In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

Youth involved in 4-H projects have been engaged in science-related endeavors for years. Since 2006, 4-H has invested considerable resources in the advancement of science learning. The new Minnesota 4-H Science of Agriculture Challenge program challenges 4-H youth to work together to identify agriculture-related issues in their communities and to…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…

Word problems have been well recognised for their pedagogical value in mathematics teaching and learning. The authors of this paper examined Fijian primary mathematics teachers' mathematical knowledge by analysing 34 teachers response to three word problems. The teachers were enrolled in a primary mathematics teaching methods course at a Fijian…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

Recommending educational resources to groups of students is a common task in collaborative learning contexts. However, differences in within-group motivational factors might lead to conflicts in students' intention to use the resources. Previous methods fail to achieve high goodness of recommendation for the majority of students in heterogeneous…

The aim of this study is to determine the teaching activities of pre-service teachers in the course of mathematics teaching methods. All of the pre-service teachers have selected an attainment content from the primary (1-4) mathematics education curriculum at the beginning of the semester in the scope of mathematics teaching methods course. Data…

The aim of this study was to analyze middle school students' metacognition awareness levels and problem solving skills. The research was carried out with a total of 1595 middle school students studying in the 5th, 6th, 7th, and 8th grades in a middle school in a city of the Central Anatolia Region. The metacognitive awareness scale (MAS) form B…

A blog page is a vital tool to share and discuss information in real-world problem-solving. Unfortunately, this potential of blogs rarely was used to facilitate the problem-solving in specific physics topics. This study aimed to describe and examine a blog transformation in improving students' problem-solving. Through 40 university students, this…

Australian science teachers are asked to involve their students in the scientific processes of inquiry and investigation. The abilities needed for scientific problem-solving ("doing") and the capacity to reflect on the process of problem-solving at a meta level ("understanding") are defined as scientific reasoning competencies…

The present study took a reciprocal learning approach to examine Canadian and Chinese elementary school students' (N=40) mathematics problem posing and problem solving. Data included student performance, Skype meeting videos, meeting notes, and interviews transcripts through direct and indirect interactions between a pair of Canadian and Chinese…

We live in the challenging times of the 21st-century with the increased need for humans to possess specific skills that will help them to be successful in this era. This means that education should in learners, develop these skills effectively. Different global countries have begun to recognize the significance of multiple solutions tasks in the…