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STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS - Teaching experiment Mia Peltomäki 26.5.2008

STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS - Teaching experiment Mia Peltomäki 26.5.2008. Teaching experiment at a Finnish high school (upper secondary school) years 2001-2005 starting year test group control group 2001 25 24 2002 28 23 Classification:

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STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS - Teaching experiment Mia Peltomäki 26.5.2008

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  1. STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS- Teaching experiment Mia Peltomäki 26.5.2008

  2. Teaching experiment at a Finnish high school (upper secondary school) years 2001-2005 • starting year test group control group • 2001 25 24 • 2002 28 23 • Classification: • basic education certificate • grade in mathematics • starting level exam • test group students interested in computer science

  3. Background • Lessons at the same time • Same text book/exercise book • Same exams • Different teacher • Test group: structured derivation’s method • Control group: traditional method • Matriculation Examination Board accepts semiformal notation

  4. Teaching • the basic notation of propositional logic (5h) • structured derivation method was used on the whiteboard and with a computer • when using computer subderivations were hidden and replaced with a link giving more detailed view of the partial solution • computer was used when checking homework • some students changed the groups

  5. Teachers observations: • the method makes it easier to follow the teaching process • time was diminished when correcting exams • easy to notice where students loose the idea • forces the student to be explicit about what strategies and rules they use • students in the testgroup argued their answers more precisely than those in the control group

  6. More observations • forces the student to be explicit about what strategies and rules are used • suitable for talented students • the notation should be somewhat lighter at the high-school level

  7. Students proposals • more logic • many good examples • more examples from difficult parts • more calculating during lessons • good text book (part of the students) • short motivations

  8. Conclusions • difficult for less talented students to produce large wholenesses so that logic woud work correctly • lightening of the method

  9. Matriculation examination in spring 2004 70 % of the test group got one of the two highest degrees (laudatur or eximia) while in the whole country this was 21%.

  10. The grades results BEC Basic education certficate C1-C10 Compulsory courses MEP Matriculation exmination points

  11. BEC – Basic education certificate C1 - Functions and equations I C2 - Functions and equations II C3 - Geometry C4 - Trigonometry and vectors C5 - Analytic geometry C6 - Calculus I C7 - Calculus II C8 - Integrals C9 - Statistics and stochastics C10 - Sequences and series MEP – Matriculation examination points

  12. Future? • Method seems to be suitable at least to average and talented students • Continuing the use of the method with the suitable level for each group • Follow same students in the programming course • Follow same students even today in the mathematics and programming courses at the university

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