The purpose of this study was to determine the effectiveness of early diagnosis and a summer program to strengthen precalculus skills before students enrolled in Engineering Calculus I. A meta-synthesis of interventions to increase success in college calculus was conducted, with a meta-analysis of studies that contained sufficient quantitative data to calculate Hedge's g effect sizes. Content validity for a mathematics placement exam was confirmed by an expert panel, and internal consistency of scores from 2008-2011 was verified using Cronbach's alpha. Effectiveness of a summer program to strengthen precalculus skills was measured by Hedge's g effect size. Results of content analysis of surveys given to tutors and students in the summer program were presented. ANOVA was used to compare mean GPA's of participants and nonparticipants of the summer program. The meta-synthesis revealed that numerous strategies, some in precalculus and some in calculus, were successful for increasing success in college calculus. For the studies in the meta-analysis, the highest effect sizes were found in studies that used a more comprehensive approach (e.g., collaborative groups and projects) rather than a single strategy (e.g., computer skills practice). An expert panel determined that the exam was a good measure of requisite knowledge for calculus. One question was considered unnecessary for calculus and was not of a type addressed in precalculus and was eliminated from further analysis. Cronbach's alpha was consistently above .8 for each year's scores 2008-2011 and for each subset of scores by gender, ethnicity, and selected majors for 2008-2011. The 122 students who participated in the summer program increased the average score by 6.45 points (total of 33), with 81% of the students raising their scores above the cut score to take Engineering Calculus I. Results of ANOVA to compare mean GPA's for students in the summer program and students who did not participate, both with placement exam scores in the range 16 to 21, inclusive, showed no significant difference. The summer program was successful in allowing some students the opportunity to strengthen their precalculus skills and take Engineering Calculus I a semester earlier than the control group.

Many students face tremendous difficulty in high school and/or college level calculus courses. The author hopes that by introducing students to the following nontraditional three topics prior to calculus, students' understanding of calculus will be enhanced. This thesis focuses on the following topics: Tangent Lines to Conics Maxima and Minima Biquadratic Equations Because these topics are not generally covered in precalculus courses, there are several possible uses for them. An instructor could use the material as: An added classroom resource Project assignments for outside classroom study A student resource for precalculus advanced studies, or An independent study This thesis assumes that the student is well prepared for the precalculus course by having a good understanding of foundational algebra skills.

Grounded in Freire's (1970) notion that the purpose of education in an unjust society is to bring about equality and justice, Critical Mathematics (CM) scholars consider mathematics to be a tool to understand, critique, and change the world by deconstructing power structures that marginalize certain groups. In particular, Gutstein's (2006) framework for integrating students' Community, Critical, and Classical mathematics knowledge bases (3 Cs) advocates for mathematics instruction that incorporates students' informal and everyday experiences. This involves investigations into social phenomena that draw on students' perspectives and experiences to inform critical analysis, while developing mathematical power. This dissertation presents the findings from a critical ethnographic study of a veteran teacher of color's approach to integrating the 3 Cs in his Precalculus class. In addition to discussing the creation and implementation of CM activities, this study examined the perspectives and participation of students of color during these curricular units. Data from 12 students of color, including interviews, focus groups, classroom observations, and student work, were collected over the course of a school year. Detailed descriptions are presented of three CM activities (i.e., Local Poverty Unit, AIDS Lab, Gini Coefficient Unit).Analysis of student participation found that students engaged most fully when units integrated transparent mathematical concepts into non-traditional social investigations. CM activities that lacked mathematical activity and/or reproduced traditional instructional norms resulted in high levels of open and passive resistance. Analysis of student perspectives found that repeated opportunities to integrate the 3 Cs promoted shifts in students' orientation toward mathematics. Some students came to see new ways of learning and using mathematics that included various means of participation and connections to one's personal life. In the end, students recognized that mathematics could be relevant and powerful for making sense of the world (reading the world), and acknowledged its potential for bringing about change (writing the world). Findings point to the essential role personalization plays in helping students develop a sense of social agency. That is, by prioritizing Community knowledge and inviting students to incorporate personal and family stories, teachers promote students' integration of their personal perspectives and experiences into their critical analyses.

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The quality of mathematics knowledge attained by students entering university in Science, Technology, Engineering and Mathematics (STEM) fields has been decreasing. There is a need to enhance students’ mathematical knowledge in order to maintain the standards of STEM curriculum at university. The rationale of this study was to investigate the influence of Pre-Calculus Mathematics Refreshment module taught using Meta-cognitive skills and Co-operative Learning (MCL), or Co-operative Learning (CL) only, or Traditional lecture (T) intervention method to First Year pre-engineering Students on their Applied Calculus 1 in an Ethiopian university. The study further investigated the influence of Pre-Calculus Mathematics Refreshment module for MCL, or CL, or T intervention method on male and female students’ achievement. The refreshment module and Applied Calculus 1 scores were measured through posttest and normal class room score of Applied Calculus 1 result. The dependent variables were student achievement in pre-calculus refreshment Module and Applied Calculus 1. Out of 29 universities in Ethiopia only four were selected to participate in this study. Population of this study was all pre-engineering first year students in those universities in 2016/2017. The sample consisted of 200 pre-engineering university students who studied in four of Ethiopian universities and one class was randomly selected by lottery method from existing pre-engineering classes in each university. Two experimental groups which were taught MCL and the other CL intervention method and two of them were control groups upon whom the control novice with traditional lecture method and control without intervention was applied. In each group 50 students of 25 males and 25 females were purposely selected from sampled class. A pre-calculus mathematics Pre-test was administered first, where the average scores of all students Pre-test result was below 33%. Then, first MCL and CL intervention methods were discussed and exercised for one week before implementing the study. For the study, selected pre-calculus mathematics topics was taught in all classrooms for 32 periods i.e. 50min x32= 26.7hrs at the beginning of the first semester parallel with Applied Calculus 1 for the academic year 2016 / 2017. The statistical tools used under this procedure include descriptive statistics percentage, mean and standard deviation and inferential statistics, T-test, and one-way analysis of variance (one-way ANOVA). The results show statistically significant differences (Sig 0.00) at the significance level (0.05) between students that learnt pre-calculus refreshment module and control group which did not. Among the students those learned pre-calculus refreshment module through MCL, CL and T method students in the MCL and CL groups’ posttest scores significantly different from T group in pre-calculus results both with Sig of 0.00. But there was no significant difference between MCL & CL groups were Sig is 0.97. Additionally, the female students in the MCL group was not significant different from CL and T group, on an impact of refreshment module, in Applied Calculus 1 mathematics where Sig is 0.994 and 0.237 respectively, and CL female group scores significantly different from T group in Applied Calculus 1 results with Sig 0.042. The male students in the MCL and CL groups were significantly different from T group in Applied Calculus 1with Sig of 0.07 and 0.012 respectively. Also, there was a positive correlation between Pre-Calculus refreshment module and Applied Calculus 1 with correlation coefficient of 0.835. Lastly, the result of pre-calculus mathematics posttest scores with the female students in MCL relatively increased than male students, than in CL and T groups, which indicated that MCL benefit more female students than male students. The differences were more in favor of pre-calculus mathematics refreshment with MCL intervention method. To improve success in engineering participation of all students, recommended that a pre-calculus module should be offered by all universities for first year engineering students, structured co-operative learning with purpose has significant gains for effective instruction, and to increase the success rate of female students this study has proven that they are trainable and therefore, meta-cognition skills have to be nurtured for female students. / Mathematics Education / D. Phil (Mathematics Education in Science and Technology)