Integrated learning of engineering and mathematics modules CDIO Conference 2009

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

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

our motivation to link engg and math modules using a formulae booklet CDIO Standard 3 integrated curriculum CDIO Standard 7 Integrated learning experience 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

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

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

Math Module Integration (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) examples from the formulae booklet

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

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

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

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

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

example – math module Link to formulae booklet -page 3 Formula 7 (Structural Mechanics) and page 15 Formula 103 (Theory of Structure) Linkage to the formulae booklet. 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 Example 3

another example – math module STRAINSECTIONSIMPLIFIED STRESS Math module needs to fill up the ‘gaps’ in engg modules Filling up the ‘gaps’ in engg module Example: Concrete Design

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

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

SURVEY FINDINGS. Carried out a survey last year on 135 students Each student was given a copy of the formulae booklet 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

room for improvement Students want more formulae to be included in the formulae booklet – from Geomatics and Structural Analysis *** The compilation of the formulae booklet is creative and a task well done. 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 road ahead time consuming – not all all formulae have been linked need to realign math modules to meet the requirements of engg modules some formulae in the booklet could not be linked directly further improve on the layout of the formulae booklet

Q & A Thank You