ALICE IN RANDOMLAND: A RESOURCE FOR IMPROVING ATTITUDES TOWARDS PROBABILITY AND ITS TEACHING

This article presents the results of a study aimed at examining how primary school teachers’ attitudes towards probability and its teaching are influenced by their use of an interactive story focused on sparking interest in probability and providing opportunities for learning this mathematical topic. A scale of attitudes towards probability and its teaching was applied to 40 prospective primary school teachers, before and after reading the book. This instrument was implemented with two focus groups. Preliminary results revealed significant changes in pre-service teachers’ attitudes, particularly in their feelings towards probability. This evidence attested to the potential of the book, especially considering that the participants had only studied the basics of this topic in previous courses. Abstract: Spanish En este artículo se presentan los resultados de un estudio que busca indagar sobre cómo las actitudes hacia la probabilidad y su enseñanza de futuros profesores de Educación Básica, se ven influenciadas al interactuar con un cuento interactivo que busca estimular el interés y a la vez brindar oportunidades para el aprendizaje de las probabilidades. Para el estudio se aplicó una escala de actitudes hacia la probabilidad y su enseñanza a 40 futuros profesores de Educación Básica, antes y después de la lectura del libro, lo que fue complementado con dos grupos focales. Los resultados preliminares muestran cambios significativos en sus actitudes, particularmente en el componente afectivo hacia la probabilidad. Esta evidencia muestra el potencial que tiene la lectura del libro, más aún considerando que los estudiantes solo han estudiado, en cursos anteriores, nociones básicas de probabilidades. En este artículo se presentan los resultados de un estudio que busca indagar sobre cómo las actitudes hacia la probabilidad y su enseñanza de futuros profesores de Educación Básica, se ven influenciadas al interactuar con un cuento interactivo que busca estimular el interés y a la vez brindar oportunidades para el aprendizaje de las probabilidades. Para el estudio se aplicó una escala de actitudes hacia la probabilidad y su enseñanza a 40 futuros profesores de Educación Básica, antes y después de la lectura del libro, lo que fue complementado con dos grupos focales. Los resultados preliminares muestran cambios significativos en sus actitudes, particularmente en el componente afectivo hacia la probabilidad. Esta evidencia muestra el potencial que tiene la lectura del libro, más aún considerando que los estudiantes solo han estudiado, en cursos anteriores, nociones básicas de probabilidades.

Enhanced Language Model with Hybrid Knowledge Graph for Mathematical Topic Prediction

Understanding mathematical topics is important for both educators and students to capture latent concepts of questions, evaluate study performance, and recommend content in online learning systems. Compared to traditional text classification, mathematical topic classification has several main challenges: (1) the length of mathematical questions is relatively short; (2) there are various representations of the same mathematical concept(i.e., calculations and application); (3) the content of question is complex including algebra, geometry, and calculus. In order to overcome these problems, we propose a framework that combines content tokens and mathematical knowledge concepts in whole procedures. We embed entities from mathematics knowledge graphs, integrate entities into tokens in a masked language model, set up semantic similarity-based tasks for next-sentence prediction, and fuse knowledge vectors and token vectors during the fine-tuning procedure. We also build a Chinese mathematical topic prediction dataset consisting of more than 70,000 mathematical questions with topics. Our experiments using real data demonstrate that our knowledge graph-based mathematical topic prediction model outperforms other state-of-the-art methods.

O espaço e suas relações: uma sequência de atividades em construção Space and its relations: a sequence of activities under construction

ResumoEste artigo apresenta um recorte de nossa tese de doutorado. Apresenta o episódio de discussão que envolveu a participação das professoras dos anos iniciais na produção de uma sequência de atividades, com a finalidade de trabalhar em sala de aula o tema matemático Espaço e suas relações. Para subsidiar essa discussão, como aporte teórico, recorreu aos estudos que discutem o desenvolvimento profissional docente e o trabalho colaborativo. Esse episódio assinalou a necessidade de o professor ampliar e aprofundar seus conhecimentos dos conteúdos que espera ensinar, e a contribuição significativa do trabalho em um grupo colaborativo para o desenvolvimento profissional das professoras.AbstractThe present article is a cut-off of our doctoral thesis. It shows the episode of discussion that involved the participation of elementary school teachers in the production of a sequence of activities aiming to work on the mathematical topic Space and its relations in their classrooms. In order to support that discussion theoretically, we searched for studies that discuss professional teacher develoment and collaborative work. Such episode emphasized the necessity for the teachers to increase and deepen their knowledge on the contents they expect to teach and the meaningful contribution of collaborative group work for the teachers’ professional development.

Students’ Recognition of Function Transformations’ Themes Associated with the Algebraic Representation

<p>The topic of function transformations is a difficult mathematical topic for school and college students. On the other hand, GeoGebra is a new technological tool for mathematics teaching and learning, so we wanted to experiment with this new tool in teaching non-basic function transformations to middle school students. Specifically, we wanted to examine how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned, with the help of GeoGebra translations, reflection and stretch. During their learning, the participants worked with transformations on the absolute function, the cubic function, and the quartic function. After they finished the transformation unit, the participants solved mathematics problems by means of function transformations. This research is interested in the participants’ solution of problems that included two non-basic functions: the absolute value of the quadratic function and the rationale function. The research findings show that the participants were generally able to solve successfully mathematical problems, by means of transformations on new and non-basic functions. Furthermore, the participants encountered difficulties in working with translations. These difficulties were due to the special algebraic form of the functions. We recommend that mathematics teachers expose middle school students to transformations on different types of non-basic function during learning this mathematical topic. Future researches could examine the impact of activities that include such functions and that are GeoGebra based on students’ conceptions and behavior when performing translations is involved.</p>

Technology Tips: Squaring the Circle with The Geometer's Sketchpad

The study of the history of mathematics can be an important approach to engaging students in learning mathematics. At the same time, mathematics history provides a context that will help students understand how and why certain types of mathematics were developed and used. The study of p has as rich a history as any mathematical topic.

Ensinar para aprender ou para avaliar? / Teach to learn or to evaluate?

ABSTRACTWith this work we propose to reflect on the motivations that lead teachers in the planning and selection of materials they use in class. The text gives us some analysis about an exploratory study with two teachers who were followed in introductory classes to the same mathematical topic in classes the seventh grade. Through classroom observation, interviews and analysis of a narrative produced by one of the teachers, it was revealed their conceptions and allowed to know their practices, featuring the approaches that have been adopted, as well as the positions they choose to face assessment of student learning. From here, to problematize the different approaches used and the intentions that guide the light of the "new" educational paradigm, whereby the student must be the center of the teaching-learning process, being the teacher the responsibility to create conditions for that to happen, especially in terms of reconstruction and contextualization of the curriculum and promoting mechanisms for systematic evaluation.RESUMOCom o presente trabalho pretendemos refletir sobre as motivações que conduzem os professores na seleção e planificação dos materiais que utilizam nas aulas. O texto devolve algumas análises realizadas num estudo exploratório com duas professoras que foram acompanhadas, em aulas de introdução a um mesmo tópico matemático, em turmas do sétimo ano de escolaridade. Pela observação de aulas, entrevistas e análise de uma narrativa produzida por uma das professoras, foi possível perceber as suas conceções e conhecer as suas práticas, caraterizando as abordagens que foram adotadas, assim como as posições que escolhem face à avaliação das aprendizagens dos alunos. Partindo daqui, problematizam-se as diferentes abordagens utilizadas e as intenções que as norteiam, à luz do “novo” paradigma educativo, segundo o qual o aluno deve ser o centro do processo de ensino-aprendizagem, cabendo ao professor a responsabilidade de criar condições para que isso aconteça, nomeadamente ao nível da reconstrução e contextualização do currículo e da promoção de mecanismos de avaliação sistemática.