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"Mathematics Activities"
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Introducing Learning Creative Mathematical Activity for Students in Extra Mathematics Teaching
Abstract The objective of the research is determined by the need to introduce creative learning mathematics activities for school students, because that is one of the ways of ensuring the effective acquisition of knowledge at the intersubject level and further successful adaptation while choosing a future career. Moreover, the resources of extra mathematics teaching at a general secondary school can be widely used. Thus, the purpose of the research is a) studying the theoretical basis for stimulating creative learning mathematics activities for the students and b) developing the teaching techniques of this stimulation in extra mathematics teaching at general secondary schools. The leading methods are a) modeling the task systems ensuring the development of the five types of learning activities: reproductive, productive, research, project, and project-research and b) the system analysis of the selections of experimental data based on estimating three criteria: fluency - the ability to generate a lot of ideas; flexibility - the ability to produce different ideas; ingenuity - the ability to react unconventionally. The experimental research has been carried out since 2001 and the problem systems characteristic of the five types of learning activities have been used. Subsequently, methodological approaches in extra mathematics teaching have been developed introducing creative mathematics activities for students. Resumen La actualidad de la investigación está determinada por la necesidad de introducir un aprendizaje creativo en las actividades matemáticas para los estudiantes de las escuelas, porque es una de las formas de asegurar la adquisición efectiva de conocimientos a nivel inter-sujetos y una adaptación más exitosa al elegir la futura carrera. Además, porque los recursos adicionales de enseñanza de matemáticas, en la escuela secundaria, pueden ser ampliamente utilizados. El objetivo de la investigación es estudiar la base teórica de estimulación del aprendizaje creativo de las actividades matemáticas en los estudiantes, y desarrollar las técnicas didácticas de su estimulación en la enseñanza adicional de matemáticas en la escuela secundaria. Los métodos principales son: a) modelación de sistemas de tareas que aseguren el desarrollo de los cinco tipos de actividades de aprendizaje (reproductivo, productivo, investigativo, de proyecto y proyectivo-investigativo), b) análisis sistémico de la selección de datos experimentales, basado en la estimación de tres criterios: fluidez en la capacidad de generar muchas ideas, flexibilidad de producir ideas diferentes e ingenio para reaccionar de forma no convencional. La investigación experimental se ha desarrollado desde el 2001, utilizándose los sistemas de problemas característicos de los cinco tipos de actividades de aprendizaje. Posteriormente, los enfoques metodológicos en la enseñanza adicional de matemáticas han sido desarrollados por la introducción de actividades de matemáticas, creativas, para los estudiantes.
Journal Article
I see a pattern here
\"Patterns are fascinating! They can be so beautiful that people come from all over the world to see them, or so familiar you hardly notice them. They appear everywhere: beehives, dinner plates, even the bottoms of your shoes! With stunning photographs that show diverse examples from nature and artwork around the world, Bruce Goldstone reveals the secrets behind patterns--and gives you some fun ideas for making your own\"-- Provided by publisher.
Book
Integration of computational thinking in K-12 mathematics education: a systematic review on CT-based mathematics instruction and student learning
There has been substantial research undertaken on the integration of computational thinking (CT) in K-12 mathematics education in recent years, particularly since 2018 when relevant systematic reviews were conducted on the topic. Many empirical studies in this area have yet to elaborate clearly and explicitly on how CT may support mathematics learning, or otherwise, in CT-based mathematics activities. Addressing this research gap, we conducted a systematic review on the integration of CT in K-12 mathematics education with a focus on CT-based mathematics instruction and students learning under such instruction. The Web of Science database was searched for in terms of studies published from 2006 to 2021, from which 24 articles were selected to provide illustrations of CT-based mathematics instruction and related student learning, and they were further analyzed according to education levels and contexts, programming tools, learning outcomes in CT and mathematics, and the mutual relationship between CT and mathematics learning. Among the results, this review found that geometrized programming and student-centered instructional approaches were facilitators of productive learning in CT and mathematics. Moreover, CT-based mathematics learning entails an interactive and cyclical process of reasoning mathematically and reasoning computationally, which can occur when: (1) applying mathematics to construct CT artefacts; (2) applying mathematics to anticipate and interpret CT outputs; and (3) generating new mathematical knowledge in parallel with the development of CT. The findings contribute to an in-depth understanding of what, and how, CT-based mathematics instruction impacts student learning in K-12 contexts.
Journal Article
A knotty problem
\"When Stephanie finds out her soccer team has a tournament on the same day as the district math competition, an upset Justin offers her a choice: choose Math Kids or leave the club. Dismayed by his attitude, Stephanie quits and Catherine goes with her. With their club in shambles, the future of their friendships further threatened by the news that Justin's dad has been offered a new job and wants to move his family to St. Louis. Jordan, Justin, Catherine, and Stephanie may face the permanent fracture of their friend group and a bleak end to their school year--unless they can come together to overcome some impossible situations. Problem-solving skills apply to much more than homework in the latest addition to the Math Kids series.\"-- Back cover.
CHILDBOOK
Creativity as a function of problem-solving expertise: posing new problems through investigations
This study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.
Journal Article
The Culture of Exclusion in Mathematics Education and Its Persistence in Equity-Oriented Teaching
The author investigates the influence of the dominant culture characterizing mathematics education—which she terms the culture of exclusion—on efforts to teach for equity. Analyzing a year of observations in an urban high school mathematics department, she found that this culture structured everyday instruction even for teachers who expressed a strong commitment to equity and who participated in ongoing equity-oriented professional development.
Journal Article
Mediation Relationships Among Gender, Spatial Ability, Math Anxiety, and Math Achievement
In this review, findings from studies investigating gender differences in spatial ability, math anxiety, and math achievement, the relationship between spatial ability and math anxiety, between spatial ability and math achievement, and between math anxiety and math achievement are synthesized. As a result of this synthesis, a sequential mediation model that allows simultaneous testing of two mediational relationships has been derived. Within this model, paths from gender to spatial ability, from spatial ability to math anxiety, and from math anxiety to math achievement are more strongly supported by prior studies than the paths from gender to math anxiety, from gender to math achievement, and from math achievement to math anxiety.
Journal Article
Equity Analytics: A Methodological Approach for Quantifying Participation Patterns in Mathematics Classroom Discourse
Equity in mathematics classroom discourse is a pressing concern, but analyzing issues of equity using observational tools remains a challenge. In this article, the authors propose
equity analytics as a quantitative approach to analyzing aspects of equity and inequity in classrooms. They introduce a classroom observation tool that focuses on relatively
low-inference dimensions of classroom discourse, which are cross-tabulated with demographic markers (e.g., gender, race) to identify patterns of more and less equitable
participation within and across lessons.
Journal Article
Initiating a conversation about expertise in designing elementary mathematics methods courses for equity
Many elementary education programs have only one mathematics methods course designed for preservice teachers (PTs). Such courses typically cover a range of content and present a challenge for mathematics teacher educators (MTEs) who strive to prepare their PTs to teach mathematics in equitable and humane ways. Due to the “stand-alone” nature of these semester-long courses, additional expertise is required for MTEs who desire to intentionally and authentically attend to equity and support PTs in developing pedagogy that aims for equity as outlined by (Gutiérrez, in: Herbel-Eisenmann, Choppin, Wagner, Pimm (eds) Equity in discourse for mathematics education, Springer, Berlin, 2012). In this paper, we take a first step at outlining this expertise by proffering a framework for conceptualizing MTE curricular knowledge for designing mathematics methods courses for equity. Using 12 syllabi for stand-alone elementary mathematics methods courses in initial teacher licensure programs from MTEs who have demonstrated expertise in the field of equitable mathematics teaching (MTE-EEs), we examined how aspects of their curricular expertise were evidenced in course descriptions, goals, objectives, assignments, topics, and related readings. Findings indicated that MTE-EEs often included similar design features in their courses and concentrated their attention to equity on access and identity. Implications and future directions for research are discussed.
Journal Article