Dialog Internasional 4 Pendidikan Matematika

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Group: Math, Math Education, Math Culture

The current issue for "Focus on Mathematics and Pedagogy" is now online. Please see http://distance-ed.math.tamu.edu/newsletter/newsletters_new.htm#current_issue

Marsigit Dr MA:
@Donald: I have searched the newsletter you indicated. I found one interesting topic you have written in the Volume 4, Number 2, April 2012 i.e. Why Study Math when I Have Technology? I want to hear directly from you, may it is in brief sentences, the most basic reason why study math when we have technology? Thank


G Donald Allen:
I detailed the key point to study math in the article you referenced. Perhaps what I didn't say is that the study of math and problem solving gives anyone a methodology for the solution of even non-math problems. One learns to isolate the question, decide the variables, put the variables together, create a model, and then work to solve mathematically. This is what people do (except maybe the math part) in their own professions and lives. Math shows and teaches students the discipline; many use this throughout their lives. Let me cite Thomas Jefferson, who recommended to an inquiry, that the study of math, particularly geometry, was an important step in developing general thinking skills. Thanks,
Don

Marsigit Dr MA:
@Donald: I appreciate your quick response. I totally agree with your description both in your Newsletter and in your above answer. If you agree, because you start to pose and open the discussion, I also wish to share the ideas of math and its teaching, not in the spirit of negatively reducing them into a meaningless notions, but in the spirit of positively constructing them intensively and extensively in such away that we as math teachers are to self improve of our professionalism. From your works, I am really looking for the strong foundation of both math and teaching math. A certain foundation affects to everything related to math, its teaching and technology. I understand that because the phenomena of math and teaching math has its complex dimension, it is little bit difficult to expect a certain foundation from different stage of dimension. I you don't mind I wish to say that your description of the reason why study math when we have technology reflects the pragmatical one. Somethings pragmatical means that they closer to the stage of implementation. Don't misunderstand, because I also totally agree with your position. However, whenever there are peoples who want more from us e.g. I expect more from you about how really you define math, I think you need to elaborate them intensively and extensively. Of course, some one will use a certain criteria in trying to develop his/her (math) knowledge, as you use citing of Thomas Jefferson. I may use Paul Ernest's criteria on how you define math, before I can trace your rational in elaborating your ideas i.e. its relationship between math and technology.
In sum, I am spying you, by learning your works, whether you tend to be math body of structuralist, math body of knowledge, math creationist, math structuralist, math interactionist, math activitionist, or math pragmatist. I wish to hear your response further. Thank's.

G Donald Allen:
Dear Sir/Madam,
You ask if i tend to be a math body of structuralist, a math body of knowledge, a math creationist, a math structuralist, a math interactionist, a math activitionist, or a math pragmatist. I guess the answer is all of these. Most importantly, I favor a balanced approach to math education. There are mitigating factors such as teacher competency, school system desiderata, and countless other factors. Teachers do what they are asked. As to the various forms of constructivism, I suggest that such teaching is almost the most difficult to exact and to implement. Such teaching requires a consummate teaching skill and dedication. Can we ask for this realistically?

G Donald Allen:
Sorry, this email was trucated. Let me include a recent article I written on this subject for both the USA and the African audience. My views are universal. Class sizes are an important factor not generally recognized by various constituencies. This mitigates everything. Best wishes,
Don allen

Marsigit Dr MA:
@Donald: I also do agree with your further explanation. I may just want to make such an argument that a certain position in taking the foundation of math or math educ., influences the perception on others related aspects e.g. perception of how to teach math and how to relate math with technology. I am trying to reconstruct your ideas of math, math educ and its supporting technology, while on the same time I am trying to examine my prior knowledge of them; and then to develop it into the more objective and realistically relative to each of our context. On the other hand, I am optimistic that I and you may find or compromise on the available references. Of course, it needs such kind of openness from us. So before somebody may examine your notions related to the reason why study math when we have technology, it needs a clear picture about your perception on the foundation of math and math education; because, the different starting points imply to the the different implementation. I am talking about something ideal where as you may expect something realistic. That is one difference. Again, I totally agree with your elaborations. I am just trying to match or compare between our knowledge and experience of math and math educ. in order to get better one.

Realistically, I may wish to say that though we have technology we still need to learn math because there are at least three factors: the nature of math, the method of math, and the value of math. I also agree with you that the various forms of constructivism, is almost the most difficult to exact and to implement. Such teaching requires a consummate teaching skill and dedication. I perceive that constructivism is the best for democratic societies. To construct in math can be extended to construct in life. So technology as a tool, to some extent, can not substitute the students architectonic in building their own math (life). If we refer to Immanuel Kant that mathematics is a synthetic a priori knowledge, it mean that the student should built their own math logic while on the other hand they need to validate their math knowledge with e.g. empirical evidences. Technology can contribute much to everything, however it has limited contribution in building math logic and in providing evidences. That's why the students still need to learn math; and the role of technology is to support it.

In sum, my question to you on how you may define math and math educ. is still relevant. Your further elaboration will be useful to continue our constructive discussion. Thank you.

Marsigit Dr MA:
@Donald: I am waiting for your response for a moment. May be you are very busy. However, I may want to say that ACCOUNTABILITY in education is very important. It can not be limited in the space and time. Once you publish your works, you must ready to communicate with theirs readers. If you fail to communicate with them then you may have a problem with accountability in your works. If you have a problem with your accountability then your legitimate in authorizing your works will also be questioned. So then I have a question for you as a Professor of pure math. What is the relationship between (pure) MATH and EDUCATION? Which is the first, Math or Education? My next question is what kinds of legitimation of (pure) Mathematician talk about Education? Or What kinds of legitimation/rationals that (pure) Mathematician have a business with Math Education. It this just because the term "Math Educ". What do you opinion if I reverse the term "Education Math". Again, I am waiting for your response. Thank's.

Zor Shekhtman:
Firstly, I totally agree with Donald's statement "study of math and problem solving gives anyone a methodology for the solution of even non-math problems". I do believe that developing creativity, inventiveness, analytical thinking in students is more important as a goal of studying math than filling their minds with formulas they, most likely, forget after passing an exam. And whatever they will need in practical life, they will find and learn on "as needed" basis.

Secondly and unfortunately, existing system of education in public schools with standardized programs is directed more to teaching certain math skills and memorization of properties and formulas. This system does not develop students' minds. At best, it trains their memory, and, I am sure, there are better ways to train memory than studying math.

What can be done to return math education back into the realm of disciplines directed towards developing students' creativity, critical thinking, intelligence, analytical abilities? Two things: freedom of education and a rich repertoire of systems of education, in particular, math education as a powerful tool to develop young minds. The former is (unfortunately) in the hands of politicians, at least so far. The latter might be easier to address using Internet, and there are many good resources available on the Web that facilitate such development.

Personally, I have decided to contribute my modest efforts and started a Web site Unizor Education, dedicated to teaching math to teenagers interested in developing their ability to solve problems. Obviously, it's not for everybody, but bright and curious students don't have much of a choice now to develop their intelligence in the framework of the current system. Unizor, a completely free site, free of advertizing, is aimed precisely on this type of development, offering not only relatively rigorous theoretical material in a form of video lectures, but also a large amount of problems with solutions offered also in a form of lectures, where I offer my solutions to these problems.

Registered Unizor students are offered exams on each topic and also can be guided by a parent, a supervisor or a teacher, who can enroll a student into this or that part of a program, check the exam score and mark that part as completed. I believe, it's a valuable feature for homeschooling and for teachers practicing "flipped classroom" approach.

Obviously, I'd like to spread information about Unizor education to as many students as possible and appreciate any critical comments about this site.

Zor Shekhtman, Founder of Unizor Education Creative Mind through Art of Mathematics http://www.unizor.com
    
Marsigit Dr MA:
@Zor Shekhtman : I totally agree with Donald's and with your elaboration. It seem we have similar vision on how the students learn math. I also agree with you about the goal of studying math. I also in the similar position with you on criticizing the current system and looking for better system for math educ. However, I am little bit surprise with your notion " there are better ways to train memory than studying math". Ok I keep it. Yes I do agree with your notion " return math education back into the realm of disciplines directed towards developing students' creativity, critical thinking, intelligence, analytical abilities? " I also totally agree with you on the freedom of education and a rich repertoire of systems of education".

However, after having learned your Unizor web, I am little bit disappointed with how you introduce, manage and operate the way the younger learn math. In my opinion, your Unizor Web is good enough to develop a perception and perception. But it is not enough in promoting the nature of students learn math. Your videos have their limitation just to show how adult peoples learn math; so the student just as a spectator. This is not really the nature of students learn math. The nature of students' learn math should the students themselves who as the doer in learning math. So the students should be the actors.

Five Guiding Principles of Mathematics Education
It's high time we put grand ideas back into mathematics curricula.
By Natasha
Article link: http://www.eimacs.com/blog/2012/08/algebra-is-not-the-problem-part-2/.


Marsigit Dr MA:
@Natasha: Thank's for the link of your web. I have read a glance about your Five Guiding Principles of Math. I am very concerned and uncomfortable on how you defined Math. Your definition of math seems partial and unfair if you mean them as for they are related to education. In my opinion, your definition of math (and then I just call it as your math) are true only for ADULT or University level. And, they will be a big problems if they are related to education.

Natasha Chen:
@Marsigit: IMACS, through a long history of predecessor organizations, has been successfully teaching mathematics as "defined" in our blog post to talented children as young as 6 since the 1960s.

Our youngest students learn through puzzles, stories, and games. As their mathematical intuition and ability to read grow, we introduce more complex ideas and additional layers to concepts previously taught. By the time they reach late middle school, our students are ready for our university-level course in mathematical logic. With the powerful logical reasoning skills they've developed, our high school aged students are able to excel in university-level courses such as group theory and real analysis.

With all due respect, we know from decades of experience that learning the mathematics we described need not be restricted to adults or to the years at university.
 
Marsigit Dr MA:
@Natasha: Thank for the quick response. I may still argue about your claim of the "success". It it was really happened we further need to clarify on the criteria of the success. The success as a means of short term, long term, entering university criteria, or fulfilling a certain criteria? Further, I may suspect that its success due to your students are very talented or your intensive method. However, it may not related significantly to the purpose of your math teaching related with your math definitions. As you know that the way you define math will influence your understanding, attitude and scheme of teaching. Or it can be that your definition of math is meaningless in term of the pedagogical aspects. Even, if we don't care of the nature of math concepts, we may still get a success in teaching math due to the mechanically or technically procedure and schema of teaching. However, again, in the long term time it may be can not be said to be a success.
 
Marsigit Dr MA:
@Natasha: Natasha, specifically I wish to comment about your math definition as follows:

#1. Mathematics is an important intellectual discipline and not merely a collection of algorithms for performing calculations.
My comment:
It is an adult/expertise claim of the characteristics of math. The young's thinking of math has no relation with the truth of math to be claimed by the adult. So this definition has no psychological impact to the learning of math. It is also merely the characteristic of math; not about the concept of math.

#2. The subject-matter of mathematics is ideas, not notation. 
My comment:
The younger students will confuse to differentiated the ideas and notation. Again, it will be meaningful only for the adult.

#3. Mathematics is an organized body of knowledge. 
My comment:
Body of knowledge is something perfect, ultimate, final and very complicated structure. Again, it also only be understood by experienced mathematician. Even the younger math teacher can not imagine the animal of math as body of knowledge.

#4. Mathematics gives us understanding and power over "the real world"
My comment:
I reverse your logic, i.e. the real world consist of math concepts.

#5. Mathematics is a form of artistic expression.
My comment:
The critical student will say damn you the adult. It is you who said that math is artistic. For me math is a monster.

So I conclude that your success of teaching has not been supported yet by the strong foundation of the nature of math.