Parte-todo na fração: reflexões sobre o erro na resolução e na argumentação dos estudantes

Internationally, the need to modernize school curricula and introduce the concepts of modern physics into schools has been accepted in recent years. Research on introducing Einsteinian physics (EP) to the most effective school age is lagging. The present study aims to evaluate a short intervention in Einstein’s physics and determine the school level at which the concepts of EP are optimally comprehended. Therefore, a teaching intervention was carried out to 325 Greek students; 83 students in 6th grade (11–12 years old), 116 students in 9th grade (14–15 years old), and 126 students in 11th grade (16–17 years old). All students completed pre—and post—conceptual and attitudinal questionnaires. According to data analysis, the conceptual performance of students concerning EP improved significantly. In concrete, students of 11th grade have exceeded the conceptual scores, compared with general changes identified to the majority of school grades. Moreover, the study participants had a positive attitude towards science, mostly towards Einstein’s physics, before the teaching intervention, which remained at a high level after the intervention. The study generates useful results for introducing modern physics in primary and secondary education.

The purpose of this study was to examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebra-related misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used in order to analyze sixth- and eighth-grade student responses on a statewide standardized assessment. Secondary data sources consisted of Algebra I student responses which were also analyzed qualitatively using document analysis and follow-up interviews with key informants. The primary analysis indicated that (l) numerous misconceptions and errors identified in the review of literature were present on both the sixth- and eighth-grade open-responses; (2) basic computational errors with whole numbers (a secondary skill), were found consistently throughout the sixth- and eighth-grade open-responses; (3) a greater number of misconceptions and errors identified in the review of the literature were present on the eighth-grade items than were found on the sixth-grade items; (4) students often lost points for reasons other than mathematical misconceptions or errors; and (5) some refinement and reorganization of Welder's (2007) framework could prove beneficial when using the framework for data analytic purposes. The results of this study provided information about the common misconceptions and errors students possess on prerequisite algebra skills. The findings revealed common algebra misconceptions and trends that can help guide instruction for middle school mathematics teachers. The findings have direct implications for classroom practice and further confirm the need for strong and knowledgeable teachers of mathematics at the elementary and middle grades. The researcher suggests that schools, both in the state whose standardized assessment was examined as well as other states, use this information to help build awareness of common prerequisite algebra-related misconceptions and errors in elementary and middle grades mathematics teachers.

Background: Research has indicated that an aesthetic perspective on movement is lacking in physical education and that exploratory teaching assignments are rare. Purpose: The aim of the paper is to explore how PE teachers approach the issue of teaching expressive dance and which learning processes students are involved in while dancing. Participants, research design and data collection: Sixty-eight students from three different secondary school classes and four PE teachers at one municipal school in Sweden participated in a pedagogical intervention. A dance education unit built around Rudolf Laban’s framework of movement was video recorded. Careful attention was paid to ethical considerations. Data analysis: Using Dewey’s transactional perspective as a holistic starting point contributed to dissolve the dualism between individuals and the environment (1949/1991). The analysis was informed by practical epistemology analysis [Wickman, P.-O., and L. Östman. 2002. “Learning as a Discourse Change: a Sociocultural Mechanism.” Science Education 86 (5): 601–623], where the terms gaps, relations and encounters were applied to distinguish various types of transactions. The concept of risk [Biesta, G. 2013. The Beautiful Risk of Education. Boulder: Paradigm Publishers] was utilised to explore how teachers’ pedagogical methods interacted with the environment in the pedagogical intervention. Findings: Most transactions occurring during the dance unit were interpreted as narrow transactions, meaning that the students’ actions followed responses to the teachers’ initiation of a dance assignment. Expanded transactions occurred when the students were given the opportunity and responsibility to find their own solutions to dance assignments. This is interpreted as leading to an expanded purpose, which involves new ways of moving. Interrupted transactions, i.e. when actions were stopped and no encounters occurred, were observed in the form of students hesitating or avoiding participation. Teaching methods involving a certain degree of risk enable creative and non-predetermined movements. The use of unfamiliar music avoided a reproduction of stereotypical dance styles. Dimmed lighting in the sports hall and the opportunity to work in separate rooms helped the students negotiating environmental risks by attending to the organisation and aesthetics of the space. Conclusions: Expressive dance assignments can take teaching in PE in new and expanded directions. The teachers programmed gradually more risks into their lessons, which in line with Biesta’s understanding (2013) enabled the students to explore new and unpredictable movements. The students developed new ways of expressing themselves and were able to focus on the meaning of the movements. Expressive dance assignments are well suited to an exploratory method of teaching and this interplay can challenge existing logics of competition and ranking in PE.

O objetivo deste trabalho é propor uma metodologia para o ensino de física, explorando as inteligências múltiplas, sendo elas; linguística, lógico matemática e visuoespacial. A análise e coleta de dados foram realizadas na escola pública municipal Francisco Sá Sobrinho, onde eram ministradas as aulas, localizada na cidade de São João dos Patos Maranhão no nono ano do ensino fundamental, a escolha deste ano se dá em razão de ser nele que os discentes têm o primeiro contato com as especificações da disciplina de física. A metodologia utilizada foi pesquisa bibliográfica e em seguida uma pesquisa de campo com intervenções pedagógicas e aulas diferenciadas, as quais possibilitaram obter informações sobre como se dão as dificuldades dos discentes na disciplina de física frente a situações de estímulo das inteligências linguística, lógico matemática e visuoespacial. Os dados obtidos receberam um tratamento quantitativo e qualitativo. Com as intervenções pedagógicas os alunos mostraram bons resultados, manifestaram mais interesse, gostaram das aulas, e durante as mesmas eles podiam se sentir à vontade para manifestar-se, questionar, mostrar seus pontos de vistas, além disso, nas atividades avaliativas os discentes não ficam com o mesmo peso de uma avaliação, onde geralmente ficam nervosos. Assim a pesquisa pretende utilizar as Inteligências Múltiplas de Gardner para o ensino e aprendizagem na disciplina de Física.

Effects of the evidence-based history teaching on Turkish primary students’ perception of history and related concepts

In this chapter, we present illustrations of second grade students’ reasoning about patterns and two-part function rules in the context of an early algebra research project that we have been conducting in elementary schools in Toronto and New York City. While the study of patterns is mandated in many countries as part of initiatives to include algebra from K-12, there is a plethora of evidence that suggests that the route from patterns to algebra can be challenging even for older students. Our teaching intervention was designed to foster in students an understanding of linear function and co-variation through the integration of geometric and numeric representations of growing patterns. Six classrooms from diverse urban settings participated in a 10–14-week intervention. Results revealed that the intervention supported students to engage in functional reasoning and to identify and express two-part rules for geometric and numeric patterns. Furthermore, the students, who had not had formal instruction in multiplication prior to the intervention, invented mathematically sound strategies to deconstruct multiplication operations to solve problems. Finally, the results revealed that the experimental curriculum supported students to transfer their understanding of two-part function rules to novel settings.

The objective of this research was to evaluate the level of knowledge about adolescence, pubertal development and sexuality among adolescents from 10 to 14 years old at municipal public schools in Feira de Santana-Bahia, 2000. Cross-sectional study, with a randomized and proportional sample out of a population of 6,419 students in the municipal Public System. The level of knowledge was analyzed according to age, sex and educational level. Data was collected by means of a specific confidential questionnaire, which was pre-tested. A scale of values (score--satisfactory, reasonable and unsatisfactory) was established according to the percentage and proportional number of right answers regarding general and specific topics. Statistical inference was calculated by chi-square with a significance of 5% as well as the bivariate and multivariate analysis, calculating the simple and adjusted prevalence, through stratified analysis. Adolescents showed unsatisfactory level of information about terms, particularly those at the age of 10 (69.2%) and 11 years (70.6%), female (61.7%) and the ones in the 4th (82.8%) and 5th (61.1%) grades. The level of knowledge according to sex, adjusted by age and educational level, showed that females are 1.3 and 1.27 times more likely to present an unsatisfactory level of knowledge than males. The level of knowledge according to educational level, adjusted by age, showed that those subjects between 4th and 5th grades are 2.32 times more likely to present an unsatisfactory level of knowledge if compared to students of 6th and 8th grades, with significant differences (p<0.05). The high prevalence of unsatisfactory level of knowledge with significant association between 4th and 5th grades and females points to the necessity of educative actions regarding health and sexuality in the beginning of adolescence at municipal public schools.

Como crítica à perspectiva da Educação Física Escolar voltada à aptidão física e ao desenvolvimento técnico-esportivo, a partir da década de 1980 surge o Movimento Renovador. Ao longo dos anos, essas propostas foram incorporadas aos cursos de formação e aos documentos oficiais de ensino. Era de se esperar que as aulas representassem as propostas desse movimento, mas paradoxalmente temos visto intervenções difusas e até aleatórias, muitas vezes representadas pelo “rola a bola”. Diante da necessidade de investir em práticas inovadoras e a fim de abolir o caráter de estudos que apenas promovem denúncias, este estudo buscou professores que, alinhados ao movimento renovador, procuram desenvolver aulas que se aproximam e representam tais propostas. Assim, buscou-se investigar a influência do movimento renovador na intervenção pedagógica de 3 professores de Educação Física da rede municipal de ensino do Rio de Janeiro. Utilizou-se uma ficha de observação sistemática composta por indicadores didático-metodológicos. Conclui que o grupo analisado parece ter superado o esporte como conteúdo hegemônico da Educação Física, além disso, os dados revelam possibilidades de contextualização dos conteúdos da cultura corporal valorizando a diversidade, identidade e patrimônio cultural dos estudantes como possibilidade de formação cidadã.&#x0D;

O presente artigo tem como objetivo, investigar as contribuições do uso do Facebook mediante uma intervenção pedagógica nas aulas de Química, com alunos da 2ª série do Ensino Médio, de uma escola Estadual da Zona Norte da cidade de Manaus - AM. A pesquisa fez uso da Fanpage, criando-a para os alunos discutirem, postarem e tirarem dúvidas sobre os conteúdos de Química, visto que a partir dos registros, constatou-se algumas das dificuldades encontradas pelos alunos em entender os conteúdos deste componente curricular eram devido às aulas monótonas, o que justificava a falta de estímulo e interesse deles. Após a intervenção pedagógica, com o uso do Facebook nas aulas apurou-se, por meio das falas dos alunos, que a aprendizagem dos conteúdos foi satisfatória, uma vez que auxiliou o professor, e a eles próprios, que puderam tirar dúvidas e interagir nos fóruns, enviando vídeos e perguntas sobre os conteúdos estudados, contribuindo para o maior envolvimento de todos. Evidenciou-se que o uso das redes sociais, no caso o Faceboock, pode ser utilizado para analisar e resolver questões e exercícios de conteúdo programático, solucionando as dúvidas de maneira mais rápida, havendo a troca de conhecimento e informação. Destaca-se nesta pesquisa a importância na relação entre aluno e professor, e a necessidade de estimular a livre expressão dos discentes e o uso dos aplicativos e softwares para o seu processo educativo, em todas as disciplinas.

Undergraduate students in introductory biology classes are typically saddled with pre-existing popular beliefs that impede their ability to learn about biological evolution. One of the most common misconceptions about evolution is that the environment causes advantageous mutations, rather than the correct view that mutations occur randomly and the environment only selects for mutants with advantageous traits. In this study, a significant gain in student understanding of the role of randomness in evolution was observed after students participated in an inquiry-based pedagogical intervention based on the Luria-Delbruck experiment. Questionnaires with isomorphic questions regarding environmental selection among random mutants were administered to study participants (N = 82) in five separate sections of a sophomore-level microbiology class before and after the teaching intervention. Demographic data on each participant was also collected, in a way that preserved anonymity. Repeated measures analysis showed that post-test scores were significantly higher than pre-test scores with regard to the questions about evolution (F(1, 77) = 25.913, p < 0.001). Participants' pre-existing beliefs about evolution had no significant effect on gain in understanding of this concept. This study indicates that conducting and discussing an experiment about phage resistance in E. coli may improve student understanding of the role of stochastic events in evolution more broadly, as post-test answers showed that students were able to apply the lesson of the Luria-Delbruck experiment to other organisms subjected to other kinds of selection.

Writing skills are one of the important competencies in learning Indonesian as a foreign language, especially in international school environments such as Nida Suksasat School, Thailand. This study aims to analyse language errors in grade X students' writing and identify the factors that cause these errors. This study uses a descriptive qualitative approach with data collection techniques through documentation of student writing results, interviews with subject teachers, and observations of learning activities in the classroom. Data were analysed by classifying errors based on linguistic aspects, namely phonology, morphology, syntax, and semantics. The study results showed that the most common errors were related to spelling, sentence structure, and improper punctuation. In addition, errors were found in word choice and paragraph arrangement that were less coherent, thus disrupting the logical flow of the writing. The factors that cause these errors include interference from the mother tongue (Thai), limited mastery of Indonesian vocabulary, and minimal structured writing practice in class. The lack of interactive learning media, varied learning resources, and a less contextual teaching approach also contributes to students' low writing skills. Based on these findings, the researcher recommends strengthening the learning of language basics through directed writing exercises and applying teaching strategies that are more communicative, contextual, and appropriate to the background of foreign students. In conclusion, systematic, sustainable, and student-needs-based pedagogical interventions are needed to improve writing skills in international schools' learning of Indonesian as a foreign language.

This study aimed to investigate the performance and common errors of fifth grade students in equivalent fractions. The study was conducted with 435 fifth grade students from two different middle schools in Salihli, which is a district of Manisa province, in the spring semester of the 2021 – 2022 academic year. In the study, survey design, one of the descriptive research models, was used. As a data collection tool, a test was developed by the researchers. Equivalent Fractions Knowledge Test, which consists of six open – ended questions, was administered to all fifth grade students at once. Students’ responses were analysed with descriptive statistical methods (frequency and percentage values). According to the results, the overall performance of students in the test was low. It was observed that the students showed the highest performance in a question which includes area model, and the lowest performance in a question given in context which includes set model. Additionally, the most common error was that students consider multiplying a fraction by 2 and expanding it by 2 as the same algorithm while they also think similarly dividing a fraction by 2 and simplifying it by 2 as the same algorithm.

This study was carried out with the purpose of researching the causal attributions of literacy teachers from municipal and state schools in the outskirts of Uberlândia, MG, in relation to their students' academic failure in literacy, using a qualitative instrument to survey causal attributions about their students' academic failure (Study 1), and a standardized instrument for attributing causality in hypothetical situations of success or school failure (Study 2). For this purpose, 4 teachers from a municipal school and 11 teachers from a state school were interviewed (Study 1), the standardized Causality Assignment instrument was applied to 24 teachers from municipal schools and 27 teachers from state schools, whose responses were submitted to analysis of variance and the Duncan's test. The main results of Study 1 that, when focused on municipal and state schools, compared teachers □ ro n tn a m more internal causes to explain the first accentuate uwx2 school failure, while the latter place more emphasis on external causes. In relation to Study 2, the causes related to stable effort were more valued, both in situations of success and in relation to failure, with no significant differences between teachers in the state and in the municipality. These results point to the need to better understand and research the causal attribution processes of teachers regarding the students' expectations of success or failure, in order to minimize the selectivity of teaching observed in the initial grades of the program elementary School.

Abstract: The aim of the research was to determine the effect of learning models on mathematics achievement viewed from the student self-regulated learning. The learning models compared were MURDER (Mood Understand Recall Detect Elaborate Review) using RME (Realistic Mathematics Education) approach, MURDER, and direct learning. This study was a quasi-experimental research. The population of this study was students in grade XI science of Senior High School in Ponorogo on academic year 2015/2016. Instruments used were mathematics achievement test and questionnaire. Two ways anova with 3x3 of factorial design and significance level 0,05 are used for hypothesis test. The conclusions of the research were as follows. (1) MURDER RME gives better achievement than MURDER and direct learning, and MURDER gives the same achievement as direct learning, (2) students with high self-regulated learning has the same achievement as those who has middle self-regulated learning. Students who have high and middle self-regulated learning have better achievement than low self-regulated learning, (3) in the MURDER RME and MURDER, students who have high, middle, and low self-regulated learning have the same achievement. In the direct learning, students who have high self-regulated learning have the same achievement as those who have high and low self-regulated learning, and students who have high self-regulated learning have better achievement than those students who have low self-regulated learning, (4) for high self-regulated learning, MURDER RME produces better achievement than MURDER; MURDER RME and MURDER produce the same achievement as direct learning. For middle and lowself-regulated learning, MURDER RME, MURDER, and direct learning produce the same achievement which is categorized as good. Keywords: MURDER, RME, Self-Regulated Learning

ABSTRACTThe objective of this study was to determine whether the incorporation of group work in a teaching intervention can effectively foster students’ critical thinking skills. Building upon Kuhn’s critical thinking model, the research involved comparison of pretest and post-test results for 140 secondary four (10th grade) students in Hong Kong on two measures of critical thinking ability and investigation of their engagement in argumentative dialogues. The findings illustrate the efficacy of group work, relative to whole-class instruction, in helping students develop critical thinking. In addition, the findings highlight the efficacious role of the teacher in breaking the deadlocks that may arise during small-group debates.