Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

Road map problems ask students to integrate their knowledge of organic reactions with pattern recognition skills to "fill in the blanks" in the synthesis of an organic compound. Students are asked to identify familiar organic reactions in unfamiliar contexts. A practical context, such as a medicinally useful target compound, helps…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

This article discusses five generally accepted reasons to use data as a part of an educator's ongoing professional practice. Of course, there are many other more specific reasons one might look at data, but these five cover the overarching need in an educational setting. The five major purposes for using data are: (1) To enhance understanding and…

This paper deals with two types of logical problems--recognition problems and reverse engineering problems, and with the interrelations between these types of problems. The recognition problems are modeled in the form of a visual representation of various objects in a common pattern, with a composition of represented objects in the pattern.…

Many people believe that environmental factors promote giftedness and invest in many programs to adopt gifted students providing them with challenging activities. Intellectual giftedness is founded on fluid intelligence and extends to more specific abilities through the growth and inputs from the environment. Acknowledging the roles played by the…

The purpose of this quantitative study was to investigate how Rhode Island high school principals rate success in implementing 21st century skills in their schools. Secondly, this study investigated how high school principals rate the influence of implementing of 21st century skills in curriculum and instruction in their schools. The high…

In this paper we consider important factors influencing different curricular approaches to the study of numerically and geometrically defined pattern-type problems in the middle school curriculum. Our analysis involves the consideration of recommendations from national standards documents and their influences on state framework documents…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…

The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

A basic and classical assumption in the machine learning research area is "randomness assumption" (also known as i.i.d assumption), which states that data are assumed to be independent and identically generated by some known or unknown distribution. This assumption, which is the foundation of most existing approaches in the literature, simplifies…

As teachers plan instruction--even instruction about punctuation--they have the opportunity to engage students' minds and create new labels: question-asking, problem-solving. How teachers teach embeds a vision of who they think kids are and what they think kids are capable of. Are they destined for a future of critical thinking, questioning,…