This paper presents the results of a research, which proposes the introduction of the teaching by Research and Study Paths (RSPs) into Argentinean secondary schools within the frame of the Anthropologic Theory of Didactics (ATD). The paths begin with the study of "Q[subscript 0]: How to operate with any curves knowing only its graphic…

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about…

This study focuses on mathematics teachers' professional development through elements of Japanese lesson study. The teachers designed a research lesson with regard to sense-making of the derivative using the integration of GeoGebra. In the second year of the four-year lesson study project, seven secondary school teachers--from different Dutch…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

This study focuses on the role of multiple solution tasks (MST) incorporating multiple learning tools and representation systems (MTRS) in encouraging each student to develop multiple perspectives on the learning concepts under study and creativity of thought. Specifically, two types of MST were used, namely tasks that allowed and demanded…

Many researchers found that students have difficulties in understanding area measurement. Students mostly focus on applying formula to find the area of certain shapes without knowing what the area is and why the formula works. It is important for the students to know what attribute being measured and to construct the unit for area measurement.…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

This article showcases the benefits of the alliance the authors have established during the past two years with the Barnes Foundation to add more mathematics activities to their repertoire and to integrate more art into their mathematics lessons. Recently, they decided to focus on activities at the K-grade 2 level that could be used as an on-site…

This paper reports a study on designing and testing an instructional sequence for the teaching and learning of the concept of angle in Indonesian primary schools. The study's context is employing the current reform movement adopting "Pendidikan Matematika Realistik Indonesia" (an Indonesian version of Realistic Mathematics Education).…

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry…

Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there are dimensions involved in the emergence of mathematical knowing and the production of mathematical…

A number triangle, discovered using a recurrence formula similar to that of Pascal's triangle, yields sequence A077028 from the Online Encyclopedia of Integer Sequences.