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Paradigma Pembelajaran Matematika Berbasis NCTM
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Pembelajaran matematika di sekolah selayaknya sudah bergeser dari cara-cara lama. Pembelajaran matematika harus sesuai dengan kebutuhan dunia yang semakin pesat perkembanganya. NTCM sebagai organisasi/perkumpulan guru, ahli, dan praktisi pendidikan matematika yang di akui telah merumuskan 5 kemampuan dasar yang harus dimiliki anak untuk belajar matematika. Kelima kemampuan itu adalah (1) Problem Solving; (2) Reasoning and Proof; (3) Mathematical Connection; (4) Mathematical Communication; (5) Mathematical Representation. Kelima kemampuan dasar ini akan di bahas dalam buku ini, beserta contoh rancangan pembelajaran yang bisa di terapkan dalam kelas.
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... Pada pembelajaran matematika terdapat beberapa kemampuan matematis yang mesti dimiliki oleh siswa. Dalam NCTM 2000, di Amerika, disebutkan bahwa ada lima kemampuan dasar matematika yang merupakan standar yakni pemecahan masalah, penalaran dan bukti , komunikasi, koneksi, dan representasi (Maulyda, 2020). Menurut Ega Edistria "Matematika tidak hanya sekedar alat bantu berpikir, tetapi matematika juga sebagai alat komunikasi antar siswa dan antara guru dengan siswa" (Maulyda, 2020). ...
... Dalam NCTM 2000, di Amerika, disebutkan bahwa ada lima kemampuan dasar matematika yang merupakan standar yakni pemecahan masalah, penalaran dan bukti , komunikasi, koneksi, dan representasi (Maulyda, 2020). Menurut Ega Edistria "Matematika tidak hanya sekedar alat bantu berpikir, tetapi matematika juga sebagai alat komunikasi antar siswa dan antara guru dengan siswa" (Maulyda, 2020). Komunikasi matematis menurut Riyadi (2021) adalah kemampuan atau keterampilan siswa dalam mengartikan pengetahuan ke dalam bentuk bahasa simbol, grafik atau gambar, tabel, atau diagram. ...
ABSTRAKMatematika merupakan ilmu yang menjadi induk dari segala pengetahuan. Pada pembelajaran matematika terdapat kemampuan komunikasi matematis, dimana kemampuan komunikasi matematis menjadi suatu hal yang penting dalam proses pembelajaran agar siswa mampu menyatakan gagasan dengan simbol-simbol matematika, gambar, diagram serta membuat model matematika untuk menyelesaikan suatu permasalah. Tujuan dari penelitian ini mendeskripsikan kemampuan komunikasi matematis siswa SMP Plus Panumbangan dalam menyelesaikan soal-soal materi segiempat dan segitiga dengan soal berbasis Museum Bumi Alit. Penelitian ini menggunakan metode pendekatan kualitatif deskriptif. Bersifat deskriptif karena mendeskripsikan kemampuan komunikasi matematis siswa. Teknik sampling yang digunakan pada penelitian ini adalah purposive sampling. Subjek dalam penelitian terdiri dari 3 siswa dengan kemampuan awal matematis(KAM) yang berbeda dengan rincian 1 siswa KAM tinggi, 1 siswa KAM sedang dan 1 siswa KAM rendah. Hasil penelitian menyatakan bahwa siswa KAM tinggi mampu memenuhi dan menyelesaikan semua indikator kemampuan komunikasi matematis yaitu indikator Written text, Drawing dan Mathematical expressions,sedangkan siswa dengan KAM sedang mampu memenuhi dan menyelesaikan dua indikator kemampuan komunikasi matematis yaitu pada indikator Written text dan Drawing, dan siswa dengan KAM rendah hanya mampu memenuhi dan menyelesaikan satu indikator saja yaitu pada indikator Drawing.Kata Kunci : Kemampuan Komunikasi Matematis, Museum Bumi Alit, Segiempat dan Segitiga DAFTAR PUSTAKAAhmat Fatoni Rizal, Purwaningrum, J. P., & Rahayu, R. (2021). Pengembangan E-Modul Berbasis Etnomatematika Untuk Menumbuhkan Kemampuan Komunikasi Matematis Dan Minat Belajar Siswa. Koordinat Jurnal MIPA, 2(2), 1–14. https://doi.org/10.24239/koordinat.v2i2.26Bishop, A. (1994). Cultural Conflicts in Mathematics Education: Developing a Research Agenda. For the Learning of Mathematics, 14(2), 15–18.Hafidhoh, N., & Marlina, R. (2021). Kemampuan Komunikasi Matematis Siswa SMP Pada Materi Sistem Persamaan Linear Dua Variabel (SPLDV). Delta-Pi: Jurnal Matematika Dan Pendidikan Matematika, 10(1), 139–146. https://doi.org/10.33387/dpi.v10i1.2785Hasanah, R. (2018). Analisis Kemampuan Komunikasi Matematis Siswa dalam Menyelesaikan Masalah Geometri Berbasis Etnomatematika. 1–90.Kusuma, D. A. (2019). PENINGKATAN KOMUNIKASI MATEMATIS SISWA MENGGUNAKAN PEMBELAJARAN KONTEKSTUAL BERBASIS ETNOMATEMATIKA DENGAN PENERAPAN MOZART EFFECT (Studi eksperimen terhadap siswa Sekolah Menengah Pertama). TEOREMA : Teori Dan Riset Matematika, 4(1), 65. https://doi.org/10.25157/teorema.v4i1.1954Maula, I., Setyaning Pambudi, A., & Rohmah, Z. (2018). Perkembangan Matematika dalam Sejarah Peradaban Islam. Prosiding Konferensi Integrasi Interkoneksi Islam Dan Sains, 1(September), 115–119.Maulyda, M. A. (2020). Paradigma Pembelajaran Matematika NCTM. In Paradigma Pembelajaran. Mufida. (2022). Analisis kemampuan siswa pada materi segiempat dan segitiga ditinjau dari koneksimatematika (studi kasus pada siswa kelas vii smp unismuh makassar).Nurhanifah, S., Effendi, A., & Nuraida, I. (2021). Analisis Kemampuan Komunikasi Matematis Siswa Smp Melalui Pembelajaran Blended Learning Ditinjau Dari Tipe Kepribadian. J-KIP (JurnalKeguruan Dan Ilmu Pendidikan), 2(3), 111. https://doi.org/10.25157/j-kip.v2i3.6173Putri, Meilinda, L., Toto, Bara, S., & Susi, S. (2022). Analisis Kemampuan Komunikasi Matematis Dalam Menyelesaikan Masalah Pokok Bahasan Bangun Datar Segi Empat Ditinjau Dari Kecerdasan Emosional Siswa Kelas Viii-D Smp Negeri 1 Sumbermalang. Analisis Kemampuan Komunikasi Matematis Dalam Menyelesaikan Masalah Pokok Bahasan Bangun Datar Segi Empat Ditinjau Dari Kecerdasan Emosional Siswa Kelas Viii-D Smp Negeri 1 Sumbermalang,10(1), 1–52. Https://Doi.Org/10.21608/Pshj.2022.250026Riyadi, S., Noviartati, K., & Abidin, Z. (2021). Kemampuan komunikasi matematis tulis siswa Samindalam memecahkan masalah geometri. Ethnomathematics Journal, 2(1), 31–37.https://doi.org/10.21831/ej.v2i1.36192Sakti, R. K., Rahardjo, S., & As’ari, A. R. (2017). Komunikasi Matematis Siswa Dalam MenyelesaikanMasalah Persamaan dan Pertidaksamaan Linear Satu Variabel. 1(1), 419–423.Septiani, D. T., Septian, A., & Setiawan, E. (2020). Analisis Kesalahan Siswa Pada Kemampuan Komunikasi Matematis Dalam Pembelajaran Yang Menggunakan Pendekatan Saintifik. Jurnal Edukasi Dan Sains Matematika (JES-MAT), 6(2), 65. https://doi.org/10.25134/jes-mat.v6i2.2832 Solihah, S., Amam, A., & Zakiah, N. E. (2021). Meningkatkan Kemampuan Komunikasi Matematik Serta Self Confidence Siswa Dengan Menggunakan Model Brain-Based Learning Pendahuluan Kemampuan komunikasi matematik memiliki peranan yang penting untuk merefleksikan kemampuan matematik yang merupakan bagian da. Teorema: Teori Dan Riset Matematika, 6(1),48–58.Sopia, N. (2021). Kemampuan Komunikasi Matematis Siswa Terhadap Materi Persamaan Linear Satu SVariabel. Jurnal Riset Pendidikan Matematika Jakarta, 3(2), 1–7. https://doi.org/10.21009/jrpmj.v3i2.22261Sopiah, P., Erlin, E., & Amam, A. (2022). Hubungan Self Confidence Dengan Kemampuan Komunikasi Matematis Siswa. J-KIP (Jurnal Keguruan Dan Ilmu Pendidikan), 3(2), 476. https://doi.org/10.25157/j-kip.v3i2.6956Wijaya, R., Zakiah, N. E., & Sunaryo, Y. (2022). Studi Literatur: Peran Etnomatematika TerhadapPendidikan Matematika Berbasis BudayaGammanatconference.Unigal.Ac.Id, https://gammanatconference.unigal.ac.id/administrator/data_prosiding/Studi Literatur Peran Etnomatematika Terhadap Pendidikan Matematika Berbasis Budaya Lokal Di Nusantara.PdfYunita, D. (2020). Pengaruh Pembelajaran Luar Kelas dengan Teknik Scaffolding Terhadap Kemampuan Komunikasi Matematis Siswa. Jurnal Pendidikan Matematika Raflesia, 05(01), 112–126. https://ejournal.unib.ac.id/index.php/jpmr/article/view/10663
... Pembelajaran matematika tidak hanya berfokus pada pemahaman pada materi-materi matematika semata, namun juga melatih peserta didiknya untuk memiliki keterampilan bermatematika melalui proses berpikir dengan mengembangkan kemampuan matematika yang beragam (Dwirahayu et al., 2020). Seperti disebutkan dalam NCTM terdapat 5 standar kemampuan matematika yaitu kemampuan pemecahan masalah, kemampuan komunikasi, kemampuan koneksi, kemampuan penalaran, dan kemampuan representasi (Maulyda, 2020). Banyaknya kemampuan matematis yang diukur dalam pembelajaran matematika, salah satu yang menjadi fokus dalam penelitian ini yaitu kemampuan penalaran. ...
Rendahnya kemampuan penalaran matematis peserta didik sangat dipengaruhi oleh berbagai faktor baik itu faktor internal maupun faktor eksternal. Penelitian ini bertujuan untuk mengetahui faktor-faktor yang mempengaruhi terhadap kemampuan penalaran matematis peserta didik secara signifikan dan membuat model prediksi dari faktor-faktor yang teridentifikasi. Penelitian ini merupakan penelitian deskriptif kuantitatif dengan teknik analisis menggunakan Machine learning software RapidMiner. Sample dalam penelitian ini yaitu peserta didik kelas XI di SMAN 9 Tangerang Selatan sebanyak 207 responden. Data yang terkumpul dari sample dibagi menjadi data training sebagai data uji coba dan data testing sebagai data untuk menguji hipotesis. Instrumen yang digunakan berupa kuesioner terkait faktor-faktor belajar dan instrumen tes berupa butir soal uraian dengan indikator kemampuan penalaran matematis. Hasil penelitian menunjukkan bahwa, dengan menggunakan analisis chi square ditunjukkan faktor yang paling signifikan mempengaruhi kemampuan penalaran adalah kemandirian belajar. Pada analisis data training perbandingan kinerja model algoritma yang paling baik kinerjanya adalah decision tree dengan nilai akurasi sebesar 81,93%, sehingga model ini dapat digunakan dalam memprediksi data testing untuk mengetahui keakuratan antara data aktual dengan data prediksi. Selanjutnya, dengan menggunakan data testing, nilai akurasi model algoritma decision tree menjadi 78,05%, sehingga terjadi overfitting sebesar 3,88%. Namun, overfitting tersebut tidak memiliki perbedaan yang signifikan artinya kemungkinan besar belum menunjukkan overfitting yang parah. Jadi, kesimpulannya model algoritma decision tree ini cukup baik digunakan untuk menentukan faktor yang mempengaruhi kepada kemampuan penalaran matematis secara signifikan.
... In 2000, the National Council of Teachers of Mathematics (NCTM) revised the Principles and Standards for School Mathematics, continuing the global evolution of mathematics education since the 1980s (Maulyda, 2020). These revisions underscored the centrality of problemsolving in the curriculum, influenced by developmental psychology theories such as those of Piaget (Siagian, 2019), emphasizing that understanding mathematics, not mere memorization, is the primary educational objective, with the teacher serving as a facilitator. ...
Penelitian ini memfokuskan pada perbandingan pengaruh Problem Based Learning (PBL) dan Direct Instruction (DI) terhadap kemampuan pemahaman matematis peserta didik, dengan mempertimbangkan tingkat minat belajar mereka. Desain faktorial 3x2 digunakan, menggabungkan tingkat minat belajar (rendah, sedang, tinggi) dengan model pembelajaran (PBL dan DI). Hasil analisis menunjukkan perbedaan signifikan antara kedua metode pembelajaran, dengan interaksi antara metode dan tingkat minat peserta didik memengaruhi peningkatan pemahaman matematis. Peserta didik dengan minat tinggi cenderung mengalami peningkatan yang lebih signifikan. Temuan ini menekankan pentingnya responsif dan diferensiatif dalam pendekatan pembelajaran matematika, sesuai dengan kebutuhan individual peserta didik. Implikasi praktisnya adalah penyesuaian metode pembelajaran untuk mencapai hasil optimal. Studi ini memperkaya pemahaman tentang hubungan kompleks antara metode pembelajaran, minat belajar, dan pemahaman matematis. This study investigates the comparative impact of Problem-Based Learning (PBL) and Direct Instruction (DI) on students' mathematical understanding, considering their levels of interest in learning. A 3x2 factorial design was employed, incorporating varying levels of learning interest (low, medium, high) and learning models (PBL and DI). Statistical analysis reveals significant distinctions between the two instructional approaches, with the interaction between method and students' interest levels influencing improvements in mathematical understanding. Notably, students with high interest tend to demonstrate more substantial advancements. These findings underscore the importance of adapting instructional strategies to accommodate individualized student needs in mathematics education. The practical implication suggests tailoring teaching methods to optimize educational outcomes. This research enhances our understanding of the intricate dynamics among instructional methods, student interest, and mathematical comprehension.
... Suliawati, Jamal Fakhri, 2020) Matematika merupakan ilmu universal yang mendasari untuk perkembangan teknologi modern yang mempunyai peran penting dalam berbagai disiplin ilm dan kemajuan daya pikir manusia. (Maulyda, 2019) Matematika adalah ilmu yang tidak dapat dipisahkan dari dunia pendidikan yang mempunyai peran yang sangat penting dalam menciptakan sumber daya manusia yang berkualitas. Oleh karena itu matematika sebagai mata pelajaran wajib dipelajari disemua jenjang pendidikan. ...
Penelitian ini bertujuan untuk mengetahui apakah terdapat pengaruh Model Pembelajaran Matematika Knisley Berbantuan Media Video Pembelajaran Terhadap Pemahaman Konsep Matematis ditinjau dari gaya belajar peserta didik. Penelitian ini merupakan penelitian jenis kuantitatif dengan pendekatan Quasi Eksperiment Desain. Populasi dalam penelitian ini adalah seluruh peserta didik kelas VIII SMP Negeri 7 Krui, sebagai sampel menggunakan dua kelas terpilih dengan menggunakan teknik cluser random sampling dan terpilih kelas VIII B sebagai kelas eksperimen yang diberi perlakuan dengan Model Pembelajaran Matematika Knisley (MPMK) berbantuan Media Video Pembelajaran dan kelas VIII C sebagai kelas kontrol yang diberi perakuan Model Pembelajaran Direct Instruction. Teknik analisis data menggunakan uji prasyarat yaitu uji normalitas dan homogenitas. Adapun uji hipotesis menggunakan ANOVA dua jalur dan uji lanjut dengan uji komparasi ganda dengan metode scheffe. Hasil penelitian menunjukkan bahwa: (1) Terdapat pengaruh Model Pembelajaran Matematika Knisley (MPMK) berbantuan video pembelajaran terhadap pemahaman konsep matematis, (2) Terdapat perbedaan pemahaman konsep antara peserta didik yang memiliki kategori visual, auditorial dan kinestetik, (3) Tidak terdapat interaksi antara faktor model pembelajaran dan gaya belajar terhadap pemahaman konsep matematis.
... Salah satu kemampuan matematis yang dimuat dalam SK Kemendikbud RI Nomor 033/H/KR/2022 yakni pemecahan masalah matematis. Pemecahan masalah dapat dimaknai sebagai proses identifikasi solusi (Archi, 2019: Archi, 2020Polya, 1985;Seidouvy & Schindler, 2020) melalui langkah-langkah yang berlandasan dan tepat. Secara spesifik kompetensi pemecahan masalah dispesifikasi kedalam Permendikbud No. 37 Tahun 2018 yang menyatakan bahwa kemampuan pemecahan masalah dapat dicapai dengan memahami, menggunakan, menganalisis, serta menerapkan pengetahuan faktual, konseptual, dan prosedural yang dapat digolongkan sebagai indikator pemecahan masalah secara general. ...
The need for embodiment of progressive learning assisted by educational technology products was needed in the implementation of learning in research locations, departing from the need assessment conducted which shows that the results of previous learning carried out conventionally or not digitally based are classified as not optimal. This research aimed at designing the development of interactive multimedia to empower mathematical problem solving abilities in trigonometry comparison material. The research method used in this study is R&D research which refers to the ADDIE theory by focusing on the Analysis and Design aspects of the ADDIE development model. The ineffectiveness of learning activities carried out previously in the implementation of mathematics learning on trigonometry comparison material, especially in the problem-solving aspect, became the basis for the formation of digital-based learning multimedia development designs, considering that previous learning was carried out conventionally, innovations in making website-based interactive multimedia designs and their application in learning were assessed as the approach used to transition the scale of achievement of academic achievement for students towards a progressive one assisted by educational technology output.
The purpose of this study was to determine the thinking processes of students with special needs through three stages of thinking, namely the formation of understanding, the formation of opinions, and the conclusion of solving fraction problems. This research is a qualitative descriptive study with the research subject being a male student with mild mental retardation. The data analysis method was made in the form of data triangulation, which aims to test the wetness of the data. From the results of the analysis, it was found that the thinking processes involved in solving fractional problems by mentally disabled male students (1) involve the formation of understanding and can form understanding thru their thinking processes; (2) at the opinion formation stage, they need direction to be able to determine what strategies or methods will be used in solving problems.
This descriptive qualitive research aims to describe the forms of mathematics representation that appear among college students whom try to understand the relation between the change of trigonometry function coefficient and its graph through GeoGebra media. A class consists of 30 college students choosen as research subjects and they are given worksheets. From their work, it can be seen that there are 3 types of tendency of representation forms which is used by college students to solve their worksheet. From each type of tendency, a worksheet of student is choosen randomly for further investigation since it can represent others’ work. The research result shows that college students represent GeoGebra view in 3 forms. They are verbal representation, mathematics expression representation, and visual representation.
Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and meaningfulness of what they learn, they also are connected with their prior knowledge. The focus of this research is exploring the used of mathematical representations in solving ill-structured problems involving quadratic functions. The topic of quadratic functions is considered necessary in mathematics teaching and learning in higher education. It's because many mathematics education students have difficulty in understanding these matters, and they also didn’t appreciate their advantage and application in daily life. The researchers' explored mathematical representation as used by two subjects from fifty-four mathematics education students at the University of Nusantara PGRI Kediri by using a qualitative approach. We were selected due to their completed all steps for solving the ill-structured problem, and there have different ways of solving these problems. Mathematical representation explored through an analytical framework of solving ill-structured issues such as representing problems, developing alternative solutions, creating solution justifications, monitoring, and evaluating. The data analysis used technique triangulation. The results show that verbal and symbolic representations used both subjects to calculate, detect, correct errors, and justify their answers. However, the visual representation used only by the first subject to detect and correct errors.
We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N = 160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the shift-problem condition. The quality of the mathematical discussions in the shift-problem condition was better compared to that in the conventional textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the shift-problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that shift-problem lessons are powerful for eliciting mathematical discussions in seventh-grade shift-problem early algebra lessons.
This study was conducted among 269 student teachers at 11 primary teacher training colleges in the Netherlands. To investigate their competence in integrating theory and practice in their reflections on mathematics teaching, a learning environment was designed to evoke theory use in reflections on practice. To be able to systematically describe the use of theory, we distinguished two dimensions, which we called the nature and level of theory use. A Reflection Analysis Instrument was used to univocally code the nature and level of the student teachers’ theory use in the reflective notes of their final assessments into 1740 meaningful units. We found that nearly all student teachers used theory. However, they differed markedly in the way they linked theory and practice and with which depth they used theoretical concepts in their reflections. A remarkable finding of the study was the important influence of prior mathematics education on the nature and level of theory use, especially the low results of the third-year student teachers in their level of theory use. The outcome may have consequences for the design of the teacher education curricula and for the intake of first-year student teachers.
Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students' mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students' work with their knowledge or thought.
In a three-phase study, with a total of 40 third-grade teachers and their 830 students, teachers were supported to use classroom assessment techniques (CATs) to reveal their students’ knowledge of number operations. In phase I, four teachers and 66 third-grade students participated in five monthly workshops in which CATs were co-designed and their use was discussed. In phase II, the first phase was replicated with four workshops with six different teachers and 148 third-grade students. In these two exploratory phases, we evaluated student achievement on a standardized national mathematics test in a pre-/posttest design and compared changes herein to changes in the national norm sample. In phase III, a control condition was added to the design to experimentally investigate the effect on student achievement with 30 teachers and 616 third-grade students. Teachers were randomly assigned to participate in 0, 1, 2, or 3 1-hour workshops. In all three phases, we found a significant increase in students’ mathematics achievement scores on the standardized mathematics test. In phase III, the increase was significantly larger in the classes of teachers participating in three workshops than in classes with less workshops. Additionally, results from the analysis of classroom observations, feedback forms, and interviews indicate that teachers could easily integrate the CATs into their practice and could gather valuable information on their students. The results from the different phases of this study combined indicate that supporting teachers in their development and use of classroom assessment in mathematics may contribute to the improvement of students’ mathematics achievement.
Collaboration is an increasingly popular topic in mathematics education due to its potential to foster students’ learning. The purpose of this article is to draw attention to the semantic philosophical theory of inferentialism and its value for investigating students’ collaboration. We suggest that Brandom’s inferentialism can serve as a valuable theoretical resource to overcome certain issues of existing theoretical viewpoints on student collaboration. In particular, we argue that inferentialism may help to understand the individual and social nature of collaboration as intertwined. We illustrate our inferentialist approach using data from two scenes taken from video-recorded group work sessions from a fifth and seventh grade primary school class in Sweden. The topic in both classes was data generation in statistics.
This study contributes insights into how task design with different elements of guidance may influence students’ utilization of dynamic software for problem solving and reasoning. It compared students’ solving of two tasks with different designs supported by the dynamic software GeoGebra. Data analysed examined students’ approaches to utilizing GeoGebra, the characteristics of their reasoning and their ability to prove the validity of their solutions after solving the problems. The results showed that students who solved the task with less guidance (without instructions about a specific solving method) were better able to utilize GeoGebra’s potential to support their reasoning and problem solving. These students reasoned more creatively and presented more advanced proofs for their solutions than the more guided ones.
Purpose
Learning mathematics is a complex process, requiring many conceptual lenses and rich data sources to document and understand students’ construction of knowledge. The purpose of this article is both to introduce a unique database on students’ mathematical learning and to describe analytical techniques used to study students’ growth of the knowledge of mathematics and language.
Design/Approach/Methods
Our approach includes the following aspects: First, we describe a unique collection of video-taped recordings of longitudinal and cross-sectional studies of diverse, U.S. students, learning mathematics (Video Mosaic Collaborative, VMC). Second, we introduce our analytical methods, which utilize the database for collaborative study of students’ learning. These methods include video-narrative analyses that display fine-grained examinations of interactions among students who are solving engaging problems that require them to reason mathematically and to represent their understandings with language and non-language forms. These analyses, referenced as VMCAnalytics, demonstrate the accessibility and flexibility of the database to study relationships among students’ mathematics and language learning.
Findings
The findings generated are illustrated by two examples demonstrating the accessibility and flexibility of the database to study relationships between mathematics and language learning (mathematics register).
Originality/Value
The contribution of our work is illustrated by describing the rich database; employing a collaborative research approach; and signifying our understanding of relationships among students’ mathematical and language learning.