USING EXCEL TO INDIVIDUALISE BASIC MATHEMATICS ASSIGNMENTS DEE Conference, Cambridge, Sept 2007 Mike Rosser Department of Economics, Finance and Accountancy Coventry University Coventry CV1 5FB UK

Overview of Method Individualised questions are created for each student based on their ID number All students get same assessment sheet, but letters represent digits in ID number An easily readable answer grid for manual marking is generated via Excel. Note: This presentation just summarises method. See paper for specific examples and formulae.

Rationale Students need to practise examples to develop their mathematical skills. Weaker students are often reluctant to put in the effort required unless their work is assessed. Collusion is likely if students are set the same questions for coursework.

Other Advantages Manual marking is relatively quick but still gives students feedback on specific errors. Can ask students to interpret results. Can set more time consuming questions than in time constrained or on-line tests Can include problems requiring students to construct their own spreadsheets

Background Following Coventry 2006 degree revision: Mathematical Techniques taught to all Yr 1 Economics students in same module Most do not have A-level Maths, some have weak GSCE Maths, so a very mixed ability group Accountancy students also attend term 1, which focuses on financial mathematics

Teaching Philosophy Objective to get all students practising worked numerical examples. Used in lectures and formative practice questions, as well as the summatively assessed individualised questions Approach based on Mike Rosser (2003) Basic Mathematics for Economists 2 nd Edition, Routledge

Converting student ID numbers Use Excel to convert ID number to digits Specify letters B to H in questions instead of numbers (Col A used for ID). For example : If question specifies TR = 5EFq – 1Gq 2 For student ID TR = 545q– 16q 2 (Note the mix of numbers with letters.)

Dealing with Student 007 To ensure acceptable values for students answers, some actual numbers may be used with the letters representing ID digits. For example, for student ID , if digits DE represent the interest rate in an investment problem, a rate of 0% may lead their calculations into a dead end If interest rate is specified as 5.DE% then this student would use 5.00% in his problem.

From Digits to Question Parameters Excel can convert ID numbers to individual digits by dividing by 10, 100, etc., and rounding down. ( One off task) Parameters can then be created by multiplying by 10, 100, etc. For example, for An amount invested £8FGH =8, x x = £8,567

Full Workings Spreadsheet Page Before producing Answer Grid, best to create Full Workings page, with columns showing: Actual numbers created for each student ID Intermediate steps in complex answers For students who get answers wrong, this will enable tutor to check: If students started off with the wrong number At what stage answer started to go wrong.

Calculating Answers From the tutors perspective, perhaps the most difficult task is devising an Excel a formula that will provide the mathematical solution to each question For most teachers of mathematics for economists this will not be too difficult a mathematical challenge Can devise formulae based on standard algebraic solutions to mathematical economics problems.

Example : Full Workings For demand function P = 2CD E.5Q and the supply function P = 2F + 3.G Q find equilibrium price P and quantity Q. When full list of ID numbers is pasted into column A the formulae for the numbers each student uses and their answers can then be copied down the worksheet page

Answer Grid Need to eliminate intermediate stages to get answers to fit on one page Make second worksheet page and delete unwanted columns off Full Workings to get:

Answer Grid – Coventry Assignment 1 Example First few columns shown (with fictitious IDs) Includes spreadsheet investment problems. Illustrates range of numeric answers

Marking Students Work Manual marking of method relatively quick if answers are correct If answer incorrect the tutor can use Full Workings to help check if error not obvious Allows feedback on where went wrong Can over-ride and type in if student inputs a wrong digit ( and adjust mark appropriately)

Evidence - Coventry Results June pass rate up from 69% to 80% Student survey satisfaction with assessment methods 81% Several students made basic errors Eg plus/negative signs mixed up Manual marking allowed feedback on where students need to improve / take more care

Conclusions First Coventry trial of Excel generated maths for economists individualised questions has shown some success in pass rates. Lessons have been learned from the experience in setting questions, constructing and using the Answer Grid Method will be used again and refined. Feedback from others using it are welcomed.