Background: This article focuses on a course in mathematics for first year undergraduate materials engineering students of which I have been a teacher now in two successive years. Students in the materials engineering programme have a wide range of mathematical qualifications and experience ranging from A* at A level, achieved just prior to entering university, to GCSE mathematics, achieved several years earlier with no mathematical study since then. The cohort this year includes 72 students who are taught together over two semesters in two lectures and 1 tutorial per week over about 27 weeks. They are assessed through 8 computer-based tests (40%) and a final examination (60%). I was responsible for all the teaching in the first semester (15 weeks). This is the first year recently in which the whole cohort is taught together and separately from other engineering students. Last year, and several years before this, the students with less experience or lower qualifications were taught separately from the rest who were taught mathematics together with students in electrical engineering. I was responsible, last year, for the students with lesser experience or lower qualifications, a small group of just 16 students, and a reduced curriculum (including basic algebra, trigonometry, functions, calculus and statistics). I engaged in practitioner research as I taught this group, in order to discern, reflect on and analyse the issues that arose in relation to the approach used [5]. The main findings from this research concerned my use of investigative tasks1 to promote mathematical thinking and its relation to the mainstream teaching of course topics. Briefly, students engaged well with these tasks and showed evidence of enjoying them and engaging seriously with the mathematics. However, these same students struggled with course topics, especially with basic algebra, and when we came to exponential and logarithmic functions demands of the topic took up all our time at the expense of investigative tasks. Thus, a central issue for me as a teacher is how to design a course to integrate a focus on mainstream topics that enables students to develop mathematical fluency and an emphasis on mathematical thinking that encourages conceptual understanding. Before introducing my approach this year, in which I have used GeoGebra, I will say a little about the theoretical principles behind these aims...
Background
This article focuses on a course in mathematics for first year undergraduate materials engineering students of which I have been a teacher now in two successive years. Students in the materials engineering programme have a wide range of mathematical qualifications and experience ranging from A* at A level, achieved just prior to entering university, to GCSE mathematics, achieved several years earlier with no mathematical study since then. The cohort this year includes 72 students who are taught together over two semesters in two lectures and 1 tutorial per week over about 27 weeks. They are assessed through 8 computer-based tests (40%) and a final examination (60%). I was responsible for all the teaching in the first semester (15 weeks). This is the first year recently in which the whole cohort is taught together and separately from other engineering students. Last year, and several years before this, the students with less experience or lower qualifications were taught separately from the rest who were taught mathematics together with students in electrical engineering. I was responsible, last year, for the students with lesser experience or lower qualifications, a small group of just 16 students, and a reduced curriculum (including basic algebra, trigonometry, functions, calculus and statistics). I engaged in practitioner research as I taught this group, in order to discern, reflect on and analyse the issues that arose in relation to the approach used [5]. The main findings from this research concerned my use of investigative tasks1 to promote mathematical thinking and its relation to the mainstream teaching of course topics. Briefly, students engaged well with these tasks and showed evidence of enjoying them and engaging seriously with the mathematics. However, these same students struggled with course topics, especially with basic algebra, and when we came to exponential and logarithmic functions demands of the topic took up all our time at the expense of investigative tasks. Thus, a central issue for me as a teacher is how to design a course to integrate a focus on mainstream topics that enables students to develop mathematical fluency and an emphasis on mathematical thinking that encourages conceptual understanding. Before introducing my approach this year, in which I have used GeoGebra, I will say a little about the theoretical principles behind these aims.
