Analysing Probability Teaching Practices in Primary Education: What Tasks Do Teachers Implement?

This study analyses probability tasks proposed by primary education teachers to promote probabilistic literacy. To this end, eight class sessions at various levels of the Chilean educational system were recorded on video and analysed through the ”probability tasks” dimension from the “Observation Instrument for Probability Classes” (IOC-PROB), which includes five components: use of resources, probabilistic contexts, cognitive challenge, procedures and strategies, and probability meanings. The results show that probability tasks focus mainly on technical knowledge, causing the probability class to become an arithmetic class in which only formulas are applied, mechanically and with no meaning. As a result, we see no use of technological resources, a low use of physical materials, and an absolute predominance of solving decontextualised exercises. We conclude that it is necessary to enhance the probability teaching practices based on lesson plans that consider a wide variety of resources and contexts to gradually advance towards a representation of probabilistic knowledge that relies on conventional procedures and notations.

Conhecimento Profissional de Professores dos Anos Iniciais do Ensino Fundamental Sobre Espaço Amostral e Quantificação de Probabilidades

ResumoNeste texto, discutiu-se parte de uma investigação de Doutorado que teve o objetivo de analisar o desenvolvimento profissional de professores que lecionam Matemática para os Anos Iniciais do Ensino Fundamental em seu trabalho com Probabilidade. Para este artigo, focou-se nos conhecimentos dos participantes referentes à compreensão de espaço amostral e quantificação de probabilidades, manifestados em uma tarefa proposta durante uma formação. Adotando uma metodologia qualitativa, procurou-se descrever e interpretar as resoluções, registradas nos protocolos dos professores, e suas discussões, coletadas em vídeos e áudios gravados. Analisou-se os resultados à luz de teorias e investigações a respeito do ensino e da aprendizagem de Probabilidade e do conhecimento matemático para o ensino da temática. As resoluções, as discussões e as reflexões acerca das noções probabilísticas implicadas na situação analisada desenvolveram e ampliaram os Conhecimentos Comum de Conteúdo e também os Conhecimentos Especializados dos professores, o que, certamente, permitir-lhes-á, no ensino, antecipar erros de seus alunos, identificar possíveis causas, justificá-las do ponto de vista da Matemática e, consequentemente, buscar estratégias de intervenção que favoreçam sua compreensão e sua aprendizagem. Ressaltou-se, nesse processo de desenvolvimento e/ou ampliação dos conhecimentos, a importância de cursos de formação que conduzam à reflexão de questões ligadas tanto ao ensino como à aprendizagem, neste caso, de conceitos matemáticos e, mais especificamente, de noções probabilísticas com crianças em fase inicial de escolarização. Palavras-chave: Formação Contínua. Conhecimento Profissional Docente. Anos Iniciais do Ensino Fundamental. Ensino de Probabilidade. AbstractIn this text, it is discusses part of a Doctoral investigation which aimed analyzing the teachers professional development that teach Mathematics for Elementary School Initial Series, on its work with Probability. For this article, we focused on the participants’ knowledges regarding the comprehension of sample space and probabilities quantification, expressed in a purposed during a formation. Adopting a qualitative methodology, it was aimed to describe and interpret the resolutions, registered in the teachers protocols and their discussions collected in recorded videos audio. The results were analyzed based on theories and investigations regarding the Probability teaching and learning and the mathematical knowledge for the thematic teaching. The resolutions, the long discussions and lots of reflection about the probabilistic notions implied in the analyzed situation, have developed and amplified the teachers´ Content Common Knowledge as well as the Specialized Knowledges, what certainly will enable them to anticipate mistakes from their students, identify possible causes, justify them from the Mathematics point of view and, consequently, look for interventional strategies that promote the comprehension and learning. Iin this process, the knowledge development and/or amplification, the importance of formative courses that take the reflection of issues related to both teaching and learning, in this case, the mathematical concepts and, more specifically, the probabilistic notions whith children in schooling initial phase. Keywords: Continuous Formation. Teacher Professional Knowledge. Elementary School Initial Series. Probability Teaching.

The Teaching Proposal of Probability in a Brazilian Elementary School Textbook Collection

We present in this article the analysis of the probability teaching proposal ofa textbook collectionused in the initial years of Brazilian elementary school, approved by the National Program of Textbooks (PNLD) in 2016. This work is related to the study group of Didactics of the Mathematics (DDMat). As a theoretical and methodological contribution, we used the anthropological theory of didactic, developed by Yves Chevallard and collaborators, that allows us to model and analyze the choices regarding mathematics and didactics present in the teaching of probability in the collection adopted. By the production and analysis of data, we noticed that some notions regarding probability were proposed from the volume referring to the second year of elementary school, in activities about possibilities. The formalization of the probability concept was presented in the last volume of the collection with activities associated with the idea of ​​fraction, ratio and percentage.

PENGEMBANGAN PERANGKAT PEMBELAJARAN STATISTIKA DAN PELUANG DENGAN METODE PENEMUAN TERBIMBING BERORIENTASI KURIKULUM 2013 UNTUK SISWA KELAS X

Tujuan penelitian ini adalah menghasilkan perangkat pembelajaran statistika dan peluang untuk siswa SMA kelas X semester 2 dengan metode penemuan terbimbing yang terdiri atas RPP, LKS, dan instrumen penilaian yang memenuhi kriteria valid, praktis, dan efektif. Model pengembangan dalam penelitian ini adalah model 4D, terdiri atas tahap pendefinisian, perancangan, pengembangan, dan penyebaran. Analisis data kevalidan dan kepraktisan dilakukan dengan cara mengkonversi data kuantitatif berupa skor hasil penilaian menjadi data kualitatif skala lima. Analisis data keefektifan dilakukan dengan cara menentukan persentase ketuntasan belajar siswa berdasarkan hasil tes dan angket. Hasil validasi menunjukkan bahwa RPP yang dikembangkan memperoleh kategori baik, sedangkan LKS dan instrumen penilaian yang dikembangkan mencapai kategori sangat baik. Hasil observasi keterlaksanaan pembelajaran menunjukkan bahwa keterlaksanaan pembelajaran statisika mencapai 94,12% sedangkan peluang mencapai 84,29%. Berdasarkan hasil tes dan angket, perangkat pembelajaran termasuk dalam kriteria efektif.Kata Kunci: perangkat pembelajaran, penemuan terbimbing, statistika, peluang. DEVELOPING STATISTICS AND PROBABILITY TEACHING KIT WITH GUIDED DISCOVERY LEARNING METHOD ORIENTED TO CURRICULUM 2013 FOR GRADE X AbstractThis research aimed to produce statistics and probability teaching kit for grade X students of Senior High School in 2nd semester with guided discovery learning consist of lesson plans, student worksheets, and assessment instruments which valid, practical, and effective. The developing model in this research was 4D model consist of define, design, develop, and disseminate. Validity and practicality were analyzed by converting the actual scores obtained into five scales of qualitative data. Effectiveness analyzed by determining the percentage of students’ completeness in a test and in the questionnaires. Validation result shows that the lesson plans have good category, the student worksheet and the assessment instrument have very good categories. The result of the application shows that the statistics application was 94,12% than the probability application was 84,29%. Based on the test and questionnaires result, the teaching kit was in effective term.Keywords: teaching kit, guided discovery, statistics, probability