Similarity is a crucial concept introduced in the 8th grade, and it is further developed and reinforced through associations during high school. This research aims to investigate how 8th grade students construct the concept of similarity using concrete manipulative support within the framework of APOS theory. The research was conducted as a…

This article investigates the incorporation of loose parts as a means to enhance student creativity within educational environments. Loose parts refer to flexible, movable objects that can be manipulated, combined, and repurposed in various ways. The study delves into the theoretical underpinnings that support the connection between loose parts…

This work seeks to understand the emergent nature of mathematical activity mediated by learners' engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of…

Positioning teachers as designers of curricular resources invites opportunities for exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic…

This case study aims to describe the learning characteristics of a child and evaluate his preferences for using physical manipulatives (PM) and virtual manipulatives (VM) to solve fraction problems. The participant in this study was a fourth-grade child. The child was given similar problems to solve using PM and VM. Data sources were observations…

The use of manipulatives to develop conceptual understanding appears to be a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. This study evaluates the impact of mathematical manipulatives on young children's attitudes towards mathematics (YCATM). The modified three-dimensional model of…

In this research, it is aimed to determine the status of the preschool manipulative story books containing the activities which are placed before the stories, inside of the stories or after the stories, in terms of date of publications, subject of the stories and kind of the activities in the story. For this purpose, 188 books were investigated…

Research examining teachers' decision making is abundant for pedagogical activities, yet a neglected area is the study of factors influencing teachers when selecting mathematical games. This article sheds light on the factors considered when teachers' select a specific game to use in their primary mathematics classroom. Data from 248 Australian…

Teaching geometry courses for preservice elementary teachers, we observed that difficulty with classifying shapes (and, in particular, composite 3-D shapes) persists even after work with simple shapes to support the writing of accurate and unambiguous definitions. We conducted a self-study of our teaching of 3-D concepts to uncover the concept…

This pilot project explored the extent to which a pre-literate child can identify and record basic statistical concepts of shape, spread, and center represented by blocks in the form of a frequency distribution. A simple apparatus consisting of a ruler, pencil, and set of blocks was designed to engage a child in playful exercises under the…

Spatial ability is an important tool in chemistry and this ability can be improved. Various technologies have been used to improve spatial ability. However, it is not clear if viewing technologies should take the place of the model kit; the traditional method of learning about molecular structures. Our research aims to address this gap. In our…

This lecture discusses how the careful preparation of the observer, control of conditions, and precise use of materials will allow the child to "be free to manifest the phenomena which we wish to observe." This lecture was delivered at the International Training Course, London, 1921. [Reprinted from "AMI Communications" (2008).]

Time is an area of measurement that is difficult for children. This interview study addresses the question: What are children's solution approaches to position the hands of an analog clock? To explore this, we investigated problem solving when using a clock manipulative with mechanically linked hands. We compare overall success rates among…

The recent proliferation of technological devices with natural user interfaces (e.g., touchscreen tablets) is regenerating scholarship on the role of sensorimotor interaction in conceptual learning. Some researchers of mathematical education have adopted views from constructivism, phenomenology, enactivism, and ecological dynamics to interpret…

Tangible user interfaces (TUIs) are frequently used to teach children abstract concepts, in science and mathematics. TUIs offer a natural and immediate form of interaction that promotes active and hands-on engagement and allows for exploration and reflection. Tangible objects are representational artifacts in their essence, and they increase the…