Many students are being left behind by an educational system that some people believe is in crisis. Improving educational outcomes will require efforts on many fronts, but a central premise of this monograph is that one part of a solution involves helping students to better regulate their learning through the use of effective learning techniques. Fortunately, cognitive and educational psychologists have been developing and evaluating easy-to-use learning techniques that could help students achieve their learning goals. In this monograph, we discuss 10 learning techniques in detail and offer recommendations about their relative utility. We selected techniques that were expected to be relatively easy to use and hence could be adopted by many students. Also, some techniques (e.g., highlighting and rereading) were selected because students report relying heavily on them, which makes it especially important to examine how well they work. The techniques include elaborative interrogation, self-explanation, summarization, highlighting (or underlining), the keyword mnemonic, imagery use for text learning, rereading, practice testing, distributed practice, and interleaved practice. To offer recommendations about the relative utility of these techniques, we evaluated whether their benefits generalize across four categories of variables: learning conditions, student characteristics, materials, and criterion tasks. Learning conditions include aspects of the learning environment in which the technique is implemented, such as whether a student studies alone or with a group. Student characteristics include variables such as age, ability, and level of prior knowledge. Materials vary from simple concepts to mathematical problems to complicated science texts. Criterion tasks include different outcome measures that are relevant to student achievement, such as those tapping memory, problem solving, and comprehension. We attempted to provide thorough reviews for each technique, so this monograph is rather lengthy. However, we also wrote the monograph in a modular fashion, so it is easy to use. In particular, each review is divided into the following sections: General description of the technique and why it should work How general are the effects of this technique?  2a. Learning conditions  2b. Student characteristics  2c. Materials  2d. Criterion tasks Effects in representative educational contexts Issues for implementation Overall assessment The review for each technique can be read independently of the others, and particular variables of interest can be easily compared across techniques. To foreshadow our final recommendations, the techniques vary widely with respect to their generalizability and promise for improving student learning. Practice testing and distributed practice received high utility assessments because they benefit learners of different ages and abilities and have been shown to boost students' performance across many criterion tasks and even in educational contexts. Elaborative interrogation, self-explanation, and in...

Aos meus pais, Rogério e Lucia, com extremo amor, responsáveis por toda essa caminhada.À minha esposa, Adriana, Por ter suportado momentos de privações, mas sempre lapidava palavras que serviram de incentivo e encorajamento. AGRADECIMENTOSAo Prof. Marcelo Bairral, que com toda sua simplicidade, mostrou-me preciosos caminhos para (des)construção de concepções acerca da Educação Matemática e por se tornar um grande amigo e cúmplice nessa árdua jornada. À Profª. Márcia Pletsch pelos inesquecíveis momentos vigostikianos, sua alegria, seu otimismo e por ter aceito o convite para compor a banca. À Profª. Janete Bolite Frant pelas valiosas sugestões para a corporeidade dada ao texto. Ao Prof. Aristóteles Berinio pelas frutíferas reflexões acerca da Educação na Contemporaneidade. Ao grande amigo Wagner pelo constante incentivo, carinho nas leituras e suas preciosas contribuições. À querida Bárbara Caroline pela parceria em momentos de pesquisas e reflexões. Aos integrantes do Observatório da Educação Materiais Curriculares Educativos Online (OBEDUC -MCEO), GEPETICEM e Observatório de Educação Especial e Inclusão Escolar (OEEIEs). Aos demais professores do corpo docente do PPGEduc/UFRRJ por proporcionar situações de pesquisa e desenvolvimento. Aos colegas de turma de mestrado pelos ricos momentos com compartilhamento de saberes, sem destaque para não cometer injustiça. Aos diretores do Instituto de Educação Rangel Pestana (IERP) que permitiram o desenvolvimento dessa pesquisa no ambiente escolar. Aos alunos do curso normal do IERP, com um carinho especial aos alunos participantes, pelos momentos de aprendizagem mútua. A CAPES pelo apoio financeiro. RESUMO ASSIS, ALEXANDRE RODRIGUES DE. Alunos do Ensino Médio trabalhando no GeoGebra e no Construtor Geométrico: Mãos e rotAções em touchscreen. 2015. 158p. Dissertação (Mestrado em Educação).

This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problem-solving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students' strategies and errors as the basis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external representations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.A commonly held belief about story problems at both the arithmetic and algebra levels is that they are notoriously difficult for students. Support for this belief can be seen among a variety of populations including the general public, textbook au-

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This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade-offs in problem-solving performance. In prior research with high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations-students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a "symbolic advantage" emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed "verbal advantage" on simple problems was replicated. We thus provide empirical support for a trade-off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems.