Algebraization Levels in the Study of Probability

The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic approach is applied to identify the different objects and processes involved in the resolution of a selection of probabilistic problems. As a result, we describe the possible progression from arithmetic and proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization in the study of probability. The method of analysis developed can help to establish connections between intuitive/informal and progressively more formal approaches in the study of mathematics.

Exploring Mathematical Concepts and Philosophical Values in Jember Batik

Ethnomathematics are different ways of doing mathematics taking into account the academic mathematical knowledge developed by different sectors of society as well as taking into account the different modes in which different cultures negotiate their mathematical practices (ways of grouping, counting, measuring, designing tools, or playing). Based on this research, this study aims to describe the results of ethnomathematics exploration in Jember batik motifs. The method of analysis used in this research was a qualitative approac with an ethnographic design. Data collection techniques were observation, documentation, and interviews. This research was conducted at Rumah Batik Rolla Jember and Rezti'z Batik Tegalsari Ambulu Jember. The research was conducted for one week. The results of this study indicate that the ethnomathematics in the Jember batik motif has a philosophical value that describes the natural wealth of Jember Regency in each of its motifs, and there are mathematical concepts in the form of geometric transformation concepts (reflection, translation, rotation, and dilation) along with the concept of number patterns.

Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process.

Connecting expectations of Te Whāriki and The New Zealand Curriculum: Examples of mathematical practices

The first year of primary school aims to be closely connected with early childhood education, yet this is often invisible in the curriculum of specific subjects. This paper sets out an approach that uses mathematical practices as a curriculum tool that reconceptualises school mathematics. Using the early childhood mathematics framework of Te Kākano, the strands of mathematical practices are important descriptors of mathematical activity for children. We describe examples of mathematical learning from both early childhood and the first year of school, and make a case for using mathematical practices as a conceptual tool for designing a mathematics curriculum in the first years of school.

Comparing the Mathematical Practices Pre-Service Teachers and Mathematics Teacher Educators Identified as Relevant to Problems and Tasks

In the U.S., state adopted or developed college- and career-ready mathematics standards, including the Common Core State Standards for Mathematics, not only impact districts, students, and their teachers, but also university teacher preparation programs. In order to attain and sustain Common Core’s vision of developing mathematically competent citizens, teacher preparation programs must support pre-service teachers’ development of practical conceptions of the Standards for Mathematical Practice. In this article, we examine the mathematical practices middle grades pre-service teachers (grades 4-9 licensure) and mathematics teacher educators identified as playing a role in attempts to make sense of and work toward solutions to mathematics problems. In addition, we compare the mathematical practices indicated both within and across pre-service teachers and mathematics teacher educators. Results identify pre-service teachers’ potential difficulties operationalizing six specific mathematical habits of mind. Finally, we describe how such comparisons can guide the design of future teacher education and professional learning by describing a process for identifying problems and tasks with the greatest potential to support pre-service teachers’ development of practical conceptions of mathematics or other content-specific habits of mind.

Mathematics Heritage Project: An Exploration Empowering Students' Mathematical Identities

The International Study Group on Ethnomathematics (ISGEm) supports incorporating cultural diversity of mathematical practices to promote the teaching and learning of school mathematics. Through The Mathematics Heritage Project, students at a middle school in the southeastern United States developed unique creations to connect with the mathematics connected to their identities and self-identified cultural group. Upon reflection, students reported an increased awareness of the relevance of mathematics in their lives and a sense of ownership that is both meaningful and modern.