultures. The appendices provide lists of selected resources for Spa...
Summary This article describes the linguistic work of Felipe Arroyo de la Cuesta (1780–1840), a F... more Summary This article describes the linguistic work of Felipe Arroyo de la Cuesta (1780–1840), a Franciscan missionary from Spain who lived and worked in the missions of Alta California for some 32 years. He was the most prolific chronicler of the indigenous languages of Alta California during the mission period, writing a vocabulary and grammar of the Costanoan/Ohlone language Mutsun, taking notes on a Yokuts language he called Nopthrinthres, and compiling shorter word lists and religious texts in numerous other languages. The present work seeks to bring together and analyze what information is available about Arroyo de la Cuesta’s life and writings and place these within the broader field of missionary linguistics.
International Journal for mathematics teaching and learning, 2018
Research in second language acquisition and the learning of mathematics has matured through long,... more Research in second language acquisition and the learning of mathematics has matured through long, albeit disconnected, histories. This study examines how theories and models of second language acquisition can be applied to the learning of mathematics and, through this, develops a novel framework defining stages in the learning of mathematics. This framework considers dimensions of language (social and academic), cognitive level (undemanding and demanding), locus of activity (student and teacher), and primary mode of communication (listening, reading, speaking, and writing) and leads to the mathematical learning stages: receiving mathematics, reading and replicating mathematics, negotiating meaning; communicating mathematics; and producing mathematics. This framework has numerous implications for the learning and assessment of mathematics.
This study investigates representational code-switching (RCS) by considering three high school st... more This study investigates representational code-switching (RCS) by considering three high school students’ communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical representations, practicing language learning, and linguistic code-switching (LCS). Attention is given to assessing student mathematical understanding based on frequency and type of RCS performed. This investigation concludes that RCS demonstrates either weaker or stronger mathematical performance depending on whether the RCS evidences semantic elaboration, isomorphic and transcendent connections, and domain register knowledge.
While one branch of literature is replete with investigations of problem solving and another bran... more While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated during either problem-solving experiences or DME use and only a handful of studies consider cognitive processes associated with problem solving when working in a DME. This paper reports a novel approach to investigating, defining, and categorizing the cognitive processes used by students in mathematical problem-solving while working in a DME with examples found in student work. Using this approach, problem-solving is found to be nonlinear, iterative, and idiosyncratic. Insights gained by this analysis have both theoretical and practical applications in mathematics education.
espanolFelipe Arroyo de la Cuesta, un fraile espanol nacido en la provincia de Burgos, paso la ma... more espanolFelipe Arroyo de la Cuesta, un fraile espanol nacido en la provincia de Burgos, paso la mayoria de su vida en la Alta California, territorio espanol y luego mexicano. Un analisis cuidadoso de su vocabulario manuscrito espanol-mutsun, el Alphabeticus Rivulus Obeundus (c. 1815), demuestra que Arroyo de la Cuesta emplea una gran variedad de terminos que se consideran tipicos del espanol mexicano. Tambien utiliza en su vocabulario terminos regionales espanoles y terminos de la lengua californiana mutsun, pero en menor grado. Este analisis apoya la afirmacion de que el espanol hablado en la Alta California tenia origenes fundamentalmente mexicanos, y contradice la afirmacion de que la influencia mexicana comenzo sobre todo despues de 1830. EnglishFelipe Arroyo de la Cuesta was a Spanish priest born in the province of Burgos who spent most of his adult life in the Spanish and then Mexican territory of Alta California. Careful analysis of his manuscript Spanish-Mutsun vocabulary, th...
Indigenous languages of the Americas are spoken by millions of people 500 years after the initial... more Indigenous languages of the Americas are spoken by millions of people 500 years after the initial period of European conquest. The people who speak these languages and the customs they continue to practice form a rich cultural texture in many parts of Spanish America and can be important components of an instructor’s Standards-based teaching. This article discusses the influence of Maya and Nahuatl languages and cultures on the language, literature, and history of Mexico and Central America. Examples of this influence range from lexical and phonological traits of Mexican Spanish to the indigenous cultures and worldviews conveyed in texts as varied as the Mexican soap opera “Barrera de Amor” and the stories by Rosario Castellanos of Mexico and Miguel Angel Asturias of Gua temala. The examples given here relate to classroom teaching at multiple levels, particularly as they apply to the Standards of Communication and Cultures. The appendices provide lists of selected resources for Spa...
Uploads
Papers by Catherine Fountain