Book Review: Adding depth to portraits of mathematical inquiry Karin Brodie (2010) Teaching mathematical reasoning in secondary school classrooms

2011 ◽  
Vol 79 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Victoria Hand
Keyword(s):  
Secondary School ◽  
Mathematical Reasoning ◽  
Mathematical Inquiry

Analisis Kemampuan Penalaran Matematis Mahasiswa Calon Guru Matematika Sebagai Kajian Evaluasi

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Hanifah Nurus Sopiany
Keyword(s):  
High School Students ◽  
Secondary School ◽  
Mathematical Reasoning ◽  
Mathematics Learning ◽  
Good Reason ◽  
School Level ◽  
Real Analysis ◽  
Reasoning Ability ◽  
School Students ◽  
Secondary School Level

Penalaran matematis menggunakan pola pikir logis dalam menganalisa suatu masalah yang nanti pada akhirnya akan ditandai dengan aktivitas menyimpulkan atas masalah tersebut. Seseorang yang memiliki penalaran yang baik, tentunya akan berhati-hati dalam bertindak dan memutuskan sesuatu. Materi-materi pada kalkulus merupakan materi yang ada pada tingkat sekolah menengah yang nantinya menjadi lahan mengajar mahasiswa calon guru matematika S-1. Kemampuan penalaran yang dikaji mempengaruhi pembelajaran mahasiswa kedepannya karena berlaku pada matakuliah lanjut, contohnya pada kemampuan pembuktian akan selalu digunakan pada matakuliah persamaan diferensial, struktur aljabar, analisis  vektor, analisis real, dll. Sedangkan sebagai calon guru yang nantinya mengajar pada tingkat sekolah menengah, maka kemampuan penalaran ini menjadi salah satu capaian pembelajaran matematika bagi siswa sekolah menengah, maka oleh karena itu guru yang mengajarnya haruslah memiliki kemampuan penalaran yang baik. Analisis kesalahan sangat penting untuk melakukan evaluasi dan refleksi pada struktur soal maupun pada perlakuan dalam pembelajaran dalam upaya memperbaiki kemampuan penalarannya.   Mathematical reasoning uses a logical mindset in analyzing a problem that will eventually be marked by concluding activity on the problem. Someone who has good reason, will certainly be careful in acting and deciding something. The material content on the calculus is the material that exists at the secondary school level which will become the field of teaching the prospective master of math teacher bachelor. The reasoning ability studied influences student learning in the future as it applies to advanced courses, for example in the ability of proof will always be used in the course of differential equations, algebraic structure, vector analysis, real analysis, etc. While as a teacher candidate who will teach at the secondary school level, then this reasoning ability becomes one of the achievements of mathematics learning for high school students, therefore teachers who teach it must have good reasoning ability. Error analysis is very important to evaluate and reflect on the problem structure as well as on the treatment in learning in order to improve the reasoning ability.

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

The Effectiveness of Collaborative Learning In The Teaching of Form Four Mathematical Reasoning

2011 ◽  
Author(s):  
Hong Kian Sam ◽  
Geok Shim George Tan
Keyword(s):  
Collaborative Learning ◽  
Secondary School ◽  
Teaching Methods ◽  
Instructional Methods ◽  
Mathematical Reasoning ◽  
Gender Effects ◽  
Control Group ◽  
Learning Group ◽  
Learning Mathematics ◽  
Based Instruction

Pembelajaran kolaboratif merujuk kepada organisasi bilik darjah di mana pelajar bekerjasama dalam kumpulan yang kecil melakukan aktiviti yang dikongsikan tetapi mempunyai matlamat yang sama. Kajian ini mengkaji keberkesanan pembelajaran kolaboratif dalam pengajaran topik “Penaakulan Matematik” tingkatan empat dan kesan jantina kepada keberkesanan kaedah pengajaran ini di sebuah sekolah menengah kerajaan Malaysia. Kajian ini juga melihat kesan jantina ke atas minat pelajar terhadap pembelajaran matematik dan persepsi kepada kaedah pengajaran. Kajian ini dijalankan menggunakan kajian berbentuk ujian pra–pasca kuasi–eksperiment dengan satu kumpulan kajian dan satu kumpulan kawalan. Kajian ini menggunakan dua kelas di sebuah sekolah menengah kerajaan di Kuching, Sarawak, Malaysia. Kelas kajian telah diajar menggunakan pembelajaran kolaboratif manakala kelas kawalan telah diajar menggunakan pembelajaran secara lisan. Alat ukur kajian adalah ujian pra, ujian pasca dan borang soal selidik. Keputusan kajian menunjukkan kumpulan pembelajaran kolaboratif menunjukkan keputusan yang lebih baik berbanding dengan kumpulan pembelajaran tradisional. Tambahan pula. pelajar perempuan mendapat keputusan yang lebih baik jika dibandingkan dengan pelajar lelaki dalam kedua–dua kaedah pengajaran. Majoriti pelajar juga lebih gemar pembelajaran kolaboratif dan kumpulan kolaboratif menunjukkan minat yang tinggi dalam pembelajaran matematik. Akan tetapi, keputusan menunjukkan bahawa tiada kesan jantina terhadap kaedah pengajaran, minat pelajar terhadap pembelajaran matematik dan persepsi kepada kaedah pengajaran. Kata kunci: Kolaboratif; pembelajaran kolaboratif; keberkesanan; jantina; penaakulan Matematik Collaborative learning refers to the form of classroom organization in which students work together, in small groups, on a shared activity and with a common goal. This study focused on looking at the effectiveness of collaborative learning in the teaching of form four mathematical reasoning, and the possible effects of gender on the instructional methods in a Malaysian government secondary school. This study also looked at the gender effects on interest toward learning mathematics and perceptions of the teaching methods. The study was carried out using a pretest–posttest quasi-experiment research design with one treatment group and one control group. The study used two intact classes at a government secondary school in Kuching, Sarawak, Malaysia. The treatment class was taught using collaborative learning while the control class was taught using lecture–based instruction. The research instruments used in the study to collect data consisted of a pretest, posttest and questionnaire. The result showed that the collaborative learning group outperformed the traditional instructional group. In addition, female students obtained better results compared to male students in both of the instructional method. Majority of the students also preferred collaborative learning and collaborative learning group also showed higher interest in learning mathematics. However, the result showed that there were no gender effects on the instructional methods, interest toward learning mathematics and perceptions of the teaching methods. Key words: Collaborative; collaborative learning; effectiveness; gender; mathematical reasoning

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