Change Laboratories are a methodology to deal with complex problems in society in order to both better understand these problems as well as to find potential solutions. They typically involve collaborative problem solving and solution seeking from practitioner's perspectives, conducted in a series of successive, structured workshops informed by…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

This research was conducted to facilitate the conceptual understanding of the solutions that contain abstract concepts and not to understand easily. The aim of this research is to determine the effect of applied methods on the achievement level of prospective science teachers and conceptual understanding level at the particulate nature of matter…

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to…

This study was conducted during the first semester of 2016, from March 21st to June 30th, with 104 students, in eight educational centers or "polos," in the states of Minas Gerais and São Paulo. Previously, these mathematics teacher education students had no opportunity to study in higher education in Brazil. They were enrolled in a…

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

In this article, the authors describe how a theoretical framework--the modeling cycle of Bliss, Fowler, and Galluzzo (2014)--came to life in their classroom as students struggled with an open-ended modeling task. The authors share their high school students' work--warts and all. They explain how they used their students' ideas and errors to help…

Mathematics can be viewed as complex structures comprising intricate and profoundly useful webs of relationships. Students can experience mathematics in this way when working on mathematical tasks such as problem-solving, modelling, investigations or problem posing. Yet these kinds of tasks are seldom implemented in many upper-secondary and…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…

In May 2016, the office of Finance and Sponsored Projects at The Research Institute at Nationwide Children's Hospital conducted a 5-day design sprint session to re-evaluate and redesign a flawed final reporting process within the department. The department sprint was modeled after the design sprint sessions that occur routinely in software…

Design tasks are difficult to teach, due to large, unstructured solution spaces, underspecified problems, non-existent problem solving algorithms and stopping criteria. In this paper, we comment on our approach to develop KERMIT, a constraint-based tutor that taught database design. In later work, we re-implemented KERMIT as EER-Tutor, and…

Science, Technology, Engineering, and Mathematics (STEM) education initiatives have placed pressure on teachers to bring technology tools into classroom, including three-dimensional (3D) printing. Yet, little research has examined what specific math skills are required for 3D printing technology. This article describes a follow-up analysis of…

To date, many instructional systems are designed to support learners as they progress through a problem-solving task. Often these systems are designed in accordance with instructional design models that progress the learner efficiently through the problem-solving process. However, theories from various fields have discussed failure as a strategic…

Research in computer-based learning environments has long recognized the vital role of adaptivity in promoting effective, individualized learning among students. Adaptive scaffolding capabilities are particularly important in open-ended learning environments, which provide students with opportunities for solving authentic and complex problems, and…

Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly…