1. 1 Embedded Math as an Effective Tool for Smooth Transition from High School into Integrated Engineering: Teacher  and E  Centered Learning Riadh W. Y. Habash1, PhD, P.Eng, Mustapha Yagoub1, PhD, P.Eng, Christine Suurtamm2, EdD, Ghanim Ibrahim1, PhD1, Gilles Delisle, PhD, P.Eng1 1 School of Information Technology and Engineering, Faculty of Engineering 2. Faculty of Education

2. 2 The problem A particular challenge currently faces engineering schools is students having an insufficient understanding of mathematics to fully and actively engage in engineering programs. Engineering schools face the problem that currently students from high schools are reluctant to choose engineering because of their insufficient knowledge of science and mathematics plus their role in engineering. Furthermore, students who do choose engineering often do not have the necessary mathematical knowledge to fully engage in engineering. Quite often students have a procedural knowledge of mathematics but do not have a deep enough understanding of how to apply it. This creates a challenge for students in an engineering program.

3. 3 Our Goal Good solutions to problems must be integrated systems that mesh with existing structures. Our goal through our pilot project is not to develop advanced technical concepts, but to recognize the need of students for effective tools and techniques (in particular mathematics) that make them master foundations of engineering. Mathematics has been taught for many years in a traditional way, with the main focus on analytical solutions to simplified problems. Currently, University of Ottawa and other universities provide review of mathematics to the students during the summer. Applied courses and their problem solving techniques are then adapted to the students’ abilities gained in mathematics. From our experience as instructors, we feel that the way mathematics is taught now works well for certain number of students, however, a good number of students still can not realize the link between mathematics and engineering.

4. 4 Pilot Project Imbedding Math in all Aspects of Engineering In order to address the students’ lack of math knowledge and to ease the transition of students from high school into a university engineering program several different tools and methods could be used: Our pilot project attempts to assist students by embedding necessary math concepts in engineering contexts within the engineering courses. Additionally, learning engineering depends critically on the student’s experience of learning math and by the process of embedding math with foundations of engineering, the students can make the connection to math that is required in engineering applications.

5. 5 Primary Goals The purpose of this project is: to examine the relationship between high school and science and engineering studies, to identify areas critical for a smooth transition from high school to science and engineering studies, to identify discrepancies between the high school and university curriculum, to make recommendations for improvements in the transition, and importantly, to develop an education program (summer school and an interactive E-learning portal) for training high school students before they join their university studies.

6. 6 The Means for Achieving these Goals are: Training in problem-solving and mathematical skills. Good knowledge of theory of math and science. Engineering competence. Sufficient insight into physics, chemistry, and biology. A dynamic and creative academic environment. Various means of learning: instructor-based teaching, hands-on, and E-learning.

7. 7 Current Trends in Mathematics Education Mathematics in Context Use of technology as a tool in mathematics Mathematical modelling Connections between strands of mathematics and mathematics and other disciplines Changes in assessment – focus on projects, performance-based assessment

8. 8 Mathematics and Engineering Modelling in engineering subjects makes greater use of computers MATLAB and SIMULINK are used as the vehicle for analyzing engineering problems Focus on student projects that include developing mathematical models of engineering systems to predict the performance. Greater integration is required

9. 9 Areas that Need Greater Attention Mathematical modelling and analysis Complex algebra Differential and integral calculus Differential equations Transformations Matrix calculations

10. 10 Learning Foundations of Engineering through Mathematics This project provides a new way to learn and understand foundations of engineering. A wide range of students will benefit from this learning process. Hundreds of students apply to the engineering program of the University every year. We strongly believe among other instructors that a significant percentage of these students need the kind of learning proposed in this project before they join the engineering program. In fact, many students suffer in the program from a lack of appropriate knowledge in math. This particular problem may be amplified by the province of Ontario adopting a new curriculum framework with one less year at the secondary level. Through Phase I of this program, we plan to bridge the existing gap of knowledge, especially in math.

11. 11 The Vision! The project is not intended, at the moment, to substitute for teaching engineering courses, however, it is an additional tool that can be used. Our teaching experience for many years shows the need to establish bases of an elementary understanding in all areas of engineering in addition to many other areas, which are related to the profession of engineers. Therefore, students may understand the fundamental engineering phenomena that occur in the real world in terms of their physical, mathematical, and operational signification before learning advanced topics. In addition other instructors in the faculty will benefit from this activity. We are even thinking to extend the scope of the project in the future to include a kind of training to high school teachers.

12. 12 Basic SciencesMathematics Build up the connection: ability to mathematically model engineering problems Phase I E-Learning Portal Phase II Summer Training Phase III Evaluation Specialty knowledge: ability to solve engineering problems Integrated Engineering Goal: produce graduates who will be ready to assume engineering tasks upon graduation

13. 13 Phase I: E-Learning Portal This phase of the project is granted two funds in November 2003 and February 2004 in order to build up an E-learning portal. Our focus is develop a number of engineering modules with special emphasis on related mathematics. We should have the portal ready in July 2004.

14. 14 Phase II: Summer Training Program Between 50 and 100 high school students who are admitted to various disciplines of engineering (Electrical, Computer, Civil, Mechanical, and Chemical) will participate in the training program in summer 2004. The length of each training session is one week (6 hours per day). Students will be taught basic courses in engineering with emphasis on mathematics. We will utilize the E-learning portal as an integrated educational tool in order to ease the process of transition into the engineering. The objectives of the training program are: Identify, interpret, and simulate engineering problems through mathematical modelling. Carry out and analyse advanced engineering exercises. Manage both engineering language and the language of mathematics.

15. 15 Phase I and Phase II Bilingual Education Program Interactive E- Learning Portal To be developed by the E-Learning Unit Engineering Summer School First pilot project will be conducted in summer 2004

16. 16 Research: Dynamic Evaluation Dynamic evaluation will help to inform the program as it progresses and will include: Analysis of Curriculum Gaps Pre-program questionnaire for students Observation, de-briefing sessions with instructors E-learning questionnaire Post-program questionnaire for students Accordingly, adjustments will be made to the topics covered in the training, the materials provided to the students, and the class activities which enhance the educational experiences of the students.

17. 17 Innovation Use of embedded mathematics to review key mathematics concepts and to introduce students to the context of engineering. Strong connections between K-12 education and the needs of engineering students Development of engineering modelling applications that could be used in secondary school mathematics class