Parametric equations are used to represent the pathway of an object in terms of time or another changing variable. This allows, for example, for equations that are written using two variables to be examined in terms of the passage of time. In this paper the author examines two traditional application problems whose solutions can be enriched through the use of parametric equations. In the first, the falling ladder problem, a ladder is leaned against a wall then pulled away with a constant velocity. Deriving parametric equations for this scenario permits the pathway of the ladder to be plotted. Parametric equations also make it possible for the horizontal and vertical velocities of the ladder to be examined separately. The second problem is that of maximizing the length of a ladder that can fit around a hallway corner. In this problem an envelope algorithm is first developed, then parametrized to further investigate this scenario. Using these two situations, this report ultimately shows how parametric equations can be used to give a more thorough approach to some of today’s most classic calculus problems. / text

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)