This study examines the power of cognitive and noncognitive variables to predict students' performance in algebra. We investigated students' prior year's assessment scores and demographic characteristics to predict eighth-grade algebra scores. Using California statewide assessment data, we explored predictive factors in three regression models. These analyses reveal that the seventh-grade mathematics test scores account for 61% of the variance in eighth graders' algebra test scores. Analyzing subscores of the seventh-grade mathematics test, the assessment content focus of rational numbers is a major predictor, contributing 48% of the variance in eighth graders' algebra test scores. On the other hand, students' demographic variables show little predictive power for eighth-grade algebra scores. This study provides empirical evidence for understanding the factors that impact a student's success in learning algebra.

In California, an increasing number of 8th graders have taken algebra courses since 2003. This study examines students ' California Standards Test (CST) results in grades 7 through 11, aiming to reveal who took the CST for Algebra I in 8th grade and whether the increase has led to a rise in students' taking higher-level mathematics CSTs and an improved performance in following years. Results show that the pipeline of 8th-grade algebra and following years' higher-level mathematics CSTs has a significant leak in it. Furthermore, the longitudinal analysis reveals that 9th-grade students have a 69% greater chance of succeeding in algebra if they passed the CST for General Mathematics in 8th grade compared to those who failed the CST for Algebra I.

Since 2003, California has enacted a policy through its education accountability system that encourages schools and districts to place all 8th grade students into algebra courses and therefore, be tested in algebra in the statewide assessment program. Ten years later, there are a great many more 8th graders taking algebra now. However, there are also many students repeating algebra, instead of going on taking higher level mathematics tests. This article aims to provide the historic context of this policy, previous and recent studies on 8th grade algebra, and our study based on the California Standardized Testing and Reporting (STAR) data. We analyzed 8th grade algebra test-taking and the following years� higher level mathematics test-taking to examine the college preparation course taking pipeline. Our longitudinal study compared two groups of students� performance on 9th grade algebra between those who previously scored below proficient on algebra at 8th grade and those who scored proficient or above on general mathematics at 8th grade. Further, another longitudinal study linked 7th grade mathematics sub-scores to 8th grade algebra achievement. The results show that �algebra for all� policy increased the number of students taking algebra at 8th grade and subsequently, taking higher level mathematics tests. However, the pipeline of the college preparation course taking has a significant leak because the number of students taking higher level mathematics decreased dramatically after algebra. Longitudinal study shows that students who pass the general mathematics test at 8th grade have a 69% greater chance to pass the algebra test at 9th grade compared to their peers who failed the algebra test at 8th grade. We also find that the sub-score rational numbers is a strong predictor of 8th grade algebra achievement. Alternatives to help all students achieve in mathematics learning are also discussed in addition to recommendations for future research.

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Based on the generate mechanism of rolling bearing fault signal and its modulation model in the process of spreading, an improved method that combining Hilbert transformation and Stochastic Resonance (SR) is proposed for rolling bearing fault features extraction. Subsequently, the method is used to extract fault signal features from three kinds of typical faults, the surface damage of the inner ring, outer ring stripping injury and roller electrical erosion. First, low frequency envelope components are acquired from rolling bearing vibration signals through Hilbert transformation. Then, depending on the advantage of SR that SR is immune to noise and sensitive to periodic signal, cyclical faults signal of the low frequency envelope is highlighted by using the variable step size solution that can overcome adiabatic condition limitation of SR system. The experimental results show that the algorithm can extract the fault feature and identify the fault type effectively.