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

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 Peltomäki 26.5.2008

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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 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:
- basic education certificate
- grade in mathematics
- starting level exam
- test group students interested in computer science

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

- 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

- 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

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

- 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

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

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%.

The grades results

BEC Basic education certficate

C1-C10 Compulsory courses

MEP Matriculation exmination points

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

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