Mathematical problem solving in didactic institutions as a complex system

Pichat, Michaël; Ricco, Graciela

doi:10.1016/s0732-3123(01)00061-x

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…Berikut ini adalah berbagai kesulitan yang merupakan masalah umum dalam pembelajaran kalkulus; (1) konsep bilangan tak hingga (Tall, 2001), (2) menggambar grafik (Pichat & Ricco, 2001), (3) manipulasi aljabar (Aspinwall & Miller, 2001), (4) konsep limit fungsi (Tall & Vinner, 1981;Williams, 1991;Cornu, 1991;Szydlik, 2000;Juter, 2005;Naidoo & Naidoo;2007;Susilo, 2011;Syaripuddin, 2011;Denbel, 2014), (5) konsep limit dan kekontinuan fungsi (Bezuidenhout, 2001;Karatas et al, 2011), (6) memahami konsep turunan fungsi (Tarmizi, 2010;Tall, 2010;2012;Pepper et al, 2012;Hashemi et al ;, dan (7) konsep integral fungsi (Orton, 1983;Tall, 1993;Kiat, 2005;Metaxas, 2007;Yee & Lam, 2008;Mahir, 2009;Rubio & Gomez-Chacon, 2011;Usman, 2012;Salazar, 2014;Zakaria & Salleh, 2015;Serhan, 2015;Yudianto, 2015;Ferrer, 2016). Berbagai jenis kesulitan yang dialami oleh para mahasiswa ini akan berdampak pada hasil belajar dan juga pada kemampuan mahasiswa untuk berpikir secara logis, analitis, sistematis, kritis, dan kreatif.…”

Section: Unnes Journalsunclassified

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

Susilo

Darhim

Prabawanto

2019

Kreano

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Penelitian ini bertujuan untuk mendeskripsikan kesulitan belajar yang dialami mahasiswa pada materi aplikasi integral untuk luas daerah dalam perspektif disposisi matematis. Penelitian ini menggunakan metode deskriptif eksploratif dengan instrumen skala, tes, dokumentasi, dan catatan lapangan. Data diambil dari 80 mahasiswa dari program studi S1 pendidikan matematika di sebuah universitas di Jawa Tengah. Hasil penelitian menunjukkan bahwa mahasiswa dengan disposisi matematis positif sedang dan tinggi memiliki jenis kesulitan yang sama yaitu (1) kesulitan dalam menggambar grafik, (2) kesulitan dalam menentukan daerah yang dicari luasnya, (3) kesulitan dalam menentukan batas integral, (4) kesulitan dalam menggunakan rumus integral, dan (5) kesulitan dalam memahami integral. Mahasiswa dengan disposisi matematis positif rendah selain mengalami kelima kesulitan tersebut, juga mengalami kesulitan dalam menghitung integral. Terdapat tren atau kecenderungan peningkatan persentase pada 2 jenis kesulitan, dan penurunan persentase pada 1 jenis kesulitan, sedangkan pada 3 jenis kesulitan yang lain bersifat fluktuatif.The purpose of this research was to described the learning difficulties experienced by students in integral application material for the area in the perspective of mathematical dispositions. This research used descriptive exploratory methods with scale, tests, documentation, and field notes instruments. Data was taken from 80 undergraduate students from the mathematics education study program at a university in Central Java. The results showed that students with moderate and high positive mathematical dispositions had the same types of difficulties, namely (1) difficulties in drawing graphics, (2) difficulties in determining the area to be searched for, (3) difficulties in determining integral boundaries, (4) difficulties in using integral formulas, and (5) difficulties in understanding integrals. Students with low positive mathematical dispositions in addition to experienced these five difficulties, also experienced difficulties in calculating integrals. There is a trend or tendency to increase percentage in 2 types of difficulties, and a decrease in percentage in 1 type of difficulty, while in 3 other types fluctuating.

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Section: Unnes Journalsunclassified

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

Susilo

Darhim

Prabawanto

2019

Kreano

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“…The commonly pursued line of research on the assessment of students' mathematical thinking about derivative addressed how secondary (e.g. Pichat & Ricco, 2001) and/or undergraduate (e.g. García, Llinares & Sánchez-Matamoros, 2011) students think about the differentiation situation by documenting and/or representing their mathematical ideas, particularly using open-ended tasks in the instruments.…”

Section: Introductionmentioning

confidence: 99%

The Thinking-About-Derivative Test for Undergraduate Students: Development and Validation

Aydın

Ubuz

2014

Int J of Sci and Math Educ

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Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises 6 mathematical thinking aspects, enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, demonstrates acceptable levels of reliability and validity. Followed by additional cross-validation studies, the TDT may be a useful tool for mathematics education researchers and mathematicians. Directions for future research and implications for educational practice are discussed.

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“…It was the idea that what we call knowledge does not and cannot have the purpose of producing representations of an independent reality… (Glaserfeld, 2005, p. 3) Putting aside the constructivist appropriation to Piaget, it is at least clear many have tried to develop it in relation to Vygotsky in order to emphasize peer collaboration. Pichat and Ricco (2001), psychologists at the University Paris 8, noted that there are three poles in the classroom: the student, teacher and knowledge. For Vygotsky, upon whom they rely, cognitive mediation (contractual expectations) is the main factor in understanding (Piachat & Ricco, 2001).…”

Section: Introductionmentioning

confidence: 99%

Constructivism and Peer Collaboration in Elementary Mathematics Education: The Connection to Epistemology

Gupta

2008

EURASIA J MATH SCI T

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In this paper, an attempt is made to determine if peer collaboration increases student achievement in teaching elementary mathematics. Empirical evidence and philosophical problems with constructivist epistemology are considered. Two things are argued: first, it is reasonable to think, for elementary mathematics, peers collaboration is useful (especially in heterogeneous groups). Peer collaboration is an appendage to instruction, not a replacement for the didactics of an expert, or individual problem solving (which occurs both at its inception, when mathematics is discovered as well as advanced levels). There is reciprocity between individual and social settings in learning mathematics. Second, for the teaching of mathematics an adequate epistemology will guide, to some extent, a successful pedagogy.

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Mathematical problem solving in didactic institutions as a complex system

Cited by 5 publications

References 20 publications

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

The Thinking-About-Derivative Test for Undergraduate Students: Development and Validation

Constructivism and Peer Collaboration in Elementary Mathematics Education: The Connection to Epistemology

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