Because of a greater need to focus on early achievement in mathematics and increased global competition in this area, emphasis is increasingly being placed upon screening and monitoring of math development in early elementary to ensure progress for all students. Although protocols for early literacy assessment exist, research of psychometrically sound and instructionally useful early numeracy assessment methods is still developing. Thus, the current study was undertaken to further develop and examine early numeracy measures. In a two-year investigation, 72 kindergarten and 57 first-grade students completed a set of existing and newly developed early numeracy curriculum-based measurement (EN-CBM) tools. Reliability and validity of these measures were examined both within and across years. The nature of score change across the academic year was also analyzed. Findings were generally similar to those published in previous EN-CBM research. Alternate-form reliability estimates were largely adequate for screening purposes. Although concurrent and predictive validity estimates varied as a function of screening period and the outcome criterion, these estimates were generally moderate to strong. EN-CBM discriminant validity evidence was mixed for the kindergarten measures but more evident for first-grade tools. All measures demonstrated score change that was statistically significant over time with at least moderate to large effect sizes for most measures. Implications for EN-CBM use as screening tools are discussed. Study limitations are presented as are suggestions for future EN-CBM research.

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應用模糊調查與統計方法去瞭解國中數學評量試題在教師與學生間以及學生不同背景（性別、對數學喜歡程度、課後數學練習時間及有無參加數學相關課外活動）對試題難易度的認知差異。結果顯示：在教師與學生之間、性別、學生對數學喜歡程度及課後數學練習時間方面有顯著差異，但是在參加課後數學相關活動方面對於數學科試題的難易度認知並沒有顯著的差異性存在。 / Using fuzzy statistical methods to understand whether the cognitive difficulty scales of the junior high school mathematics assessment questions shows difference between those given by teachers and students, by students with different genders, with different preferences, with different amounts of time spent on math practice after school, with participation or not in various math related seminars. Result demonstrates that significant difference between teachers and students, between students with different genders, between students with different preferences, and between students with different amounts of time spent on math practice after school. However, there is no significant difference between students with participation or not in various math related seminars.

Although traditional college students are more prepared for college-level math based on college admissions tests, little data have been collected on nontraditional adult learners. The purpose of this study was to investigate relationships between math placement tests and community college students' success in math courses and persistence to degree or certificate completion. Guided by Tinto's theory of departure and student retention, the research questions addressed relationships and predictability of math Computer-adaptive Placement Assessment and Support System (COMPASS) test scores and students' performance in math courses, persistence in college, and degree completion. After conducting correlation and regression analyses, no significant relationships were identified between COMPASS Math test scores and students' performance (n = 234) in math courses, persistence in college, or degree completion. However, independent t test and chi-squared analyses of the achievements of college students who tested into Basic Math (n = 138) vs. Introduction to Algebra (n = 96) yielded statistically significant differences in persistence (p = .039), degree completion (p < .001), performance (p = .008), and progress (p = .001), indicating students who tested into Introduction to Algebra were more successful and persisted more often to degree completion. In order to improve instructional methods for Basic Math courses, a 3-day professional development workshop was developed for math faculty focusing on current, best practices in remedial math instruction. Implications for social change include providing math faculty with the knowledge and skills to develop new instructional methods for remedial math courses. A change in instructional methods may improve community college students' math competencies and degree achievement.