The Effects of a Professional Development Program for Technology Integrated Algebra Teaching

This study examined technological pedagogical content knowledge change of middle school mathematics teachers who participated in a professional development program designed to integrate technology into teaching algebra. Twenty-eight middle school teachers from 20 different schools participated in the study. The data collection tools were technological pedagogical content knowledge survey, reflective journals, lesson plans, and program evaluation forms. The data analysis showed that the participants’ technological pedagogical content knowledge increased significantly. In addition, participants wrote lesson plans that included effective use of technology to teach algebra contents. The positive effects of the professional development program seem to be related to the following components of the program: the usability of the program activities in middle school classrooms, program’s focus on using technology in teaching algebra, the introduction of new technological tools and software related to mathematics, and the interactive nature of the program.

From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations

The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to algebra and giving more prominence to conversions among different representation registers than treatments as simplifications and expansions. Nowadays, the daily practice in teaching algebra is still influenced by the traditional approach, and there is a need to offer teachers examples of activities that can give meaning to algebraic computations. This study proposes a set of interactive activities for eighth grade students, with a functional approach to formulas in a geometric context. The goal of the study is to investigate how similar activities can help students to develop multiple approaches to problems, understand algebraic formulas, and discern which main problems they face. The activities were tested with about 300 students, and qualitative and quantitative data were analyzed to answer the research questions.

Learning opportunities experienced by mathematics teachers: unveiling actions and role of the teacher educator during a formative process

Context: One of the research challenges related at the professional learning of mathematics teachers is to understand the importance of the role and actions of the teacher educator during a formative process. Objective: This research seeks to understand what the role was and how the actions of the teacher educator took place, in a process of continuing education with teachers of basic education, about the teaching of patterns and regularities, with a view to providing learning opportunities to the teachers involved. Design: It is a qualitative-interpretative study aligned to an intervention research. Settings and Participants: We developed the research in a formative process involving 33 mathematics teachers and future teachers, and 3 teacher educators. Data collection: We use data from audio and video recordings of planning and enacting of the formative process, and protocols from teachers’ tasks and planning from teacher educators. Results: We found that teacher educators, since planning the formative process, sought to provide opportunities for participating teachers professional learning, since he/she structured the process through professional learning tasks, using videos of mathematics lessons to highlight the classroom practice, as well as encourage discussions among teachers about patterns and regularities in and for the teaching of algebra. Conclusions: We identified that teacher educators played a mediating role in the orchestration of the discussions and an articulator between mathematics and didactics, thus providing opportunities for professional development and the learning of teaching algebra.

Problematika Guru dalam Mengajar Materi Aljabar di Era Pandemik Coronavirus Disease 2019 (Covid-19)

<p class="06IsiAbstrak">Keharusan dalam pelaksanaan pembelajaran <em>online</em> yang disebabkan oleh pandemik Covid-19 menimbulkan munculnya masalah-masalah dalam pembelajaran matematika khususnya materi aljabar. Penelitian ini bertujuan untuk mengetahui problematika yang dihadapi guru dalam mengajarkan materi aljabar di era pandemik Covid-19. Metode penelitian menggunakan penelitian kualitatif deskriptif. Sumber data berasal dari tujuh guru matematika Sekolah Menengah Pertama (SMP) di Kudus dan Tangerang yang memberikan jawaban atas pertanyaan dalam google form. Hasil penelitian ini menunjukkan problematika yang dialami guru dalam mengajar materi aljabar di era pandemik Covid-19 adalah keterbatasan alat penunjang pembelajaran sehingga guru sulit menerangkan penerapan operasi hitung aljabar, soal aplikasi aljabar, dan menyederhanakan bentuk aljabar secara <em>online</em>. Terbatasnya ruang dan waktu, jaringan internet yang tidak stabil serta kuota yang tidak memadai mengakibatkan interaksi antara guru dan siswa tidak dapat optimal dilakukan.</p><p class="06IsiAbstrak"> </p><p class="06IsiAbstrak"><span lang="IN">The necessity of implementing online learning caused by the Covid-19 pandemic has created problems in learning mathematics, especially algebraic material. This study aims to find out the problems faced by teachers in teaching algebra material in the Covid-19 pandemic era. The research method uses descriptive qualitative research. Sources of data came from seven junior high school mathematics teachers (SMP) in Kudus and Tangerang who provided answers to questions in the google form. The results of this study indicate that the problems experienced by teachers in teaching algebra material in the Covid-19 pandemic era are the limitations of learning support tools so that teachers find it difficult to explain the application of algebraic arithmetic operations, algebra application questions, and simplify algebraic forms online. Limited space and time, unstable internet networks, and inadequate quotas have resulted in the interaction between teachers and students not being optimal.</span></p>

Diseño de una app como herramienta de apoyo para la enseñanza-aprendizaje del álgebra básica

Algesquares is an innovative method based on the algebraic tiles created by Caleb Gattegno, which seeks a more dynamic student experience, instead of teaching algebra by the traditional method. The present work aimed to present the design of an application that functions as a teaching tool for students and teachers, in Basic Algebra topics, through a board with colored cards marked with a positive and negative sign that solve issues such as reduction of terms like, multiplication, factoring, etc. Students will be the protagonists of their own learning and will play an active role in and out of the classroom, obtaining points through solving interactive algebraic exercises, increasing levels and difficulty. Algesquares, seeks to capture the student's attention, motivate and interest them, encouraging students to be self-taught, advancing in the application gradually and advancing at their own pace, building meaningful learning in students, developing mathematical skills, knowledge and skills, to continue their school training.

Virtual Manipulatives for Teaching Algebra: A Research-to-Practice Guide for Secondary Students with a Learning Disability

Many forms of assistive and instructional technology exist to support secondary students in mathematics education. Classroom technology provides particular benefits to students who frequently struggle learning academic content such as procedural and conceptual skills in algebra. One tool studied in mathematics to support the needs of students with or at-risk for a mathematics learning disability is virtual manipulatives. Research shows virtual manipulatives support cognition by providing visual representations of mathematical concepts and are an age appropriate technology solution for secondary students that promote autonomy inside and beyond the classroom setting. The aim of this article is to highlight research on virtual manipulatives for secondary students with a learning disability in mathematics and discuss techniques for teachers to incorporate these tools into their classrooms to support students.

As mudanças geradas pela Base Nacional Comum Curricular na abordagem do pensamento algébrico nos anos iniciais do Ensino Fundamental

ResumoEste artigo trata de uma pesquisa bibliográfica que tem por objetivo analisar dissertações e teses que investigaram o pensamento algébrico nos anos iniciais do Ensino Fundamental. O referencial teórico salienta um modelo dominante de ensino da Álgebra reduzido a uma Aritmética generalizada no Ensino Fundamental, que será bruscamente algebrizado no Ensino Médio. E na atual proposta da BNCC temos a algebrização do currículo desde os anos iniciais. Foram adotadas algumas palavras chave relacionadas ao pensamento algébrico para o levantamento dos trabalhos no banco de teses e dissertações da Coordenação de Aperfeiçoamento de Pessoal do Nível Superior (Capes). Em relação ao tema pensamento algébrico nos anos iniciais do Ensino Fundamental, foram encontrados onze trabalhos sobre sequências didáticas ou a produção escrita dos alunos e dois trabalhos sobre o professor dos anos iniciais. E podemos dizer também que nenhum dos estudos está relacionado à análise de materiais didáticos e existe, nesse levantamento, apenas um trabalho envolvendo a BNCC. Palavras-chave: Pensamento algébrico; Anos Iniciais; BNCC.AbstractThis article refers to a bibliographic research that aims to analyze dissertations and thesis that investigated algebraic reasoning in the early years of Elementary School. The theoretical framework highlights a dominant model of teaching Algebra reduced to a generalized Arithmetic in Elementary School, which will be sharply algebraized in High School. And the current proposal of the Base Nacional Comum Curricular (BNCC) (National Common Curricular Base) present an algebraized curriculum since the early years. Some keywords related to algebraic reasoning were adopted to survey the work in the thesis and dissertation database of the Coordenação de Aperfeiçoamento de Pessoal do Nível Superior (Capes) (Coordination for the Improvement of Higher Education Personnel). Regarding the theme algebraic reasoning in the early years of Elementary School, eleven works were found on didactic sequences or the student’s' written production and two works on the teacher of the early years. And we can also say that none of the studies is related to the analysis of teaching materials and there is, in this survey, only one work involving BNCC.Keywords: Algebraic reasoning; Elementary Education; BNCC.