When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense-related problems. An online three-tier diagnostic test was administered to 125…

Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with…

Several investigations have revealed that students tend to exclude their real-world knowledge when solving simple, routine-like mathematical word problems. The current research is a cross-sectional developmental analysis with students from grade 2 to 10 (N=1346). Other than describing the development (or lack thereof) in students' realistic…

This paper introduces and summarises a programme of German research into teaching started 20 years ago. This research draws on Herbart's analysis of teaching with its focus on 'Bildung' (formation) which is distinguished from the measurement/psychometric tradition. It offers the possibilities of a deeper empirical understanding of pedagogical…

This article explores the concept of being an intrapreneur and a hybrid professional. An intrapreneur is a person who fills a need and starts programs, products, or services inside of a company or nonprofit as opposed to starting from nothing, which is what entrepreneurs do. A hybrid professional is someone who integrates multiple professional…

Estimation skills are critical for students in the 21st century. The ability to estimate or approximate is widely accepted as fundamental to problem solving, and important for checking the reasonableness of results. (Dowker, 2003; Reys & Reys, 1989). Therefore, estimation should be an important aspect of problem solving in all year levels but…

The aim of this study is to analyze the relationship between intellect and creativity level of students with gifted, and to understand the relationship between their creativity level and creative problem solving skills. The target group of this study consists of a total of 20 primary school students between the ages 7 and 10; it is determined by…

This article reports on a 4th-grade problem activity implemented as part of a 4-year longitudinal, design research study across grades 3-6. The activity integrated the four STEM disciplines through a focus on design. Following investigations of their feet measurements and shoes, two classes of 9-year-olds explored the roles of designers and…

Productive failure is an instructional approach that requires learners to struggle as they attempt to generate solutions to problems before, rather than after, receiving direct instruction on a targeted concept. Studies demonstrate that productive failure prepares students for later learning of new, related knowledge. Our study explored the…

Mathematical Communication Skills (MCS) refer to the students' ability to (1) arrange and link their mathematical thinking through communication; (2) communicate their logical and clear mathematical thinking to their friends, teachers, and others; (3) analyze and assess mathematical thinking and strategies used by others; and (4) use mathematical…

The ability to correctly interpret data is an important skill in modern knowledge societies. The present study investigates adults' ability to interpret covariation data presented in bar graphs. Drawing on previous findings that show that the problem context influences the interpretation of contingency tables (grounded and concrete problems are…

The purpose of this study is to examine organizational decision-making processes of problem-solving groups. This experimental design study utilized a case study method bounded by a fictional problem-solving scenario to illicit problem solving in groups. Fourteen undergraduate pre-service teachers were placed into six groups and given 45 minutes to…

Reasoning and problem solving skills are not just for researchers; they are also progressively significant for making knowledgeable decisions in our everyday lives. Showing variations in learning styles have any influence on these skills? The current state of research address the learning styles in context of reasoning and problem solving ability.…

Heat and enthalpy are challenging topics for general chemistry students because they are conceptually complex and require avariety of quantitative problem-solving approaches. Expert chemists draw on conditional knowledge, deciding when and under what conditions a certain problem-solving approach should be used. Decision-based learning (DBL)…

Reflection and recalibration, two key hallmarks of metacognition, are important elements of productive problem solving in scientific research. Often, training in these skills is obtained informally through direct exposure to independent research after college. Although some undergraduate students participate in extra- or co-curricular research…