A visit to the elementary school

I visited the Elementary School Attached to Seoul National University of Education (that is the name of the school!). This school is really physically attached to Seoul National University of Education and it is just separated by the gate. The students can use the field and the track at the university.

Here are some interesting facts about this elementary school:

1. Named as research school by the Ministry. Teachers do research on developing materials for effective teaching, develop and verify curriculum, methodology , textbooks and educational materials.

2. Have a special need class and return class (for Korean students returning from overseas)

3. It is a small school with 36 teachers but there are 6 Drs there. Some of them have subject specific doctorate , fore example, Doctorate of Chemistry or Music.


TEDS-M Teacher Education and Study in Mathematics

TEDS-M 2008 is a comparative study of teacher education with a focus on the preparation of teachers of mathematics at the primary and lower secondary levels.It provides a cross-national data-based study about initial mathematics teacher education. TEDS-M is both relevant to educators and policy makers.In this study, the MCK (Mathematical Content Knowledge) and MPCK (Mathematical Pedagogical Content knowledge) of the would-be teachers are investigated. MPCK consists of (1) Mathematical curricular knowledge (Big idea), (2) Knowledge of planning for mathematics teaching and learning (Activities, possible misconceptions) and (3) Enacting mathematics for teaching and learning (Explaining mathematics concepts). For more info, please visit: http://teds.educ.msu.edu/


The Chaos Theory

Chaos theory is  popularized by Lorenz’s butterfly effect: “does the flap of a butterfly’s
wings in Brazil set off a tornado in Texas?” Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions (From wikipedia).

It is actually not new and this ideal can be found in some famous Mathematician quotes:

“We ought then to consider the present state of the universe as the effect of its previous
state and as the cause of that which is to follow. An intelligence that, at a given instant,
could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be
uncertain, and the future, like the past, would be open to its eyes.” (Laplace, 1814)

“There is a maxim which is often quoted, that ‘The same causes will always produce the
same effects.’ To make this maxim intelligible we must define what we mean by the same
causes and the same effects, since it is manifest that no event ever happens more that once,so that the causes and effects cannot be the same in all respects. […]
There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when
small variations in the initial circumstances produce only small variations in the final state
of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course.” (Maxewell, 1876)

India National Presentation

(1) Introducing history would make mathematics education more complete and help develop social cultural perspective.

(2) Traditional Pathshala (Hindi world of school) culture of learning numbers : Local orientation and a strong sense of functionality; recollective memory was the primary mode of learning.

(3) India has a strong Mathematical tradition. The major challenge in Mathematics education is the divisions in India society. Schools are stratified (poor schools for ppor students)

(4) Critical perspective : Problem posing pedagogues, folk tales, stories

(5) Face challenge in development of Maths teachers (viewed as “2nd rate” profession)

(6) A group of passionate mathematicians has come together to from National Initiative on Mathematics Education . I applaud their enthusiasm and their passion for mathematics education in their home country.

(7) Mathematics Assessment : Lots of questions and you have only 2 to 3 minute to solve each question.Extremely high stakes (Gang steals papers. Students commit suicide) . Emphasize on procedures and manipulative skills , heavy dependance on memorization
(8) Mathematics Training and Talent Search (MTTS) . Highly interactive. Think along with teacher. Do not allow the students to take notes

(9) More information on India Mathematics Education can be found at : http://nime.hbcse.tifr.res.in/uploads/INP-Book.pdf

Constructionism : theory of learning or theory of design?

By Chronis Kynigos
(Director of Educational Technology Lab, National and Kapodistrian University of Athens School of Philosophy, Faculty of Philosophy, Pedagogy and Psychology Department of Pedagogy)

(1) More info about the projects in Educational Technology Lab, can be found in : http://etl.ppp.uoa.gr/_content/Erga_R@D/Index_research_en.htm

(2) Constructionism is first coined by Seymour Papert “”The word constructionism is a mnemonic for two aspects of the theory of science education underlying this project. From constructivist theories of psychology we take a view of learning as a reconstruction rather than as a transmission of knowledge. Then we extend the idea of manipulative materials to the idea that learning is most effective when part of an activity the learner experiences as constructing a meaningful product.”

(3) Constructionism can be addressed as an epistemology of learning associated with a theory of learning and design

(4) Constructionism is relevant since digital society is full of objects to be tinkered with and tools for collective mathematical activity and communication.

(5) Constructionist media : A digital media as an expressive medium for students. Designed for students and teacher

(6) Useful Links:


TSG Gp 18 : Session 2

(1) Use of Internet In a Mathematics Assessment System
– SMAPP (Singapore Mathematics Assessment and Pedagogy Project)
– Assessment for Learning
– More information can be found at SMAPP
– Positive response from teachers and students

(3) Written math exams with Internet Access : A teacher’s perspective on the impact on day to day Math Teaching

– Denmark conducted exams in 2008 to 2010 in which students can use Internet
– For Mathematics, the use of Internet exam is not relevant as students can solve problems easily without using Internet
– However, the pupils are now currently equipped with laptops with CAS (Computer Algebra System) . Teachers use the laptop for classroom teaching.

(4) Identifying Cognitive Appropriate Technological Tasks based on Students’ level of Geometric Thinking
– There are different geometry applets/animations. Teachers need to use them properly
– The teachers can use geometry-related technology tasks for(1) Developing Analysis Dynamic Activities , (2) Developing Abstraction Dynamic Activities (3) Developing Deduction Dynamic Activities. These tasks are based on the the geometry learning as proposed by van Hiele (http://en.wikipedia.org/wiki/Van_Hiele_model)

(5) How to use video in a class?
–    As an informative tool
–    trigger a formative process about a given mathematical content?
– Teacher must know when to use in class
–    http://www.m3.mat.br/ (Website in Brazil)
–    Video-least used resource (lack of training for teachers to use video)


Developing free computer-based learning objects for high school mathematics

Fluminense Federal University of Brazil is tasked to develop mathematics resources for secondary school. Such learning objects are developed by mathematicians.  One of the strong point of these learning object is the provision of feeback. The URL is : http://www.uff.br/cdme/index-en.html. Some of the software developed using GeoGebra.

Some of the possible uses in secondary mathematics:

1. Triangle Classification Game

2. Function : How b depends on A?



TSG Gp 18 – Session 1

Integrating CAS and course management systems for undergraduate mathematics

– Using Moodle with Maxima (Computer Algebra System)

– Need to modify the code of Moodle to make it Maths Moodle

Postmodern DeConstruction in Mathematics Education

– PreCalculus : Constant Change and Numbers can be taught as polynomia.

– More info can be found at : http://mathecademy.net/intro/


Mathematicians and Didacticians

I learn a new term today. I m a didactian (teaching mathematics).So, do not call me a maths teacher. Call me a didactician of Mathematics.

In this lecture, Bernard R. Hodgson argues that there should be link between mathematicians and didacticians. In the history of Mathematics, 3 mathematicians had made contributions to the teaching of mathematics

(1) Archimedes

(2) Leonhard Euler (Published books for the teachers like ents of Algebra, Letters to a German Princess, Introduction to the art of reasoning )

(3) George Polya (The Ten Commandments for Teachers)



Regular Lecture : Computer Aided Assessment of Mathemtics

By Chris Sangwin (School of Mathematics, University of Briningham)

There are 2 strands of mathematical activity : the use of routine techniques and problem-solving. Computer Aided Assessment (CAA) is more meant for use of routines. Formative and meaningful  feedback can be given to the students by using CAA. Automation allows for follow through error and open ended question. He has designed, STACK  (an open-source system for computer-aided assessment in Mathematics and related disciplines. For more information, do visit the http://www.stack.bham.ac.uk/ .  STACK has moodle plug-in :-)

For CAA, we should have random questions, articulate the properties in central issues and test for properties different than calculation