STRUCTURED DERIVATIONS IN HIGH-SCHOOL MATHEMATICS

- Teaching experiment

Mia Peltomäki

26.5.2008

Teaching experiment at Kupittaa high school (Turku) 2001-2005

year test group control group 2001 - 04 25 24 2002 - 05 28 23

Tried to make test group and control group as similar as possible:

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

Background

• Lectures at the same time• Same text book/exercise book used in both

groups• Same exams• Different teachers• Test group: structured derivation’s method• Control group: traditional method

• Matriculation Examination Board approval for structured derivations

Teaching methods

•basic notions 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 proofs where the logic would work correctly

• lightening up of the method

Test Control Whole Wholegroup group school country

N 20 12 47 12494Laudatur % 25,00 0,00 10,64 6,31Eximia % 45,00 8,33 23.40 14,64Sum of L and E % 70,00 8,33 34,04 20,95Average points 5,70 4,17 4,47 3,92

70 % of the test group got one of the two highest degrees (laudatur or eximia) while in the whole country this was 21% (7 grades scale)

Matriculation examination in spring 2004

5,00

6,00

7,00

8,00

9,00

10,00

test group 9,73 8,77 8,00 8,09 7,91 8,59 8,41 7,68 8,95 8,59 8,00 8,77

control group 9,17 7,75 6,00 7,42 6,50 7,00 6,42 6,00 6,33 6,92 7,17 7,17

BEC C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 MEP

The grades results

BEC Basic education certficate

C1-C10 Compulsory courses

MEP Matriculation exmination points

BEC – Basic education certificateC1 - 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 seriesMEP – 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