We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom's taxonomy and then used to code exam problems. We have analyzed historical and recent exam problems in both algebra-based and calculus-based exams. In…

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…

An augmented reality (AR) application and an activity worksheet have been developed to support students in visualizing the concepts involved when solving [superscript 1]H NMR problems. This instructional resource was designed to encourage conceptual problem-solving and prevent memorization by eliminating the use of chemical shift tables. It uses…

Background: The assessment of cross-curricular skills is gaining attention in many countries. In Japan, the 'Information Literacy Survey for Upper Secondary Students' (the ILSUS) was designed to measure information literacy through Computer-Based Testing (CBT). It was the first large-scale survey based on Item Response Theory (IRT) implemented by…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

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…

Innovations in Science, Technology, Engineering, and Mathematics (STEM) are a cornerstone of the United States' economic prosperity, yet national and international assessments paint a poor picture of students' STEM competencies (reference 1; reference 2). These data have led to transformative approaches to improve STEM education including…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

Understanding how struggling students approach math is vital to designing effective math lessons. Many low achieving students rely on a weak knowledge of procedures and attempt calculations without adequate consideration of the problem. We investigated how enabling or preventing premature calculations affected learning math. Students were…

In this article we present our arguments in favor of a teaching of mathematics by means of problematization and investigation, one that includes in the classroom multiple ways and meanings for the students to read the world around them. In this respect, we propose a teaching-learning process of mathematics grounded on the relationships between…

In this study, we continue our efforts to address students' difficulties understanding organic chemistry, particularly in connecting structure to function and using the language of chemistry to explain how and why reactions occur. For the first time, we have characterized students' work and problem-solving strategies on familiar and unfamiliar…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

This study examined the impact of Classworks® Individualized Learning math instruction on second-grade students performing below the 25th percentile in math. The research, conducted during the 2021-2022 school year, involved 1,367 students from 45 schools across seven districts. A quasi-experimental design compared 941 students who had any use of…

Research and development of Learning Analytics (LA) have created new ways to support students' learning. However, our understanding of teachers' roles when implementing LA in classroom practices remains nascent. This study investigates how teachers can implement LA to support students' agency in directing their own inquiry, when engaging in a…