quo vadis latvian school mathematics?

Quo Vadis Latvian School Quo Vadis Latvian School Mathematics?Mathematics?

Janis MencisJanis Mencis LULU

the director of professional studythe director of professional study programme of secondaryprogramme of secondary mathematics mathematics teachersteachers

Tallinn 2009Tallinn 2009

Reviewed points in presentation „Ouo Reviewed points in presentation „Ouo VVadis adis LLatvian atvian SSchool chool MMathematics? ”athematics? ”

report of school education system report of school education system

novelty in documents of education regultationnovelty in documents of education regultation

methodical resources for teaching of mathematics methodical resources for teaching of mathematics

Schools and studentsSchools and students

Children attend school from age 7 in Children attend school from age 7 in Latvia.Latvia. They learn to learn, and they study They learn to learn, and they study from 1from 1stst grade grade to 12 to 12thth grade grade at school. at school. Theoretical children were prepared for Theoretical children were prepared for successful work in primary school at successful work in primary school at kindergarten. Practically students at 1kindergarten. Practically students at 1stst gradegrade have different level of have different level of reading and reading and counting skills and counting skills and behavioral norms. behavioral norms.


Students learning in three stagesStudents learning in three stages Primary school (1Primary school (1stst – 3 – 3rdrd grade), grade), Elementary school (4Elementary school (4thth – 9 – 9thth grade) grade) Secondary school (10Secondary school (10thth – 12 – 12thth grade) grade)

Note. Practically Note. Practically Primary school (1Primary school (1stst – 4 – 4thth grade grade),), Elementary school (5Elementary school (5thth – 9 – 9thth grade grade)) Secondary school (10Secondary school (10thth – 12 – 12thth gradegrade))Students take state examination at the end of grade of 3., Students take state examination at the end of grade of 3.,

6., 9. and 12.6., 9. and 12.


Students learn basic level of mathematics four Students learn basic level of mathematics four lessonslessons at week, except grade of 5. and 6., at week, except grade of 5. and 6., whewhenn they learn mathematics five times at they learn mathematics five times at week. Still it is not clear, why and when week. Still it is not clear, why and when mathematics, which is almost every student mathematics, which is almost every student favorite lesson at grade of 1, favorite lesson at grade of 1, isis turning into the turning into the worst nightmare, where teachers actions looks worst nightmare, where teachers actions looks like magics at blackboardlike magics at blackboard

DDocuments of education ocuments of education regulationregulation

Year 2011 will be Year 2011 will be the first year, when final the first year, when final exams of secondary school exams of secondary school will be will be made in made in accordance with new curriculum for secondary accordance with new curriculum for secondary school, which was established in year 2008. school, which was established in year 2008. Accents of curriculum were putted on Accents of curriculum were putted on understanding of mathematics but not on understanding of mathematics but not on formal algorithms. After some time we will see formal algorithms. After some time we will see how new curriculum, which recommends how how new curriculum, which recommends how teacher have to work, works (not works) in teacher have to work, works (not works) in exam exercises.exam exercises.


OOver all of that as the sword of Damocles is ver all of that as the sword of Damocles is plans of plans of the Ministry of Education and Science:the Ministry of Education and Science:

to terminate 4000 teachers;to terminate 4000 teachers; to raise hour rate;to raise hour rate; to reduce to reduce amountamount of schools and finances for of schools and finances for

educationeducation..

Note. Of course, some of points of plans are Note. Of course, some of points of plans are useful, but way, how it will be done, is useful, but way, how it will be done, is miserably.miserably.


There is other idea to create various There is other idea to create various study programs with professional study programs with professional orientation at the group of orientation at the group of gradegrade 7 7 -- 9 9 Therefore there will be entrance Therefore there will be entrance examination at the examination at the gradegrade 10, and there is 10, and there is a possibility that secondary school will a possibility that secondary school will not be mandatory any more just like not be mandatory any more just like higher education.higher education.

MMethodical resources for ethodical resources for teaching of mathematicsteaching of mathematics

Irrespective of global economical crisis, Irrespective of global economical crisis, that affects Latvia very much, high school that affects Latvia very much, high school lecturers and teachers continue to work lecturers and teachers continue to work with hope, that priority of education with hope, that priority of education changes from words to works.changes from words to works.


European project “European project “MMaths and aths and SScienceciencess” was ” was done large job, which includes courses, where done large job, which includes courses, where took part almost all teachers of maths, in Latvia took part almost all teachers of maths, in Latvia since year of 2005 till year of 2008. Project since year of 2005 till year of 2008. Project explain:explain:

that teacher have to teach according with that teacher have to teach according with curriculum,curriculum,

newest teaching methods and their usagenewest teaching methods and their usage,, skilful IT usageskilful IT usage..


The questions appear:The questions appear: Will teachers actually change something in Will teachers actually change something in

their teaching work?their teaching work? Is lost of student interest about maths also not Is lost of student interest about maths also not

because of teachers? because of teachers? Will predictable competition of work place Will predictable competition of work place

change positively work style of teachers?change positively work style of teachers?

Note. These questions are common for all of us.Note. These questions are common for all of us.


European project provides secondary European project provides secondary schools not only with interactive visual schools not only with interactive visual aids of blackboard, bur also with aids of blackboard, bur also with interactive study materials. In my opinion, interactive study materials. In my opinion, there are not good textbooks for there are not good textbooks for secondary school, but it is not bad secondary school, but it is not bad because teacher has to teach math not to because teacher has to teach math not to teach textbook.teach textbook.


Interesting, that in education of Interesting, that in education of elementary school, you can find part of elementary school, you can find part of all of it, that now is in curriculum of all of it, that now is in curriculum of secondary school, but for unknown secondary school, but for unknown reason some things were ignored in reason some things were ignored in elementary school, for example, science elementary school, for example, science work and decision proving.work and decision proving.


Now there is a plan to create large Now there is a plan to create large project, which will be oriented to rise of project, which will be oriented to rise of competence of teachers which work in competence of teachers which work in system of professional system of professional educationeducation..

SummarySummary

In conclusion, let’s note that in the better In conclusion, let’s note that in the better situation are students, which learns at grade of situation are students, which learns at grade of 5. and 6. There exists full study package:5. and 6. There exists full study package:

TextbookTextbook Teacher bookTeacher book Work exercise-bookWork exercise-book Collection of exercises, tests and exercises of Collection of exercises, tests and exercises of

self-controle self-controle

SummarySummaryNote. I can to reveal, that Note. I can to reveal, that exercises, which implicitly exercises, which implicitly orienting students to science orienting students to science work, that will be at grade of work, that will be at grade of 7.-9., are including in work 7.-9., are including in work exercise-book. But details exercise-book. But details about it next time. about it next time.

See youSee you in Tallin again! in Tallin again!

Advanced education at Advanced education at schools: achievements schools: achievements

and trendsand trends

Laura FreijaLaura Freija LULU

A.Liepa’s Correspondence mathematics school A.Liepa’s Correspondence mathematics school Tallinn 2009Tallinn 2009

The system of out-of-school activities, The system of out-of-school activities, being less formal and conservativebeing less formal and conservative than than school curriculaschool curricula, therefore is playing an , therefore is playing an increasing role in advanced education.increasing role in advanced education.

Out-of-school activitiesOut-of-school activities Such activities as Such activities as

correspondence courses, correspondence courses, correspondence contests, correspondence contests, Olympiads, Olympiads, students’ research clubs etc., students’ research clubs etc.,

run by enthusiastic teachers and university run by enthusiastic teachers and university students, essentially complement the official students, essentially complement the official curricula. curricula.

The material covered by these activities is much The material covered by these activities is much broader; the scientific standards are higher; and broader; the scientific standards are higher; and the possibilities to compare one’s achievements the possibilities to compare one’s achievements with those of counterparts in the whole Latvia are with those of counterparts in the whole Latvia are broader.broader.

Origin of CMSOrigin of CMS

A.Liepa’s Correspondence mathematics school - A.Liepa’s Correspondence mathematics school - a a scientific/methodical laboratory is functioning at the scientific/methodical laboratory is functioning at the University of Latvia. University of Latvia.

It was founded in 1969 to prepare high school It was founded in 1969 to prepare high school students for the entrance examination in the students for the entrance examination in the University of Latvia, Faculty of Physics and University of Latvia, Faculty of Physics and Mathematics. As the entrance examinations were Mathematics. As the entrance examinations were very hard these days, there was a need for extra very hard these days, there was a need for extra studies to prepare to them. CMS mainly practiced studies to prepare to them. CMS mainly practiced extramural math teaching – there was extramural math teaching – there was correspondence between students and CMS on correspondence between students and CMS on the university’s entrance examination level.the university’s entrance examination level.

For few years there are no more entrance exams to theFor few years there are no more entrance exams to the UniversityUniversity - - if you want to enter it you have to pass if you want to enter it you have to pass graduation exams after the High school very well. graduation exams after the High school very well.

CChanges in the education of Latvia through 30 years hanges in the education of Latvia through 30 years have had a great effect to these exams. As there aren’t have had a great effect to these exams. As there aren’t many essential topics in the school curricula, the exams many essential topics in the school curricula, the exams are getting easier and the level of students’ knowledge is are getting easier and the level of students’ knowledge is getting worse. getting worse.

CMS has followed all the changes in the school curricula CMS has followed all the changes in the school curricula all these years and it has also changed, but in quite all these years and it has also changed, but in quite different waydifferent way - - CMS has noticed that there are many CMS has noticed that there are many issues missing from the school program which are issues missing from the school program which are essential for the entire math comprehension. essential for the entire math comprehension.

So CMS now tries to give a chance to study these So CMS now tries to give a chance to study these issues organizing correspondence contests and issues organizing correspondence contests and supporting activities for these contests.supporting activities for these contests.

““Extramural studies for high Extramural studies for high school students” (ESH)school students” (ESH)

On September at the beginning of school year an application to the running ESH year is announced in the internet website of CMS http://nms.lu.lv . Any 9th to 12th grade Latvian schools’ student can join the ESH.

Through the school year there are 4 or 5 ESH lessons so there are 4 or 5 booklets formed and sent to students which have decided to participate. Booklets contain elements of theory, examples and problems for independent solution.

The students have one month to cope with them, The students have one month to cope with them, then they send their solutions to CMS. then they send their solutions to CMS.

The supervisor of this contest collects the sent-in The supervisor of this contest collects the sent-in solutions. Usually the checking is done by CMS solutions. Usually the checking is done by CMS collaborates and students of University of Latvia. collaborates and students of University of Latvia. Supervisor also gives some hints to these people. Supervisor also gives some hints to these people.

After thAfter the checkinge checking the next booklet is sent out. It the next booklet is sent out. It contains not only the theory, examples and contains not only the theory, examples and problems but also solutions to the previous problems but also solutions to the previous booklet’s problems. The checked papers are booklet’s problems. The checked papers are returned to the participants, too.returned to the participants, too.

Over the years ESH lessons’ issues have changed according Over the years ESH lessons’ issues have changed according to the necessity. As CMS already many years deals with to the necessity. As CMS already many years deals with students’ education it has great experience of the problems students’ education it has great experience of the problems the students have. So ESH can choose the issues that are the students have. So ESH can choose the issues that are fundamental in mathematics but still are difficult for the fundamental in mathematics but still are difficult for the students.students.

Analyzing research papers in mathematics and computer Analyzing research papers in mathematics and computer science, we have concluded that following general methods science, we have concluded that following general methods are of especially importance:are of especially importance: method of mathematical induction,method of mathematical induction, mean value method (generalized Pigeonhole Principle),mean value method (generalized Pigeonhole Principle), invariants,invariants, interpretation method (the problem is “translated” into interpretation method (the problem is “translated” into

appropriate language).appropriate language). extremal element method (the set is analyzed by investigating extremal element method (the set is analyzed by investigating

its extremal elements),its extremal elements), · ·

Out-of-school activities for Out-of-school activities for junior studentsjunior students

““Club of Professor Littledigit”Club of Professor Littledigit” (for students up to 9th (for students up to 9th grade) grade)

““Contest of Young Mathematicians” Contest of Young Mathematicians” (for students (for students up to 7th grade)up to 7th grade)

A lot of teachers, students and parents have A lot of teachers, students and parents have expressed interest and necessity of similar expressed interest and necessity of similar contests for primary school pupils. So contest “So contests for primary school pupils. So contest “So much or… How much?” for 4much or… How much?” for 4 thth grade grade students was students was established. established.

· ·

Other activitiesOther activities

There are organized also mathematical There are organized also mathematical summer camps for students in some summer camps for students in some regions.regions.

In some back-country regions monthly In some back-country regions monthly sessions for students and teachers are sessions for students and teachers are organized during school year.organized during school year.

Teaching aidsTeaching aids

Beside the present-time activities and Beside the present-time activities and competitions, a lot of teaching aids are competitions, a lot of teaching aids are prepared and published for advanced math prepared and published for advanced math education. There are education. There are methodical materials on some topics methodical materials on some topics volumes of problems with extended solutions of volumes of problems with extended solutions of

Latvian math olympiads and other contestsLatvian math olympiads and other contests Teaching aids are published both in a “hard Teaching aids are published both in a “hard

copy” version and on the Internet. A lot of copy” version and on the Internet. A lot of books are written and published within the books are written and published within the Latvian – Icelandic project “LAIMA”. Some of Latvian – Icelandic project “LAIMA”. Some of them are translated into English too.them are translated into English too.

Thank you for attention!Thank you for attention!

Jānis Mencis (e-mail: [email protected])Laura Freija (e-mail: [email protected])

University of Latvia http://www.lu.lvCorrespondence mathematics school http://nms.lu.lv