Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008
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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 yeartest group control group 2001 25 24 2002 2823 Classification:

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

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Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS- Teaching experiment

Mia Peltomäki

26.5.2008


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

  • Teaching experiment at a Finnish high school (upper secondary school) years 2001-2005

  • starting yeartest group control group

  • 2001 25 24

  • 2002 2823

  • Classification:

  • basic education certificate

  • grade in mathematics

  • starting level exam

  • test group students interested in computer science


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

  • 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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

  • 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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

  • 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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

  • Conclusions

    • difficult for less talented students to produce large wholenesses so that logic woud work correctly

    • lightening of the method


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

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%.


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

The grades results

BEC Basic education certficate

C1-C10 Compulsory courses

MEP Matriculation exmination points


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

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


Structured derivations in high school mathematics teaching experiment mia peltom ki 26 5 2008

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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