Integrated learning of engineering and mathematics modules

1. CDIO Conference 2009 Integrated learning of engineering and mathematics modules

2. our team fan kee sengyoong yuen soo, nashatar singh,ng geok ling Singapore Polytechnic School of Architecture & the Built Environment Department of Mathematics & Science

3. problem • in engg modules, formulae are given to students to solve engg problems • the concepts and principles of some of these formulae are not explained to students in the engg modules as they are taught in math modules • however, students can’t relate the math modules and the engg modules • hence they do not have a good understanding of some of the engg formulae

4. our motivation • to link engg and math modules using a formulae booklet • to realign the math content to make it more explicit in its applications to engg so that students are able to relate and apply mathematical concepts and principles to solve engineering problems CDIO Standard 3 integrated curriculum CDIO Standard 7 Integrated learning experience

5. methodology • module coordinators of engg modules were asked gathered the formulae used their modules • a total of 210 formulae – compiled into a formulae booklet • each formula in the booklet is indicated with a reference to a math module • similarly in each math chapter, references to the formulae booklet are also indicated

6. examples from the formulae booklet • Module Name: Structural Mechanics (Engineering Module) • Module Code: BE752Y • Module Coordinator: Rose Huang • Formulae used: 1 Direct stress Linkage to mathematics module is shown in the yellow box. 2 Direct strain 3 Young’s modulus Math ModuleIntegration (MS322Z, Chapter 4) 4 Bending stress 5 Moment of inertia

7. examples from the formulae booklet Math ModuleIntegration (MS322Z, Chapter 8) 6 Euler’s buckling load 7 Deflection of beam Math Module Integration (MS322Z, Chapter 8) There are 210 formulae in our formulae booklet (25 pages)

8. example – math module Chapter 8 Solving Differential Equations of the form Example 1 Link to formulae booklet -page 3 Formula 7 (Structural Mechanics) and page 15 Formula 103 (Theory of Structure) Example 2 Math module: Reference booklet on Mathematical Modelling Structural Mechanics: Finding Reactions Total load Reaction at each support

9. example – math module To find M --- use the free body diagram below Structural Mechanics: Free body diagram Take moment about point C

10. example – math module Math module: Reference booklet on Mathematical Modelling Integrate wrt x Integrate wrt x

11. example – math module To find the constant A, the boundary condition is: Concept of boundary conditions as applied to the deflection at the mid-span of a simply support beam That is, the gradient is zero when the deflection is maximum Hence equation (2) Math module: Application of Differentiation MS3126 Chapter 5 becomes Math module: Simplification MS3126 Chapter 1

12. example – math module Concept of boundary conditions at a support To find B, the boundary condition is: when x = 0, v = 0 i.e. no deflection at the support Hence equation (3) Math module: Substitution and Simplification MS3216 Chapter 1 becomes Hence the deflection equation is Maximum deflection occurs at the mid span i.e. Hence, becomes

13. example – math module Linkage to the formulae booklet. Example 3 Link to formulae booklet -page 3 Formula 7 (Structural Mechanics) and page 15 Formula 103 (Theory of Structure) When loading condition is changed ………. When support is changed ………. Carry out project work that may involve the use of these concepts to solve more difficult problems

14. another example – math module SECTION STRAIN SIMPLIFIED STRESS Filling up the ‘gaps’ in engg module Example: Concrete Design Math module needs to fill up the ‘gaps’ in engg modules

15. another example – math module Missing basic concepts from from the entire course Example: Concept of dA Math modules need to be realigned to include important basic concepts

16. hence, there are cross references of engg and math modules • some of the concepts and principles of engg formulae are explained in math modules moreexplicitly • hence this will promote students’ understanding of engg content better

17. SURVEY FINDINGS Each student was given a copy of the formulae booklet Carried out a survey last year on 135 students • 90% of the students felt that the formulae booklet helped them learn engineering modules better • 85% of the students felt that the booklet helped them relate better how mathematical concepts are applied in engineering modules • 77% felt that, with the help of the booklet, they were motivated to learn mathematics . • 93% of the students felt that it was very convenient for them to refer to the booklet whenever they needed the formulae • 81% felt that they would use the booklet in their work or in their further studies after graduation

18. room for improvement Students want more formulae to be included in the formulae booklet – from Geomatics and Structural Analysis The meaning of each term or symbol used in the booklet should be given. Provide soft copy of the formulae booklet with the necessary links to engineering and math module. Provide reference booklet e.g. mathematical modelling for self-directed learning. *** The compilation of the formulae booklet is creative and a task well done.

19. the road ahead • time consuming – not all all formulae have been linked • some formulae in the booklet could not be linked directly • need to realign math modules to meet the requirements of engg modules • further improve on the layout of the formulae booklet

20. Q & A Thank You