Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary students. The author investigated this relationship by separating performance in openended and closed situations. Findings of the study indicated that the cognitive abilities explained 32.3% (open-ended) and 48.2% (closed) of the variance in mathematical problem solving performance as a whole. Mathematical knowledge and general intelligence were found to be the only variables that contributed significant variance to closed problem solving performance. General creativity and verbal ability were found to be the only variables that contributed significant variance to open-ended problem solving performance.

A persistent problem in education is underrepresentation of certain cultural and linguistic groups such as American Indian, African American, and Hispanic, in special programs for exceptionally talented students, especially in science, technology, engineering, and mathematics (STEM). An assessment with demonstrated reliability and validity as an instrument to identify exceptionally talented students was included with new instruments created in the X project. A continuum of problems, including closed, semi-open, and open-ended, was an important component of the assessment, enabling the assessment of creativity as well as understanding of mathematics concepts. The math assessment was field tested in five high schools in high poverty areas that also had high percentages of American Indian or Hispanic students. It was implemented as part of a battery of instruments to identify students to participate in a special internship program. The test–retest reliability and construct, concurrent, and predictive validity need to be investigated in future studies.

In this qualitative study the researchers explored children's perceptions of their participation in a science class in which an elementary science curriculum, the Full Option Science System (FOSS), was combined with an innovative teaching model, Real Engagement in Active Problem Solving (REAPS). The children were capable of articulating views about their learning experiences during science classes. Meaningful experiences with deep levels of engagement were those that involved hands-on activities, such as experiments, provided by the FOSS curriculum; and problem-solving and model building, which were components of the REAPS model. Students' perceptions demonstrated in their drawings were similar to their interviews, which were evidence of their meaningful science learning experiences. Incorporating students' voices, as a type of feedback for teaching and learning, is important for teachers and practitioners; innovative pedagogical models contribute to meaningful and long-lasting science learning.

Using the test scores of more than 2,250,000 students who participated in the American Mathematics Competitions (AMC) from 2009 to 2019, this study examined the direction and magnitude of the trends in gender disparity in participation and high achievement in self-select mathematics exams. The results of this study indicated that the male to female ratio among the AMC participants increased significantly from 2009 to 2019. The findings also showed an established disparity that favored males for each year and for all competitions in both the top 1% and 5% levels, while the trend in the male to female ratios over a decade was stable, except for the top 1% of the population in the AMC 8, in which there was a significant increasing trend that favored males. The possible impacts of these findings within the context of the underrepresentation of women in STEM (science, technology, engineering, and mathematics) fields are discussed.

Using the test scores of more than 1,000,000 students who participated in the Advanced Placement Computer Science (AP CS) exams from 1997 to 2020, this study examined the direction and magnitude of the trends in gender disparity in participation and top achievement in advanced exams. The findings indicated that the male-to-female ratio (MFR) among AP Computer Science (CS) exam participants declined from 4.87 to 2.26 between 1997 and 2020. Similarly, the MFR among top scorers (students who scored 5 out of 5) in any type of AP CS exams declined rapidly, in favor of female students, from 8.00 to 2.14 during the same period. Possible implications of these findings for educators, particularly for AP CS teachers and school counselors, were also discussed in the context of the underrepresentation of females in computing fields.