To develop critical reasoning skills potentially advances students' ability to critically consume information, make informed decisions, and actively participate in a democracy. An inquiry-based pedagogical approach to science teaching remains an effective means to develop critical reasoning skills. Participating in scientific inquiry requires students to generate arguments and test alternative hypotheses using experimental evidence. Scientific inquiry demands that students use their critical reasoning skills. Unfortunately, many teachers fail to allocate an adequate amount of time for genuine experimentation in science classes. As a result, science classes often leave students unprepared to think critically and apply their knowledge in a practical manner.

The focus of this study was to investigate the extent to which an inquiry-based professional development experience, including a two-day summer workshop and 18 weeks of follow up Professional Learning Community (PLC) support, affected the attitudes and pedagogical skills regarding scientific inquiry among six high school biology teachers. A concurrent mixed methods, action research design was used to measure changes in teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy was measured throughout the 22 weeks of the study. A survey instrument, card sorting activity, classroom observations using the Reformed Teacher Observation Protocol (RTOP), individual interviews, and PLC observations were used to gather data. Results indicated the professional development was effective in transforming the participating teachers' attitudes, perceptions, and skills regarding inquiry-based pedagogy.

Industry, academia, and government have spent tremendous amounts of money over several decades trying to improve the mathematical abilities of students. They have hoped that improvements in students' abilities will have an impact on adults' mathematical abilities in an increasingly technology-based workplace. This study was conducted to begin checking for these impacts. It examined how nine adults in their workplace solved problems that purportedly entailed proportional reasoning and supporting rational number concepts (cognates).

The research focused on four questions: a) in what ways do workers encounter and utilize the cognates while on the job; b) do workers engage cognate problems they encounter at work differently from similar cognate problems found in a textbook; c) what mathematical difficulties involving the cognates do workers experience while on the job, and; d) what tools, techniques, and social supports do workers use to augment or supplant their own abilities when confronted with difficulties involving the cognates.

Noteworthy findings included: a) individual workers encountered cognate problems at a rate of nearly four times per hour; b) all of the workers engaged the cognates primarily via discourse with others and not by written or electronic means; c) generally, workers had difficulty with units and solving problems involving intensive ratios; d) many workers regularly used a novel form of guess & check to produce a loose estimate as an answer; and e) workers relied on the social structure of the store to mitigate the impact and defuse the responsibility for any errors they made.

Based on the totality of the evidence, three hypotheses were discussed: a) the binomial aspect of a conjecture that stated employees were hired either with sufficient mathematical skills or with deficient skills was rejected; b) heuristics, tables, and stand-ins were maximally effective only if workers individually developed them after a need was recognized; and c) distributed cognition was rejected as an explanatory framework by arguing that the studied workers and their environment formed a system that was itself a heuristic on a grand scale.