1
PROMOTI NG MATHEMATI CAL THI NKING IN FI NNI SH MATHEMATI CS
EDUCATI ON
Heidi Krzywacki, Leila Pehkonen & Anu Laine
University of Helsinki
Abstract
In this article, we outline some of the main characteristics of the mathematics education in the
Finnish educational context. In Finland, at both primary and secondary school levels
teachers are educated to be autonomous and reflective academic experts. This policy means
there is a strong emphasis on teachers’ independence and autonomous responsibility and it
also has many consequences for teaching mathematics. We start by discussing the main
features of Finnish mathematics education through the outline stated in the National Core
Curriculum and reflecting on the features of teacher education, which prepares academic,
pedagogically thinking teachers for school work. In Finland, mathematics education is highly
dependent on teachers and their understanding of teaching and learning mathematics.
Secondly, we elaborate the practical and environmental aspects influencing schooling and the
way mathematics is taught in Finnish comprehensive schools. The central aspects
characterising Finnish mathematics education, such as the distribution of lesson hours, the
availability of pedagogically well-structured learning materials and the principles of school
assessment, are discussed. To conclude, Finnish teachers responsible for teaching
mathematics play a significant role in maintaining and developing the quality of school
mathematics education.
Keywords: mathematics education, comprehensive school, curriculum, teacher education
1 Introduction
In Finland, basic education in mathematics is carried out by primary school teachers,
responsible for the first six years of schooling, i.e., grades 1-6 when pupils are 7 to 12 years
old, and by specialised subject teachers, who teach mathematics at secondary school level in
grades 7-9 when pupils are 13 to 16 years old. In practice, Finnish primary school teachers
teach more than two thirds of mathematics lessons in comprehensive school. The
achievements of Finnish pupils are, at least to some extent, based on the high-level academic
teacher education implemented in Finland (see more about teacher education in chapter X).
Obviously, the number initial teacher education courses, which are intended to give student
teachers expertise in teaching and learning mathematics as well as those for special interests
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in mathematics education, differ for teachers at different school levels. Especially, primary
teacher education programmes have always been popular; only about 10 per cent of the gifted
and talented applicants are accepted. Even though becoming a mathematics teacher at the
secondary school level is less popular, there is no lack of qualified subject teachers in
mathematics in Finland. Teachers in Finnish comprehensive schools are not only well
educated academic experts with university master’s degree, but they are also motivated,
autonomous professionals, who are relatively committed to their work (Simola & Hakala
2001; Simola 2002).
The outcomes of Finnish mathematics education have proved to be outstanding according to
PISA testing (OECD 2004?, see more in chapter X). The success is actually not surprising
considering the development of mathematics education during the past twenty years. From the
late 1980s, serious efforts were made to develop mathematics teaching and learning in
schools. At that time, an informal voluntarily established committee, ‘Mathematics teaching
in the 1990s, was formed by experts in mathematics teaching at different levels, publishers,
researchers and administrators. Teachers had an essential role in the committee, which
discussed the future and the need for reforms in mathematics education. After two years of
continuous informal meetings, a booklet about the main outcomes and recommendations for
the further development of Finnish mathematics education, for example, some practical ideas
and examples of exercises, was published (Halinen et al. 1991). The committee was
successful in sketching upcoming and current developmental trends in mathematics
education. The booklet became an important trailblazer for future reforms – among others the
curriculum reform in 1994.
There has been a clear trend to improve Finnish mathematics and science education in
general. In 1995, the National Board of Education launched a national development project,
the LUMA –project (LU refers to science and MA to mathematics) that lasted from 1996 until
2000 (Heinonen 1996). The aim was to strengthen knowledge and skills in mathematics and
science education at all levels of schooling, while providing special attention to the
significance of learning the respective subjects. There have not been dramatic changes in
Finnish education in the 21st century; although the spirit of developmental work and special
attention to mathematics and science education is still there. The national LUMA Resource
Centre coordinated by the University of Helsinki has continued the developmental work as an
organisation that oversees cooperation between schools, universities and industry. The aim of
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the activities is to promote and improve education in natural science, mathematics, computer
science and technology at all levels. However, some critical voices can be heard when
discussing the quality and competence of the students entering mathematical programmes in
higher education institutions. According to the responsible providers of education, the
computational skills and mathematical routines of students starting at their institutions do not
meet all their expectations, and therefore the challenge still remains of how to achieve the
learning aims set by the respective study programmes.
In this article, we outline the characteristics of Finnish mathematics education by discussing
teaching and learning school mathematics, the core idea of mathematics education described
in the national curriculum and the school environment influencing the implementation of
school mathematics. We elaborate on Finnish mathematics education especially from the
perspective of the teachers, who can be seen as autonomous professionals, meaning that they
are responsible for the planning, implementation, and assessment of teaching and learning
mathematics. As a result of the autonomous role of the teachers, the nature of teaching
mathematics in Finnish classrooms is highly dependent on individual teachers.
2 The starting point of Finnish mathematics education
There are two essential aspects, which have an impact on the way mathematics education is
carried out in Finland: the outline of mathematics education described in the National School
Curriculum, by which teachers are bound when teaching mathematics in their classrooms, and
teacher education organised by the universities. Teachers, both at the primary and secondary
school levels, have an essential role in implementing the core ideas of mathematics education.
The core idea of mathematics education according to the national curriculum
The previous national core curriculum, the Framework Curriculum for the Comprehensive
school (FCCS 1994) published in 1994 by the National Board of Education was an important
basis for successful mathematics education in Finland. Before that, in the 1980s, the National
School Curriculum was a more detailed document setting the aims for and describing the
contents of various school subjects. The main change took place when the curriculum was
written giving special emphasis to the spirit of constructivism. The 1994 FCCS was much
more flexible, less centralised and detailed than its predecessors (see more in Chapter X). All
Finnish teachers truly became involved in curriculum planning and writing, although not all
the teachers were responsible for mathematics.
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Problem solving – both as a method and as content - was set as an underlying principle along
with mathematical-logical requirements. In addition, teaching geometry, statistics and number
concept as well as proper basic counting skills were widely discussed. Stress was laid on
pupils’ thinking and understanding mathematics, and co-operative learning methods were
emphasized. In addition, it is clarified in the curriculum that: ‘pupils of all ages and all levels
should be allowed to build and make models with their hands in order to form correct mental
pictures and concepts’ (ibid. 83). Various, easy-produced, non-expensive and self-made
manipulatives and a range of exercises were introduced in the support material. In practice,
the ethos and practical examples provided in the documents are consistent with the tasks used
in PISA testing.
The latest educational and psychological research on learning mathematics was taken
seriously into consideration in the 1994 FCCS and consequently, the main changes in
mathematics education took place almost 20 years ago. However, it was found to be to put
into practice, the main ideas of Finnish school education described in the broad outline, even
if additional support materials (Opetushallitus 1995) were provided to support understanding
and practically implementing the new ideas of mathematics education. The current core
curriculum (NCCB 2004) differs from the previous one in some ways, even if neither the
spirit of Finnish comprehensive school in general, nor the underlying ideas of constructivist
mathematics education have changed. The current curriculum takes more control over the
contents of teaching and learning, and consequently, the overall outline of education is
described in more detail. Mathematics education is considered as the basis for developing
mathematical and logical thinking, which are seen to be potentially important for societal
activities in the future. Since learning mathematics is seen to be abstract and challenging for
children to understand, the need to use didactical models and concrete materials such as
manipulatives should be addressed in good mathematics teaching. In addition to transforming
mathematics into something more visible and concrete, applying mathematical thinking in
practice and emphasising the importance of reasoning are also at the focus of the learning
goals. Students should learn how to reason their thinking and communicate mathematical
processes with other learners. The essential aim of learning mathematics is to acquire a
thorough understanding of mathematical concepts and based on that, learn how to apply the
acquired knowledge in different situations. To conclude, the current national curriculum still
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outlines only the main principles of teaching mathematics in Finnish schools without going
into detail. The details are elaborated in the local level curricula.
Teacher education and the main principles of good mathematics education
Finnish teachers have a comparatively autonomous role in teaching mathematics in their
classrooms, and therefore, teachers’ beliefs, skills and knowledge-base of mathematics
education and their potential to put the ideas into practice matter (Krzywacki 2009). Teachers
face challenges at many levels when they teach mathematics. However, Finnish teachers are
committed to addressing these demands and they do so in their own individual ways. This, in
turn, puts weight on the quality of teacher education, and how well the initial education of
teachers manages to provide a starting-point for expertise in teaching mathematics. Since each
Finnish university is allowed to design its teacher education programmes a bit differently,
there are minor differences between the implementation, amount and contents of mathematics
education courses (Laine & Kaasila 2007; see more about teacher education in chapter X).
Here, we will use teacher education at the University of Helsinki as an example.
In the initial primary school teacher education, mathematics education is a special focus
among the multidisciplinary courses providing readiness for teaching all school subjects at
primary school level. In practice, the extent of mathematics education course at the University
of Helsinki is 7 credit points (cp) out of the total 300 credit points comprising the overall
programme. In addition to the basic course compulsory for all student teachers, they all teach
mathematics during their teaching practice periods that provide actively mentored and
supervised teaching experience (20 cp). Only some of the teacher students specialize in
teaching mathematics through extended studies. Some 10 to 15 percentage of the primary
school teacher students complete 25 credit points of advanced mathematics education courses,
comprising of mathematical courses and the courses dealing with teaching and learning
mathematics, such as special needs in mathematics education. It is also possible to complete a
minor (60 credit points) specialising in teaching mathematics at lower secondary school. Only
5 per cent of the students complete these studies comprising mostly of the mathematical
courses provided at the Department of Mathematics and Statistics.
In secondary school teacher education, at the University of Helsinki as well as other Finnish
universities, a major in university mathematics is the main component of the degree that takes
approximately five or six years to complete (see more about teacher education in chapter Y).
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The programme is grounded on building up strong mathematical content knowledge, i.e., the
programme consists of university mathematics as a major (150 cp), another school subject
such as chemistry or physics (60 cp), and one year of pedagogical studies (60 cp) that
includes supervised teaching practice modules (20 cp). Pedagogical issues are discussed in
general educational courses (20 cp), as well as special features of teaching and learning
mathematics in the special courses of mathematics education (20 cp). The production of a
small-scale pedagogical dissertation in mathematics education is also part of the studies.
Here, we introduce four themes characterising the spirit of mathematics education that are
mediated in pre-service teacher education at Finnish universities. Even if the structure of the
teacher education programmes are varied, a common foundation is laid for quality
mathematics teaching and learning. First, affective aspects are considered important to
studying and learning mathematics. Traditionally, both in Finland and internationally, the
outline of mathematics education has been established through describing cognitive aspects
and the aims of learning outcomes regarding mathematical skills and knowledge. However,
recently, Finnish educators have started to underline the importance of views and attitudes
towards mathematics (Hannula 2004; Pietilä 2002). The need for improving positive attitudes
and interest towards mathematics is also mentioned in the current national curriculum (NCCB
2004). When affective aspects are also considered in outlining educational aims there is a
broadening of the traditional learning aims in mathematics education.
Second, the use of concrete materials and didactical models for improving the understanding
of mathematical concepts is also seen as an underlying theme of Finnish mathematics
education. This is discussed during the teacher education courses, for example, in group
activities and when piloting the use of concrete materials in teaching practice. In the teacher
education programme at University of Helsinki, the main idea behind number systems are
elaborated with the help of concrete materials, which help students to understand the main
mathematical concepts and consider how to take this special viewpoint into consideration in
their teaching, especially through identifying the difficulties that learners might face when
learning the ten-base system.
Third, problem solving and the significance of reasoning and thinking processes are also
addressed in the pre-service teacher education. Traditionally, the process of teaching and
learning mathematics, whether in Finnish schools or internationally, has not underlined the
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importance of oral communication and co-operative methods in mathematical processes.
However, since interaction with peers enhances the need for communicating about the
processes and the reasons underpinning them, co-operative learning and working in pairs or in
small groups are regarded as workable methods for promoting skills in problem-solving
(Good, Mulryan & McCaslin 1992). The emphasis is on learning to process complex
mathematical situations in a flexible and creative manner. When working together with
others, learners are in a situation, where speaking about mathematical problems and the
phases of the solution process is necessary. It is natural to speak about processes and give
reasons for making decisions on how to carry out procedures when sharing one’s
understanding with others.
The fourth theme is related to understanding and supporting students, who have learning
difficulties with, and special needs for, mathematics learning. Teachers in comprehensive
schools, especially those teaching the first grades of primary school, should have a basic
knowledge about learning difficulties and dyscalculia, and based on that, be able to recognise
learners who might need some extra support in learning mathematics. Often the question is
not about serious learning problems but recognising some common misconceptions and minitheories, i.e., rules and misconceptions developed by the pupils themselves that are common
in mathematics (Claxton 1993). In addition to recognising pupils with challenges in learning
mathematics and providing extra support in problematic situations, it is essential to possibly
prevent difficulties in learning through taking into consideration the most common minitheories related to different mathematical content, for example, through using manipulatives
in teaching and learning fractions and providing parallel tasks, which help learners in the
conceptual changes associated with understanding the characteristics of rational numbers
(Merenluoto & Lehtinen 2004).
3 Implementation of mathematics education in Finnish comprehensive schools
In the following, we outline some environmental and practical features that influence the way
mathematics is taught and studied in Finnish comprehensive schools.
Distribution of lesson hours in mathematics
In the OECD countries, the total number of hours devoted to mathematics teaching in Finnish
schools is only larger than those of the Netherlands (Välijärvi et al. 2002, 262), i.e., 32 hours
of lessons hours a week are allocated for teaching and learning mathematics during the nine
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years of comprehensive school. Time is not wasted on mathematics education in Finnish
comprehensive schools, although the number of mathematic lesson hours is higher than that
given to most other school subjects. In fact, only mother tongue studies have more lessons
hours than mathematics. The Council of State gave its latest decision on the distribution of
lesson hours in 2001 (Distribution of Lesson Hours for Basic Education 2001), which
increased the minimum amount of mathematics by one lesson compared to the previous
decision.
According to the decision, mathematics must be taught for at least 18 lesson hours a week
(i.e. 18 times 45 minutes) during the first five years at the primary level of comprehensive
school, and at least for 14 hours a week during the four years at the upper level of
comprehensive school. This means approximately 3 to 4 hours a week at the primary school
level as well as at the lower secondary level. In a similar way, minimum hours per week were
given for all school subjects as well as the maximum hours pupils were allowed to work at
school. However, no hourly maximum limits were set for any school subject. In addition, the
local curriculum level must be set so that pupils are eligible to continue their studies at the
next school level even if they had studied the minimum amount of mathematics set by the
decision of the Council of State. Within these constraints, the schools are responsible to make
their own decisions about the distribution of lesson hours.
Learning materials as a resource for teaching and learning
Learning materials, especially pupils’ textbooks have an important role in Finnish
mathematics education. Finnish primary school teachers are especially very loyal to their
mathematics textbooks – as are teachers all over the world. In Finland, primary school
teachers have always been very satisfied with the mathematics textbooks and teacher’s
support materials. According to a study by Niemi (2004), 53% of teachers in the sixth grade
found that textbooks are a better base for the planning mathematics teaching than the school’s
own curriculum. This is in conflict with the underlying principle of local level curriculum
work. Secondary school teachers have a slightly different attitude towards ready-made
learning materials. They rely on their expertise in mathematical content knowledge and
specialisation in teaching and learning mathematics, and therefore, the need for support
material and ready-made pedagogical ideas is different at the primary and secondary school
levels. This can be seen also in the supply of support materials.
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In Finland, learning materials are produced by ordinary teachers, who are interested in
mathematics education and currently working at schools. Therefore, they are very familiar
with the conditions in schools. Currently, there are several parallel textbooks from different
publishers, i.e., 5 or 6 textbooks at the primary level and 4 to 6 at the secondary school level.
Even if the textbooks differ slightly from each other, all the learning materials and textbooks
are generally speaking rather similar. All textbooks provide various materials for problem
solving and statistics, ideas for group work and projects. They also provide a good supply of
basic exercises as well as more complicated tasks for all the pupils. There are also collections
of challenging tasks for those pupils who are more advanced or/and interested in mathematics.
It is the teachers’ responsibility to choose the textbooks and other materials for their pupils as
well as the teaching methods. It is noteworthy that the quality of the learning materials is not
directly equivalent to the quality of teaching, as the teacher can use all kinds of materials
either appropriately or otherwise. They can also choose to teach without textbooks if they
want to, although this alternative is seldom used.
Teachers’ conceptions of teaching and learning materials in mathematics reveal something
about Finnish mathematics education. In a case study (Pehkonen 2004b), nine primary
teachers were interviewed about what constitutes good and stable elements in school
mathematics teaching and learning. The mathematics textbooks were seen as important tools
for teachers in maintaining their teaching at an appropriate level and providing ideas for new
ways to teach. This justification was revealed by the teachers speaking appreciatively about
the textbooks and their use in mathematics education and of positive accounts of using
textbooks. Teachers claim that the textbooks guarantee a stable quality of teaching, since they
are considered to be logical and explicit. They contain the essential facts and the tasks are
connected to everyday life. In addition, the use of textbooks was seen as a means for teachers
to keep their teaching logical and coherent. Mathematics textbooks help teachers with their
workloads, because the books provide ready and sensible structures for lessons and enough
exercises for the pupils.
Actually, mathematics textbooks were considered to be written for pupils and their learning
processes. Moreover, textbooks were seen to be a source of motivation; they are colourful and
the exercises are varied. The pupils’ keen interest was seen as evidence of their high quality.
Teachers of the youngest children claimed that children love their mathematics books. As
nowadays most schoolwork is organised in small groups, teachers find that pupils love those
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peaceful moments when they are allowed to work alone and proceed at their own pace. The
shared belief is that, with the help of textbooks, children can study the facts they are expected
to learn.
Nowadays, other kinds of learning materials and computer-aided facilities are increasingly
used in Finnish schools. Teachers can choose what they use and how to use these modern
facilities in a way that suits their personal teaching styles. Even if Finnish schools are rather
well equipped (Eurydice 2004; Eurydice 2011), the challenge lies in using these resources in
meaningful ways from the perspective of learning mathematics. The technological materials
are often related in a complementary way to existing learning materials, such as book series.
In accordance with the underlying idea of using concrete materials and didactical models in
teaching and learning mathematics, textbooks also include some print versions of
manipulatives, for example, materials for illustrating the ten-base system and basic
calculations during the first grades in primary school. There are also additional materials
attached in teacher guidebooks, for example, geometrical obstacles to be used by teachers in
teaching and learning geometry.
In Finland, teacher guidebooks are structured to support teachers in their everyday teaching
work. The main idea of the guidebooks are to provide help in designing mathematics lessons
and give ideas for implementing the main underlying ideas of mathematics education in
Finland. In practice, the pedagogical ideas provided in the teacher guidebooks are presented in
parallel with a learner’s page view and structured in accordance with traditional parts included
in mathematics lessons (see Illustration 1: Best practice example).
Illustration 1. Best practice example: a mathematics lesson in a teacher’s guidebook (Lilli et
al. 2010).
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Teaching mathematics in Finnish classrooms
We cannot claim that Finnish mathematics education uses very innovative teaching
approaches. The fact is that teaching in general as well as especially in mathematics education
is rather traditional in Finnish classrooms (Norris et al. 1996). In mathematics, teaching is
mainly teacher-centred frontal teaching of the whole group of pupils but nevertheless the
frequency of pupil activity and involvement are high. Although there is a good deal of
conservatism in the teaching methods, focusing on this alone does not give the whole truth.
Finnish teachers avoid being too hasty and want to guarantee learning opportunities for their
pupils. They try to avoid ‘educational entertainment’ (Pehkonen 2007). However, teachers do
adopt new ideas and methods that they find meaningful and useful. For example, some
teachers have a special mathematics lesson with problem solving or project work once a
week. According to Niemi (2004), more than 60% of primary school teachers state that they
use a lot or quite a lot of various co-operative teaching methods in their mathematics lessons.
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It seems that Finnish teachers have found a successful way to combine traditional teaching
methods with some innovative approaches. Some traditions and routines have proved to be
very fruitful and the structure of an average mathematics lesson is rather unchangeable. It has
been a tradition for decades that a short time, about a 5-minute session at the beginning of a
mathematics lesson is devoted to mental calculation or some other orientation activity. All
teachers’ support materials provide a collection of mental exercises for every lesson to help
the teachers. Even if the time used for this kind of practising is short, it is repeated from
lesson to lesson from one year to the next.
Usually, what follows is checking the homework that is given after each mathematics lesson
in order to repeat the main points of the previous lesson. However, even if Finnish pupils use
less time on their regular mathematics homework than their peers in most OECD countries
(Välijärvi et al. 2002, 262), homework has a special role in Finnish mathematics classrooms.
Most teachers make a quick round of the classroom and make sure that all the pupils have
completed their homework. Usually, difficult or complicated tasks are explained by selected
pupils to the rest the class. Consequently, the pupils are regularly given plenty of feedback
about their homework. Negative feedback is not given if pupils are unable to complete their
homework but their parents are informed if they do not do their homework.
The lesson continues with the teacher introducing and teaching new topics, which is followed
by individual work through tasks that help the learners study and acquire the knowledge set in
the lesson aims. The guidebook highlights some essential pedagogical ideas that a teacher
should take into consideration when discussing a topic. A large proportion of mathematics
lessons are devoted to silent, individual work. The pupils can practise at their own pace and
teachers help those who need support. Individual work is very consistent with the ideas of
constructivism, although it is not a new and modern way of working. Homework is usually
given to the pupils at the end of the lesson to promote the learning process.
Assessment policy
As Finnish teachers have a considerable amount of decision-making authority in schools they
can, among other things, determine quite a lot of their course contents and pupil assessment
policies. Finnish pupils are not assessed by national tests or examinations, which emphasise
the importance of teacher-conducted assessment practice. On the national level, the outcomes
of the Finnish comprehensive school are followed only by sample-based surveys at the end of
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the sixth and ninth grade of comprehensive school. The results are published only at the
system level, while the results of individual schools are delivered exclusively to the schools
concerned.
In the 1990s, the principles of pupil evaluation were reformed in conjunction with the
curriculum reform. The main principle was no longer to find differences between pupils - as it
had been earlier - but to improve pupils’ learning. The main goal was to determine how to
help pupils better understand mathematics. Various methods in pupil assessment were
introduced, for example, how to evaluate pupils’ mathematical processes and how to evaluate
products. At that time, pupil self-assessment was a totally new idea in Finnish education, but
very soon it was adopted at all school levels.
All Finnish teachers are taught to design and implement assessment in mathematics during
their pre-service teacher education. Primary school teachers are capable of designing their
own tests and assessment tools. All primary school mathematics textbooks provide collections
of ready-made tests, and teachers can use them if they want as an additional resource.
Naturally, the use of these tests is one method to reach some uniformity in assessment.
Anyway, as all teachers are involved in the process of planning the school curriculum the fact
is that Finnish primary teachers are very well aware of the curricular goals for mathematics.
In addition, they know what contents and to which level children are expected to learn
mathematics.
Talent development for all students
A law (Basic Education Act 1998/628) regulates the compulsory education of all Finnish
children. The central point of the Basic Education Act is that education and teaching must be
arranged so that it respects and takes into account the pupils’ ages and talents. The law
guarantees the right of pupils to be educated in a manner that is best suited to them. The same
principle can be seen in the Development Plan in Education and Research published by the
Ministry of Education for the years 2007-2012. This document states that
‘The premise in developing general education is to secure basic educational rights for all pupils and students
according to their abilities and special needs’ (ibid. pp. 22).
One of the leading principles in the Finnish education policy has been to provide all pupils
with equal and high-quality educational opportunities and to remove obstacles to learning
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especially among the least successful pupils (Ministry of Education 2004). Help is given most
during the first school years. This has been the Finnish educational mission for decades. It can
be seen as an ideological standpoint, but it has its pragmatic perspective as well. Educational
equality has been seen as an investment in human capital. Small nations, like Finland, cannot
afford to waste any reserve of talent. In the light of PISA findings, we seem to have managed
very well in these aims (e.g., OECD 2004, 144-145).
According to the Basic Education Act, schools must cooperate with parents. These principles
create the opportunities for education of all pupils’ with different capacities – those with
learning difficulties as well as those who are gifted and talented. The sooner special needs as
a learner are recognised, the better schoolteachers can provide support in learning process and
possibly avoid difficulties in the future.
Gifted pupils are not mentioned as a special group in any law or official document regulating
Finnish school education. Gifted education pedagogy as such is not typical to the Finnish
school system, meaning that it is not taken into consideration significantly in everyday
schooling. However, it can be said that opportunities are provided for developing the talents
of all pupils in accordance with their needs (Pehkonen 2004a). Although, it must be said that
there still are, particularly at primary level, academically gifted pupils who are not given
special attention. The sizes of teaching groups vary, and there are different kinds of learners
integrated in heterogeneous classes. Therefore, much is dependent on a teacher's interests and
talents. Especially at the primary school level, it might be difficult for primary school teachers
who have not specialized in mathematics to provide academic challenges for any of their
pupils who are exceptionally gifted in mathematics.
To conclude, the Finnish view on education and giftedness is to concentrate more on talent
development than on gifted education. This does not mean leaving the most able and capable
pupils without special nurturing, but the main concern is to develop the talents of all the
pupils and take also care of those with learning difficulties. The full use of all talent reserves
is a challenge to Finnish education and an investment for the future. Educational equality is
promoted by providing special needs education in mathematics as part of mainstream
schooling. The idea is to support students with different talent profiles individually in mixed
classes, not by grouping the pupils based on their mathematical talents but dealing with their
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individual needs through special lessons and exercises designed in cooperation with special
needs education teachers.
Concluding remarks
Finnish pupils seem to like mathematics especially at the primary school level based on
studies that have found pupils’ attitudes towards mathematics to be quite positive. According
to Kupari (1999), mathematics is one of the five most popular subjects among 4th and 6th
graders. The attitudes are most positive during the first school years. However, over time
attitudes seem to turn less positive. Niemi (2004) has found that sixth-graders had still mildly
positive attitudes (scale from 1 to 5; M = 3.3) and one-third of sixth graders claimed that
mathematics was their favourite school subject. It is noteworthy that expressing strong
emotions or feelings is not typical in Finnish culture, and consequently, learning mathematics
is not considered in an emotional manner either. Finnish pupils have mostly very sensible and
neutral attitudes towards schooling and mathematics is seen as an important and useful school
subject rather than something to be emotional about (Niemi 2004, 151-152).
We have presented the outlines of teaching and learning mathematics in Finnish
comprehensive schools in order to describe the facilities influential to functional mathematics
education in Finland. One of the features characterising mathematics education in the Finnish
education system is the independent role of the teacher. Although primary school teachers are
not usually experts in mathematics, they are professionals in teaching and education. All
teachers have a solid knowledge base in education and appropriate skills for self-development
in work. At the secondary school level, specialised subject teachers are responsible for
teaching mathematics. They are experts in their respective subject, and most of them are
deeply interested in developing their methods of teaching mathematics and promoting
learners’ interest in mathematics learning. Teachers know how to develop skills, nurture talent
and to take care of the overall wellbeing of a child. Even if mathematics teaching seems to be
quite traditional in Finnish classrooms (Norris et al. 1996), the teaching and learning process
is guided by professionals who are aware of the learning objectives within the core curricula.
It is one of the teachers’ responsibilities to choose appropriate activities and materials to
implement these objectives. Using teacher-conducted assessments instead of national tests
and examinations especially gives teachers enough scope to independently plan and teach
mathematics. Teaching and learning mathematics at the primary school level seem to provide
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a good and sound basis for studies at the upper secondary level. Finnish teachers have shown
that there are many ways to teach mathematics well.
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