Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-06T13:40:54Z No. of bitstreams: 1 davidsonmendesferreiradepaula.pdf: 1155298 bytes, checksum: 9e0a8999b7a791620c60d74d75c4915e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T13:21:42Z (GMT) No. of bitstreams: 1 davidsonmendesferreiradepaula.pdf: 1155298 bytes, checksum: 9e0a8999b7a791620c60d74d75c4915e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T14:08:17Z (GMT) No. of bitstreams: 1 davidsonmendesferreiradepaula.pdf: 1155298 bytes, checksum: 9e0a8999b7a791620c60d74d75c4915e (MD5) / Made available in DSpace on 2017-02-07T14:08:17Z (GMT). No. of bitstreams: 1 davidsonmendesferreiradepaula.pdf: 1155298 bytes, checksum: 9e0a8999b7a791620c60d74d75c4915e (MD5) Previous issue date: 2016-08-18 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O conceito de Limite é uma das ferramentas fundamentais no ensino de cálculo diferencial e integral no ensino superior, mas que normalmente não é lecionado no ensino básico, embora esse tema tenha feito parte dos livros do ensino médio por um longo tempo. Este trabalho visa mostrar a importância de se abordar esse assunto nesse nível, como um elo que une o ensino médio e a graduação, pois, o conteúdo ensinado até o ensino médio, não é completamente eficiente para estudar matemática mais avançada. Ele é composto por vários planos de aula que tratam desde a noção inicial de limite, passa por derivada, e finda nas somas de Riemann e noções de integral, além de uma síntese sobre esses assuntos. Temas como máximos e mínimos de funções, áreas e volumes, tornam a introdução do tema menos impactante e abrem caminho para resolvermos problemas mais avançados. / The Limit concept is one of the fundamental tools in teaching differential and integral calculus in higher education although it is not usually taught at basic education level, although this theme has been part of high school books for a long time. This work aims to show the importance to deal with Limit at this level, so it can work as a link between high school and higher education, once the content taught at elementary and high school are not really efficient for the study of more advanced mathematics. This work consists of several lesson plans that deal from the initial concept of limit, go through derivative, and end in Riemann’s sums and integral notions, as well as offer an overview of such issues. Topics such as maximum and minimum of the functions and also areas and volume make the introduction of the topic less impactful and pave the way to the solution of more advanced problems.

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)

Mathematics achievement has been of great concern to researchers involved in mathematics education. This concern has resulted in research seeking to determine for example, the factors that positively or negatively contribute to student performance in mathematics. Many of the reported studies in the literature have investigated the factors within the context of mathematics teaching and learning in general. Very few studies have investigated the factors contributing to student achievement in mathematics when learning takes place in a computer aided environment. With the pervasiveness of computers in education in general, studies in this direction become imperative. The present study fills this gap in the literature by examining the extent to which selected variables (mathematics attitude, mathematics aptitude, computer attitude, computer prior experience, computer ownership, proficiency in language of instruction, and learning style) contribute to students' achievements in pre-calculus algebra classes that are supplemented with a computer lab program. The participants in the study were 120 students sampled from the population of students enrolled in the second pre-calculus algebra course at the preparatory year program of King Fahd University of Petroleum & Minerals during the 2003/2004 academic session. The instruments used to measure the study constructs were the mathematics attitude scale (Aiken, 1979), the computer attitudes scale (Loyd & Gressard, 1984a), and the learning styles questionnaire (Honey & Mumford, 1992). New instruments to measure computer prior experience and computer ownership were developed for the present study. Hypotheses formulated for the study were tested using multiple regression and other statistical techniques. The results show that mathematics aptitudes and English language proficiency are the most significant contributors to students' mathematics achievement. No other variables show statistically significant effects on students' achievement. Together, the selected variables explain more than 41 percent of the total variance of students' achievement. Theoretical and policy-making implications of the results are outlined and discussed. / Mathematical Sciences / D. Phil. (Mathematics, Science and Technology Education)

Mathematics achievement has been of great concern to researchers involved in mathematics education. This concern has resulted in research seeking to determine for example, the factors that positively or negatively contribute to student performance in mathematics. Many of the reported studies in the literature have investigated the factors within the context of mathematics teaching and learning in general. Very few studies have investigated the factors contributing to student achievement in mathematics when learning takes place in a computer aided environment. With the pervasiveness of computers in education in general, studies in this direction become imperative. The present study fills this gap in the literature by examining the extent to which selected variables (mathematics attitude, mathematics aptitude, computer attitude, computer prior experience, computer ownership, proficiency in language of instruction, and learning style) contribute to students' achievements in pre-calculus algebra classes that are supplemented with a computer lab program. The participants in the study were 120 students sampled from the population of students enrolled in the second pre-calculus algebra course at the preparatory year program of King Fahd University of Petroleum & Minerals during the 2003/2004 academic session. The instruments used to measure the study constructs were the mathematics attitude scale (Aiken, 1979), the computer attitudes scale (Loyd & Gressard, 1984a), and the learning styles questionnaire (Honey & Mumford, 1992). New instruments to measure computer prior experience and computer ownership were developed for the present study. Hypotheses formulated for the study were tested using multiple regression and other statistical techniques. The results show that mathematics aptitudes and English language proficiency are the most significant contributors to students' mathematics achievement. No other variables show statistically significant effects on students' achievement. Together, the selected variables explain more than 41 percent of the total variance of students' achievement. Theoretical and policy-making implications of the results are outlined and discussed. / Mathematical Sciences / D. Phil. (Mathematics, Science and Technology Education)