math education for stem disciplines in the eu
TRANSCRIPT
Math education for STEM disciplines in EU
Seppo Pohjolainen Tampere University of
Technology (TUT)
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Contents
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• Importance of mathematics • Pisa and Timms and consequences • From content to competence • Reform in math education • Role of technology
Mathematics
• “The remarkable development of the natural sciences and engineering since the
Renaissance is a consequence of the fact that all nature’s known laws can be expressed as
mathematical equations.”
• (OECD 2008)
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• “Mathematics offers business a formula for success.“
– (Financial Times, February 2006)
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• Know-how on mathematical and natural sciences must be emphasised more strongly as
a part of common cultivation and their valuation must be improved in the society
• (Finnish Association of Graduate Engineers 2009)
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Quality of school math education
• The Programme for International Student Assessment
(PISA) is an internationally standardized assessment for15-year-olds in schools. PISA aims at testing literacy in three competence fields: reading, mathematics, science.
• TIMSS (Trends in International Mathematics and Science Study) collects educational achievement data at the 4th and 8th grades to provide information quantity, quality, and content of instruction.
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Targets of TIMSS and PISA • The PISA mathematics test asks students to apply their
mathematical knowledge to solve problems set in various real-world contexts.
• TIMSS, on the other hand, continues to measure more traditional classroom content such as an understanding of fractions and decimals and the relationship between them.
http://www.edinformatics.com/timss/TIMSS_PISA_test.htm TEMPUS MetaMath Kazan 8-10.12.2014
http://www.theguardian.com/news/datablog/2013/dec/03/pisa-results-country-best-reading-maths-science
Quatar
Luxembourg
Singapore
China (Shanghai)
Peru
Europe
USA
Pisa 2012
Vietnam
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http://www.theguardian.com/news/datablog/2013/dec/03/pisa-results-country-best-reading-maths-science
Pisa 2012: Results
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Education versus economical growth
Hanushek, Wößmann:The Role of Education Quality in Economic Growth World Bank Policy Research Working Paper 4122, February 2007
• “The existing research provides strong reasons to believe that quality of education is causally related to economic outcomes.
• To be sure, quality may come from formal schools, from
parents, or from other influences on students. • But, a more skilled population – almost certainly
including both a broadly educated population and a cadre of top performers – results in stronger economic performance for nations.”
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OECD REPORT: Added-variable Plots of Growth and Education
Hanushek, Wößmann:The Role of Education Quality in Economic Growth TEMPUS MetaMath Kazan 8-10.12.2014
PISA and TIMMS
• Asian countries are doing well: criticized for teacher centered education, large amounts of homework, rote learning etc..
• European countries are doing well, but lagging behind. Pedagogical and instructional reforms.
• Developing countries at the bottom.
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University engineering mathematics
• Facing the same problems as in schools
• The problems from school will transfer to university level
• We need to educate all engineering students to a sufficient level.
• We can not escape the problems by concentrating only on good students
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Evolution of Student Interest in Science and Technology Studies, Global Science Forum, OECD, May 2006.
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AUSTRALIA • Period 1997-2005 has experienced a 52% growth
in employment demand for the mathematical sciences. The number of students taking a mathematics subject has decreased by 34 %.
• Henderson,Broadbridge:Engineering Mathematics Education in Australia, (2009)
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Australia
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Europe
• At the 1998 meeting of the SEFI Mathematics Working Group the decline in entry competencies of students was a common theme, from across Europe and beyond.
• In 1997 only 54% of A-level UK students tested at the start of their university studies, could correctly identify the graph of the cosine function. In 1991 all comparably qualified students could do this.
• SEFI “Report on “Mathematics for the European Engineer - a Curriculum for the twenty-first Century”(2003)
• SEFI= European Society for Engineering Education
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SEFI (Report 2003)
• Universities taken measures to handle the problem:
• 1. Reducing syllabus content, replacing some of the harder material with more revision (or, for some students, vision) of lower level work,
• 2. Developing additional units of study, • 3. Establishing mathematics support centres, • 4. Doing nothing.
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Finland • Despite PISA results teachers at Finnish
universities are worried about degrading mathematical skills of incoming students.
• In PISA survey (2003) Finland showed highest mathematical literacy performance in OECD and second highest among all 41 countries.
• In PISA (2012) Finland dropped 12 th in mathematics.
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Changes in Finnish comprehensive school (1980-2000)
Näveri (2009)
numerical, math structural, evaluation, application
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Aamulehti (2014) News on PISA 2012 :Every Finn has 500 competitors in mathematics from China and India
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A student’s comments in the Aamulehti newspaper
• I have studied mathematics at TUT and my opinion is that current math teaching does not improve one’s problem solving skills. • It is more about rote learning of mathematical procedures and routine calculations. • Student motivation is lost somewhere when they are asked to solve assignments that have nothing to do with their future. Only 1% of students need this kind of mathematics in their future life. • Others will forget math as unnecessary stuff after graduation. The idea that problem solving skills are dependent on mathematics is absurd. • One can learn logical thinking with but also without mathematics.
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TUT Teacher’s opinions
• Manipulation skills are weak – some students do not know even how to handle fractions
• Weakest students do not know basic rules of algebra: sin(a+b)=sin(a)+sin(b)
• Too much work with formula books and calculator • No idea about mathematical proof. • If asked to prove A implies B they assume B is true and try to
show that A is true.
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Pedagogical reform
• Engineering education similar to schools: we have to
teach for all kind of students • We cannot drop out the weakest students
• From content to competencies • What do students learn ?
• Motivate students to do their job ? • Use ICT a tool
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Reports on school reform in science for EU
EURYDICE: Mathematics Education in Europe: Common Challenges and
National Policies 2011
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Recommendations on how to increase motivation to learn mathematics and encourage the take-up of mathematics-related careers. Many European countries are confronted with declining numbers of students of mathematics, science and technology, and face a poor gender balance in these disciplines.
• The mathematics curriculum (contents->competences, math in everyday life)
• Teaching approaches and methods (PBL, Inquiry based mehods, contextualization....)
• Addressing low achievement • Improving student motivation(extra curricular activities,
companies, gender issues)
• Education and professional development of mathematics teachers
• Promoting evidence-based policies (collection and evidence on best practices)
Mathematics in Europe:Common Challenges and National Policies (EURYDICE 2011)
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SEFI (2013): Pedagogical reform
• The main message is that although contents are still
important, they should be embedded in a broader view of mathematical competencies that the mathematical education of engineers strives to achieve.
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SEFI: A Framework for Mathematics Curricula in Engineering Education 2013
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Mathematical Competence for Engineers
”the ability to understand, judge, do, and use mathematics in a variety of intra- and extra-mathematical contexts and situations in which mathematics plays or could play a role” SEFI (2013): ”A Framework for Mathematics Curricula in Engineering Education”
General Mathematical Competencies for Engineers
– Competencies
• thinking mathematically • reasoning mathematically • posing and solving mathematical problems • modelling mathematically • representing mathematical entities • handling mathematical symbols and formalism • communicating in with and about mathematics • making use of aids and tools
– Dimensions (of extent) – Clusters (reproduction, connections, reflection)
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• Symbolic calculators • Learning platforms (Moodle,...)
– distribution of material – collaboration and feedback – motivation (links to applications and
other sources) • Mathematical Software (Matlab, R-,
Octave, Maple, Mathematics, Wolfram Alpha...) – application of mathematics to ”real”
world problems – visualization of results
• Course delivery & cognitive support (MatBridge,...)
The role of ICT
The Role of ICT • The design of a computer-based instructional system
should be based on content specific research of learning and comprehension and pedagogical model of the learner and the learning process.
• In designing computer-based teaching and learning environments real didactic tasks should be considered. One should think thoroughly what to teach and how to teach.
• Reusser, K.: “From Cognitive Modeling to the Design of Pedagogical Tools”; (1995).
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Teacher’s role • Teacher’s role may change, but they can not be replaced by peer/
independent learning or technology.
• In Norway curriculum for compulsory school 1997, emphasized that students should be independent, proactive and 'learn by doing'.
• Analysis of declining results revealed that students were sometimes left alone to construct their knowledge from a multitude of experience and the teacher's role was being reduced to facilitator.
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Conclusion
• Importance of mathematics is well understood.
• Deterioration in the students’ skills is recognized.
• Pedagogical and school reforms are the way EU is going.
• Technology can play a important role here.
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• Thanks !