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## Quo Vadis Latvian School Mathematics?

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**Quo Vadis Latvian School Mathematics?**Janis Mencis LU the director of professional studyprogramme of secondarymathematics teachers Tallinn 2009**Reviewed points in presentation „Ouo Vadis Latvian School**Mathematics? ” • report of school education system • novelty in documents of education regultation • methodical resources for teaching of mathematics**Schools and students**Children attend school from age 7 in Latvia.They learn to learn, and they study from 1st grade to 12th grade at school. Theoretical children were prepared for successful work in primary school at kindergarten. Practically students at 1st grade have different level ofreading and counting skills and behavioral norms.**Schools and students**Students learning in three stages • Primary school (1st – 3rd grade), • Elementary school (4th – 9th grade) • Secondary school (10th – 12th grade) Note. Practically • Primary school (1st – 4th grade), • Elementary school (5th – 9th grade) • Secondary school (10th – 12thgrade) Students take state examination at the end of grade of 3., 6., 9. and 12.**Schools and students**Students learn basic level of mathematics four lessons at week, except grade of 5. and 6., when they learn mathematics five times at week. Still it is not clear, why and when mathematics, which is almost every student favorite lesson at grade of 1, is turning into the worst nightmare, where teachers actions looks like magics at blackboard**Documents of education regulation**Year 2011 will be the first year, when final exams of secondary school will be made in accordance with new curriculum for secondary school, which was established in year 2008. Accents of curriculum were putted on understanding of mathematics but not on formal algorithms. After some time we will see how new curriculum, which recommends how teacher have to work, works (not works) in exam exercises.**Documents of education regulation**Over all of that as the sword of Damocles is plans of the Ministry of Education and Science: • to terminate 4000 teachers; • to raise hour rate; • to reduce amount of schools and finances for education. Note. Of course, some of points of plans are useful, but way, how it will be done, is miserably.**Documents of education regulation**There is other idea to create various study programs with professional orientation at the group of grade 7-9 Therefore there will be entrance examination at the grade 10, and there is a possibility that secondary school will not be mandatory any more just like higher education.**Methodical resources for teaching of mathematics**Irrespective of global economical crisis, that affects Latvia very much, high school lecturers and teachers continue to work with hope, that priority of education changes from words to works.**Methodical resources for teaching of mathematics**European project “Maths and Sciences” was done large job, which includes courses, where took part almost all teachers of maths, in Latvia since year of 2005 till year of 2008. Project explain: • that teacher have to teach according with curriculum, • newest teaching methods and their usage, • skilful IT usage.**Methodical resources for teaching of mathematics**The questions appear: • Will teachers actually change something in their teaching work? • Is lost of student interest about maths also not because of teachers? • Will predictable competition of work place change positively work style of teachers? Note. These questions are common for all of us.**Methodical resources for teaching of mathematics**European project provides secondary schools not only with interactive visual aids of blackboard, bur also with interactive study materials. In my opinion, there are not good textbooks for secondary school, but it is not bad because teacher has to teach math not to teach textbook.**Methodical resources for teaching of mathematics**Interesting, that in education of elementary school, you can find part of all of it, that now is in curriculum of secondary school, but for unknown reason some things were ignored in elementary school, for example, science work and decision proving.**Methodical resources for teaching of mathematics**Now there is a plan to create large project, which will be oriented to rise of competence of teachers which work in system of professional education.**Summary**In conclusion, let’s note that in the better situation are students, which learns at grade of 5. and 6. There exists full study package: • Textbook • Teacher book • Work exercise-book • Collection of exercises, tests and exercises of self-controle**Summary**Note. I can to reveal, that exercises, which implicitly orienting students to science work, that will be at grade of 7.-9., are including in work exercise-book. But details about it next time. See you in Tallin again!**Advanced education at schools: achievements and trends**Laura Freija LU A.Liepa’s Correspondence mathematics school Tallinn 2009**The system of out-of-school activities, being less formal**and conservative than school curricula, therefore is playing an increasing role in advanced education.**Out-of-school activities**• Such activities as • correspondence courses, • correspondence contests, • Olympiads, • students’ research clubs etc., run by enthusiastic teachers and university students, essentially complement the official curricula. • The material covered by these activities is much broader; the scientific standards are higher; and the possibilities to compare one’s achievements with those of counterparts in the whole Latvia are broader.**Out-of-school activities**• Such activities as • correspondence courses, • correspondence contests, • Olympiads, • students’ research clubs etc., run by enthusiastic teachers and university students, essentially complement the official curricula. • The material covered by these activities is much broader; the scientific standards are higher; and the possibilities to compare one’s achievements with those of counterparts in the whole Latvia are broader.**Origin of CMS**• A.Liepa’s Correspondence mathematics school - a scientific/methodical laboratory is functioning at the University of Latvia. • It was founded in 1969 to prepare high school students for the entrance examination in the University of Latvia, Faculty of Physics and Mathematics. As the entrance examinations were very hard these days, there was a need for extra studies to prepare to them. CMS mainly practiced extramural math teaching – there was correspondence between students and CMS on the university’s entrance examination level.**For few years there are no more entrance exams to**theUniversity - if you want to enter it you have to pass graduation exams after the High school very well. • Changes in the education of Latvia through 30 years have had a great effect to these exams. As there aren’t many essential topics in the school curricula, the exams are getting easier and the level of students’ knowledge is getting worse. • CMS has followed all the changes in the school curricula all these years and it has also changed, but in quite different way - CMS has noticed that there are many issues missing from the school program which are essential for the entire math comprehension. • So CMS now tries to give a chance to study these issues organizing correspondence contests and supporting activities for these contests.**“Extramural studies for high 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 CMShttp://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, then they**send their solutions to CMS. • The supervisor of this contest collects the sent-in solutions. Usually the checking is done by CMS collaborates and students of University of Latvia. Supervisor also gives some hints to these people. • After the checking the next booklet is sent out. It contains not only the theory, examples and problems but also solutions to the previous booklet’s problems. The checked papers are returned to the participants, too.**Over the years ESH lessons’ issues have changed according**to the necessity. As CMS already many years deals with students’ education it has great experience of the problems the students have. So ESH can choose the issues that are fundamental in mathematics but still are difficult for the students. • Analyzing research papers in mathematics and computer science, we have concluded that following general methods are of especially importance: • method of mathematical induction, • mean value method (generalized Pigeonhole Principle), • invariants, • interpretation method (the problem is “translated” into appropriate language). • extremal element method (the set is analyzed by investigating its extremal elements), • ·**Out-of-school activities for junior students**• “Club of Professor Littledigit” (for students up to 9th grade) • “Contest of Young Mathematicians” (for students up to 7th grade) • A lot of teachers, students and parents have expressed interest and necessity of similar contests for primary school pupils. So contest “So much or… How much?” for 4th grade students was established. • ·**Other activities**• There are organized also mathematical summer camps for students in some regions. • In some back-country regions monthly sessions for students and teachers are organized during school year.**Teaching aids**• Beside the present-time activities and competitions, a lot of teaching aids are prepared and published for advanced math education. There are • methodical materials on some topics • volumes of problems with extended solutions of Latvian math olympiads and other contests • Teaching aids are published both in a “hard copy” version and on the Internet. A lot of books are written and published within the Latvian – Icelandic project “LAIMA”. Some of them are translated into English too.**Thank you for attention!**Jānis Mencis (e-mail: jmencis@gmail.com) Laura Freija (e-mail: laura.freija@gmail.com) University of Latvia http://www.lu.lv Correspondence mathematics school http://nms.lu.lv