Quiz (Math Ed 525, Unit 3)

✨ Math Ed 525, Unit 3✨

Answer all questions, then submit with your details.

Full Name Exam Symbol Number

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Quiz (Math Ed 525, Unit 2)

✨ Math Ed 525, Unit 2✨

Answer all questions, then submit with your details.

Full Name Exam Symbol Number

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Quiz (Math Ed 525, Unit 1)

✨ Math Ed 525, Unit 1✨

Answer all questions, then submit with your details.

Full Name Exam Symbol Number

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Embeded Plane

Definition: Embedded plane

If $\sigma=(\mathscr{P,L,I})$ and $\sigma'=(\mathscr{P',L',I'})$ are two planes then we say $\sigma$ is embedded to $\sigma'$ if

1. $\mathscr{P} \in \mathscr{P'}$
2. For every line $L \in \mathscr{L}$ there exists a line $L' \in \mathscr{L'}$ such that $L =L' \cap \mathscr{P}$

Definition: Subplane

If $\sigma=(\mathscr{P,L,I})$ and $\sigma'=(\mathscr{P',L',I'})$ are two planes then we say $\sigma$ is a subplane of $\sigma'$ if

1. $\sigma$ is embedded to $\sigma'$.
2. For every line $L' \in \mathscr{L'}$ and if $L' \cap \mathscr{P}$ contains two points then there exists a line $L \in \mathscr{L}$ such that $L =L' \cap \mathscr{P}$

Definition: Principal subplane

If $\sigma=(\mathscr{P,L,I})$ and $\sigma'=(\mathscr{P',L',I'})$ are two planes then we say $\sigma$ is a principal subplane of $\sigma'$ if

1. $\sigma$ is a subplane of $\sigma'$.
2. $\mathscr{P}=\mathscr{P'}/L'$ for some line $L' \in \mathscr{L'}$

Note: Principal subplane

A subplane $\sigma$ can be a principal subplane of $\sigma$ if and only if the plane differs by exactly one line and all belonging points on it.

Example:

A complete four-point is a principal subplane of fano-configuration because the configurations are differ by exactly a line and all belonging points on this line.

Theorem: Any principal sub-plane of a projective plane is an affine plane.

Proof:

Let $\sigma'=(\mathscr{P',L',I'})$ be a projective plane. Now we construct:

• $\mathscr{P}=\mathscr{P'}/D$ for some $D \in \mathscr{L'}$
• $M=\{p\in L' ∶ p \notin D\}$ for all $L\in \mathscr{L'}/D$
• $L=\{L:L' \in \mathscr{L'}/D\}$

Then $\sigma=(\mathscr{P,L,I})$ is a principal sub-plane of $\sigma'$ obtained by removing $D \in \mathscr{L'}$. Now we show that $\sigma$ is an affine plane.

1. Two points in $\sigma$ determine a line:
   Let $p,q\in \sigma$. By construction, $p,q\in \sigma'$. By [P1], $p$ and $q$ determine a line $L' \in \sigma'$. By construction, $p$ and $q$ determine a line $L \in \sigma$.
2. If $L$ is a line and $p \notin L$ is a point, there is exactly one line on $p$ parallel to $L$:
   Let $L$ is a line and $p \notin L$ be a point. By construction $L' \in \sigma'$ is a line not containing the point $p$. Since $D$ is already a line in $\sigma'$, by [P2], we say $D \cap L'=q$. By [P1], $p$ and $q$ determine a line, say $M' \in \sigma'$. By construction, $M'$ corresponds to a line $M \in \sigma$ not containing the point $q$. Hence, $M$ is the required line on $p$ parallel to $L$.
3. There is a set of three non-collinear points:
   Since $\sigma'$ is a projective plane, there is a four-point, say $a_0 a_1 a_2 a_3$. Now three cases arise:
   1. Case 1: If $D$ contains no points from $a_0, a_1, a_2, a_3$, then $\sigma$ contains the same four-point.
   2. Case 2: If $D$ contains one of the points from $a_0, a_1, a_2, a_3$, then the remaining three points are not on $D$ and so are in $\sigma$. Hence $\sigma$ contains three non-collinear points.
   3. Case 3: If $D$ contains any two points from $a_0, a_1, a_2, a_3$ say $a_0, a_1$, then by construction $a_2 a_3$ are not on $D$ and so are in $\sigma$. Also, the point $a_0 a_2 \cap a_1 a_3$ is not on $D$ and so in $\sigma$. Thus $\sigma$ contains three non-collinear points $a_2 a_3, a_0 a_2 \cap a_1 a_3$.

Thus $\sigma$ is an affine plane. This completes the proof.

Theorem: Show that every affine plane is a principal sub-plane of some projective plane.

Proof:

Let $\sigma=(\mathscr{P,L,I})$ be an affine plane. By [A2], for any line $L \in \sigma$ and a point $p \notin L$, there is exactly one line on $p$ parallel to $L$. Let such a parallel line on $p$ meet $L$ at an ideal point, say $p_L$. Now we construct:

• $L'=L \cup p_L$ for each $L$
• $L_\infty=\{p_L:L \in \mathscr{L}\}$
• $\mathscr{P'}= \mathscr{P} \cup L_\infty$ and
• $\mathscr{L'}=\{L':L \in \mathscr{L}\} \cup L_\infty$

Then $\sigma'=(\mathscr{P',L',I'})$ is an extended plane of $\sigma=(\mathscr{P,L,I})$ so as $\sigma=(\mathscr{P,L,I})$ is a principal subplane of $\sigma'=(\mathscr{P',L',I'})$. Now we show that $\sigma'=(\mathscr{P',L',I'})$ is a projective plane.

1. Two points on $\sigma'$ determine a line:
   Let $p$ and $q$ be two points in $\sigma'$
   1. Case 1: If $p,q \in \sigma$, by [A1], they determine a line in $\sigma$, say $L \in \sigma$. By construction, $p$ and $q$ determine a line $L' \in \sigma'$.
   2. Case 2: If any one point, say $q \notin \sigma$, by construction $q$ is an ideal point. By construction, there is a line on $p$ and $q$ in $\sigma'$.
   3. Case 3: If both points $p,q \notin \sigma$, then both $p$ and $q$ are ideal points so there is a line $pq=L_\infty \in \sigma'$.
   Hence two points in $\sigma'$ determine a line.
2. Two lines on $\sigma'$ always meet:
   Let $L',M' \in \sigma'$
   1. Case 1: If both $L'$ and $M'$ are ordinary lines in $\sigma'$. By construction $L, M \in \sigma$ and they do meet either in a finite point [if L and M do intersect] or in an ideal point [if L || M].
   2. Case 2: If any one line, say $L'$ is an ideal line in $\sigma'$. By construction they [$L'$ and $M'$] do meet at an ideal point.
   Hence two lines on $\sigma'$ always meet.
3. There is a four-point on $\sigma'$:
   Since $\sigma$ contains a four-point, $\sigma'$ contains the same four-point.

Hence $\sigma'=(\mathscr{P',L',I'})$ is a projective plane. This completes the proof.

Theorem: Show that $\alpha_R$ is a principal subplane of $\pi_R$.

Proof:

Let us remove a line $⟨0,0,1⟩$ and all its belonging points $[x,y,0]$ from $\pi_R$. Then all points in $\pi_R$ can be written as $[x,y,1]$ and all lines in $\pi_R$ are of the form $⟨a,b,c⟩$ with the property that $a,b$ both are not zero.

Now we define:

• $f(x,y) \to [x,y,1]$
• $F(ax+by+c=0) \to ⟨a,b,c⟩$

Which are both one-one onto.

This completes the proof.

Order of plane

Let $\sigma$ be a finite affine plane. The **order of $\sigma$** is the number of points on any line in $\sigma$. It is denoted by $O(\sigma)$. Since any affine plane $\sigma$ has the form
$\sigma: (n^2_{n+1}, n^2+n_n)$ for some $n \ge 2$
The order of an affine plane with this form is
$O(\sigma) = n$

Let $\pi$ be a finite projective plane. The **order of $\pi$** is the order of any principal sub-plane of $\pi$. It is denoted by $O(\pi)$.

Prove that the order of a finite projective plane $\pi$ with the form $(n^2+n+1_{n+1})$ for $n \ge 2$ is $n$.

Proof

Let $\sigma$ be a finite affine plane with the form $(n^2_{n+1}, n^2+n_n)$ for $n \ge 2$. By definition,
$O(\sigma) = n$
Now, we extend $\sigma$ to a projective plane $\pi$ so that $\sigma$ is a principal sub-plane of $\pi$. Then $\pi$ is a finite projective plane, in which $\pi$ has $n^2+n+1$ lines, each on $n+1$ points. Since every projective plane has duality, it has the form
$(n^2+n+1_{n+1})$ for $n \ge 2$
Hence, a projective plane with the form $(n^2+n+1_{n+1})$ for $n \ge 2$ has order $n$.

Note: Order

If a projective plane has order $n$, then it has the form $(n^2+n+1_{n+1})$ for $n \ge 2$ and conversely.

Example

The order of the fano configuration is 2.

If $F$ is a finite field with $q$ elements, then $O(\pi_F) = q$.

Proof

Let $F$ be a finite field with $q$ elements. Then $\pi_F$ is a finite projective plane. The points in $\pi_F$ are denoted by triples $[x_1, x_2, x_3]$ for $x_1, x_2, x_3$ not all zero, and proportionality is preserved. The first element of the triples can be chosen in $q$ different ways, and similarly for the second and third elements.

Since $[0,0,0]$ cannot be a point in $\pi_F$, there is a total of
$ \frac{q^3 - 1}{q - 1} = q^2 + q + 1 $
number of non-proportional and not all zero triples in $\pi_F$. Thus,
$O(\pi_F) = q$
This completes the proof.

Let $\pi = (\mathscr{P}, \mathscr{L}, \mathscr{I})$ be a projective plane of order $n$. Then the number of points/lines in it is $n^2+n+1$.

Proof

Let $\pi = (\mathscr{P}, \mathscr{L}, \mathscr{I})$ be a projective plane of order $n$. If $p$ is any point of the projective plane, then each of the $n+1$ lines through $p$ contains $n$ additional distinct points. Thus, we have altogether
$(n+1)n+1$ points.
By duality, this proves that the number of lines is also the same.
This completes the proof.

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ICME

Mathematics Education Conferences

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International Congress on Mathematical Education (ICME)

In 1952, the newly formed IMU re-established the ICMI and Prof. A. Chatelete was elected as the first president of IMU. The former president of ICMI was Felix Klein and former secretary was Hanri Fehr. The first 1962, second 1966 and third 1970 elected presidents of ICMI were Lichnerowicz, Freudenthal and Lighthill. Not until 1969, did ICMI start the new International ICME congresses after the New Math movement took place in different countries. The first three congress mainly dealt with new curricula and ongoing projects.

The first International Congress on Mathematical Education (ICME) was held in Lyons, France, from August 24-30, 1969. This event was a significant landmark in the history of the International Commission on Mathematical Instruction (ICMI), which decided to establish ICMEs as a permanent institution, arranging them regularly every four years between the International Congresses of Mathematicians (ICMs).

The establishment of ICME was driven by the opinion of Hans Freudenthal, who became President of ICMI at the beginning of 1967. He believed that the role of ICMI at the ICMs was not sufficiently significant. Freudenthal argued for the need of:

A congress devoted solely to mathematics education, where invited talks could be given and opportunities for personal contributions would be presented.

The Executive Committee of ICMI accepted this idea, and the first ICME was organized with financial support from the French Government and UNESCO. Although this initiative was taken without informing the IMU Executive Committee initially, the IMU later decided to continue its policy of paying special attention to educational questions through ICMI, aiming to ensure that creative mathematicians and educators remained connected.

The first ICME was launched in 1969 in Lyon, France, at the initiative of ICMI President Hans Freudenthal (1905-1990) and has been held since then in leap years.

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ICMI	Year	Location	Message	Countries
ICME-1	1969	Lyon (France)		42
ICME-2	1972	Exeter (UK)		73
ICME-3	1976	Karlsruhe (Germany)		76
ICME-4	1980	Berkeley (USA)	Mathematics for All / Everyday life mathematics	73
ICME-5	1984	Adelaide (Australia)		68
ICME-6	1988	Budapest (Hungary)		40
ICME-7	1992	Quebec (Canada)		57
ICME-8	1996	Sevilla (Spain)		83
ICME-9	2000	Tokyo (Japan)		79
ICME-10	2004	Copenhagen (Denmark)		83
ICME-11	2008	Monterrey (Mexico)
ICME-12	2012	Seoul (Korea)
ICME-13	2016	Hamburg (Germany)
ICME-14	2021	Shanghai (China)
ICME-15	2024	Sydney (Australia)

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Organization of ICME in different Countries

Mathematics education is a distinct discipline rather than mathematics. It has its own history. In the history of mathematics education, one might find different movements and trends in different civilizations and countries. The explosion of science and technology has changed social and human life day by day. The world slowly becomes a narrow place due to the dominant role of information technology.

To face the new problems related to new technologies, mathematics education in different countries needs to have a broad vision, and it was necessary to create unity in mathematical activities to fulfill their global needs in the field of mathematics education. So, different commissions, conferences, and seminars were established and organized in various places at various times for the concerned subject matter.

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International Conference on ICSTME

The International Conference on Science Technology and Mathematics Education for Human Development, held from 20-23 February 2001, in Panaji (Goa), India, was hosted by the Homi Bhabha Centre for Science Education (HBCSE), a national Centre of the Tata Institute of Fundamental Research, Mumbai, devoted to science and mathematics education. Financial support was provided by UNESCO; Commonwealth Association for Science and Technology Educators (CASTME); Commonwealth Secretariat (COM-SEC); the Departments of Science and Technology and Biotechnology of the Government of India and Indira Gandhi National Open University.

The conference was targeted mainly at educational planners and administrators; curriculum developers; teacher educators; teachers, researchers and specialists in science, technology and mathematics education (STME) as well as representatives of concerned voluntary organizations. Its aims and objectives were as follows:

1. To provide a forum for exchanging ideas on various themes focusing on the role of STME in human development.
2. To assess the impact of projects promoting scientific and technological literacy and numeracy and to work out targeted programmes for the next decade.
3. To identify new strategies to narrow the gap between developed and developing countries in the field of STME.
4. To work out how new ICTs can be used for enhancing the reach of STME for all.
5. To develop a consortium of international organizations working in STME.
6. To promote access and participation, notably of girls and women, in STME and related areas.

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Regional Conferences on Integral Curriculum

This conference was sponsored by the International Commission of Mathematical Instruction and India Science Academy and was supported by IMU, Unesco, University Grants Commission (UGC) and National Council of Educational Research and Training. It was held from December 15 to 20 in 1975 at Allahabad and hosted by Mehta Research Institute of Mathematics and Mathematical Physics.

Themes of the Conference

The main themes of the conference were to develop Integrated curriculum Integration within mathematics, Integration with application, Integration with other subjects, and Integration with everyday daily life situations. Other topics discussed in the conferences were as follows.

1. Structures of Schools according to Age level
   • ME at pre-school and primary level of years 4 to 12 years
   • ME at upper primary and junior higher school students of ages 10-15 years
   • ME at senior high school, college and university transition students of ages 15 to 20 years
   • The training and the professional life of mathematics teachers.
2. Curriculum and evaluation system on mathematics education
   • A critical analysis of curriculum development in mathematics education
   • Methods and result of evaluation with respect to mathematics teaching.
   • Overall goals and objectives for mathematics
   • The role of algorithms and computer in teaching mathematics at school.
3. Recent trends in Mathematics Education
   • Professional life for teacher
   • Mathematics for all
   • The role of technology in teaching mathematics education.
   • Curriculum development and application and modeling
   • Problem solving in mathematics education
   • Psychology of mathematics learning
   • Mathematics education for the gifted and culturally deprived children.

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Arkansas Conference

The conference was organized by the University of Arkansas, USA on 7, 8 and 9 August in 1969. This conference made a difference in the mathematics congress in different countries like the school mathematics programmed in Africa, teaching mathematics in Latin America, teaching mathematics in the Soviet Union and Communist China. The conference was attended by about 100 delegates from various parts of the world.

Issues and Problems of ME

1. Reformation to curriculum from time to time.
2. Teacher Oriented teaching.
3. Unify elementary and secondary mathematics curriculum (National and International).
4. Creativity and logical thinking.
5. How to impose mathematical knowledge on a large scale of students.

Recommendation from Arkansas Conference

1. Preparing the textbook, teacher Guide.
2. Separate book for Algebra and Geometry.
3. Pre-service Programs for Teachers.
4. International Co-operation in school mathematics education.
5. To publish the mathematical bulletin.
6. Compulsory and optional mathematics.

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The Psychology of Mathematics Education

The traditions of developmental theorists (Bruner, Dienes, and Piaget) are taken from the traditions of Behaviorists (Skinner, Gagne, Carroll, and Bloom). In 1976, Prof. Efraim Fischbein of the University of Tel Aviv formed an international study group of psychologists and educators for research work. The International Group for the Psychology of Mathematics Education was formed with the following missions:

1. To promote international contacts and the exchange of scientific information in the psychology of mathematics education.
2. To promote and stimulate inter-disciplinary research in the aforementioned area with the co-operation of psychologists, mathematicians and mathematics teachers.
3. To further a deeper and better understanding of the psychological aspects of teaching and learning mathematics and the implications thereof.

Since 1976 PME conferences have been held annually. Usually, 200 to 500 educators and psychologists attend the annual conferences which provide an annual forum for the world's leading mathematics education researchers. The two most common methodologies used by psychologists were experimental (using inferential statistics) and developmental studies (using qualitative tools). PME became a major shift away from theory-driven research to theory generation research in which social, cultural and linguistic dimensions are emphasized.

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Themes of Regional Conferences

The main themes of the conferences were to develop Mathematics for All for high-level mathematical activities. Issues and Problems of Regional Conferences are raised under the following headings:

1. Mathematical

   The main problem of transition is necessarily of introducing important issues:

   • How variable and function can be introduced in elementary school.
   • How to judge the theoretical status of mathematical knowledge at the elementary level.
2. Cognitive

   The transition deals with the change from child to adult behavior under different domains:

   • How to balance the learning of mathematics with the developing knowledge and interest of students of school level and higher level.
   • How to develop on situated teaching of mathematics within suitable fields of experience and mathematical knowledge with students and teachers in a positive interaction framework at school and a higher level?
3. Cultural

   The learning of mathematics evolves differently in different countries with the following issues:

   • How the technological evaluation changes the ways mathematics can be taught. For example, new technologies?
   • How the various ways of looking at maths inside and outside school influence its teaching?
   • How is the teaching of maths influenced by the organization of the school?
   • How is the teaching of mathematics determined by that of other disciplines like natural sciences and first language.
4. Political

   Nautical view point can be visualized by the following bullets:

   • How the evolution of the school organization: teaching of mathematics in lower secondary school (LSS) in different countries evolved?
   • How Mathematics Education suggests politicians to improve mathematics education?

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ICME-1: Lyon in France

Different ICMEs have different focuses and with different views regarding the issues emerged at that period. In the case of ICME VI, the most expected slogans and "Mathematics for All" and "Everyday life mathematics". These slogans can finally get the support of the public and the media, but they lead to no mathematics.

Mathematics by its nature is not that of the so-called "Everyday life". Mathematics can be for all, Mathematics can be a simple and lovely subject when the students can understand it. Since 1972 (ICME 2) different ICMEs were organized every four years.

The first ICME was held at Lyon, France, 1969. Approximately 700 mathematicians and mathematics educators from 42 countries. The main objectives of the conferences were to differentiate the mathematics education from mathematics and discuss about the changes that brought by the “New Math”.

The Issues and Problems of ME

The contemporary mathematical society faced the great trouble to develop mathematics education and its change. They discussed the following problems regarding with change in mathematics education.

1. Unification of mathematics curriculum and subject matter: Mathematics curriculum should be same in the members' countries for similar level, teaching method, attitude towards mathematics, relation of mathematics to other subjects.
2. Change Process: The leading idea how they develop in the course of years, how they were actually realized increasing the mathematical literacy and excellence.
3. Training for elementary teachers.
4. How to encourage the interest towards the public about 'new math" which was extending all over the world.

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ICME-2: Exeter in UK

The second ICME was held at Exeter University in England, 1972 and participated by about 1400 mathematicians and mathematics educators from 73 countries.

The Issues and Problems of ME

In the second ICME conference there were active discussion and comment about the following issues:

1. Mathematics Curriculum: The issue was about the suitable mathematics curriculum to fulfill the mathematical needs in contemporary society.
2. Research in Mathematics Education: To find out the existing problem in mathematics curriculum and suggest the solution of the problem.
3. Teacher Training: Supply of researchers finding by means of training to the elementary teachers.
4. Assessments in Mathematics: Different methods of assessments in curriculum.
5. Application in Mathematics (Beauty and Utility): New mathematical topics in application, applied mathematics for non-mathematicians’ co-operation between industry, schools and universities, applied mathematics in schools, application of mathematics to school science were brought for discussion.
6. Mathematical Competition: National competition, international Olympiads in different part of the world were exercised.
7. Technology in Mathematics Teaching: Discussion held on “How to use the production of advanced technology like calculator, compute, in mathematics teaching”.
8. Language and Mathematics: Writing and speaking, mathematics should have uniformity, the relation between language of mathematics and mother tongue of the children must be investigated. They must be learned through children own experienced.
9. Creativity, Investigation and Problem Solving: Creativity and discovery in elementary mathematics trying of thinking, role of heuristics, discovery teaching, undergraduate research, and workshop investigation were discussed.
10. Mathematics and Slow Learner: Every child learn but with different rate of learning and with different styles. So, slow learner must be included.

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ICME-3: Karlsruh in Germany

The third ICME was held at Karlsruh, Germany, 1976. Approximately 1800 participant were take part from 76 countries.

The Issues and Problems of ME

The issues and problem of ICME III were focused on the following topics:

1. Rate of psychology in learning mathematics
2. Heuristic and problem solving mathematics
3. Relation of mathematics with other subjects
4. Grading of problem in sequential order
5. Application of mathematics in real situation

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ICME-4: California in USA

The Issues and Problems of ME

The fourth ICME was focused on the following topics:

1. Mathematics in Biology curriculum
2. Mathematics and nature mathematics teaching
3. The teaching mathematics through the arts as a pedagogical technique
4. Gender and modeling
5. Problem of teaching mathematics in a language other than the mother tongue.

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ICME-5: Adelaide in Australia

The fifth ICME was held at Adelaide in Australia, 1984. The conference was attended by 2000 delegates from 68 countries. It talks about "Methods as well as Modelling", Micro-computer, calculator, and culturally deprived and gifted students.

The Issues and Problems of ME

1. Problem solving in mathematics
2. Micro-computer and calculators in mathematics education
3. History an pedagogy in mathematics education
4. Women and mathematics
5. Psychology of mathematics learning
6. Mathematics education of culturally deprived children
7. Mathematics education for the gifted
8. Training for mathematics for industry
9. Mathematical Modelling
10. Language and Mathematics

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ICME-6: Budapest in Hungry

Major themes were Math for all, ethnomathematics and mathematics education in the global village. The shortage of math teacher was one problem among many. The causes for this shortage were identified as

The Issues and Problems of ME

1. low salaries as compared to industry.
2. discouragement of students from entering the profession.
3. negative attitude of society towards education.
4. teacher stress; and
5. teacher burnout (tired).

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ICME-7: Quebec in Canada

Major goal of constructivism as a method as well as the philosophy.

The Issues and Problems of ME

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ICME-8: Seville in Spain

Major goal of constructivism and mathematical research. Adult numeracy, Collaborative learning, curriculum Development, Interdisciplinary Math, Math for employment, NCTM standards were more topics dismissed!

The Issues and Problems of ME

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ICME-9: Tokyo in Japan

The ninth ICME was held in Mukuhari, Japan (2000). The ICME IX was attended by 1840 participants from 79 countries.

The Issues and Problems of ME

1. To balance the learning of mathematics with the developing knowledge and interest of students, part attitude towards mathematics has been negative because of different complex reasons.
2. In many countries, there is a big jump between the ways mathematics is framed from elementary to secondary school, different types of interactions in the class be organized with in different frame.
3. How to develop a situated teaching of mathematics within suitable fields of experiences that contact deep mathematical knowledge with that of students and teachers in a positive interaction framework?
4. Effectively use of technology (Internet, calculators, and computer) to advance problem solving research; and
5. How to tackle mathematics problems and "Good Problems" be developed using historical context and computer simulations?

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ICME-10: Copenhagen in Denmark

The tenth international congress mathematics education (ICME X) was held in Copenhagen, Denmark in 2004. It focused the great majority of students in all countries concerned continue their studies in upper secondary school. The special needs of different students, integration with other subjects, "mathematics for all" and the mathematical literacy necessary for further study and everyday life are vital issues in all countries and have given rise to a multitude research and development projects.

The Issues and Problems of ME

1. Mathematics education from future teachers differs from mathematics education for future mathematicians;
2. Valuable mathematical and pedagogical competencies of primary and secondary mathematics teachers;
3. Different beliefs, values and cultural backgrounds of teachers affect their teaching and its development;
4. Can teachers and educators undertake in service education with a constructivist orientation?
5. Research into teaching and teaching development act as a catalyst for development itself;
6. Mathematical literacy and "Mathematics for everybody";
7. Relationship between different levels of knowledge;
8. Different approaches of geometry;
9. The role of technology and electronic tools; and
10. Role of algebra in lower secondary school. Mathematics educators also argue that algebra is a part of cultural heritage and is needed for informal and critical citizenship.

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ICME-11: Menterry in Mexico

Preparation for the Centennial of the Commission, to be celebrated in 2008, was in 2004. Ferdinando Arzarello has been appointed as the chair of the IPC and the current plans are for a symposium to be organized in Rome around May 2008 just prior to ICME XI. The aims of the symposium are to reflect on the evolution of mathematics education during the last 100 years and identify the emerging trends in the field.

The Issues and Problems of ME

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ICME-12: Seoul in Korea

The Issues and Problems of ME

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ICME-13: Hamburg in Germany

The Issues and Problems of ME

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ICME-14: Shanghai in China

The Issues and Problems of ME

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ICME-15: Sydney in Australia

The Issues and Problems of ME

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ICMI

International Commission on Mathematical Instructions (ICMI)

Devoted to the development of mathematics education at all levels, the International Commission on Mathematical Instruction (ICMI) is an international non-governmental and non-profit scientific organization whose purpose is to promote international cooperation in mathematics education. The scope of the Commission's work quickly expanded beyond just secondary schools to include the teaching of mathematics at all types of schools, including primary and vocational, as well as universities.

The ICMI, or its predecessor known as the International Commission on the Teaching of Mathematics, was established in 1908 during the International Congress of Mathematicians (ICM) held in Rome. The proposal for its creation was initiated by David Eugene Smith from New York. The Rome Congress accepted a resolution charging Professors F. Klein, G. Greenhill, and Henri Fehr to constitute an International Commission to study these questions and report to the next Congress. This three-person group named itself the "Central Committee," with Felix Klein as President, G. Greenhill as Vice President, and Henri Fehr as Secretary General. Thus, Felix Klein was the first president of ICMI (1908-1920).

The acronym ICMI became popular later, and the name "International Commission on Mathematical Instruction" was officially adopted by the IMU General Assembly in 1952. Following interruptions in activity as a result of the First and Second World Wars, ICMI was reconstituted in 1952 and became an official commission of the International Mathematical Union (IMU).

ICMI has considerably expanded its objectives, activities, and international reach in the years since, with increasing commitment to educational capacity building in developing countries and broadening the participation and inclusiveness in ICMI activities of mathematics educators from diverse cultural contexts.

A major responsibility of ICMI is to plan for the quadrennial International Congress on Mathematical Education (ICME). ICME is the largest international conference on mathematics education. ICMEs are the meeting point for mathematics educators, curriculum developers, mathematicians, researchers in mathematics education, teachers, teacher educators and resource producers.

ICMI was established to support better education of mathematics at all levels and to secure public appreciation of its importance. This means that the mathematicians who met in Rome in 1908 were of the opinion that the development of mathematics depends on the development of mathematics education. The work of ICMI was oriented intensively towards the emphasis of understanding of mathematics instead of the mechanical skills.

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Aims and Objectives of ICMI

The main goal of ICMI is to develop the international co-operation in the field of mathematics instruction. The specified aims and objectives of ICMI are as follows:

1. Develop mathematics practitioners, curriculum designers, decision-makers and others interested in mathematics education.
2. Provide opportunities for exchanging information on mathematics education, promoting published materials and forums.
3. Exchange and disseminate ideas and information on all aspects of the theory and practice of contemporary mathematics education as seen from international perspectives.
4. Provide the overall goals of teaching of mathematics education for any given level is to provide teachers with appropriate knowledge, skills and attitudes for teaching mathematics, at that level under the changing curricula and conditions.
5. Apply a new trend in mathematics teaching for the development of science and technology.
6. Enable students to think logically and develop the process of understanding of mathematical concepts.
7. Encourage applying new trends in mathematics teaching.
8. Give emphasis on research in learning and teaching mathematics education.
9. Discuss problems of mathematics teaching and find solutions in international conferences by sharing experiences.
10. Create a suitable environment to develop knowledge, skill and attitude in teachers to make their teaching activities meaningful.
11. Develop an integrated curriculum on mathematics for developing countries.
12. Encourage the mathematical institutions which produce Journals and Forums.

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Activities and Responsibilities of ICMI

The ICMI’s primary responsibilities are to plan for the ICME congress which entails selecting one among host countries and offering opportunities to appoint an International Program Committee (IPC). The financial organization of ICME has the independent responsibilities of a national organization committee. The following are the responsibilities of ICMI:

1. Organize the ICME every four years.
2. Organize the Regional Conference.
3. Organize the National Conference.
4. Give opportunities for mathematicians to present their papers.
5. Make an environment to discuss the problems arising from the New mathematics movement in the conferences.
6. Supervise the works done by the Study Groups affiliated with ICME.
   • The Psychology of Learning Mathematics
   • Research in the Teaching of Mathematics
   • Calculus and Analysis at School Level
   • Teaching of Probability and Statistics at School Level
   • Individual Learning Methods

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Recent Activities of ICMI

Over recent years, ICMI has been sponsoring, jointly with Unesco and other bodies, the development of a mathematical exhibition. The exhibition "why mathematics" was changed into the slogan "Experiencing Mathematics," whose aim is to improve the image of mathematics among the general public. This exhibition resulted from the work of colleagues in France and Japan, and ICMI supported it substantially.

Following a recommendation of the Ad Hoc subcommittee on “Supporting Mathematics in Developing countries” appointed in 2003, the IMU Executive Committee established in early 2004 the Developing Countries Strategy Group (DCSG) with the charge of increasing, guiding, and coordinating IMU’s activities in support of mathematics and mathematics education in the developing world. ICMI is represented in the DCSG by Vice-president Michele Artigue. The first meeting of the DCSG was held at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Italy, on 16-17 October 2004. Among the actions considered by the DCSG is the creation of a web-based Clearinghouse for African Mathematics, which will be housed at ICTP. ICMI offered to contribute to this project by collecting information about activities linked to mathematics education in Africa, in particular as regards existing associations, projects, master and doctorate programs in education, and mathematics competitions.

ICMI has co-sponsored an International Seminar on Policy and Practice in Mathematics Education organized since 2001 in Utah, USA, in the context of the annual Park City Mathematics Institutes (PCMI) hosted by the Institutes for Advanced Study (Princeton, USA). This program has engaged each year mathematics educators from a diverse set of countries in a stimulating five-day discussion about common issues and concerns in the teaching and learning of mathematics, with a particular focus on teacher preparation and development. The 2004 session took place during ICME X, where participants from the first three years shared with the large mathematics education community the outcome of the first seminars and considered with this larger group how to continue the dialogue at future Institutes.

The World Bank also expressed interest in the ICMI networking capacity with the leadership in mathematics education around the world, as it is connected to scientific societies and individuals in academic institutions and is thus complementary to the links that the Bank has with governments and ministers of education.

In a similar vein, ICMI has been invited by the Director of Education at OECD (Organization for Economic Cooperation and Development) to participate in a Forum on education and social cohesion organized by OECD on the occasion of a meeting of Education Ministers held in Dublin on March 18-19, 2004. This meeting, where ICMI was represented by the Secretary General, was a first opportunity for a direct link of ICMI with the OECD Directorate for Education.

The current ICMI affiliated Study Groups are HPM (History and Pedagogy of Mathematics, 1976), PME (Psychology of Mathematics Education, 1976), IOWME (International Organization of Women and Mathematics Education, 1987), WFNMC (World Federation of National Mathematics Competitions, 1994), and ICTMA (International Study Group for Mathematical Modeling and Application, 2003). The IICTMA 13 International Conference on the Teaching of Mathematical Modeling and Applications was held in Nepal on 23-27 July 2007 at Dhulikhel, Kathmandu University. ICTMA is held biannually with the support of ICMI.

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Quiz (Math Ed 525, Unit 4)

✨ Math Ed 525, Unit 4✨

Answer all questions, then submit with your details.

Full Name Exam Symbol Number

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