Previous research on problem diagrams suggested that including a supportive diagram, one that does not provide necessary problem solving information, may bring little, or even negative, benefit to students' problem solving success. We tested the usefulness of problem diagrams on 12 different physics problems (6A/B experiments) in our massive open…

This study aimed at developing a module in physics based on the assessment of the learning progression of students in physics and science teachers' formative assessment practices. The participants in this study were the Grade 11 students and Junior High School science teachers for the data gathering, science teachers for the design and development…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

Despite the importance placed on how children come to solve single-digit addition problems, many children count on to solve these problems when they are expected to use accurate retrieval-based strategies. In this study, we assessed if a subitising intervention improved the rate at which problem-solving practice promoted retrieval, using a…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks…

The relationship between metacognition in real life situations and study skills and habits was examined using a sample of college students. Results showed no significant relationship between these two variables nor was there a significant relationship between study skills and reaction time as measured on the metacognitive test. However, there was…

This paper describes the results achieved by high school seniors on an item which involves translation of the equation P = kT into a corresponding pictorial external representation. The majority of students (the classes of 2011, 2012 and 2013) did not give the correct answer to the multiple choice part of the translation item. They chose pictorial…

In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

"Low threshold, high ceiling" tasks are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone's mathematical reasoning. In this article, the authors present a family of Brick Pyramid problems as examples of "low threshold, high ceiling"…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

This paper presents a case study of how the interactive whiteboard (IWB) may facilitate collective meaning-making processes in group work in engineering education. In the case, first-year students attended group-work sessions as an organised part of a basic physics course at a Norwegian university college. Each student group was equipped with an…

The purpose of this study is to analyse from the perspective of a history teacher and of a geography teacher the use of a photo at a history lesson. The task of designing learning activities associated with a photo was given at the discipline "Models and Paradigms of Teaching and Learning" to the first year students of the Curricular…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…