Supervisor and Teacher Educator Perceived Relevance of Recommendations in the NCTM Curriculum Standards

Based on judgments of mathematics supervisors and teacher educators, the findings of this empirical study confirm that the Curriculum and Evaluation Standards (National Council of Teachers of Mathematics [NCTM], 1989) reflect content that is relevant to mathematics instruction. However, some concern did exist about the relevancy of teaching statistics and probability at the elementary level. Despite the general consensus about the Standards, total agreement was not evident. Respondents with asecondary-school focus rated many of the standards and criteria across grade levels significantly lower in importance than did other respondents; elementary- and middle-school respondents judged several K-8 standards and criteria to be more important than did some higher-education and secondary respondents, while secondary-and middle-school respondents judged the 9–12 standards and critera to be more important than did elementary and some higher education respondents. Respondents with 30 or more years of experience or who were less familiar with the standards rated the K-8 standards and criteria to be lower in importance than did other respondents.     

The Integration of Math and Science Via Centroids

Science problems enhance and promote math functions to establish some formulas to solve them; conversely, many math results give the explanation and the development of science phenomena and their related situation. From Archimedes’ Law of the Lever, together with some properties of vector's representation, the geometrical construction of the weighted centroid of gravity of finite particles is given, the new proving of Ceva's and Menelaus's results is explored, and a related result to spacial shape is set up. These presentations are important in math, physics, chemistry, statistics, and engineering. The ideas are significant to these fields for the integration of multifarious curricula.     

Enriching Science and Math Through Engineering

This case study reviewed the collaborative efforts of university engineers, teacher educators, and middle school teachers to advance sixth‐ and seventh‐grade students' learning through a series of project‐based engineering activities. This two‐year project enriched regular school curricula by introducing real‐world applications of science and mathematics concepts that expanded opportunities for creativity and problem‐solving, introduced problem‐based learning, and provided after‐school programming (for girls only) led by engineering students from the local university. This engineering education initiative showed significant impact on students' (1) confidence in science and mathematics; (2) effort toward science and mathematics; (3) awareness of engineering; and (4) interest in engineering as a potential career. With regard to gender, there were no significant differences between boys' and girls' responses. The girls' confidence in their own skills and potential, however, was significantly more positive than the boys' confidence in the girls. These results gave rise to new questions regarding mentor/mentee relationships and the overall effect of “girls only” mentoring.