The notion of algorithm may be perceived in different levels of abstraction. In the lower levels it is an operational set of instructions. In higher levels it may be viewed as an object with properties, solving a problem with characteristics. Novices mostly relate to the lower levels. Yet, higher levels are very relevant for them as well. We…

This study evaluated the effectiveness of the Mathematics Infusion into Science Project (MiSP), which integrated science and mathematics in an engaging middle school science curriculum that fostered improvements in science content knowledge, higher-level problem solving, and affective domains related to mathematics. The project design was based…

This study explores the affordances that the open-ended questions hold in comparison with those of closed-ended questions through examining 6th grade students' performance on a mathematics test. For this purpose, a questionnaire including 2 open-ended and 2 closed-ended questions was applied to 36 6th grade students. The questions were prepared in…

This paper extends prior work establishing an operationalized framework of mathematical sense making (MSM) in physics. The framework differentiates between the object being understood (either physical or mathematical) and various tools (physical or mathematical) used to mediate the sense-making process. This results in four modes of MSM that can…

This article introduces the concept of adaptive intelligence--the intelligence one needs to adapt to current problems and anticipate future problems of real-world environments--and discusses its implications for education. Adaptive intelligence involves not only promoting one's own ability to survive and thrive, but also that of others in one's…

This study investigated the effectiveness of using a sequence of worked examples as part of the feedback cycle. Worked examples were either presented as full worked examples or partial worked examples (single-step and completion formats). In two experiments, grade 8 students completed a learning phase on a mathematics topic, which was immediately…

The present study aims to examine the pedagogical effectiveness of a Chinese mathematical dialogue-based intelligent tutoring system used for teaching mathematics. The mathematical unit 'multiplication and division of time expressions' was taught to 134 fifth-grade students in three types of instruction conditions: the intelligent tutoring system…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

We investigated the feasibility of using automatic speech recognition (ASR) and natural language processing (NLP) to classify collaborative problem solving (CPS) skills from recorded speech in noisy environments. We analyzed data from 44 dyads of middle and high school students who used videoconferencing to collaboratively solve physics and math…

In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

This guide is a revised and updated edition of "Making It Count." This version contains much of the information from the earlier publication but also includes strategies for using project-based learning and Web-based instructional programs to support the development of mathematics proficiency for youth in short-term juvenile correctional…

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

Information and communication technology (ICT) is an integral aspect of the current Australian Curriculum: Mathematics. The language, strategies and resources required in mathematics education today can be very different to the mathematics lessons experienced by current teachers when they themselves were at school (Sousa, 2015). Learning…

In this study, it was aimed to investigate the primary mathematics teacher candidates' perceptions about the equal sign within the scope of neuroscience studies. To reveal their perceptions about the equal sign, three types of addition operations were asked to the participants: a+b=[], []=a+b, a+b=[]+c. Their brain waves were recorded by EEG…