This research aimed to examine the difficulties and failures of eleventh-grade students regarding probability concepts. With this aim, ten different open-ended probability problems were asked to the 142 eleventh-grade students. Each of these problems requires using different basic probability concepts. It is qualitative research, and the data…

Recent findings show that after studying a text, teaching the learned content on video to a fictitious peer student improves learning more than restudying the content. This benefit may be in part due to increased arousal associated with the teaching activity. The present experiment investigated whether teaching on video is also effective for…

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

The concept of intrinsic complexity explains why different problems of the same type, tackled by the same problem solver, can require different times to solve and yield solutions of different quality. This paper proposes a general four-step approach that can be used to establish a model for the intrinsic complexity of a problem class in terms of…

Fractions are perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity are fractions having five interrelated constructs (part-whole, ratio, operator, quotient and measure) and teachers' pedagogical approaches to address these constructs. The present…

Developing textbooks of optimal quality is crucial for enriching the students' learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…

In collaborative learning, the intuition "the more device, the merrier" is somehow widely acknowledged, but little research has investigated the relationship between device-student ratio and the learning outcome. This study aims to investigate not only the main effect of different device-student ratio, also to identify the moderators in…

Nowadays, students are becoming familiar with the computer technology at a very early age. Moreover, the wide availability of the internet gives a new perspective to distance education making e-learning environments crucial to the future of education. Intelligent tutoring systems (ITSs) provide sophisticated tutoring systems using artificial…

The objective of this study is to analyze the ability of students of the University Center for the Economic Administrative Sciences which forms part of the University of Guadalajara from different economic-administrative undergraduate programs, to solve distinct problems in the area of probability, applying a multiple-choice instrument aligned to…

Providing test questions after an initial study phase is a common instructional technique. In theory, questions that require higher-level (deep) processing should be more beneficial than those that require lower-level (shallow) processing. However, empirical evidence on the matter is inconsistent. To shed light on two potential reasons for these…

Problem solving is an integral part of doing science, yet it is challenging for students in many disciplines to learn. We explored student success in solving genetics problems in several genetics content areas using sets of three consecutive questions for each content area. To promote improvement, we provided students the choice to take a…

Scaffolding techniques, such as sequencing and fading, used in online video lectures may help mitigate the negative relationship between complex contents represented by intrinsic load and content understanding represented by germane load. This study analyzed survey responses from university students (n = 2365) who participated in online classes in…

The article aims to determine the academic performance and errors in the resolution of types of problems of application of the quadratic function, of high school students from the Los Lagos Region and Los Rios Region in Chile. The approach is qualitative and descriptive with case studies. A math test with open response problems and an opinion…