This monograph offers an overview of the current research work carried out in Croatia and the surrounding countries, and specifically an interesting insight in teaching and learning issues in these countries. The authors discuss the need of the general population for becoming good problem-solvers in society of today, which is characterised by…

Scope and method of study: The purpose of this study was to unpack the understandings pre-service elementary teachers have pertaining to the ideas of pattern and function. The intent was to bring insight into how mathematics teacher educators can use patterning activities to prepare pre-service elementary teachers to support the development of…

Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic…

The author has been prompted to write this article about finger multiplication for a number of reasons. Firstly there are a number of related articles in past issues of "Mathematics Teaching" ("MT") which have connections to this algorithm. Secondly, very few of his primary teaching students and professional colleagues appear to be aware of the…

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become…

In this article we suggest a method of evaluating learner expertise based on assessment of the content of working memory and the extent to which cognitive load has been reduced by knowledge retrieved from long-term memory. The method was tested in an experiment with an elementary algebra tutor using a yoked control design. In the learner-adapted…

This paper suggests a route to deep, long-term algebra reform that begins not with more new approaches but with elementary school teachers and the reform efforts that currently exist. This route involves generalization and expression of that generality using increasingly formal languages, beginning with arithmetic, modeling situations, geometry,…

Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…

Describes a lesson taught in primary school based on the use of linking cubes. Shows how meaningful mathematics can be made accessible to children and how fundamental issues of variant and invariant properties might be developed. (KHR)

The purposes of this paper are to present research related to the development of new instructional games (named Survivor's Games), and measure the effectiveness of these games to help students (K-5) master basic fact operations (single-digit additions or factor and single- or double digit sums or products), stimulate the exploration of…

Improving teacher effectiveness is high on the list of most education reformers in Colorado, as it is nationally. Effective teaching in the elementary years is of vital importance to ensure not only that children master fundamental skills, but that performance gaps narrow rather than widen beyond repair. Disadvantaged students can catch up…

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

Presented are example activities which are typical of the topic focus and methods of approach evident in the Algebraic Thinking in Children (ATIC) project. This project is aimed at assisting children to ultimately make sense of formal algebra when it is presented. (CW)