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Joseph N. Grima & Alfred J. Vella

Adequacy of pre-university mathematics curriculum as a preparation for chemistry undergraduate studies. Joseph N. Grima & Alfred J. Vella. Department of Chemistry, Faculty of Science, University of Malta, Msida MSD 06, MALTA E-mail: joseph.grima@um.edu.mt Tel: (+356) 2340 2274

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Joseph N. Grima & Alfred J. Vella

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  1. Adequacy of pre-university mathematics curriculum as a preparation for chemistry undergraduate studies Joseph N. Grima & Alfred J. Vella Department of Chemistry, Faculty of Science, University of Malta, Msida MSD 06, MALTA E-mail: joseph.grima@um.edu.mt Tel: (+356) 2340 2274 WWW: http://staff.um.edu.mt/jgri1

  2. Malta & its University Malta: Size: 126 square miles, Population: 380,000 The University:Traces its origin to the founding of the Collegium Melitense in 1592. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  3. Science & Mathematics: • “Without mathematics the sciences cannot be understood, nor made clear, nor taught, nor learned.” • “Mathematics is the door and key to the sciences” Roger Bacon (1214-1292) … chemistry is no exception! http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  4. Chemistry … (1) Is math really required? Chemistry is no exception … Math is required! A non specialist looking at some physical chemistry textbooks may think these are textbooks in advanced mathematics! Atkins & de Paula, Atkins' Physical Chemistry 7th edition , Ch. 23 http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  5. Chemistry … (1) Is math really required? ‘A facility in mathematics is an essential part of the armoury for all chemists.’ Mathematics in Chemistry Degree Courses – The Royal Society of Chemistry, UK, Sept. 1996 http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  6. Chemistry … (2) What math is required? A chemist’s minimum math skills must include skills in: • The handling of indices and logarithms; • Equations functions and graphs; • Differentiation and integration (including partial differentiation and differential equations); • Basic trigonometry (including trigonometric identities and polar coordinates); • Statistics, regression analysis and error calculations; • Vectors; etc.. Mathematics in Chemistry Degree Courses – The Royal Society of Chemistry, UK, Sept. 1996 http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  7. Chemistry … (2) What math is required? … Topics range: From ones normally covered in some 16+ syllabi (e.g. indices) to others that are usually part of mathematics degree courses (e.g. partial differentiation). Required proficiency:Students must have grasped the math to the extent that they can use it with confidence in their chemistry courses. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  8. Chemistry … (3) When should math training be given? Ideally before and during degree course. 1 Many universities include math courses as part of their ‘chemistry’ curriculum. • University of Exeter (UK), University of Bologna (Italy): About 25% of their first year. • University of Perugia (Italy):About 25% of their first two years. Importance of an adequate pre-university math education is often reflected in the entry requirements for chemistry degree courses. 2 http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  9. Entry Requirements for Chemistry Degree Courses … University of London, Imperial College, UK ‘Candidates should normally offer three A levels including chemistry and mathematics.’ University of Cambridge, UK ‘If you plan to take chemistry through to the second year and beyond, we recommend strongly that you have A level maths (or an equivalent) — AS is not sufficient.’ http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  10. ASIDE: What is an A-Level Exam? A chemistry A-Level syllabus is similar to the syllabus in a US first-year BS course with some additional organic chemistry. Typical question: UoM June 2003 Chemistry A-Level, Paper II, Q6 http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  11. Scope of paper: • To investigate how well the education system in Malta is preparing its pupils for degrees in chemistry by providing them with the appropriate mathematical skills; • To make a few suggestions on how this important minority can be provided with the required mathematical skills. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  12. Chemistry Degrees in Malta: ‘Joint Honors’ BSc(Hons) / Science BEd(Hons) Students choose two principal subject areas from: Biology – Chemistry – Computer Science – Informatics – Mathematics –Statistics & Operations Research – Physics Common combinations involving chemistry include: • Chemistry & Biology • Chemistry & Physics Favorite combination No ‘single honors’ Chemistry program offered! http://home.um.edu.mt/science/ http://www.educ.um.edu.mt http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  13. ‘Joint Honors’ Chemistry Degrees … The problems • Teaching time is severely limited … hardly enough time for all ‘core chemistry’ … Finding enough time for Math classes at university is extremely difficult! • Impossible to impose any stringent mathematical entry requirements: • Second subject taken as ‘major’ will inevitably require a different preparation; • No. of students majoring in chemistry is small http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  14. The math education of Malta’s chemistry students in ‘Biology & Chemistry’ stream Pre-university math education The math education of chemistry students at university http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  15. Education System in Malta 16+ exam 18+ exam 11+ exam 6th Form Primary Secondary University | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Age: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 General Science Chemistry ? Mathematics = Compulsory Math (optional) http://www.um.edu.mt/courses/ http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  16. Pre-University Math: Ages 16-18: The 18+ exam Mathematics NOT taught to all students. • At age 18, students take the 18+ ‘UoM Matriculation Certificate’: • Two subjects are studied at Advanced Level ** • Three subjects are studied at Intermediate Level (~ 1/3 of that of an Advanced Level) ** • Systems of Knowledge (General Studies) • ** Must include at least one from each of these three groups: • Group 1: The Languages • Group 2: Accounts / Economics / Marketing / Computing & IT • Group 3: The Sciences http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  17. Pre-University Math: Ages 5-16: The 16+ exam Mathematics taught to ALL students. … but there are still some problems! Problem: The differentiated examining mode (to make these exams more accessible to students with different strengths and abilities). It is possible to pass the mathematics 16+ examination through a less demanding examination paper based on a somewhat curtailed syllabus (Paper B) http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  18. Practical Implications: The 18+ Exam for students in the ‘Biology & Chemistry’ stream • Group 1: The Languages: • Students may freely choose 1 subject from this group at I-Level • Group 2: Accounts / Economics / Marketing / Computing & IT: • Students may freely choose 1 subject from this group at I-Level • Group 3: The Sciences: • Students must choose: • Chemistry & Biology at A-Level (the main subjects) • Physics at I-Level (reqd. for Physical Chemistry) … This leaves no space for mathematics! http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  19. The ‘Biology & Chemistry’ Stream – Problem # 1a: The mathematical skills of most students majoring in chemistry are very limited … just a pass in the 16+ exam Problem # 1b: Some students majoring in chemistry may have opted for the less demanding 16+ examination math paper based on a somewhat curtailed ‘Paper B’ syllabus as opposed to the more traditional and complete ‘Paper A’ syllabus. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  20. 25 22.2% 20 15 10.5% 10 5 0.0% 0.0% 0 1996 1997 1998 1999 Problem #1b: The ‘Paper B’ problem There seems to be a trend for more students to opt for the easier ‘Paper B’: % of Pupils who sat for Paper B = current 1st years Year of examination http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  21. 25 22.2% 20 15 10.5% 10 5 0.0% 0.0% 0 1996 1997 1998 1999 Problem #1b: The ‘Paper B’ problem % who sat for Paper B Why worry? Year of examination • Chemistry students may have then felt that their mathematical knowledge was not of high enough standard, (or students were ‘advised’ to take the ‘surer path’ to a Grade 4); • Students are not being made aware that chemistry and mathematics are inter-related http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  22. Problem #2: When do students become aware that chemistry and mathematics are inter-related? 40 34% 35 30 28% 25 21% % 20 17% 15 10 5 0 Before Form 3 Between Forms 3-5 At 6th Form At University Too late ? http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  23. Problem #3: No mathematics for the two years preceding commencement of their university course! Result: Most mathematical knowledge is difficult to retrieve from long-term memory. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  24. 70 61% 60% 59% 60 50 37% 40 30 20 10 0 1 2 3 4 Problem #3: No math for 2 years … The experiment: 1st and 2nd year chemistry undergraduates students were asked to work a set of math questions taken from 16+ past-papers The result: Average % mark in ‘experiment’ Math Grade in the 16+ exam http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  25. Problem #3: No math for 2 years … • The equal sides of an isosceles triangle are (3x-2y) cm and 2(x+y) cm. The third side is of length 3(x-3y) cm and the perimeter of the triangle is 46cm. • (a) Find the values of x and y. • (b) Calculate the length of each side. Beyond the capability of most students ! … Probable cause: mathematical knowledge is difficult to retrieve from long-term memory. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  26. Math education of chemistry undergraduates Up to year 2000-2001: Course followed: MA001 – Elementary calculus When: First year, first semester Content: General (not specifically designed for chemists) Syllabus:Cartesian coordinates, equations of lines and curves, differentiation (including partial differentiation) and integration. No. of Hours:1 hour per week x 14 weeks (2 ECTS credits = 5% of First year teaching) http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  27. Math education of chemistry undergraduates (up to 2000/2001) … Problem: With MA001 alone, students could not cope with the math contained in the core chemistry courses. Reason: (Main) Students’ inability to do very basic algebra, such as, simplifying equations, working with indices and logarithms, factorizing, etc. (These topics are usually taught at school!) http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  28. Math education of chemistry undergraduates (up to 2000/2001) … Possible causes: • Changes in 16+ math syllabus: logs no longer included, ‘index laws’ covered only in Paper A, etc.; • Time: • MA001 teaching time was too little; • Not enough time to assimilate the material (MA001 was taught over a single semester.); • Problems in transferring the ‘pure’ math learnt in MA001 to the chemistry applications. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  29. Math education of chemistry undergraduates (From to 2001/2002) The ‘solution’: CH033 – Mathematics for Chemists* • Designed specifically for chemists • Taught through examples that chemistry students could relate to; • It was made sure that no math knowledge which the students did not have was being pre-assumed; • CH033 had more time and credits allocated to it: • 4 ECTS credits = 10% of 1st Year • Run over two semesters • Given ample teaching time (one hour of lecture + two hours of tutorials per week, for 28 weeks) http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  30. Math education of chemistry undergraduates (From to 2001/2002) CH033 – Mathematics for Chemists Does it work? Test:Three months into the course, students were asked to sit for a ‘closed book’ test Result:Average mark was just 43% WHY???? http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  31. Math education of chemistry undergraduates (From to 2001/2002) CH033 – Mathematics for Chemists Why students thought they did so badly in the test: Attitude to the subject Lecturer's fault Inadequate pre-university Math Time Applying math to chemistry Too Difficult 0 5 10 15 20 25 30 35 % of students http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  32. The math problem should be tackled before students reach the university. Math education of chemistry undergraduates … The problem of time In a joint-honors degree, the number of credits that may be allocated to ‘math for chemists’ is necessarily limited: 25 % of year in a full ‘single honors’ program = more that 50% of total chemistry credits in a ‘Joint honors’ program!!! http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  33. But … Ensuring an adequate math education from schools = Difficult task: • Different students’ strengths and abilities; • Different future career pathways. • Only a moderate percentage of students will eventually make it into tertiary education • Different university disciplines require different levels of expertise in literacy and numeracy • No. of students taking chemistry at Uni is negligible!!! 3. School time-table is also full ! http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  34. Making the necessary changes The only solution is to optimize and strengthen the math education at all levels: (1) School teachers should highlight the link between chemistry and mathematics and encourage future chemists to take math seriously. (2) The introduction of a new subject at secondary school level (“Further Mathematics”, taught in parallel to the current math syllabus). http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  35. (3) Sixth Forms start requiring a Grade 3 or better in math 16+ from students taking chemistry at A-Level. (or, to oblige those students with a grade 4 or 5 to take supplementary lessons in math). This will send the right signals to the students in secondary schools!!! Making the necessary changes • (4) Make changes in the 18+ exam system: • Is it wise to allow students aspiring to enter university to halt their mathematics education (and probably also that of Proficiency in English and Maltese) at the age of 16? http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  36. Conclusions: • There are several inadequacies in the mathematical preparation at secondary and post-secondary level of education of those students who wish to further their studies in sciences. • However, there are also a number of possible solutions which could address the situation without causing major disturbance. Also, the time is right to make an effort to rectifying this particular problem which otherwise may actually worsen rather than improve in future. http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

  37. Acknowledgments • The authors would like to thank all chemistry undergraduates, especially the students of the study unit CH033 for their help in this paper. Thank you! Joseph N. Grima & Alfred J. Vella http://staff.um.edu.mt/jgri1  joseph.grima@um.edu.mt

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