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program. He has a B.S. in Civil Engineering from Virginia Tech and a Master's of Civil Engineering and an Ed.D. in Technology Education both from N.C. State University. Using his work experience in both engineering and education, he specializes in designing integrative STEM activities for K-12 students and implementing professional development programs for K-12 educators.

Background Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first‐year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose The purpose of this study was to investigate the relationship among the first undergraduate mathematics course a student completes, the grade they earn in this course, and the likelihood of graduating with a degree in engineering within six years. Method The study involved 1504 students from five consecutive cohorts of first‐year students enrolled in an engineering degree program at a medium‐sized Midwestern public university. Logistic regression was used to model the interrelationship between course and grade in predicting the relative likelihood of graduation for students enrolled in 16 different mathematics courses. Results Overall, students who take Calculus I or a more advanced mathematics course as their first mathematic course and who are more successful in their first mathematics course are more likely to graduate with a degree in engineering. However, considering grade and course together, some groups of students who are more successful in lower‐level mathematics courses are as likely to graduate as students who are less successful in upper‐level mathematics courses. Conclusions Evidence from this study helps to dispel the myth that beginning with higher‐level mathematics courses is the optimal course‐taking strategy when pursuing an engineering degree. Findings have implications for student advising, curriculum and instruction, high school course‐taking, and broadening participation in engineering.

As education works to reconnect student learning to something more than standardized testing, projectbased learning (PBL) has become a popular way to increase student engagement while providing more authentic applications of student knowledge. While research regarding PBL is bountiful, little has been done to connect this body of research with student perceptions regarding its classroom application, especially concerning authenticity and student engagement. This research focuses on the topic of ''task authenticity'' as a means to improve student outcomes. Two groups of seventh-grade students were presented the concept of slope and y-intercept in the context of engineering-based activities. The research design measures if there is a difference in student achievement and perceived importance of these mathematics concepts when presented with authentic and non-authentic approaches to the material. Given this particular methodology, the results show that although no significant difference was found in student achievement, there is a significant difference in the perception that students have regarding the importance of understanding slope and y-intercept.

Assessing the Severity of Departures from Sphericity SPSS produces a test known as Mauchly's test, which tests the hypothesis that the variances of the differences between conditions are equal. → If Mauchly's test statistic is significant (i.e. has a probability value less than .05) we conclude that there are significant differences between the variance of differences: the condition of sphericity has not been met. → If, Mauchly's test statistic is nonsignificant (i.e. p > .05) then it is reasonable to conclude that the variances of differences are not significantly different (i.e. they are roughly equal). → If Mauchly's test is significant then we cannot trust the F-ratios produced by SPSS. Correcting for Violations of Sphericity Fortunately, if data violate the sphericity assumption there are several corrections that can be applied to produce a valid F-ratio. All of these corrections involve adjusting the degrees of freedom associated with the F-value. In all cases the degrees of freedom are reduced based on an estimate of how 'spherical' the data are; by reducing the degrees of freedom we make the F-ratio more conservative (i.e. it has to be bigger to be deemed significant). There are three different estimates of sphericity used to correct the degrees of freedom: 1. Greenhouse and Geisser's(1958)