The authors propose that conceptual and procedural knowledge develop in an iterative fashion and that improved problem representation is 1 mechanism underlying the relations between them. Two experiments were conducted with 5th-and 6th-grade students learning about decimal fractions. In Experiment 1, children's initial conceptual knowledge predicted gains in procedural knowledge, and gains in procedural knowledge predicted improvements in conceptual knowledge. Correct problem representations mediated the relation between initial conceptual knowledge and improved procedural knowledge. In Experiment 2, amount of support for correct problem representation was experimentally manipulated, and the manipulations led to gains in procedural knowledge. Thus, conceptual and procedural knowledge develop iteratively, and improved problem representation is 1 mechanism in this process. Understanding the process of knowledge change is a central goal in the study of development and education. Two essential types of knowledge that children acquire are conceptual understanding and procedural skill. Competence in domains such as mathematics rests on children developing and linking their knowledge of concepts and procedures (Silver, 1986). However, competing theories have been proposed regarding the developmental relations between conceptual and procedural knowledge. The majority of past research and theory on these relations has focused on whether conceptual or procedural knowledge emerges first (Rittle-Johnson & Siegler, 1998). The developmental precedence of one type of knowledge over another has been hotly

Gestures are often considered to be valid evidence of the embodiment of language and cognition. Since people use their bodies (i.e., gestures) to express knowledge, it is argued, the knowledge itself must be deeply tied to the body (Alibali & Nathan, 2007;Gallagher, 2005;Gibbs, 2006;Hostetter & Alibali, 2004;McNeill, 2005;Nuñez, 2005). This claim may hold some truth, but to date, there have been no explicit proposals about how embodied knowledge comes to be reflected in speech-accompanying gestures. The goal of this article is to explore how gestures may arise from embodied thinking; we will approach this goal by integrating research about perception, action, cognition, language, mental imagery, and gesture production.A variety of hand and body movements can be considered to be gestures, and much previous research has sought to describe these different types of gestures (e.g., Efron, 1972;Kendon, 2004;McNeill, 1992). In this article, we limit our discussion to representational gestures-that is, movements that represent the content of speech by pointing to a referent in the physical environment (deictic gestures), depicting a referent with the motion or shape of the hands (iconic gestures), or depicting a concrete referent or indicating a spatial location for an abstract idea (metaphoric gestures). We use the term gestures to refer specifically to representational gestures. Other types of gestures, including beat gestures (movements that emphasize the prosody or structure of speech without conveying semantic information) and interactive gestures (movements used to manage turn taking and other aspects of an interaction between multiple speakers), fall outside the scope of this article.Our aim is to describe a mechanism that may possibly give rise to gestures. We do not seek to address the issue of the functions of gestures (e.g., in communication, in speech production). Although we review some ideas about the functions of gestures, we do not take a strong stance here regarding gesture function. The goal of our framework is to explain what gestures are, rather than what they do.The article proceeds in seven sections. In the first section, we review ideas about links between perception and action and how these links are important in memory and cognition. In the second section, we review evidence that language processing is tied to the body. In the third section, we review evidence that mental imagery is also an embodied process. In the fourth section, we review evidence on the relationship between gesture production and mental imagery, and in the fifth, we propose a theoretical framework that explains how gestures may arise from the activation of perception and action. In the sixth section, we compare our framework with other models of gesture production. Finally, in the seventh section, we articulate predictions that derive from the framework. Perception, Action, and Embodied CognitionMany theorists have proposed that perception is for action (J. J. Gibson, 1979;Sperry, 1952); that is, the ability to perceive evolv...

This study examined relations between children's conceptual understanding of mathematical equivalence and their procedures for solving equivalence problems (e.g., 3 + 4 + 5 = 3 +). Students in 4th and 5th grades completed assessments of their conceptual and procedural knowledge of equivalence, both before and after a brief lesson. The instruction focused either on the concept of equivalence or on a correct procedure for solving equivalence problems. Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual understanding and to adoption, but only limited transfer, of the instructed procedure. These findings highlight the causal relations between conceptual and procedural knowledge and suggest that conceptual knowledge may have a greater influence on procedural knowledge than the reverse.

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 study examined whether knowledge of arithmetic contributes to difficulties with equations. In Experiment 1, children (ages 7-11) completed tasks to assess their adherence to 3 operational patterns prevalent in arithmetic: (a) the strategy of performing all given operations on all given numbers, (b) the "operations = answer" problem structure, and (c) the concept that the equal sign means "the total." Next, children received a lesson on equations; then, they solved a set of equations. There was a negative relationship between adherence to the operational patterns and learning. In Experiment 2, undergraduates' knowledge of the operational patterns was activated or not. Students whose knowledge was activated did not perform as well on equations. Results suggest that early-learned patterns constrain future learning and performance.