Mathematics permeates almost every aspect of human life and it is a skill much needed by the increasingly complex technological world. It is necessary that this essential skill must be properly developed among students to prepare them for future academic and professional careers. An assessment of the research-based instructional strategies blending with old traditional methods with the modern technological development is a must. Due to the complexity of mathematics learning and the varied learning styles of learners, an integration of appropriate multiple instructional strategies into mathematics education will positively impact mathematical achievement of students. The purpose of this research was to examine the effects of the use of Integrated Technologies Instructional Method (ITIM) as a supplement to the traditional lecture method on mathematics achievement of the Integral Calculus students at the College of Engineering, University of Ha'il, Saudi Arabia. The ITIM includes the four instructional strategies such as the use of the Computer-Supported Collaborative Learning, the collaborative learning, the bilingual support and the study support. Different types of academic supports have been used to examine their effects on students achievement in mathematics. Mathematics, the bedrock of science and engineering, is considered a very important indicator of a student's academic success in professional higher education. Undergraduate engineering students' low achievement in the first year mathematics is an issue demands much attention. The study was undertaken to address students' weak background in mathematics and particularly their high failure rates in this particular course. A total of 218 undergraduate engineering students, comprising of both the experimental and the control groups, were involved in this experimental design study. The control group was taught by the traditional lecture method whereas the experimental group was exposed to the ITIM as a supplement to the traditional lecture method. Apart from the effects of the use of ITIM, students' performance in the previous courses (covariates) such as mathematics, computer, and the English language were compared with their final grades of the Integral Calculus course. The final grades of students were taken as the dependent variable and the ITIM and students' scores in the previous courses as the independent variables. It has been noticed from the literature review that the application of only one instructional strategy does not address the needs of the diverse learning styles of students. A mixed mode method, quantitative and qualitative, was used to collect and analyse data. The quantitative data instruments included students' final exam grades and the student questionnaires. Interviews with students were used as qualitative tools of data collection. An independent t-test, ANOVA, univariate analysis and the stepwise multiple regression analysis were performed to determine the overall statistical significance. The study concluded that there was a statistically significant difference in the performance of the experimental group of students' in terms of their end-of-course grades compared to that of the control group. The regression model revealed significance of covariates on the dependent variable. However, no significant relationship was found between the mathematics achievement and attitudes towards the use of ITIM. The study was an attempt to demonstrate the suitability of the instructional strategies on the bilingual Arab undergraduate engineering students; however, they can probably be applicable to other bilingual students.

<p>Early childhood teachers pursuing associate degrees often repeated the college algebra course, demanding, “Why do we have to take this? We don’t teach algebra!” Expectations for their training were not well-aligned with their mathematics preparation or teaching work. I have taught the mathematics courses and young children and have worked for an early childhood practice, policy, and research agency. I wanted to learn about these teachers’ experiences as mathematics learners and teachers, with a goal to share the complex nature of their work with teacher educators and other stakeholders to identify better avenues for their mathematics training. I explored the questions: (1) What role, if any, do mathematical learning experiences play in early childhood teachers’ mathematics teaching practice? (2) In what ways do their voices contribute to the professional dialogue regarding teaching mathematics with young children? </p> <p>Dewey’s (1938/1998) <i>experience</i> construct provided lenses to examine early childhood teachers’ experiences learning and teaching mathematics. <i>Continuity</i>, <i>interaction</i>, <i>social control</i>, <i>freedom</i>, <i>purpose</i>, and <i>subject matter</i> provided insights and situated teachers’ experiences within a disparate patchwork of settings and policies. Two family childcare providers participated in this narrative inquiry (Clandinin & Connelly) through an interview on their experiences learning and teaching mathematics and three classroom observations. After analyzing data for Dewey’s (1938/1998) <i>experience</i> constructs, I used narrative analysis (Polkinghorne, 1995) and teaching images (Clandinin, 1985) to write an emplotted narrative for each teacher, Josie and Patsy.</p> Josie told a turning point story (Drake, 2006) of making mathematics “real,” influencing her mathematics teaching practice as she integrated “real” mathematics into everyday activities. Patsy’s appreciation for mathematics and building was seen in her story of a child explaining he used the wide blocks for his base, elaborating, “He's telling me HOW he's building.” While Josie and Patsy had few opportunities to learn about teaching mathematics with young children, they were eager to learn. I propose a training for early childhood teachers, iteratively working as a group to investigate a personal mathematics teaching puzzle or celebration, building on their mathematical personal practical knowledge. Adding my own story to those of the teachers, like Josie’s and Patsy’s, of our work together, will add to my understanding and development of my practice as a curriculum maker (Clandinin & Connelly, 1992), as early childhood teachers’ voices contribute to the professional dialogue about teaching mathematics with young children.

Problem solving at the crossroads between chemistry and mathematics presents significant challenges for students at all levels of education. This licentiate thesis aims to enhance our understanding of such problem solving, with a focus on how university students approach problems in the context of chemical kinetics. The thesis is based on two papers. The video data analysed in these papers were collected from problem-solving sessions where second-year chemistry students worked in pairs to solve tasks centred around a key concept in chemical kinetics. The first paper aimed to develop a framework suitable for analysing problem solving at the interface of chemistry and mathematics. Deductive and inductive analysis of the collected video data resulted in the extended mathematical modelling cycle (MMC). This empirically derived framework offers a fine-grained picture of the processes and resources at play during problem solving in chemical kinetics, suggesting that students: (1) engage in a range of (sub)processes beyond those typically outlined in the classical MMC; and (2) employ extra-mathematical resources (EMRs) in all stages of the MMC. The EMRs can be divided into chemical and other resources. While chemical resources are essential in translating chemical information into mathematical relationships, they also play a crucial role during mathematical work, offering guidance to the mathematical operations. The purpose of the second paper was to further characterise the nature and roles of other resources. Findings suggest that other resources can be divided into: implicit models of results, explicit examples from experience, and superficial procedural resources. Analysing their roles in problem solving revealed that implicit models primarily influence students’ ideas of where they are going, while explicit examples and superficial procedural resources provide a basis of strategies for how to get there.

Research has shown that students achieved higher standardized test scores in mathematics and gained more positive attitudes towards mathematics after learning from reform curricula. Because these studies involve actual students and teachers, there are classroom variables that are involved in these findings (Silver and Stein, 1996; Stein et al., 1996). To understand how much these curricula by themselves contribute to higher test scores, I have studied the cognitive demand of tasks in two traditional and two reform curricula. This work required the creation of a scale to categorize tasks based on their level of cognitive demand. This scale relates to those by Stein, Schoenfeld, and Bloom. Based on this task analysis, I have found that more tasks in the reform curricula require higher cognitive demand than tasks in the traditional curricula. These findings confirm other results that posing tasks with higher cognitive demand to students can lead to higher student achievement.