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 year test group control group 2001 25 24 2002 28 23 Classification:

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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:
• 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%.

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