The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

In mathematics, learners often spontaneously draw on prior knowledge when learning new ideas. In this study, we examined whether the specific diagrams used to represent more familiar (i.e., whole number division) and less familiar ideas (i.e., fraction division) shape successful transfer. Undergraduates (N = 177) were randomly assigned to…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these…

The connection between mathematics and statistics is an important aspect in understanding college students' learning of statistics because studies have shown relationships among mathematics attitudes and performance and statistics attitudes. Statistics attitudes, in turn, are related to performance in statistics courses. Little research has been…

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

In spite of increased interest in game-based learning, relatively little is known about the learning process in games. The aim of this article is to study the process of conceptual change in the context of game-based learning in order to reveal playing behavior that triggers and facilitates it. Primary school pupils (N = 401) played a game of…

Reports on a study that examined potential links between mental models constructed by students, the organizational quality of students' prior geometric knowledge, and the use of that knowledge during problem solving. Suggests that the quality of geometric knowledge that students develop could have a powerful effect on their mental models and…

Provides an overview of research on transfer, highlighting its main tenets. Looks at interviews of two grade 5 students learning about mathematical concepts regarding operations on positive and negative quantities. Focuses on how their learning is influenced by prior knowledge and experience. (Author/MM)

Argues that inventions are of the utmost importance in knowledge development, and that conventions play an important role in inventions by providing support for their development. This position borrows from Piaget's perspective regarding figurative and operative aspects of thought. Contains 22 references. (DDR)

Reports on a study of children ages 10-11 years (N=6) exploring forces. Reveals a gap between the ways that measurement is used in mathematics and the ways it is used in science. Reviews the focus of the National Numeracy Project. (DDR)

Argues that teachers are challenged to understand how constructivism can serve as a referent for teaching. Discusses one approach that provides opportunities for teachers to practice innovative strategies while engaging in discourse about the process. Contains 25 references. (DDR)

Recommends that numeracy be better coordinated and integrated across the curriculum and that teachers examine the image of mathematics presented to children. Discusses the value of eliciting children's ideas about and experiences with numbers and measuring. (DDR)

Explains the work of a primary-research group focusing on the practical aspects of the use of scale in science. Reports on three studies that look at the impact of the representation of scale in different areas related to the Standard Assessment Tasks (SAT). (DDR)