# LinkedIn Groups

**Group:**Math, Math Education, Math Culture

Marsigit Dr MA • Outside
perception is sometime not good to the students, because they tend to judge
rather than to facilitate. Further read my web http://powermathematics.blogspot.com

And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

William Galinaitis • "Scientific American Mind" (july or august issue?)
has summary articles on how various factors affect the mind of early learners.
Brain activity related to behavior and learning seems to be composed of genetic
and environment ( cultural, family, chemical...) factors (You already know
this.) How ever I was suprised how much stress that the children experience may
affect their ability to control their classroom beahvior, and therefore their
ability to focus on a single activity. Just a thought outside the Idea that it
is only the system and not the student.

Frances Winters • Is it not perhaps that math is like walking. Thousands of years
ago our ancestors began to walk on two legs, some better than others. Took ages
before everyone was good at it and took walking for granted.

Ginetta Nistoran • I've noticed more and more these days that math is taught
using memorization and mechanical repetition, rather than an understanding of
mechanics and logic. Very often the students are able to solve a problem very
similar to the one taught in the classroom, but as soon as the layout changes,
they are not able to see a pattern, or the fact that they need to apply the
same concepts in a different form. For me, that means a superficial learning,
based more on memorization than on logic.

Henry Schaffer • @Ginetta - in some fields we call this "plug and
chug". One remembers the method, plugs in the new numbers, turns the crank
and out pops the answer.

I agree that this superficial - and should *not* be more than a small portion of math.

I agree that this superficial - and should *not* be more than a small portion of math.

Marsigit Dr MA • The
architectonic of Kant teach us that mathematics is the business of the
students' architectonic. So, for me, whatever the external criteria to measure
students mathematics is always mislead. The genesis competence of mathematics
is really their architectonic. So, the problem for the teachers is how to
uncover mathematics depth inside of the students. Until then you get the
criteria of the success of your teaching mathematics after you hear the
students' claim that mathematics really belong to them.

Further read my web http://powermathematics.blogspot.com

And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

Further read my web http://powermathematics.blogspot.com

And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

Marsigit Dr MA • Our
further perceptions on how to educate (mathematics) can be read at the
following:http://www.whohub.com/drmarsigitma

and:

http://www.whohub.com/marsigit

Thank's

and:

http://www.whohub.com/marsigit

Thank's

Henry Schaffer • @Marsigit - you seem to be saying it isn't possible to
measure a student's progress in math. Am I interpreting you post correctly?

William Galinaitis • Agree with Marsigit: An educator is important in the moment
when a learner is trying place new knowledge in to the context of their own
understanding of the world. Sometimes I can "read" the student (ask
them questions, have them try to explain a concept to others...) and provide
the appropriate stepping stones for them to integrate the new material into
their framework or modify it.

Plug and chug has its place. You have "memorized" a significant amount of material about the world. This allows you to quickly recall disjoint pieces of information and formulate them in to a sentence for communication. If you had to look up the definition of each word in the formation of a sentence, you would probably forget what you were trying to communicate.

Plug and chug has its place. You have "memorized" a significant amount of material about the world. This allows you to quickly recall disjoint pieces of information and formulate them in to a sentence for communication. If you had to look up the definition of each word in the formation of a sentence, you would probably forget what you were trying to communicate.

Susan Northridge • I agree with many of the previous comments. Practice is key
and I find that my hardest working students (not necessarily the most brilliant
ones) are the most successful. I also agree that there is something lacking in
the way basic math is being taught in the lower grades. I teach calculus and I
am always amazed at how many of my students still struggle with basic
fractions.

Anne Patterson • I agree that fractions are an ongoing issue for students at
all levels. It sure makes a case for switching over to the metric system for
ALL measurement!

Judy Dobles, MBA • My observation is that if the desire is there, people then
show the dedication to learn. In American culture it is socially unacceptable
to be illiterate but socially acceptable to be innumerate. Our first step is to
begin a culture change to show people that math is the underpinning of
everything we do so that they want to learn math.

Marsigit Dr MA • @ Henry Schaffer and others: By nature it is impossible to
measure a student's progress of math using a certain approach or criteria.
Objective test is very bad because it is gambling. I have been trying to
promote new paradigm that LEARNING is constructing activity anywhere and
anytime, not much depend on teacher. Consequently, MEASURING the students
competent of math is also in the means of anywhere and anytime, i.e.
continuously and using various approach (tools), e.g. portfolio. The criterion
test is really dangerous to the students because it is the act of REDUCTION or
simplifying of students' characteristics. This will produce partially
psychological character of students and ultimately produce problematic
students. So then I think there is no choice for the teachers to acknowledge,
trust and empower the students in term of facilitating their needs in learning
math as their effort to construct their own life (math). Thank's

Henry Schaffer • @Khaled - I think that this thread has mostly been about
counting - arithmetic - algebra and geometry. Not very theoretical math areas.

@Marsigit - I disagree that the teacher, and teachers' practices - are mostly irrelevant.

I also disagree with what I think you are saying "By nature it is impossible to measure a student's progress of math using a certain approach or criteria. Objective test is very bad because it is gambling." Asking a student 6 x 7 = ? or "Prove that the sum of the angles ..." are object tests. They are "gambling" in the sense that they are a partial sample of the entire subject area. But a (validly chosen) sample does give valid information about the universe sampled.

@Marsigit - I disagree that the teacher, and teachers' practices - are mostly irrelevant.

I also disagree with what I think you are saying "By nature it is impossible to measure a student's progress of math using a certain approach or criteria. Objective test is very bad because it is gambling." Asking a student 6 x 7 = ? or "Prove that the sum of the angles ..." are object tests. They are "gambling" in the sense that they are a partial sample of the entire subject area. But a (validly chosen) sample does give valid information about the universe sampled.

Henry Schaffer • @Anne - I use the metric system now and then - and when I
want to divide 2 liters of orange juice equally among 7 people, can I describe
this without using fractions? :-)

larens imanyuel • @Susan.

To teach fractions effectively one needs to teach division as the inverse of multiplication. For multiplication one aggregates unit squares into rectangles. For division one may need to divide unit squares into smaller rectangles. One also needs to teach that one is the multiplicative identity. Rational arithmetic and its rules naturally follows from this, so there is no need for students to have a hard time with fractions. Teachers generally switch representations when going to fractions, so leave students confused.

To teach fractions effectively one needs to teach division as the inverse of multiplication. For multiplication one aggregates unit squares into rectangles. For division one may need to divide unit squares into smaller rectangles. One also needs to teach that one is the multiplicative identity. Rational arithmetic and its rules naturally follows from this, so there is no need for students to have a hard time with fractions. Teachers generally switch representations when going to fractions, so leave students confused.

larens imanyuel • @Anne.

Scientists use different systems of measurement to naturally fit the physical system with which they are working. To omit this fact by only teaching decimal arithmetic and the metric system is to do students a disservice by alienating them from real science.

Scientists use different systems of measurement to naturally fit the physical system with which they are working. To omit this fact by only teaching decimal arithmetic and the metric system is to do students a disservice by alienating them from real science.

Marsigit Dr MA • @ Henry Schaffer: What do you expect by questioning the
student 6 x 7 =?. Do you expect that the student will deliver his answer 42 ?.
What really my concern as a problem is that if you just expect that the
students just think about 42 ? Why should, at the first stage of their
learning, we do not tolerance to look at other possibilities of answers? In my
perception, 42 is just a very static ideot answer. The better and more
brilliant answer is his STRUGLING to find out the answer 42. Why? Because it
reflect his nature of life (math). It is very good that at the early step the
students my get wrong answer. While this aspect will not emerge and not ever
emerge when you use OBJECTTIVE test or CRITERION test. That is really my
struggling how we implement mathematics education that in line with the student
NEED; no just accord with the teacher's expectation (or system outcome
expectation).

Henry Schaffer • @Marsigit - "What do you expect by questioning the
student 6 x 7 =?. Do you expect that the student will deliver his answer 42
?." Actually I do. If not, then the student has a deficiency in arithmetic
and attention should be paid to remediation.

I don't expect or want the student to "just think about 42" - but I do want them to be able to do arithmetic correctly. As far as "tolerance to look at other possibilities of answers" - well, other answers (e.g. 5 or 112 or 29 or 77) aren't correct.

"42" is the correct answer to this arithmetic - it isn't idiotic, and it shouldn't be a "STRUGGLE". If it is, then it's premature to ask the question and instead the student should review more basic arithmetic.

If we never ask such "objective" questions, and don't build one simple arithmetic as the grounding for more advanced math - we will usually fail to have our students be able to understand, let alone master, the more advanced math.

I don't expect or want the student to "just think about 42" - but I do want them to be able to do arithmetic correctly. As far as "tolerance to look at other possibilities of answers" - well, other answers (e.g. 5 or 112 or 29 or 77) aren't correct.

"42" is the correct answer to this arithmetic - it isn't idiotic, and it shouldn't be a "STRUGGLE". If it is, then it's premature to ask the question and instead the student should review more basic arithmetic.

If we never ask such "objective" questions, and don't build one simple arithmetic as the grounding for more advanced math - we will usually fail to have our students be able to understand, let alone master, the more advanced math.

Victor Guskov • @Henry, I agree with you completely.

Victor Guskov • @Marsigit, your opinion is unacceptable for me.

Gail Mills • Yes
Henry! Learning takes many forms. There is a time to experiment and ponder and
a time to master the givens of accepted fundamentals and knowledge. Operating
comfortably with numbers does not destroy the thinking and creative abilities.
Mastery provides a foundation and vocabulary to discuss abstractions.

Marsigit Dr MA • @ Henry, Victor and Gail: Thank a lot for the responses.
Ultimately, I think there is no adult or older people, including me, not to
expect that younger people should have a correct answer of 42 for math problem 6
x 7 =? Implicitly, it was stated in my previous statement. But this is not the
case that I perceived as a problem of the nature of teaching math. I in purpose
have striven to provoke you that, pedagogically, the real problem of teaching 6
x 7 is not just guessing to get or memorizing 42, but the process of getting or
producing 42. Then, the next problem is about what kinds of the PROCESS, who
and how it to be promoted amid the balance between the role of teacher and
his/her students. In many places, many teachers teach the students just to
memorize 6 x 7 = 42. That's I called it as idiotic math i.e. learn math without
understanding and processes. Some points I agree with you and I understand the
worry of Victor and Gail.

However, I still don't understand about your point of STRUGGLING in math. For me, struggling is something ontologically an aspect of our life (math). As an adult or older people we need to promote to younger people the means of struggling of every aspect of life (including math).

@ Gail Mills: No certain pedagogy action means to destroy thinking and creativity unless it is partial, not complete, and under certain motive of adult. So, there is no the best way to educate people. However, the best way to educate people is if it is without PREJUDICE.

@ Victor Guskov: Having my explanation you may change your position. I expect your elaboration.

Thank

However, I still don't understand about your point of STRUGGLING in math. For me, struggling is something ontologically an aspect of our life (math). As an adult or older people we need to promote to younger people the means of struggling of every aspect of life (including math).

@ Gail Mills: No certain pedagogy action means to destroy thinking and creativity unless it is partial, not complete, and under certain motive of adult. So, there is no the best way to educate people. However, the best way to educate people is if it is without PREJUDICE.

@ Victor Guskov: Having my explanation you may change your position. I expect your elaboration.

Thank

Henry Schaffer • @Marsigit - While I agree that the student should learn how
6 x 7 = 42 (by rectangle, etc.), they still do have to learn that 6 x 7 =42.
Yes, that is memorization - and I see nothing wrong with it. In fact, if a
student needs to go back to the derivation each time a multiplication is done,
it will take much, much too long. As far as guessing - if a student can
consistently "guess" the answers to arithmetic problems - then
perhaps it isn't really "guessing"??

As to "struggling" - perhaps we are using the word differently. To me it means need to use unusual effort with a constant stress of failure. I don't consider it is the same as, perhaps, "study diligently".

As to "struggling" - perhaps we are using the word differently. To me it means need to use unusual effort with a constant stress of failure. I don't consider it is the same as, perhaps, "study diligently".

Victor Guskov • @Marsigit, I take 5th graders and should teach them
fractions, decimals, etc. Regrettably, too many of them don't possess simple
arithmetic skills - addition and subtraction within the limits of 20,
multiplication and division within the limits of 100. I suspect that elementary
school teachers waste too much time on “the process of getting or producing”
instead of practice and memorization.

Gail Mills • With
standards-driven education teachers don't have a lot of choice. My 4th grade
grandson had 204 concepts to "learn". All the teacher could do, if
she stuck with the district's plan, was expose the students, not teach the
students. Teaching does not occur if learning does not occur.

Marsigit Dr MA • @Henry Schaffer: I am interested with your notions: guessing
that it isn't really guessing; struggling that it isn't really struggling; and
memorizing that it isn't really memorizing. Really that's all my points. The
problem is then how to realize them. Thank's

@Victor Guskov: Again, in my opinion, you too much stressing on your own expectations about what the students do or their capabilities. This is really the main problems of education i.e. predominantly employing by teachers' expectation but lack of developing and employing students' expectation. You also seem in a hurry and not be passion to wait the students to develop math and produce their own concept of math. This is also the biggest problem of math educ. because it is related to the curriculum and the educ.system.

@Gail Mills: How sad the fate of EDUCATION due to the standard-driven educ system. Yes I am aware that amongst the global interaction many countries stressing much on how to compete with others. Consequently, in educ also the system means of competing between everything. Why do we not to promote education based on COLLABORATION/COOPERATION rather than competing. You know that in every scene of competition, there will always be the LOOSER. Who will take responsibility to the looser students? No other people except that of teachers. No other people except that of the people who really think intensively and extensively about the nature of education.

@Victor Guskov: Again, in my opinion, you too much stressing on your own expectations about what the students do or their capabilities. This is really the main problems of education i.e. predominantly employing by teachers' expectation but lack of developing and employing students' expectation. You also seem in a hurry and not be passion to wait the students to develop math and produce their own concept of math. This is also the biggest problem of math educ. because it is related to the curriculum and the educ.system.

@Gail Mills: How sad the fate of EDUCATION due to the standard-driven educ system. Yes I am aware that amongst the global interaction many countries stressing much on how to compete with others. Consequently, in educ also the system means of competing between everything. Why do we not to promote education based on COLLABORATION/COOPERATION rather than competing. You know that in every scene of competition, there will always be the LOOSER. Who will take responsibility to the looser students? No other people except that of teachers. No other people except that of the people who really think intensively and extensively about the nature of education.

Bradford Hansen-Smith • The best way to overcome struggling is to begin to have some
curiosity about what we are doing to the degree that self-discipline and
responsibility becomes the result of effortless attention in learning to love
through the experience of doing.

Where does this leave math when teachers, as a generalization, do not simulate curiosity about their subject, themselves having little curiosity. No matter how many good teachers, few students will find real interest in the mathematical form. There are other ways to acquire understanding of pattern and thinking abstractly in "logical" systematic ways.

Competition kills curiosity and love for what we do by focusing on self over others. Maybe by opening beyond individual self-importance we can find curiosity enough to love and cooperate, the first step towards collaboration. Learning is grounded in curiosity, yet we still favor competition, going to war with each other to prove ourselves. It is difficult for students to learn when they are in an educational war zone.

Where does this leave math when teachers, as a generalization, do not simulate curiosity about their subject, themselves having little curiosity. No matter how many good teachers, few students will find real interest in the mathematical form. There are other ways to acquire understanding of pattern and thinking abstractly in "logical" systematic ways.

Competition kills curiosity and love for what we do by focusing on self over others. Maybe by opening beyond individual self-importance we can find curiosity enough to love and cooperate, the first step towards collaboration. Learning is grounded in curiosity, yet we still favor competition, going to war with each other to prove ourselves. It is difficult for students to learn when they are in an educational war zone.

Art DiVito • Argh.
I'm sorry, but I really don't like "competition" getting bad mouthed like
this (I say as I am about to head to a five state Regional US Tennis Assoc.
playoff!). "Competition" exists only because activities must have a
"limit" (typically the limit is time; volleyball goes with points,
tennis with sets, and baseball with outs). If you don't like it, try cricket,
... but even those games eventually end. : )

When folks, especially teachers, speak in terms of competition "killing curiosity," "focusing on self over others," and "creating losers," then it is time to reassess our understanding of "competition." Life itself is not fair. Get used to it. Courses are still passed or failed. Shall we drop that? Shall we just say, "It's okay, Johnny, you don't know dog manure (about fractions, or signed numbers, or whatever), but you're going to the next course, the next teacher, the next grade, the next school"? Real competition is about having fun, learning to cooperate with teammates, respecting your opponents, accepting defeat, being gracious in winning, and advancing the "game." Perhaps above all else, competition is about "getting it done." What students need to do today, more than ever, is to "get it done." The next time you attend a concert, do you want to listen to someone who is accomplished or someone who is not?

Education has its problems today. Competition is not one of them.

When folks, especially teachers, speak in terms of competition "killing curiosity," "focusing on self over others," and "creating losers," then it is time to reassess our understanding of "competition." Life itself is not fair. Get used to it. Courses are still passed or failed. Shall we drop that? Shall we just say, "It's okay, Johnny, you don't know dog manure (about fractions, or signed numbers, or whatever), but you're going to the next course, the next teacher, the next grade, the next school"? Real competition is about having fun, learning to cooperate with teammates, respecting your opponents, accepting defeat, being gracious in winning, and advancing the "game." Perhaps above all else, competition is about "getting it done." What students need to do today, more than ever, is to "get it done." The next time you attend a concert, do you want to listen to someone who is accomplished or someone who is not?

Education has its problems today. Competition is not one of them.

Elias Gourtsoyannis • @Art. I agree. Perhaps not with the tone. But, you're right.

I once participated in a Mathematics competition in California. At the

time, I did not even know trig identities. I revised until late night from

the textbook. Next day, I took part. Several schools. It was a big

multiple-choice test. Together with some additional questions. The top

prize was an aluminium state of the art log-log type slide rule. In the

test, I did not even make the top 50%. But, I had an idea. The competition

was sponsored by the slide rule makers. The top prize was for sale for $32.

Now, I had some pocket money I had not spent. Given to me by the AFS,

monthly. So, I promptly bought it. It had a beautiful leather case!

Perhaps one of the reasons I eventually studied math?

I once participated in a Mathematics competition in California. At the

time, I did not even know trig identities. I revised until late night from

the textbook. Next day, I took part. Several schools. It was a big

multiple-choice test. Together with some additional questions. The top

prize was an aluminium state of the art log-log type slide rule. In the

test, I did not even make the top 50%. But, I had an idea. The competition

was sponsored by the slide rule makers. The top prize was for sale for $32.

Now, I had some pocket money I had not spent. Given to me by the AFS,

monthly. So, I promptly bought it. It had a beautiful leather case!

Perhaps one of the reasons I eventually studied math?

Marsigit Dr MA • @Bradford Hansen-Smith: Your ideas are challenging. I agree
with you about curiosity and the concept of educational war zone. However, from
your explanation, I found some in-synchronize notions. Curiosity is very
difficult to be directly connected with self-discipline, responsibility and
understanding of pattern and thinking abstractly in "logical"
systematic ways. Why? Because curiosity is something happened in the very early
stage of everything and it is original. It should be free, neutral and not have
a certain burdened. Even the 7 month age baby has his/her curiosity. It is
clear that it cannot be compared with the notions of self-discipline,
responsibility and understanding of pattern and thinking abstractly in
"logical" systematic ways. While the later is coming from the very
powerful authority e.g. adult people (authoritarian teacher or pure
mathematician). I agree with you on individual self-importance as the first
step towards collaboration.

@Art DiVito: Comparing educational activity with other subjects e.g. sport, art is to some extent not proportionally appropriate. Education is sometime about long term program rather than short term program as you said because of limitation of time. If you put LIMITATION as the main factor of education, I assume that there is not appropriate foundation or theories of education. You feel you have just very limited time because you feel you have everything to teach, while you may perceive that your students have nothing. I prefer to give the small amount of knowledge to my students in which they are in a hurry running to come forward to me; rather than I bring a huge amount of knowledge but they are running leaving me. So, the concept of limitation much depend on our perception. It is you as the winner who said "Real competition is about having fun, learning to cooperate with teammates, respecting your opponents, accepting defeat, being gracious in winning, and advancing the "game."" I prefer to hear it from the looser rather than from the winner.

@Art DiVito: Comparing educational activity with other subjects e.g. sport, art is to some extent not proportionally appropriate. Education is sometime about long term program rather than short term program as you said because of limitation of time. If you put LIMITATION as the main factor of education, I assume that there is not appropriate foundation or theories of education. You feel you have just very limited time because you feel you have everything to teach, while you may perceive that your students have nothing. I prefer to give the small amount of knowledge to my students in which they are in a hurry running to come forward to me; rather than I bring a huge amount of knowledge but they are running leaving me. So, the concept of limitation much depend on our perception. It is you as the winner who said "Real competition is about having fun, learning to cooperate with teammates, respecting your opponents, accepting defeat, being gracious in winning, and advancing the "game."" I prefer to hear it from the looser rather than from the winner.

Marsigit Dr MA • @Elias Gourtsoyannis: How wonderful your experienced in the
process of learning math. However, it may be difficult for other people to
follow you. Your experience is unique and only a few, while the teacher in a
certain class should take responsibility for all of his/her students (both the
winner and the looser). Your experience is your creativity. Regrettably,
teachers can not teach CREATIVITY. They can only facilitate or develop the
scheme in order the students are to be creative. As we know that other students
are also unique. Of course it is his uniqueness that the most important of his
value.

Art DiVito • @Marsigit.
Marsigit, every winner has lost tons more than they have won. It is in losing
that we know we are human; and we generally learn more from losing than from
winning. We have to learn to handle losing (gosh, I wish I could do that when I
golf!), not shy away from the challenge. ... As for analogies with education,
... education could learn from a few. A wise man once said (I believe it was an
ancient Greek, but I cannot find it; I wonder whether Elias would recognize it)
the now very politically incorrect, but nonetheless true: "A nation that
draws too broad a distinction between its scholars and its warriors will have
its lessons taught by cowards and its battles fought by fools."

Marsigit Dr MA • Art DiVito: Thanking for the response. Again I wish to say
that it is you as the WINNER or you as the POWERFUL SUBJECT/AUTHOR/TEACHER or
you as the COORDINATOR/SPONSORSHIP of Playing Game or you as the PEOPLE who
always have the AUTHORITY to TEACH/EDUCATE ...who said that "every winner
has lost tons more than they have won. It is in losing that we know we are
human; and we generally learn more from losing than from winning. We have to
learn to handle losing (gosh, I wish I could do that when I golf!), not shy
away from the challenge.". And also again I prefer to hear it from the
LOOSER or from the STUDENTS or from the OBJECT or from the WEAKER or from THE
PEOPLE who have no authority to speak. I do really more trust to the last
because they are the MORE. As you know that at every single game there will be
always very-very few WINNER (first, second, third). You can imagine how
frustrated, sad or even feel devastated most of the looser football team in the
UK Olympiad (99 %), compare with just MEXICO who defeat Brasil in the Final
(0,001%). For the people who really love football playing (not football game)
they also feel like the looser. Imagine please!

By relating the scholar and the warrior in a very short distance, you look a very pragmatics people. In my opinion, because education is about long term program, it still needs idealistic people. As Immanuel Kant said :"Practice without theory is BLIND, and theory without practice is EMPTY". So, the scholar without its warriors is empty, and the warriors without its scholar is blind. So it is dangerous for you to be pragmatical alone without hearing me as an idealist because it can make you blind. And also it will be dangerous also for me without learning your notions because it can make me empty.

Education is for ALL. The teacher should take responsibility both the winner and the looser. It is very-very bad and inappropriate behavior for the teacher to urge the looser to give applause to the winner while the prize is only for the winner. The teacher should also consider the psychological conditions of his/her looser students, because their fate as the looser is also because of the teacher's act/behavior/schema. So again, in education, I prefer to promote COLLABORATION rather than COMPETITION.

All that I strive to prove that some of your notions are not fit with the nature of education, and so that I disagree with you.

By relating the scholar and the warrior in a very short distance, you look a very pragmatics people. In my opinion, because education is about long term program, it still needs idealistic people. As Immanuel Kant said :"Practice without theory is BLIND, and theory without practice is EMPTY". So, the scholar without its warriors is empty, and the warriors without its scholar is blind. So it is dangerous for you to be pragmatical alone without hearing me as an idealist because it can make you blind. And also it will be dangerous also for me without learning your notions because it can make me empty.

Education is for ALL. The teacher should take responsibility both the winner and the looser. It is very-very bad and inappropriate behavior for the teacher to urge the looser to give applause to the winner while the prize is only for the winner. The teacher should also consider the psychological conditions of his/her looser students, because their fate as the looser is also because of the teacher's act/behavior/schema. So again, in education, I prefer to promote COLLABORATION rather than COMPETITION.

All that I strive to prove that some of your notions are not fit with the nature of education, and so that I disagree with you.

Behnaz Herbst, MSc.OCT • We need to "teach" in the ways that the brain
"learns"! In many cases, the teaching happens, the learning may not!
I wish for our school system to become more brain - friendly. Also, our
students need to be taught how cognition takes place, how memory works, how
they can focus, and retain their attention for longer periods of time. They
need to be convinced that their brain can change and adapt and that their
perceived inability is really a myth. If we could achieve this, they might be
upset from home, but when in class, they will learn! There is no way they
won't!

William Galinaitis • People learn new things all the time when the need is there
and they are mentally capable. To be really clinical about it, I can sent up an
experiment which shows the innate curiosity of an average person (motivation)
and their ability to learn something new, when the stimulus is correct.

Marsigit Dr MA • @Behnaz Herbst, MSc.OCT: I am worry that your much pay
attention on manipulating students' brain is also really a myth?

@William Galinaitis: In my perception, stimulus-response psychology is out of date. I prefer to use various approach.

@William Galinaitis: In my perception, stimulus-response psychology is out of date. I prefer to use various approach.

Patricia Frey • Because when basic math was taught, it was mostly taught by
generalists who did not understand even the basic math! Consequently, they
taught a bunch of rules and procedures to follow without thinking! How easy is
it to remember a bunch of rules and the order in which they are to be
performed, if you have no understanding of the basis of those rules?

Dr Patricia Frey

Dr Patricia Frey

Marsigit Dr MA • @Patricia Frey: I prefer to use the sentence "...when
basic math was learned by the student...". Regrettably, what you meant by
specialist may still perceive to teach bunch of rules and procedure although
with thinking. In my perception, it is very difficult to connect younger
(primary school) with a bunch of rules and procedure; however, it can be a
certain struggling. I prefer to introduce basic math using concrete object
surrounding them.

**Marsigit Dr MA • @Elias Gourtsoyannis: I am more concerned about LEARNING MATH rather than TEACHING MATH. So I am more concerned about how the student learn math rather than WHO TEACH MATH. Hence, theories of learning math should come first; it should come before theories of teaching.**

Elias Gourtsoyannis • @Behnaz. This is the view of the 'embedded mathematics'
program advocated by George Lakoff and Raphael Nunez in their their book. I
will provide a full reference in a moment. They do seem to overstate their
case. They claim that 'brain research' has confirmed their view. This can
alienate some practitioners, however. Not enough is known as to what the
'brain' actually does. Aristotle, for example, thought it was some kind or
refrigeration system for the blood. Perhaps our present state of knowledge will
prove just as outdated, some day!

@Bill. I liked your joke on 'sending up' an experiment. It is always healthy to question 'objective' procedures!

@Pat. I agree with you. Mathematics should always be taught by Maths

graduates. However, the reality is that, until this happens, most primary

mathematics teachers would be trained practitioners. Increasingly, however,

in some countries, teacher training includes basic mathematical skills.

With the right trainer, student teachers can, and do, experience something

of the flavor of true mathematical thinking and processes. And, later, they

can pass it on to their pupils!

@Marsigit. Sorry. I just run out of time in editing my previous comment. I had to resubmit it. But, I noted your comment. And, I do not disagree!

@Bill. I liked your joke on 'sending up' an experiment. It is always healthy to question 'objective' procedures!

@Pat. I agree with you. Mathematics should always be taught by Maths

graduates. However, the reality is that, until this happens, most primary

mathematics teachers would be trained practitioners. Increasingly, however,

in some countries, teacher training includes basic mathematical skills.

With the right trainer, student teachers can, and do, experience something

of the flavor of true mathematical thinking and processes. And, later, they

can pass it on to their pupils!

@Marsigit. Sorry. I just run out of time in editing my previous comment. I had to resubmit it. But, I noted your comment. And, I do not disagree!

Elias Gourtsoyannis • @All. The reference is: 'Where Mathematics Comes From: How
the Embodied Mind Brings Mathematics into being'. By George Lakoff, and Rafael
E. Núñez 2000,ISBN 0-465-03770-4. There is a Wikipedia article on it. I am not
sure as to its accuracy. But, I have read the book itself.

Marsigit Dr MA • Thank Elias Gourtsoyannis for the information

**Behnaz Herbst, MSc.OCT • Elias, thanks for your comment, but I was not referring to enactivism or the theory of embodied mind, brought forward by Humberto Maturana. I am simply stating that there are better ways to teach math. We don't know a lot of things about how the brain works, but we know some stuff and we better start using these facts. For instance, we should teach in 15 minute sessions with a couple of minutes of rest in between and repeat every hour of teaching after an hour, the next day (a 5 minute review), in one week, and then in one month if we want the information to be submitted to the long - term memory. We need to teach our students that when it comes to learning, brain cannot multitask, so they should not be watching TV and texting their friends while doing their homework! In a recent study, children who jogged for 30 minutes 3 times a week showed significant academic improvement compared to those who did not exercise. Physical activity is a must when it comes to cognitive performance. It would be nice if the neuroscientists and educators would collaborate and do real - life research together. Don't you think?**

Elias Gourtsoyannis • @Μπενάζ. 'Νους υγιής, εν σώματι υγιεί' - a healthy mind
resides in a healthy body. Alan Turing and a friend developed a version of
chess. Where you jog around the house in between moves. And, by the time you
return, your opponent has to complete her next move!

Bradford Hansen-Smith • Art, you state “Education has its problems today.
Competition is not one of them.”

Teaching to the test is certainly competitive when the results are used to determine who gets the prize, from individual students, to teachers, to school board, to country ratings.

Marsigit, the connections I see are when children are curious is that they will stay with what engages them for as long as they need to. Over time they develop self-discipline to stay with what is of most interest and not get diverted to that of less meaning and value. Learning to love what you do is a discipline of the self to that responsibility. Anytime one is deeply interested in what they do, originally growing out of curiosity, there is understanding that expands the conceptual context and system of logic that governs that particular activity.

Individual self-importance is not the same as giving value to yourself in the same way you value others. This is what makes collaboration possible.

Teaching to the test is certainly competitive when the results are used to determine who gets the prize, from individual students, to teachers, to school board, to country ratings.

Marsigit, the connections I see are when children are curious is that they will stay with what engages them for as long as they need to. Over time they develop self-discipline to stay with what is of most interest and not get diverted to that of less meaning and value. Learning to love what you do is a discipline of the self to that responsibility. Anytime one is deeply interested in what they do, originally growing out of curiosity, there is understanding that expands the conceptual context and system of logic that governs that particular activity.

Individual self-importance is not the same as giving value to yourself in the same way you value others. This is what makes collaboration possible.

Art DiVito • @Bradford.
I'm sorry, Bradford, but I regard "teaching to the test" as a
construct brought by those who favor the collective and uniformity, ... not by
those who value the individual and creativity. If you reject competition, then
you reject assessment itself; education would reduce to absurdity. I just don't
understand this desire to paint competition as some sort of negative. The White
Sox just swept the Yankees. Doesn't that make almost all of us just a little
happier this morning? : )

Bradford Hansen-Smith • Art, I do not know about "almost all of us."

I am not a sports fan. Some team, political party, country, corporation, or individual in any field, winning over someone else dose not make my morning happier. The news is full of this sort of thing. I can certainly appreciate all that it takes for an individual or team to preform to excellence. I have done both in the competitive arena and find life to be much larger and more grand outside of the mind in competition.

I am not a sports fan. Some team, political party, country, corporation, or individual in any field, winning over someone else dose not make my morning happier. The news is full of this sort of thing. I can certainly appreciate all that it takes for an individual or team to preform to excellence. I have done both in the competitive arena and find life to be much larger and more grand outside of the mind in competition.

Marsigit Dr MA • @Art DiVito: Assessment is the most crucial problem in
education. I totally agree with the assessment if it means to collect or record
students' activities and achievements. However, it can be a big problem if it
means to evaluate, because the next important question is who has the authority
to evaluate? It will also no problem if the teacher himself evaluate his/her
students, because the teacher is the people who knows the best about his
students. The problems arise when evaluation is carried out externally or by
external institution/board.

If it does so, philosophically there will be a huge reductions or simplification. Reduction or simplification is a kind of psychologically unhealthy partially dimension of life. If education from time to time always produce a simplified generation, then we will have a problematic generation. Look at directly to the phenomena in the society not only in the certain country but also in each country all over the world. So, according to my point of view, the best assessment should be supported by keeping-record (portfolio) both by the teacher and by the students themselves. The form of it can be authentic assessment or classroom-based assessment. Thank you

If it does so, philosophically there will be a huge reductions or simplification. Reduction or simplification is a kind of psychologically unhealthy partially dimension of life. If education from time to time always produce a simplified generation, then we will have a problematic generation. Look at directly to the phenomena in the society not only in the certain country but also in each country all over the world. So, according to my point of view, the best assessment should be supported by keeping-record (portfolio) both by the teacher and by the students themselves. The form of it can be authentic assessment or classroom-based assessment. Thank you

Marsigit Dr MA • @Bradford: Because there important and strategic, so now I
am spying your notions "the connections I see are when children are
curious is that they will stay with what engages them for as long as they need
to. Over time they develop self-discipline to stay with what is of most
interest and not get diverted to that of less meaning and value. Learning to
love what you do is a discipline of the self to that responsibility. Anytime
one is deeply interested in what they do, originally growing out of curiosity,
there is understanding that expands the conceptual context and system of logic
that governs that particular activity. ". I may produce my comments later.
Thank's

Marsigit Dr MA • @Elias: The reference you indicated "Where Mathematics
Comes From: How the Embodied Mind Brings Mathematics into being'. By George Lakoff,
and Rafael E." is very strategic and important. I have just read at a
glance from the sample of excerpt. My first conclusion is that it is strategic
and important evidences and then thus as theories of the origin of math
concept. It is a very good illustration on the origin of math concept from the
early stage up to the highest stage. I am still finding of what happened and
comparing with other theories of how a certain student in a certain stage is to
construct math knowledge, what kinds of math and what kinds of the limit or
edge. As you know, according to realistic-ism, there are four stages to
construct math: concrete math, concrete model, formal model, and formal math.
In an easy way there are just two categories: horizontal math and vertical math.

Marsigit Dr MA • @Art DiVito: I really wish to know about your perception of
math? How you define math? What kinds of math? Do you have any particularity on
how to develop Pure Math-Formal Math-Axiomatic Math? or Maybe School Math?
That's all are really also my question to you. Is there any reference you may
indicate that I can read? Thank's

Marsigit Dr MA • @Bradford: After a moment I think them deeply and trying to
reconstruct your ideas, I may produce the following comment. I agree with you
about the connection between curiosity and self-discipline. The most important
point is about SELF as the aspect of discipline. As you know, or as in the
common-sense or at least it is my previous understanding , usually the term discipline
is interpreted by something that coming from outside. I now understand, by
relating with and imaging your activities with the students in searching the
pattern of circle, that SELF-discipline ultimately come out from long
engagement starting with curiosity. That the point that I really am
enthusiastic also to expect about the emerging of SELF....discipline. Of course
it needs the experienced adults to develop a scheme in such away that they are
interested and not get diverted to that of less meaning and value.

The next most crucial problem is how the self-discipline leads to a certain responsibility. Responsible of what, how, when and where? To what extent that the degree of the stage of kids mental development come into the process of curiosity-selfdiscipline-responsibility? I think it will be very complicated psychological aspect of learning. Even it has not until the stage of understanding math concept and logical system.

So I agree with you at the first stage, I am still thinking at the second stage; however, I still didn't agree with you at the last stage. I perceive that there is still a huge gap between self-discipline/responsibility and understanding of math concept and logical system. As you know that in mathematical understanding also consist of mathematical method and mathematical content as well as math attitude. I expect that self-discipline/responsibility may contribute to the math attitude; but they are still far away from math method, math concept and logical system. Thank

The next most crucial problem is how the self-discipline leads to a certain responsibility. Responsible of what, how, when and where? To what extent that the degree of the stage of kids mental development come into the process of curiosity-selfdiscipline-responsibility? I think it will be very complicated psychological aspect of learning. Even it has not until the stage of understanding math concept and logical system.

So I agree with you at the first stage, I am still thinking at the second stage; however, I still didn't agree with you at the last stage. I perceive that there is still a huge gap between self-discipline/responsibility and understanding of math concept and logical system. As you know that in mathematical understanding also consist of mathematical method and mathematical content as well as math attitude. I expect that self-discipline/responsibility may contribute to the math attitude; but they are still far away from math method, math concept and logical system. Thank

Elias Gourtsoyannis • @Marsigit @ Bradford@Art

I believe Bradford you have a point. On the principle that Mathematics teaching cannot be that different than teaching drawing, painting, or sculpture. It is another one of the 'seven liberal arts' of the Hellenistic era. In the late Middle Ages, and the Renaissance, this was the standard format for 'university' education. Let us not forget that examinations and grades were a rather late invention. Until then, a student was judged by professors orally and sometimes in writing. 'Portfolio' work. Yet, there were dedicated scholars in many fields. Other than completely practical subjects. And, advanced scholarship went on. In the Islamic world, there was already a strong tradition of studies. Based partly on the Koran but also on Greek Classics in philosophy, mathematics and science. Some may even hold the view that the transmission of Greek learning to the west occurred via the medium of Arabic. I do not know if Arabs used grades. But, I am sure they, like the ancient and medieval scholars, held debates. If learning is based on a 'collegiate' approach, in the sense of 'community of scholars', lack of assessment does not necessarily imply lack of competition. I am sure it is just as easy to to arouse jealousy and ambition by 'winning' an important disputation. As an alternative to achieving high grades. Perhaps the most rewarding acclaim is the enthusiastic approval of one's peers!

I believe Bradford you have a point. On the principle that Mathematics teaching cannot be that different than teaching drawing, painting, or sculpture. It is another one of the 'seven liberal arts' of the Hellenistic era. In the late Middle Ages, and the Renaissance, this was the standard format for 'university' education. Let us not forget that examinations and grades were a rather late invention. Until then, a student was judged by professors orally and sometimes in writing. 'Portfolio' work. Yet, there were dedicated scholars in many fields. Other than completely practical subjects. And, advanced scholarship went on. In the Islamic world, there was already a strong tradition of studies. Based partly on the Koran but also on Greek Classics in philosophy, mathematics and science. Some may even hold the view that the transmission of Greek learning to the west occurred via the medium of Arabic. I do not know if Arabs used grades. But, I am sure they, like the ancient and medieval scholars, held debates. If learning is based on a 'collegiate' approach, in the sense of 'community of scholars', lack of assessment does not necessarily imply lack of competition. I am sure it is just as easy to to arouse jealousy and ambition by 'winning' an important disputation. As an alternative to achieving high grades. Perhaps the most rewarding acclaim is the enthusiastic approval of one's peers!

Marsigit Dr MA • @Art DiVito: I am interested with your claim
"....education would reduce to absurdity".

I may interpret ABSURDITY as something not clear, not effective, not efficient, or even meaningless. In my opinion, this is very-very subjective claim. In the case of totalitarian government/institution/board, they perceive education as a tool or instrument to legitimate and achieve their interests; so they always expect that education should be very clear scheme, effective, efficient, and thus not reduce to absurdity. These also happened in the countries that implement the centralized curriculum. So for the people who are striving to promote decentralized-curriculum, your claim of absurdity can be very sensitive.

I may interpret ABSURDITY as something not clear, not effective, not efficient, or even meaningless. In my opinion, this is very-very subjective claim. In the case of totalitarian government/institution/board, they perceive education as a tool or instrument to legitimate and achieve their interests; so they always expect that education should be very clear scheme, effective, efficient, and thus not reduce to absurdity. These also happened in the countries that implement the centralized curriculum. So for the people who are striving to promote decentralized-curriculum, your claim of absurdity can be very sensitive.

Marsigit Dr MA • Marsigit Dr MA • @Elias: Your last description is inspiring
me. However, I may smooth your notion by indicating that NOT TEACHING but LEARNING
may not be differentiated by one's activities in drawing, painting, or
sculpture.

Further, you seemed made the very technical reasons for the need of learning based on a 'collegiate' approach, or may I call it as 'small group discussion'. Really, it has a very deep of philosophical grounds.

As we know that there are various definition/assumptions about the nature of "KNOWLEDGE" i.e. the nature of "math". As I asked to Art DiVito, but it has not been responded yet, there are different ways to define math. Usually, Conservatives or Old Humanist, define MATH as a body of knowledge or as a body of structure. There are also the same definition made by Pure/Axiomatic/Formal Mathematicians. They usually do not much pay attention to what happen inside the learner.

However, if we read Paul Ernest on his Philosophy of Math Educ., Socio-Constructivist or even Liberalis define Math very differently. They define math as a CREATIVITY or PROCESS OF THINKING or even as SOCIAL ACTIVITIES. Accordingly, the nature of math can be perceived as social-activities. What then the implication to the practice of teaching? There absolutely need that in learning activities the teacher should give the chance the students to do/work math in a SMALL GROUP DISCUSSION.

I do agree with you that in the sense of 'community of scholars', lack of assessment does not necessarily imply lack of competition. Further, I may add that by COLLABORATIVE approach does not also necessarily imply lack of competition. However, jealousy, ambition, and rewarding acclaim are just the impacts of working in such a certain small group.

Thank's

Further, you seemed made the very technical reasons for the need of learning based on a 'collegiate' approach, or may I call it as 'small group discussion'. Really, it has a very deep of philosophical grounds.

As we know that there are various definition/assumptions about the nature of "KNOWLEDGE" i.e. the nature of "math". As I asked to Art DiVito, but it has not been responded yet, there are different ways to define math. Usually, Conservatives or Old Humanist, define MATH as a body of knowledge or as a body of structure. There are also the same definition made by Pure/Axiomatic/Formal Mathematicians. They usually do not much pay attention to what happen inside the learner.

However, if we read Paul Ernest on his Philosophy of Math Educ., Socio-Constructivist or even Liberalis define Math very differently. They define math as a CREATIVITY or PROCESS OF THINKING or even as SOCIAL ACTIVITIES. Accordingly, the nature of math can be perceived as social-activities. What then the implication to the practice of teaching? There absolutely need that in learning activities the teacher should give the chance the students to do/work math in a SMALL GROUP DISCUSSION.

I do agree with you that in the sense of 'community of scholars', lack of assessment does not necessarily imply lack of competition. Further, I may add that by COLLABORATIVE approach does not also necessarily imply lack of competition. However, jealousy, ambition, and rewarding acclaim are just the impacts of working in such a certain small group.

Thank's

**Elias Gourtsoyannis • @Marsigit. Thank you for your kind comments.**

A noted worker in the field of ancient mathematics is Serafina Cuomo. Her

main concern is to determine the self-image of ancient mathematicians from

the professional point of view. In other words, how did these ancient

mathematicians see themselves? As practical advisers, as

researchers-scholars, or what? Daily bills had still to be paid,

presumably!

A well known book of hers can be found in

http://www.amazon.com/Ancient-Mathematics-Sciences-Antiquity-Series/dp/0415164958

<http://www.amazon.com/Ancient-Mathematics-Sciences-Antiquity-Series/dp/0415164958>

She has also written on Pappus, the Alexandrian mathematician.

Yogyakarta,
25 Agustus 2012

Aprisal

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PPs S2 Pendidikan Matematika Kelas A 2016

Assalamu Alaikum Wr.Wb

Salah satu inti yang saya dapat pahami dari percakapan di atas adalah "An educator is important in the moment when a learner is trying place new knowledge in to the context of their own understanding of the world. Sometimes I can "read" the student (ask them questions, have them try to explain a concept to others...) and provide the appropriate stepping stones for them to integrate the new material into their framework or modify it". dari pernnyataan tersebut peran seorang guru sebagai pendidik sangat dibutuhkan bagi siswa ketika para siswa mulai mencoba memahami sebuah pengetahuan baru ke dalam pengetahuan atau konteks yang telah dipahaminya. seorang guru sebagai pendidik dan fasilitator tentunya sangat dibutuhkan siswa untuk mengasimilasi dan mengakomodasi pengetahuan baru tersebut agar sesuai dengan konteks yang telah dimilikinya atau mengubah konteksnya sesuai dengan pengetahuan barunya.

Waalaikum salam wr.wb.

Erlinda Rahma Dewi

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S2 PPs Pendidikan Matematika A 2016

Fondasi matematika adalah sebuah studi tentang dasar-dasar logika dan filsafat dari matematika atau dalam arti yang lebih luas, investigasi matematis mengenai konsekuensi-konsekuensi dari teori-teori filsafat dasar tentang hakikat dari matematika itu sendiri. Ada dua pandangan bagaimana memperoleh kebanaran matematika, pertama kebenaran matematika diperoleh murni menggunakan akal pikiran, kedua kebenaran matematika diperoleh berdasarkan pengalaman. Di dalam filsafat matematika, adanya pertentangan antara kaum rasionalis dan kaum empiris menimbulkan pengakuan mendalam akan sintesis Immanuel Kant bahwa matematika adalah ilmu yang bersifat sintetik a priori.

Asri Fauzi

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Pend. Matematika S2 Kelas A 2016

Dalam mempelajari matematika sangat sering para siswa mampu memecahkan masalah yang sangat mirip dengan apa yang diajarkan di kelas, tetapi setelah perubahan tata letak, mereka tidak dapat melihat pola, atau fakta bahwa mereka perlu menerapkan konsep yang sama dalam bentuk yang berbeda. Itu berarti pembelajaran dangkal, lebih didasarkan pada hafalan dari pada logika. arsitektonis dari Kant mengajarkan kita matematika yang merupakan usaha dari siswa arsitektonis. Jadi, bagi saya, apa pun kriteria eksternal untuk mengukur siswa matematika selalu menyesatkan. Kompetensi genesis matematika adalah benar-benar arsitektonis mereka. Jadi, masalah untuk guru adalah bagaimana mengungkap kedalaman matematika dalam dari siswa. Sampai saat itu Anda mendapatkan kriteria keberhasilan mengajar matematika Anda setelah Anda mendengar klaim siswa bahwa matematika benar-benar milik mereka.

Rhomiy Handican

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PPs Pendidikan Matematika B 2016

Dari Percakapan diatas saya setuju dengan pernyataan oleh Old Humanis, mendefinisikan MATEMATIKA sebagai tubuh pengetahuan atau sebagai badan struktur. Ada juga definisi yang sama yang dibuat oleh Pure / aksiomatik / matematika formal. Mereka biasanya tidak banyak memperhatikan apa yang terjadi di dalam pelajar berbeda dengan pendapat Paul Ernest yg mendefinisikan matematika sebagai KREATIVITAS atau PROSES BERPIKIR atau bahkan sebagai KEGIATAN SOSIAL. Dengan demikian, sifat matematika dapat dianggap sebagai sosial-kegiatan. sebenarnya kedua pendapat tersebut saling mendukung tergantung dari bagian mana pandangan matematika secara menyeluruh.

Konstantinus Denny Pareira Meke

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PPs S2 Pendidikan Matematika Kelas A 2016

Matematika ibarat sebuah bangunan bertingkat. Dia punya pondasi, rangka, lantai yang bertingkat, dan unsur-unsur lain yang melekat padanya. Secara struktural bangunan itu hanya dapat dipertanggungjawabkan keberadaannya sebagai bangunan apabila dibangun di atas pondasi atau landasan yang kuat. Dengan demikian, bangunan ini akan tetap kokoh dari masa ke masa meskipun diterpa badai dan taufan. Dalam matematika, landasan berfungsi untuk memperkokoh, menyokong atau menopang bangunan matematika. Selain itu landasan matematika juga sebagai sarana yang diperlukan untuk 'merenovasi' bangunan matematika itu sendiri. Pengetahuan matematika di satu sisi bersifat subserve yakni hasil dari sintesis pengalaman inderawi, disisi lain bersifat superserve yakni mengetahui apriori sebagai hasil konsep matematika yang bersifat imannen. Dikarenakan dalam pikiran kita sudah terdapat kategori-kategori yang memungkinkan untuk memahami matematika tersebut.

Devi Anggriyani

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S2 PEP B 2016

Berdasarkan artikel di atas, dasar matematika adalah dasar logis dan filosofis matematika atau penyelidikan matematika mendasari sifat matematika. Dasar matematika dapat dipahami sebagai studi tentang konsep-konsep matematika dasar dan bagaimana mereka membentuk struktur konsep yang lebih kompleks. Dasar matematika secara keseluruhan tidak bertujuan mengandung dasar-dasar setiap topik matematika. Dasar-dasar bidang studi mengacu pada analisis sistematis lebih-atau-kurang dari konsep yang paling dasar atau fundamental, kesatuan konseptual, yang dapat membantu untuk menghubungkannya dengan seluruh manusia pengetahuan.

Fatya Azizah

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Pendidikan Matematika B PPS UNY 2016

pada artikel diatas bapak marsigit menyebutkan bahwa kedisiplinan berhubungan erat dengan rasa ingin tahu. rasa ingin tahu itu sendiri dapat dipicu dari kegiatan berkelompok siswa yang dapat meningkatkan motivasi siswa. tentunya hal ini juga harus didampingi guru agar kegiatan lebih bermakna.

MARTIN/RWANDA

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The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic. Generally, the foundations of a field of study refers to a more-or-less systematic analysis of its most basic or fundamental concepts, its conceptual unity and its natural ordering or hierarchy of concepts, which may help to connect it with the rest of human knowledge. The development, emergence and clarification of the foundations can come late in the history of a field, and may not be viewed by everyone as its most interesting part.

Mathematics always played a special role in scientific thought, serving since ancient times as a model of truth and rigor for rational inquiry, and giving tools or even a foundation for other sciences (especially physics). Mathematics' many developments towards higher abstractions in the 19th century brought new challenges and paradoxes, urging for a deeper and more systematic examination of the nature and criteria of mathematical truth, as well as a unification of the diverse branches of mathematics into a coherent whole.

Rospala Hanisah Yukti Sari

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S2 Pendidikan Matematika Kelas A Tahun 2016

Assalamu’alaikum warohmatullahi wabarokatuh.

Fondasi matematika sangat penting untuk diketahui. Ibarat sebuah bangunan, fondasilah yang akan menopang bangunan tersebut agar tidak mudah roboh. Suatu pengetahuan merupakan sintesis dari analitik a priori dan analitik a posteori. Analitik a priori memerlukan kemampuan logika untuk mendapatkan sebuah konsep. Sedangkan, analitik a posteori memerlukan banyaknya pengalaman-pengalaman yang pernah dilakukan dalam memahami konsep atau dari contoh-contoh permasalahan matematika. Maka agar konsep dapat melekat dalam pikiran kita, maka konsep tersebut di dasarkan kepada analitik a priori dan a posteori.

Wassalamu’alaikum warohmatullahi wabarokatuh.

Nanang Ade Putra Yaman

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PPs PM B 2016

Assalamualaikum

cara memperoleh kebenaran matematika dengan menggunakan akal pikiran dan diperoleh berdasarkan pengalaman yang menjadi pertentangan kaum rasionalis dan kaum empiris menimbulkan pengakuan mendalam akan sintesis Immanuel Kant bahwa matematika adalah ilmu yang bersifat sintetik a priori sehingga sintesis Kant menurut saya dapat menjadi pondasi matematika. Dari percakapan diatas Paul Ernest mendefinisikan matematika sebagai kreativitas atau proses berpikir atau bahkan sebagai kegiatan sosial. Jika merujuk pada pemikiran ini maka matematika yang abstrak. Procedural bisa disajikan dalam bentuk lain seperti seni yang mengandung nilai estetik. Sehingga subyek sebagai pembelajar matematika tidak memakasakan diri memahami matematika dengan kaku harus dibatasi ranah procedural yang terkesan menyulitkan kreatifitas bermatematika itu sendiri.

Fevi Rahmawati Suwanto

ReplyDelete16709251005

PMat A / S2

Percakapan di atas membahas tentang alasan lemahnya kemampuan dasar matematika seseorang. Banyak faktor yang menjadi penyebabnya baik secara genetik ataupun lingkungan. Faktor genetik bisa berupa aktivitas otak yang berhubungan dengan perilaku dan pembelajaran. Sedangkan faktor lingkungan banyak sekali misalnya yang berasal dari guru, keluarga, budaya, sistem pembelajaran, dst. Salah satunya pada sistem pembelajaran misalnya matematika diajarkan menggunakan menghafal dan pengulangan mekanik bukan dengan pemahaman mekanika dan logika. Hal ini mengakibatkan seseorang mampu memecahkan masalah yang sangat mirip dengan yang diajarkan, tetapi setelah perubahan tata letak, seseorang tidak dapat melihat pola atau fakta untuk menerapkan konsep yang sama dalam bentuk yang berbeda. Pengidentifikasian faktor-faktor penyebab lemahnya kemampuan dasar matematika ini diharapkan dapat dijadikan sebagai acuan dalam perencanaan dan pelaksanaan pembelajaran matematika yang akan datang, sehingga tidak terulang pada kesalahan yang sama.

Siska Nur Rahmawati

ReplyDelete16701251028

PEP-B 2016

Pecakapan di atas berisi mengenai pentingnya membentuk pondasi dasar dari matematika. Sejatinya matematika itu adalah hasil intuisi murni dari pikiran manusia. Melalui intuisi yang didasarkan pada logika dan ruang waktu, akan menghasilkan pemikiran apriori. Melalui pengamatan di luar pikiran dengan menggunakan sintetic apriori akan diperoleh kebenaran pemahaman dalam matematika.

Achmad Rasyidinnur

ReplyDelete16701251032

PEP S2 B

Mathematics as a whole can be seen as the science of all possible worlds

Mathematics is split into diverse branches, implicit or explicit frameworks of any mathematical work, that may be formalized as axiomatic theories. Mathematics is the study of systems of elementary objects, whose only nature is to be exact, unambiguous

Achmad Rasyidinnur

ReplyDelete16701251032

PEP S2 B

Paul ernest on his philosophy of math education, socio-constructivist or even liberalis define math very differently. They define math as a creativity or process of thinking or even as social activities. Accordingly, the nature of math can be perceived as social-activities. That in learning activities the teacher should give the chance the students to do/work math in a small group discussion.

Matematika identik dengan angka-angka yang rumit karena membentuk sebuah formula. Namun peran guru sangat dominan untuk menjadikan matematika lebih kreatif dan inovatif, tidak menjadi hantu menakutkan bagi siswa, apalagi pada tingkat dasar. Bila sejak awal kesan matematika sudah rumit akan terbawa pada pola pembelajaran siswa.

ReplyDeleteNur Tjahjono Suharto

PEP S3 (A)

16701261007

Azwar Anwar

ReplyDelete16709251038

Pendidikan Matematika S2 Kelas B 2016

Matematika merupakan sebagai cabang filsafat yang mempelajari berbagai macam objek dan konsep metode matematika yang meliputi kajian tentang hakekat bilangan dan bangun-bangun geometri serta hakekat objek lainnya. Jadi matematika itu harus dibangun dan mempunyai landasan atau pondasi yang kuat untuk dapat menyelesaikan suatu masalah.

Fitri Ayu Ningtiyas

ReplyDelete16709251037

S2 P.Mat B UNY 2016

Dari percakapan mengenai foundation of mathematics diatas dijelaskan bahwa sifat matematika dapat dianggap sebagai kegiatan sosial dimana dasar matematika adalah dasar logis dan filosofis matematika atau penyelidikan matematika mendasari sifat matematika. Dasar matematika dapat dipahami sebagai studi tentang konsep-konsep matematika dasar dan bagaimana mereka membentuk struktur konsep yang lebih kompleks. Selanjutnya, juga dibahas mengenai peran seorang guru sebagai pendidik agar dapat mengkondisikan siswa ketika mulai mencoba mengkonstruk pengetahuan baru ke dalam pengetahuan yang telah dimilikinya.