This literature review was conducted after it was noticed that an active instruction approach in teaching mathematics was becoming more of a standard approach. This literature review aims to analyze and synthesize existing research regarding active and direct instruction, as well as examine how these instructional strategies support the promotion of flexible thinking in students, including their promotion of the Standards of Mathematical Practice related to flexibility in thinking. This review defines both active instruction and direct instruction, as well as compares the two strategies, particularly in terms of how well they promote flexible thinking in students. It was discovered that there exists an abundance of research regarding active instruction, including its promotion of flexible thinking, yet it was difficult to find articles advocating for direct instruction. From the research conducted, it appears that a more active approach is more conducive to the learning of mathematics for students in that it encourages flexible thinking, which is a necessary component of a successful mathematician. More research is needed to determine under which conditions these instructional strategies yield optimal results.

Made available in DSpace on 2014-12-17T14:36:02Z (GMT). No. of bitstreams: 1 AlinePDpdf.pdf: 699478 bytes, checksum: d1fd21dcb47fd1fb04069e9c8121ab69 (MD5) Previous issue date: 2009-07-10 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This thesis aims to enable a wider comprehension on thought operation as well as suggest alternatives for the formation of reflexive, critical, autonomous and creative individuals. The research defends the idea that it is possible for an individual to develop vigilant attention that makes thought flexibilization and change in the course of action, possible. This operation is called Internal Dialogue and is essentially characterized by a continuous openness towards novelty and learning. This makes it possible to minimize the usual way thought operates, in a automatic fashion (automatism). The research was based on theoretical references and ideas of David Bohm (1989;1994;2005) and Michael Polanyi (1983). The main emphasis was the understanding that a crisis situation enables awareness and state of alert that favors a more flexible thought pattern (Arag?o Gomes, 1994, 1997). The methodology used was presentation and analysis of these moments through autobibliographical records with indication of crisis on behalf of the subjects. Other criteria were also used that enabled the composition of the analyzed material such as the fact that: the subjects were public and real, the data was available through accessible material; the subjects identified themselves as in crisis; these crisis were of varied kinds; they had different social, cultural and professional profiles. Thus, three auto-bibliographical elements were selected: the Infidel: the story of a woman that challenged Islam (2007), written by the political Muslim author Ayaan Hirsi; Still me: memories (2001), of the actor Christopher Reeve as well as Confessions of a Philosopher (2001), by the philosopher Bryan Magee. In these books an analysis was made related to parts that stated action an though operation that express internal dialogue. These were organized into categories that were pointed out as relevant for the identification of internal dialogue such as: Perceptions of physical reaction; emotions, beliefs and issues, individual actions, self judgment and thought, self questioning, comprehension, observation and empirical investigation, perception of the changes they performed in the world, escape of conditioning as well as action that resulted in new meaning. The analysis performed reinforces our goal once it sated that internal dialogue is an important tool that allows thought awareness, minimizing common automatism and making consciousness possible as well as favoring the occurrence of critical and reflexive thought. Thus, final considerations deal with the need for the development of teaching methodologies that address internal dialogue as a counterpoint to the many daily action that reinforce the automatism of thought / Esta tese tem como objetivo permitir maior compreens?o sobre a opera??o do pensamento e sugerir alternativas para a forma??o de indiv?duos reflexivos, cr?ticos, aut?nomos e criativos. Defendemos que ? poss?vel o indiv?duo desenvolver uma aten??o vigilante capaz de flexibilizar o pensamento e possibilitar mudan?as nas nossas a??es e pensamento. Denominada Di?logo Interno, esta opera??o caracteriza-se essencialmente pela abertura ao novo e cont?nua disposi??o para o aprendizado, minimizando o modo como o pensamento opera, na maior parte do tempo (automatismo). Este estudo teve como principais refer?ncias te?ricas as id?ias de David Bohm (1989;1994;2005) e Michael Polanyi (1983) e como pressuposto fundamental o entendimento de que situa??es de crise propiciam momentos de tomadas de ci?ncia e estado de alerta que favorecem o pensamento a operar de modo mais flex?vel. (Arag?o Gomes, 1994, 1997). Metodologicamente, optamos por apresentar e analisar estes momentos atrav?s de relatos autobiogr?ficos, cujo autor indicava vivenciar momentos de crise. Outros crit?rios foram utilizados para comporem o material a ser analisado: tratava-se de pessoas reais e p?blicas; os relatos estavam dispon?veis em obras de f?cil acesso; tratava-se de pessoas em situa??o de crise por elas identificadas; apresentavam situa??es de crise de naturezas distintas; eram pessoas com perfis s?cio-culturais, profissionais e de g?nero distintos. Assim, foram selecionados tr?s relatos autobiogr?ficos: Infiel: a hist?ria de uma mulher que desafiou o Isl? (2007), da escritora e pol?tica mu?ulmana Ayaan Hirsi; Ainda sou eu: mem?rias (2001), do ator Christopher Reeve e; Confiss?es de um fil?sofo (2001), do fil?sofo Bryan Magee. Nestas obras foram analisados diversos trechos nos quais identificamos opera??es e a??es de pensamento que expressam tra?os do Di?logo Interno, organizadas nas categorias que identificamos como relevantes para a identifica??o do Di?logo Interno: percep??o de rea??es f?sicas, percep??o dos pr?prios sentimentos, percep??o das pr?prias cren?as e pressupostos, percep??o das pr?prias a??es, percep??o e julgamento do pr?prio pensamento, a??o de questionamento, busca da compreens?o, observa??o e investiga??o emp?rica, percep??o de sua mudan?a de a??o no mundo, sa?da do condicionamento e a??o de ressignifica??o. As an?lises realizadas refor?am nosso pressuposto de que o di?logo interno ? uma importante ferramenta para acionarmos a aten??o vigilante do pensamento, minimizando o automatismo habitual e propiciando a tomada de consci?ncia e a emerg?ncia de pensamentos cr?ticos e reflexivos. Dessa forma, as considera??es finais desta tese apontam para a necessidade do desenvolvimento de metodologias de ensino que contemplem o Di?logo Interno como contraponto ?s diversas viv?ncias cotidianas que refor?am o automatismo do pensamento e a??o

Made available in DSpace on 2014-12-17T14:36:08Z (GMT). No. of bitstreams: 1 AlinePD_TESE.pdf: 699525 bytes, checksum: a35806955c1aa8e04da250ab8a863da9 (MD5) Previous issue date: 2009-08-23 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This thesis aims to enable a wider comprehension on thought operation as well as suggest alternatives for the formation of reflexive, critical, autonomous and creative individuals. The research defends the idea that it is possible for an individual to develop vigilant attention that makes thought flexibilization and change in the course of action, possible. This operation is called Internal Dialogue and is essentially characterized by a continuous openness towards novelty and learning. This makes it possible to minimize the usual way thought operates, in a automatic fashion (automatism). The research was based on theoretical references and ideas of David Bohm (1989;1994;2005) and Michael Polanyi (1983). The main emphasis was the understanding that a crisis situation enables awareness and state of alert that favors a more flexible thought pattern (Arag?o Gomes, 1994, 1997). The methodology used was presentation and analysis of these moments through autobibliographical records with indication of crisis on behalf of the subjects. Other criteria were also used that enabled the composition of the analyzed material such as the fact that: the subjects were public and real, the data was available through accessible material; the subjects identified themselves as in crisis; these crisis were of varied kinds; they had different social, cultural and professional profiles. Thus, three auto-bibliographical elements were selected: the Infidel: the story of a woman that challenged Islam (2007), written by the political Muslim author Ayaan Hirsi; Still me: memories (2001), of the actor Christopher Reeve as well as Confessions of a Philosopher (2001), by the philosopher Bryan Magee. In these books an analysis was made related to parts that stated action an though operation that express internal dialogue. These were organized into categories that were pointed out as relevant for the identification of internal dialogue such as: Perceptions of physical reaction; emotions, beliefs and issues, individual actions, self judgment and thought, self questioning, comprehension, observation and empirical investigation, perception of the changes they performed in the world, escape of conditioning as well as action that resulted in new meaning. The analysis performed reinforces our goal once it sated that internal dialogue is an important tool that allows thought awareness, minimizing common automatism and making consciousness possible as well as favoring the occurrence of critical and reflexive thought. Thus, final considerations deal with the need for the development of teaching methodologies that address internal dialogue as a counterpoint to the many daily action that reinforce the automatism of thought / Esta tese tem como objetivo permitir maior compreens?o sobre a opera??o do pensamento e sugerir alternativas para a forma??o de indiv?duos reflexivos, cr?ticos, aut?nomos e criativos. Defendemos que ? poss?vel o indiv?duo desenvolver uma aten??o vigilante capaz de flexibilizar o pensamento e possibilitar mudan?as nas nossas a??es e pensamento. Denominada Di?logo Interno, esta opera??o caracteriza-se essencialmente pela abertura ao novo e cont?nua disposi??o para o aprendizado, minimizando o modo como o pensamento opera, na maior parte do tempo (automatismo). Este estudo teve como principais refer?ncias te?ricas as id?ias de David Bohm (1989;1994;2005) e Michael Polanyi (1983) e como pressuposto fundamental o entendimento de que situa??es de crise propiciam momentos de tomadas de ci?ncia e estado de alerta que favorecem o pensamento a operar de modo mais flex?vel. (Arag?o Gomes, 1994, 1997). Metodologicamente, optamos por apresentar e analisar estes momentos atrav?s de relatos autobiogr?ficos, cujo autor indicava vivenciar momentos de crise. Outros crit?rios foram utilizados para comporem o material a ser analisado: tratava-se de pessoas reais e p?blicas; os relatos estavam dispon?veis em obras de f?cil acesso; tratava-se de pessoas em situa??o de crise por elas identificadas; apresentavam situa??es de crise de naturezas distintas; eram pessoas com perfis s?cio-culturais, profissionais e de g?nero distintos. Assim, foram selecionados tr?s relatos autobiogr?ficos: Infiel: a hist?ria de uma mulher que desafiou o Isl? (2007), da escritora e pol?tica mu?ulmana Ayaan Hirsi; Ainda sou eu: mem?rias (2001), do ator Christopher Reeve e; Confiss?es de um fil?sofo (2001), do fil?sofo Bryan Magee. Nestas obras foram analisados diversos trechos nos quais identificamos opera??es e a??es de pensamento que expressam tra?os do Di?logo Interno, organizadas nas categorias que identificamos como relevantes para a identifica??o do Di?logo Interno: percep??o de rea??es f?sicas, percep??o dos pr?prios sentimentos, percep??o das pr?prias cren?as e pressupostos, percep??o das pr?prias a??es, percep??o e julgamento do pr?prio pensamento, a??o de questionamento, busca da compreens?o, observa??o e investiga??o emp?rica, percep??o de sua mudan?a de a??o no mundo, sa?da do condicionamento e a??o de ressignifica??o. As an?lises realizadas refor?am nosso pressuposto de que o di?logo interno ? uma importante ferramenta para acionarmos a aten??o vigilante do pensamento, minimizando o automatismo habitual e propiciando a tomada de consci?ncia e a emerg?ncia de pensamentos cr?ticos e reflexivos. Dessa forma, as considera??es finais desta tese apontam para a necessidade do desenvolvimento de metodologias de ensino que contemplem o Di?logo Interno como contraponto ?s diversas viv?ncias cotidianas que refor?am o automatismo do pensamento e a??o