Analisis Sociomathematical Norms Peserta Didik dalam Pembelajaran Daring SMKN 39 Jakarta

Penelitian ini memiliki tujuan untuk menganalisis orma sosiomatematik terhadap peserta didik yang berlangsung ketika pembelajaran daring matematika. Subjek dari penelitian ini adalah peserta didik SMKN 39 Jakarta. Metode penelitian ini menggunakan metode deskriptif kualitatif. Penelitian ini menggunakan penyebaran angket melalui Google Form dan Wawancara melalui Zoom Meeting. Berdasarkan hasil penelitian, terdapat 3 peserta didik yang berkreteria tinggi dalam norma sosiomatematik, terdapat 25 peserta didik yang berkreteria sedang atau standart, dan terdapat 2 peserta didik yang berkreteria rendah. Hasil penelitian menyimpulkan bahwa kualitas interaksi yang terbentuk dalam pembelajaran daring juga mengalami penurunan, dimana peserta didik hampir tidak melaksanakan diskusi secara daring dan presentasi. Namun dapat kita lihat bahwa peserta didik yang kreteria norma sosiomatematiknya tinggi lebih percaya diri untuk menarik kesimpulan. Maka norma sosiomatematik sangat berkenaan dengan hubungan antar individu, matematika dan masyarakat yang menekankan, bahwa pemahaman dan keyakinan peserta didik dapat ditimbulkan atai dimunculkan saat proses interaksi diskusi dalam pembelajaran, namun karena interaksi yang terjadi mengalami penurunan dalam esensi, maka pemahaman dan keyakinan peserta didik juga mengalami penurunan. Selain itu norma sosiomatematik yang dimiliki peserta didik sangat berpengaruh terhadap tingginya maupun rendahnya hasil pemahaman yang di peroleh pada saat pembelajaran matematika berlangsung.

Journeys towards sociomathematical norms in the Foundation Phase

Background: The co-establishment of social and sociomathematical norms in the microculture of South African classrooms and its possible effects on early number learning has largely been unexplored. Social norms are considered to be general classroom norms that are relevant in any teaching and learning space, whilst sociomathematical norms are specific to the mathematical aspects of students’ working.Aim: In the midst of poor numeracy outcomes in South African schools, our interest lies in the connections between the establishment of particular norms and the affordances or constraints for learning that they provided. Part of our interest, in a context where sense-making, co-operative working and mathematical progression beyond one-by-one counting have been described as infrequent in Foundation Phase mathematics learning, was to explore whether it was possible to institute norms related to these aspects.Setting: We report on the social and sociomathematical norms established within group intervention sessions with two groups of four Grade 2 learners across 9 weeks of intervention in a suburban school which serves a historically disadvantaged learner population.Methods: The frequency of specific norm codes was used to determine the normative behaviour within groups across intervention lessons.Results: Two significant inferences are drawn from study results: a culture of co-operative working based on social norms was needed in the grouped learning space before sociomathematical norms could be foregrounded within the same space; and one particular sociomathematical norm – ‘use the structure of 10’ – was particularly important as the ‘hand hold’ that allowed for progression in participants’ early number skills.

Analysis of Sociomathematical Norms in Mathematics Learning at 113 Junior High School

This study aims to describe the sociomatematical norms that are owned by students when learning mathematics in class. The subjects of this study were students of class VII-A Jakarta 113 Junior High School. The research method used is descriptive qualitative method. This research uses sociomatematical norms questionnaire and interview. Based on the results of the study, there were 9 students who had very good sociomatematical norms categories with a total percentage of indicators of 81% and there were 14 students who had good sociomatematical norms categories with a total percentage of indicators of 72%. The results showed that very good sociomatematical norms owned by students would affect the high results obtained by students in mathematics learning and good sociomatematical norms would affect the moderate and low results obtained by students in learning mathematics.

STUDENT EVALUATION MATHEMATICAL EXPLANATION IN DIFFERENTIAL CALCULUS CLASS

This study aimed to determine that the failure of students to evaluate mathematical explanations based on mathematics is influenced by sociomathematical norms, teaching authority, and classroom mathematics practice. The research method used is the case study method. The research data were obtained from inside and outside the research class. The data in the research class were in the form of field notes, video recordings of the class, video recordings of student group work, and student work. Data outside the research class is the result of interviews with three interview subjects. By studying the three evaluation methods students used in evaluating explanations, it was found that each student applied a different evaluation method at different times. The three evaluation methods contributed to some of the difficulties students experience in evaluating their mathematical descriptions. The results indicate that the failure of students in evaluating explanations is not solely due to errors in choosing the method, approach, or learning model used but can be caused by sociomathematical norms, authority, and classroom mathematics practices applied in the classroom.

Doing Mathematics

Learning mathematics is a way of acting. Mathematics is something that you do, not just something you know. Yet what it means to do mathematics can depend upon the norms and sociomathematical norms in each classroom. In turn, what it means to do mathematics in a classroom affects what it means to be a student or a teacher of mathematics. This doing of mathematics can be about communicating and problem solving, or it can be about remembering and knowing. Similarly, what it means to explain, argue, or justify varies between classrooms and the opportunities for students to do mathematics are constrained by what it means to do mathematics in each and every mathematics classroom.

Mathematics in the Digital Age: The Case of Simulation-Based Proofs

Digital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.