Journal articles: 'Commognitive analysis'

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Rossydha, Faula, Toto Nusantara, and Sukoriyanto Sukoriyanto. "Commognitive Siswa dalam Menyelesaikan Masalah Persamaan Linier Satu Variabel." Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan 6, no. 1 (January 30, 2021): 1. http://dx.doi.org/10.17977/jptpp.v6i1.14367.

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Abstract: This study aims to describe the students' commognitive in solving linear problems of one variable. This study uses a qualitative approach to the type of descriptive research. The stages in this study consisted of preparation, data collection, and data analysis. The results of this study are that there are two strategies students use in solving problems when analyzed using commognitive components. Two strategies used by students are the strategy of finding patterns and trial and error strategies. Students with strategies finding patterns in using commognitive components in solving problems look systematic compared to students with trial and error strategies.Abstrak: Penelitian ini bertujuan untuk mendeskripsikan commognitive siswa dalam menyelesaikan masalah persamaan linier satu variabel. Penelitian ini menggunakan pendekatan kualitatif dengan jenis penelitian deskriptif. Tahapan dalam penelitian ini terdiri dari persiapan, pengumpulan data, dan analisis data. Hasil dari penelitian ini adalah terdapat dua strategi yang digunakan siswa dalam menyelesaikan masalah apabila dianalisis menggunakan komponen commognitive. Dua strategi yang digunakan siswa yaitu strategi menemukan pola dan stretegi coba-coba. Siswa dengan strategi menemukan pola dalam menggunakan komponen commognitive dalam menyelesaikan masalah terlihat sistematis dibandingkan siswa dengan strategi coba-coba.

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Zayyadi, Moh, Toto Nusantara, and Harfin Lanya. "The commognitive perspective of teaching skills of prospective mathematics teachers in microteaching subjects." Jurnal Elemen 8, no. 1 (January 6, 2022): 43–54. http://dx.doi.org/10.29408/jel.v8i1.4129.

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This study aims to describe the teaching skills of prospective mathematics education teachers in micro-teaching subjects from a commognitive perspective. This type of research is qualitative research. The research subjects consisted of 15 students of the 2015 Mathematics Education Study Program class, which were taking micro-teaching courses. The instrument used in this study was a rubric sheet—an assessment of prospective teachers' teaching skills. Data analysis techniques used are data reduction, data presentation, and conclusion collection. The results showed that: Prospective mathematics education teachers in preliminary activities often use the word usage component, visual mediator, routine and do not use the narrative component. In the core activities of learning mathematics, teacher candidates use four components commognitive, which are the use of words, visual mediators, routine, and narrative. In the selection of mathematics education, teacher candidates only use the word use component. Commognitive provides an overview of mathematical cognitive-communication and content in the learning carried out.

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Zayyadi, Moh, Lutfiyah Lutfiyah, and Enditiyas Pratiwi. "Analisis Commognitive Siswa dalam Menyelesaikan Soal Non Rutin." Jurnal Axioma : Jurnal Matematika dan Pembelajaran 8, no. 1 (April 13, 2023): 22–36. http://dx.doi.org/10.56013/axi.v8i1.1990.

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This study aims to describe the student's commercial analysis in resolving non-routine questions. This type of research is descriptive qualitative. The research subjects were three MTs Az-Zubair students, Sumber anyar, and Larangan Tokol. The instrument used in this study is mathematical questions and semi-structured interviews. The results showed that students have many differences in the work method or error in solving math problems from Word Use (using the right words to inform understanding, such as the basis of writing, and other symbols), visual mediators (choosing and using the right concepts and methods in the matter of non-routine. Keywords: commognitive, non-routine problems

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Et. al., Lili Supardi,. "Commognitive Analysis Of Students' Errors In Solving High Order Thinking Skills Problems." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (April 10, 2021): 950–61. http://dx.doi.org/10.17762/turcomat.v12i6.2373.

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This study aims to describe the commognitive analysis of students' errors in solving High order thinking skills problems. The problem of this study is that students have difficulty of solving mathematical problems because students do not build their own knowledge of mathematical concepts but tend to memorize concepts so that when students solve math problems students often make mistakes and do not find solutions to solve these problems. Students also taught themselves that math is difficult. This type of research is a qualitative description. The research subjects were three grade X students of Senior High school 1 Pamekasan. The instruments used in this study were mathematical problem seets and semi-structured interviews. The results showed that students experienced faults in 1) word use (mistake writting mathematical symbol and not consisstent in writting naming. the factors are hasty, inaccurate, not understanding the questions, incomplete writing is known, and asked, not understanding the material.); 2) Visual mediator (mistakes in drawing or illustrating the problem. Student is not using visual mediators, some students use visual mediators but are still wrong and use it,); 3) Narrative (not writing the formula but writing the results directly. Student mistakes also occur because students do not know the strategy that will be used to solve them, while the students' mistakes made at this stage are: students are wrong in writing the formula definition sine and wrong for not writing the formula.); 4) Routine (inaccurate in arithmetic operations so that the final answer is wrong. The mistakes of some students in general in doing routine are the students doing wrong calculations, wrong in substituting values or numbers that are known in the formula.). With this research, teachers can find out where the difficulties and misconceptions of students are in doing it so that it becomes new learning for students to improve learning outcomes and minimize errors.

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Halim, D., S. Nurhidayati, M. Zayyadi, H. Lanya, and S. I. Hasanah. "Commognitive analysis of the solving problem of logarithm on mathematics prospective teachers." Journal of Physics: Conference Series 1663 (October 2020): 012002. http://dx.doi.org/10.1088/1742-6596/1663/1/012002.

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Ioannou, Marios. "Commognitive analysis of undergraduate mathematics students’ first encounter with the subgroup test." Mathematics Education Research Journal 30, no. 2 (August 9, 2017): 117–42. http://dx.doi.org/10.1007/s13394-017-0222-6.

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Viirman, Olov. "Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis." International Journal of Mathematical Education in Science and Technology 46, no. 8 (April 27, 2015): 1165–81. http://dx.doi.org/10.1080/0020739x.2015.1034206.

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Weingarden, Merav, and Einat Heyd-Metzuyanim. "What Can the Realization Tree Assessment Tool Reveal About Explorative Classroom Discussions?" Journal for Research in Mathematics Education 54, no. 2 (March 2023): 97–117. http://dx.doi.org/10.5951/jresematheduc-2020-0084.

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One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.

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Mudaly, Vimolan, and Sihlobosenkosi Mpofu. "LEARNERS’ VIEWS ON ASYMPTOTES OF A HYPERBOLA AND EXPONENTIAL FUNCTION: A COMMOGNITIVE APPROACH." Problems of Education in the 21st Century 77, no. 6 (December 6, 2019): 734–44. http://dx.doi.org/10.33225/pec/19.77.734.

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Learners in South African schools often respond poorly in questions related to the asymptote. Despite the fact that there are only a few functions in the South African curriculum that actually explore the asymptote, learners still show some deficiency in their understanding of the concept. This research examined Grade 11 learners’ mathematical discourses about the asymptotes of the hyperbola and exponential functions. Data were analysed using the Realisation Tree of a Function, an adaptation of the Realisation Tree Assessment tool from Weingarden, Heyd-Metzuyanim and Nachlieli. While the Realisation Tree Assessment tool focused on teacher talk, the Realisation Tree of a Function focused on learner expression and responses. A qualitative research design was essentially adopted, with exploratory, descriptive and interpretive elements complementing both its data collection and analysis. A purposive sampling strategy was implemented. Data were collected by means of a test administered to a total of 112 Grade 11 participants from four selected secondary schools. Focus group interviews were conducted with 24 of the best-performing participants by using their responses from the written mathematical tests. The results revealed that the learners’ mathematical discourse is not coherent. While learners’ work on each representation was often mathematical there seemed to be a struggle when the task had an unusual orientation. Different expressions of the same mathematical object elicited different responses. The challenge is that learners exhibited a fragmented relationship between the mathematical objects of the function. Keywords: commognition, realization tree, ritualised learning, visual mediators.

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Pratiwi, Enditiyas, Toto Nusantara, Susiswo Susiswo, and Makbul Muksar. "Routines’ errors when solving mathematics problems cause cognitive conflict." International Journal of Evaluation and Research in Education (IJERE) 11, no. 2 (June 1, 2022): 773. http://dx.doi.org/10.11591/ijere.v11i2.21911.

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Many studies showed that cognitive conflict often occurs in learning and when solving mathematics problems. However, very few studies have looked at cognitive conflicts in solving mathematics problems, incredibly improper fraction problems. This descriptive qualitative study described and analyzed students’ errors in solving mathematics problems using a commognitive perspective. The data was collected using a test sheet instrument, where students do the test think-aloud. The answers on the student test sheets were analyzed by adjusting the think-aloud that was carried out, and then the interview process was carried out as a form of triangulation of the method in the study. The data analysis results showed that there was a routine error that causes cognitive conflict when solving the improper fraction problem. The error that occurred indicates that the routine can and cannot resolve the cognitive conflict that occurs. This study’s findings indicated the importance of routine procedures to be understood so that their use is appropriate for solving mathematical problems.

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Lefrida, Rita, Tatag Yuli, and Agung Lukito. "Process-Oriented Routines of Students in Heterogeneous Field Dependent-Independent Groups: A Commognitive Perspective on Solving Derivative Tasks." European Journal of Educational Research 10, no. 4 (October 15, 2021): 2017–32. http://dx.doi.org/10.12973/eu-jer.10.4.2017.

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Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students’ commognition of routine aspects in understanding derivative tasks for heterogeneous groups of cognitive styles-field dependent and independent. This qualitative study involved six third-semester mathematics education students in the city of Palu, Indonesia. We divided the subjects into two groups with field-independent (FI) and field-dependent (FD) cognitive styles. The first group consisted of two FI students and one FD student, and the second group consisted of two FD students and one FI student. Moreover, the subjects also have relatively the same mathematical ability and feminine gender. Data was collected through task-based observations, focused group discussions, and interviews. We conducted data analysis in 3 stages, namely data condensation, data display, and conclusion drawing-verification. The results showed that the subjects were more likely to use routine ritual discourse, namely flexibility on the exemplifying category, by whom the routine is performed on classifying and summarizing categories, applicability on inferring category, and closing conditional on explaining category. The result of ritual routine is a process-oriented routine through individualizing. This result implies that solving the questions is not only oriented towards the correct answers or only being able to answer, but also students need to explain it well.

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Lefrida, Rita, Tatag Yuli, and Agung Lukito. "Process-Oriented Routines of Students in Heterogeneous Field Dependent-Independent Groups: A Commognitive Perspective on Solving Derivative Tasks." European Journal of Educational Research 10, no. 4 (October 15, 2021): 2017–32. http://dx.doi.org/10.12973/eu-jer.10.4.2017.

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Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students’ commognition of routine aspects in understanding derivative tasks for heterogeneous groups of cognitive styles-field dependent and independent. This qualitative study involved six third-semester mathematics education students in the city of Palu, Indonesia. We divided the subjects into two groups with field-independent (FI) and field-dependent (FD) cognitive styles. The first group consisted of two FI students and one FD student, and the second group consisted of two FD students and one FI student. Moreover, the subjects also have relatively the same mathematical ability and feminine gender. Data was collected through task-based observations, focused group discussions, and interviews. We conducted data analysis in 3 stages, namely data condensation, data display, and conclusion drawing-verification. The results showed that the subjects were more likely to use routine ritual discourse, namely flexibility on the exemplifying category, by whom the routine is performed on classifying and summarizing categories, applicability on inferring category, and closing conditional on explaining category. The result of ritual routine is a process-oriented routine through individualizing. This result implies that solving the questions is not only oriented towards the correct answers or only being able to answer, but also students need to explain it well.

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Baek, Seungju. "Analysis of Discourse Changes due to the Introduction of Irrational Numbers in School Mathematics: Focusing on the Historical Significance of Incommensurability in Mathematics." Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics 33, no. 4 (November 30, 2023): 1041–64. http://dx.doi.org/10.29275/jerm.2023.33.4.1041.

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This study examined the method of discovering incommensurable quantities, the origin of irrational numbers, and the changes in Greek mathematics resulting from the discovery of these quantities from Sfard's commognitive perspective. In addition, in light of the history of mathematics, this study looked into changes in the discourse of school mathematics due to the introduction of irrational numbers. As a result of the analysis, the discovery of incommensurable quantities in the history of mathematics was an opportunity to change from empirical mathematics to formal and theoretical mathematics, and was an event that brought about changes in various mathematical concepts, proportion theory and roles of mathematical tools. In other words, the discovery of incommensurable magnitude transformed Greek mathematics into an incommensurable discourse. These changes in the history of mathematics appear similarly in the changes in the discourse of school mathematics due to the introduction of irrational numbers. The introduction of irrational numbers into school mathematics resulted in the application of formal definitions of numbers, changed the concepts of number and area, and led to the emergence of narratives that seemed to contradict previous discourses. It is understood that the introduction of irrational numbers has changed the discourse of school mathematics into a discourse that is incommensurable with the previous one. The analysis of this study could be basic data for the design of teaching and learning methods for students facing the task of transitioning to the incommensurable discourse of irrational number learning.

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AKÇAKOCA, Tuba, Gönül YAZGAN SAĞ, and Ziya ARGÜN. "Rituals and Explorations in Students’ Mathematical Discourses: The Case of Polynomial Inequalities." Participatory Educational Research 11, no. 1 (December 26, 2023): 178–97. http://dx.doi.org/10.17275/per.24.11.11.1.

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The study is a qualitative case study that seeks to determine whether students’ mathematical discourses in solving polynomial inequalities are more ritualistic or explorative. A comprehensive analysis of students’ routines was conducted through the observations of what they said and did (write, draw, and so on) around task situations in a small group. This study’s participants were five 11th-grade students from a public high school. These participants were chosen using the maximum diversity method of sampling. The data for this study were obtained through small-group work. The small-group interactions lasted 80 minutes and were video-recorded with two cameras. The commognitive approach was used to analyze the student routines in this study. The criteria for analyzing routines were the performers’ agentivity /external authority, focus on the goal or the procedure, and flexibility. The findings of this study revealed that the students’ routines were neither purely ritualistic nor sheer explorative. Even those whose routines were ritualistic in all task situations thought about the procedure and asked logical questions about the task. In addition, the findings indicate that teachers can play an important role in encouraging students to engage in more exploratory mathematical discourse. This study contributes to the future research on students’ discourse in the context of inequality.

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Çelebi, Emine Gül. "Exploring Mathematics Teachers’ Noticing as Pedagogical Discourse Through an Adapted Lesson Study." Journal of Education and Learning 12, no. 5 (July 20, 2023): 150. http://dx.doi.org/10.5539/jel.v12n5p150.

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Although positive effects of lesson study on teachers learning are reported, only some studies have investigated teacher noticing as an analytical tool for supporting teachers with an explicit focus, as in LS, and more empirical evidence is needed. This qualitative interpretive case study design aims to investigate the noticing processes of a group of mathematics teachers conducting a lesson study cycle focused on teaching algebraic expressions using manipulatives in middle school. Data is collected through the audio recordings of the participants’ lesson study meetings. Participants were six elementary mathematics teachers who attended a graduate course selected based on voluntariness. This study aims to incorporate Lee and Choy’s (2019) teacher noticing framework with Sfard’s (2008) commognitive theory, which views learning as changes in discourse and noticing as a discourse structure covering observation, interpretation, and reasoning processes (van Es, 2011). Results showed that teachers focused more on aspects of students’ learning than issues of their instructional practice. However, their noticing was mostly related to future decisions and actions regarding issues of teaching methods and sequencing of the lesson, whereas teachers’ dominant noticing form related to students learning was interpretive. Results illustrate the applicability of these noticing frameworks as an analytic tool where noticing is conceptualized as a pedagogical discourse for the analysis of a lesson study review discussion by a group of mathematics teachers who focus on teaching algebraic expressions.

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Roble, Dennis B., and Cherry Mae P. Casinillo. "Comparison of At-risk Students’ Mathematical Commognition in Geometry based on their Personal Attributes." Canadian Journal of Family and Youth / Le Journal Canadien de Famille et de la Jeunesse 14, no. 3 (April 11, 2022): 187–97. http://dx.doi.org/10.29173/cjfy29796.

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Students’ academic performance in Mathematics has a significant impact on their success on large scale standardized assessments as well as their eventual job choices. This study determined the level of at-risk students’ mathematical commognition in high school geometry and makes comparisons when grouped according to their family environment, language proficiency, learning style, and attitude towards learning mathematics. This study employed a mixed method research design and was conducted for select Grade 10 at-risk students of Cagayan de Oro City National Junior High School. The data gathered on students’ level of commognition was analyzed using frequency, percentage, mean and standard deviation. Correlation analysis was used to establish the association between students’ mathematical commognition and the perceived variables. The comparison of students’ level of mathematical commognition was analyzed using non-parametric tests such as Kruskall-Wallis and Mann Whitney U tests. Results reveal no significant difference of at-risk students’ level of mathematical commognition based on their personal attributes. Hence, it is recommended that further explorations of other factors that might affect students’ level of mathematical commognition. Students only have a basic level of mathematical commognition and therefore another study can be pursued on employing effective teaching methods on improving students’ mathematical commognition not only in Geometry but also in other mathematics courses across all levels.

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Kang, Suyoung, and Bomi Shin. "An Analysis of middle school students’ deductive reasoning in proof lessons: Focused on commognition perspective16)." Journal of Curriculum and Evaluation 25, no. 1 (February 2022): 143–72. http://dx.doi.org/10.29221/jce.2022.25.1.143.

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Nisa, Z., A. Lukito, and Masriyah. "Students Mathematical Discourse Analysis by Commognition Theory in Solving Absolute Value Equation." Journal of Physics: Conference Series 1808, no. 1 (March 1, 2021): 012065. http://dx.doi.org/10.1088/1742-6596/1808/1/012065.

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Nardi, Elena, Andreas Ryve, Erika Stadler, and Olov Viirman. "Commognitive analyses of the learning and teaching of mathematics at university level: the case of discursive shifts in the study of Calculus." Research in Mathematics Education 16, no. 2 (May 4, 2014): 182–98. http://dx.doi.org/10.1080/14794802.2014.918338.

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Acevedo-Arango, David, Jhony Alexander Villa-Ochoa, and Difariney González-Gómez. "Correspondence between Professional Learning Expectations and Learning Opportunities in Financial Management Textbooks." Education Sciences 13, no. 1 (December 23, 2022): 15. http://dx.doi.org/10.3390/educsci13010015.

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This research investigated the correspondence between a sample of Financial Management textbooks and professional learning expectations synthesized in the construct of Expectation of Use. To this end, a conceptual framework developed from research on professional practice was integrated with the theoretical perspective of commognition and the analysis of mathematics education textbooks. A qualitative content analysis was performed on the narrative and the end-of-chapter problems of the textbooks, which identified the experiences they can offer and their relationship with professional practice. It was evidenced that the narrative of the textbooks focuses on promoting the development of concepts, principles, and procedures of financial theory; the financial situations presented in the narrative and in the end-of-chapter problems are artificial and therefore have limited relation with professional practice. It was concluded that, according to the textbooks, the mastery of Financial Management consists of appropriating a broad set of financial concepts that excludes the use of these concepts to address problems that simulate the profession. Restructuring the narrative in Financial Management textbooks and consciously including routines that respond to the professional learning needs of the financial community is recommended.

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Lu, Jijian, Yuwei Zhang, and Yangjie Li. "Visual analysis of commognitive conflict in collaborative problem solving in classrooms." Frontiers in Psychology 14 (December 20, 2023). http://dx.doi.org/10.3389/fpsyg.2023.1216652.

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In today’s knowledge-intensive and digital society, collaborative problem-solving (CPS) is considered a critical skill for students to develop. Moreover, international education research has embraced a new paradigm of communication-focused inquiry, and the commognitive theory helps enhance the understanding of CPS work. This paper aims to enhance the CPS skills by identifying, diagnosing, and visualizing commognitive conflicts during the CPS process, thereby fostering a learning-oriented innovative approach and even giving the script of technology-assisted feedback practices. Specifically, we utilized open-ended mathematical tasks and multi-camera video recordings to analyze the commognitive conflicts in CPS among 32 pairs, comprising 64 Year 7 students. After selecting the high-quality, medium-quality, and low-quality student pairs based on the SOLO theory, further investigations were made in the discourse diagnosis and visual analysis for the knowledge dimensions of commognitive conflict. Finally, it was discovered that there is a need to encourage students to focus on and resolve commognitive conflicts while providing timely feedback. Visual studies of commognitive conflict can empower AI-assisted teaching, and the intelligent diagnosis and visual analysis of CPS provide innovative solutions for teaching feedback.

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Barnett, Janet Heine. "Primary source projects as textbook replacements: a commognitive analysis." ZDM – Mathematics Education, August 5, 2022. http://dx.doi.org/10.1007/s11858-022-01401-2.

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Weingarden, Merav, and Orly Buchbinder. "Teacher learning to teach mathematics via reasoning and proving: a discursive analysis of lesson plans modifications." Frontiers in Education 8 (August 25, 2023). http://dx.doi.org/10.3389/feduc.2023.1154531.

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Despite the importance of reasoning and proving in mathematics and mathematics education, little is known about how future teachers become proficient in integrating reasoning and proving in their teaching practices. In this article, we characterize this aspect of prospective secondary mathematics teachers’ (PSTs’) professional learning by drawing upon the commognitive theory. We offer a triple-layer conceptualization of (student) learning, teaching, and learning to teach mathematics via reasoning and proving by focusing on the discourses students participate in (learning), the opportunities for reasoning and proving afforded to them (teaching), and how PSTs design and enrich such opportunities (learning to teach). We explore PSTs’ pedagogical discourse anchored in the lesson plans they designed, enacted, and modified as part of their participation in a university-based course: Mathematical Reasoning and Proving for Secondary Teachers. We identified four types of discursive modifications: structural, mathematical, reasoning-based, and logic-based. We describe how the potential opportunities for reasoning and proving afforded to students by these lesson plans changed as a result of these modifications. Based on our triple-layered conceptualization we illustrate how the lesson modifications and the resulting alterations to student learning opportunities can be used to characterize PSTs’ professional learning. We discuss the affordances of theorizing teacher practices with the same theoretical lens (grounded in commognition) to inquire student learning and teacher learning, and how lesson plans, as a proxy of teaching practices, can be used as a methodological tool to better understand PSTs’ professional learning.

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Kontorovich, Igor’, and Sina Greenwood. "From Collaborative Construction, Through Whole-Class Presentation, to a Posteriori Reflection: Proof Progression in a Topology Classroom." International Journal of Research in Undergraduate Mathematics Education, June 2, 2023. http://dx.doi.org/10.1007/s40753-023-00217-z.

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AbstractComing from a social perspective, we introduce a classroom organizational frame, where students’ proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the mathematics community. To illustrate opportunities for mathematics learning of proof progressions, we present a commognitive analysis of a single proof from a small course in topology. The analysis illuminates the processes through which students’ proof was restructured, developed previously unarticulated elements, and became more formal and elaborate. Within this progression, the provers developed their mathematical discourses and the course teacher seized valuable teachable moments. The findings are discussed in relation to key themes within the social perspective on proof.

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Viirman, Olov. "University Mathematics Lecturing as Modelling Mathematical Discourse." International Journal of Research in Undergraduate Mathematics Education, March 24, 2021. http://dx.doi.org/10.1007/s40753-021-00137-w.

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AbstractThe lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

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Kontorovich, Igor’, and Tikva Ovadiya. "How narratives about the secondary-tertiary transition shape undergraduate tutors’ sense-making of their teaching." Educational Studies in Mathematics, March 9, 2023. http://dx.doi.org/10.1007/s10649-023-10211-6.

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AbstractDrawing on the commognitive framework, we construe the secondary-tertiary transition (STT) as a distinctive element in the pedagogical discourses of various communities. Our interest rests with university tutors in light of the emergent recognition of their impact on undergraduates’ mathematics learning in many tertiary contexts worldwide. We aim to understand the roles of STT communication in tutors’ reflections on incidents that took place in their tutorials. Our participants were undergraduate students in the advanced stages of their mathematics degrees in a large New Zealand university and who were enrolled in a mathematics education course. Throughout the semester, the participants led tutorial sessions for first-year students and wrote reflections on classroom incidents that drew their attention. Our data corpus consisted of 58 reflections from 38 tutors collected over four semesters. The analysis revealed that STT communication featured in tutors’ descriptions of classroom incidents, assisted them in making sense of unexpected events, positioned their instructional actions as replications of what was familiar to them from their own STT experience, and contributed toward generating new pedagogical narratives. We situate these findings in the literature concerning undergraduate tutoring and teachers’ perspectives on STT.

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Valenta, Anita, Kirsti Rø, and Sigrid Iversen Klock. "A framework for reasoning in school mathematics: analyzing the development of mathematical claims." Educational Studies in Mathematics, March 20, 2024. http://dx.doi.org/10.1007/s10649-024-10309-5.

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AbstractThis study introduces a framework for analyzing opportunities for mathematical reasoning (MR) in school mathematics, using MR-relevant claims and their derivation as the unit of analysis. We contend that this approach can effectively capture a broad range of opportunities for MR across various teaching situations. The framework, rooted in commognition, entails identifying necessary object-level narratives (NOLs) and the processes involved in their construction and substantiation. After theoretical development, the framework was refined through analyses of mathematics lessons in Norwegian primary school classrooms. Examples from the data illustrate how to utilize the framework in analysis and what such analyses can reveal in four typical teaching situations: the introduction of new mathematical objects, the introduction of procedures, work on exercise tasks, and work on problem-solving tasks. Drawing from the analysis of these examples, we discuss the value of the framework for analyzing MR in school mathematics and how such analysis can benefit teachers and researchers.

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Chan, Man Ching Esther, Josephine Moate, David Clarke, Ross Cunnington, Javier Díez-Palomar, Marita Friesen, Eeva Haataja, et al. "Learning research in a laboratory classroom: a reflection on complementarity and commensurability among multiple analytical accounts." ZDM – Mathematics Education, February 4, 2022. http://dx.doi.org/10.1007/s11858-022-01330-0.

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AbstractWith the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies.

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Kontorovich, Igor’, and Kim Locke. "The Area Enclosed by a Function Is Not Always the Definite Integral: Relearning Through Collaborative Transitioning Within a Learning-Support Module." Digital Experiences in Mathematics Education, November 23, 2022. http://dx.doi.org/10.1007/s40751-022-00116-z.

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AbstractLearning-support system is an umbrella term that we use for digital resources that assign students with mathematical questions and give automatic feedback on the inserted answers. Transitioning between questions and feedback is characteristic to students’ work with such systems. We apply the commognitive framework to explore the role of within-system transitions in students’ mathematics learning, with a special interest in what we term as “reroutinization”—a process of repeated development of conventional routines to be implemented in already familiar mathematical tasks. The study revolves around a digital module in integral calculus, which was designed to support undergraduates with finding areas enclosed by functions. The data comes from dyads and triads of first-year university students, who collaboratively interacted with the module. The analyses cast light on how transitioning within the module aided students to review familiar routines, amend them, confirm, and solidify the amendments. The transition process was not always linear and contained instances of students cycling back and forth between the assigned questions and feedback messages. We conclude with the discussion on the module’s design that afforded reroutinization and suggest paths for further research.

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Journal articles on the topic 'Commognitive analysis'

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