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Math, Math Education, Math Culture

Five Guiding Principles of Mathematics Education

It's high time we put grand ideas back into mathematics curricula.

Article link:

Math, Math Education, Math Culture

Five Guiding Principles of Mathematics Education

It's high time we put grand ideas back into mathematics curricula.

Article link:

*http://www.eimacs.com/blog/2012/08/algebra-is-not-the-problem-part-2/.*

**Zor Shekhtman:**

@Marsigit: I'd like to suggest an approach to young students that might justify their efforts to study math. What if we suggest to them that math is gymnastics for their minds as much as pulling weights exercises their muscles? The concept of exercising is very much familiar to them. They also understand that real exercises might not be fun, but rather hard work. People in a gym don't usually have fun, they work hard on strengthening their muscles. Working hard solving math problem will strengthen their mind or, simply speaking, will make them smarter. I try to convey this idea in some introductory lectures on my Web site, but, obviously, have no idea whether this approach works or not.

**Marsigit Dr MA:**

@Zor and Natasha: My previous explanation indicated that teaching math for the younger is not as the simple as we expected. We should have a clear understanding of the NATURE of every aspect related to the learning activities. Teaching learning activities should have their appropriate foundations: psychologically, socially, or even anthropologically. What Zor's done is good example i.e. developing the concept of gym in math. However, it can be perceived as just partially in lying the educational foundation. In my perception, the most basic problem of the foundation of math educ is how the students are to construct their own math. What we need as adults people is to develop the scheme to facilitate them. Gym in math is good as far as the students be the actors of the game. Thank's.

Bradford Hansen-Smith:

Bradford Hansen-Smith:

@Marsigit: It is not apparent to students or to math educators what the principles of mathematics are. In my 1936 Webster dictionary the first definition of “principle” is "1. A source of origin, primordial substance: ultimate bases or cause. “ In other words what is principle is what comes first, not what we think is most important. These five ideas about math education that have been presented are just ideas out of many that one might believe to be more important over others. Principles are more universal than that; more than ideas about what we think.

What is principle comes first; all that follows is principled if there is alignment to what came first. When people talk about principles there is no reference to source or essential qualities and characteristics of origin. Isn’t that really what students are asking when they want to know why they have to learn math? They want to know the principles that underlie math that make it important to learn, the higher value inherent in mathematics that is worth their time and effort. We do not have a good answer for them.

Marsigit Dr MA:

Marsigit Dr MA:

@Bradford: I do agree with you Bradford. However I may say that your opinion is only small numbers (or even just one) aspects of the nature/principle of everything. As we know that every aspect of life is dimensional. Mathematics is also dimensional. People who learn math is also dimensional. The dimension of adult math is Formal Math/Axiomatix Math; and the dimension of younger math is School Math.

So the nature/principle is the generality in its dimension. The nature/principle of math for adults is different from that of younger. The nature/principle of adults' learn of math is also different with that of the younger. The best criteria for the nature/principle is about it's INTENSIVITY and EXTENSIVITY. A certain idea can be a principle in a certain dimension if it has the deepest and the widest aspect, in such a way that it will be un-debateble.

Further, we may need to differentiate between the Principle, the Concept/Meaning, and the Method. The very basic principle is that every OBJECT has its concept and method. I then found that the Principle is really a certain object. So the Principle has its own Concept and Method. So our discussion on the Principle of Math can not be separated with the discussion of Math Concept and Math Method. Especially, for younger student, the Principle of Younger Math (School Math) consist of the Concepts School Math and the Method of School Math. Without considering those two components then you will lose your meaning.

Thank's

**NCSM: Mathematics Education Leadership**

Is it possible and advisable to have a global curriculum in Mathematics, where the best features of all existing curriculum can be incorporated?

Is it possible and advisable to have a global curriculum in Mathematics, where the best features of all existing curriculum can be incorporated?

**V R:**

Curricular development is no longer involves rational and incorporated course design. New courses are added based on faculty members’ expertise rather than students’ need. And typically, no one has a clue as to what is taught in other courses in the curriculum, and certainly no idea at all as to what has been learned in previous courses.

Anica Aleksova:

Anica Aleksova:

If we speak about primary education or grades 1 to 8, and about “prescribed curricula” (what is in the official documents) it is possible - see the TIMSS frameworks or mathematics international reports. There you can find that already more than 70% of the curricula for more than 50 different countries in the world the content is the same. The differences are in the approaches for teaching the students or in to “implemented curricula”.

Marsigit Dr MA:

Marsigit Dr MA:

Global curriculum is a crazy ideas. It's imaging to have similar and uniform people around the world. Even in a certain district, math teaching in one city should be differentiated with that of other city because of different context of learning math

**Atiya Zaidi:**

@Marsigit: Hi guys! This is a very important and interesting discussion that has caught my eye. In the light of your comments I have a few questions:

Can we categorise maths curriculum into stages to fit the education levels in every geographical region? For example: say Stage 1 refers to basic arithmetic and numeracy. Then, can we devise a Stage 1 curriculum to fit anywhere in the world where either teaching provision or student level fits this stage?

Can we devise enough stages to cover all possible levels of maths learning and teaching?

Can we devise the curriculum in English and translate it into all languages existing on the planet?

Marsigit Dr MA:

Marsigit Dr MA:

@Atiya: I perceive curriculum at least in two categories i.e first, the STAGE as you frequently stated, and second, the FORM, its content and approach. Stage is something in the vertical dimension of educational levels hierarchically existing in each educational context (a certain country or state). So there are many perspectives on how the a peoples from a certain educ system perceives educ curriculum. In the British context for example, a certain teacher can perceive that curriculum is in the level of classroom operational. So they talk about how to involve students' participation in their developing curriculum. They can do it starting form the very simple but fundamental question : " What do you expect from me as your teacher of math lesson next week? If the students are to expect some math activities and the teacher strive to fulfill their expectation, that is it that we can call it curriculum too.

However, in most countries, the situation may be very different. Even, in some countries which implement centralized curriculum, they have no ideas about the role of student in developing curriculum. So, before we talk everything about curriculum we should make sure about many things e.g. our philosophy of education and even ideology o education. Meanwhile, I really found that there are the similar philosophy and or ideology of education among the countries in the world i.e to liberate our younger generation from parental or adult generation misbehavior. We need to liberate our younger generation in order that they are able to have a free choices in each of educational event. As it was stated by the great philosopher Immanuel Kant that "free thinking" is everything and whatever to start to construct/build their knowledge/life/world.

The problem of developing curriculum on English subject as an international language is about its form, content and approach. The similarity in term of its form has no problem; however, we should put a concern in the similarity of the content and approach. As we know the the content and approach are something contextual. So they related to the foundation, ideology, philosophy up to the certain purpose of teaching English. Teaching English in Bali and Singapore will have different purposes. Teaching English in different places will have different resources potentialities.

Thank you.

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