Two suggestions for instruction in chemical equilibrium are presented, along with the evidence that supports these suggestions. The first is to use diagrams to connect chemical reactions to the effects of reactions on concentrations. The second is the use of the majority and minority species (M&M) strategy to analyze chemical equilibrium…

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Teachers typically teach subjects separately, but integrated science, technology, engineering, and mathematics (STEM) curriculums that focus on real-world practices are gaining momentum (NAE and NRC 2009). Before release of the "Next Generation of Science Standards" ("NGSS") (NGSS Lead States 2013), 36 states already had a…

Students with autism spectrum disorder (ASD), though academically capable, can have difficulty succeeding in college. Evidence-based intervention to promote effective problem solving may improve quality of life, as well as success and satisfaction in college. This study adapted and piloted a group-based cognitive-behavioral intervention program,…

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

The perception of what a teacher says s/he does in the classroom may or may not match the reality of their actual teaching practice. This case study considers one second-grade teacher's instructional methods and pedagogical decisions when teaching number sense and her perception of what informed her teaching practice. This teacher supported…

As young adolescents, middle grades students experience a wide variety of changes related to their cognitive capabilities, social and emotional well-being, and use of self-regulation strategies. Authentic performance tasks challenge students to apply their knowledge and skills to realistic problems to create products or performances--consistent…

Students in this post-industrial technological age require opportunities for the acquisition of new skills, especially in the marketplace of innovation. A pedagogical strategy that is becoming more and more popular within social studies classrooms is the use of computer and video games as enhancements to everyday lesson plans. Computer/video games…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

There have been many significant changes in education over the last fifty years, but few have been as swift and all-encompassing as the Common Core State Standards (CCSS). Discussed and debated everywhere, and now implemented in many states, the CCSS initiative set out to transform our nation's K-12 educational system by providing clear…

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

Researchers and educators support the idea of providing authentic literacy experiences to students. However, a critical misconception of the locus of authenticity exists; the focus has generally been on making tasks authentic to college, careers, or researcher-determined notions of authenticity rather than making tasks authentic to students and…

Technology-rich learning environments (TREs) provide opportunities for learners to engage in complex interactions involving a multitude of cognitive, metacognitive, and affective states. Understanding learners' distinct learning progressions in TREs demand inquiry approaches that employ well-conceived theoretical accounts of these multiple facets.…