Mar 15, 2013

Why do you think people's basic math skills are weak?

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
And also my works on, 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.

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
And also my works on, 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:

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.

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.

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 
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
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.

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.


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".

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 MillsWith 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.

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.

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.

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?

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.

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.

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.

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

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!

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

Elias Gourtsoyannis
 Δεαρ Marsigit. You can call me Elias!

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.

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.

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

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

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!

Marsigit Dr MA
 @Art DiVito: I am interested with your claim " 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.

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.


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,
A well known book of hers can be found in

She has also written on Pappus, the Alexandrian mathematician.

Yogyakarta, 25 Agustus 2012


  1. Nama : Irna K.S.Blegur
    Nim : 16709251064
    kelas : PM D 2016(PPS)
    Sedikit kesimpulan yang dapat saya tangkap dari pembicaraan (perdebatan) di atas kurang lebih mengenai berbagai alasan mengapa keterampilan matematika dasar pada masyarakat lemah. Ada yang mengatakan hal ini disebabkan dengan adanya berbagai fakor yang dapat memengaruhi pikiran siswa .Aktivitas otak yang berkaitan dengan perilaku dan pembelajaran tampaknya terdiri dari faktor genetik dan lingkungan (budaya, keluarga, gen). Pengalaman anak-anak dapat mempengaruhi kemampuan mereka untuk mengendalikan beahvior kelas mereka, dan karena itu kemampuan mereka untuk fokus pada suatu aktivitas tunggal (William Galinaitis). Matematika itu seperti sesuatu yang berjalan, terus berkembang dari masa ke masa.
    Belajar matematika tidak dapat dipaksakan, orang-orang belajar matematika karena keinginan sendiri dan karena kebutuhan yang mengharuskan mereka bersungguh-sungguh dalam belajar matematika. Belajar adalah membangun aktivitas di mana saja dan kapan saja. Meski begitu, guru tidak bisa sepenuhnya melepaskan siswa untuk mengembangkan diri. Tetap penting peran guru untuk mendampingi setiap aktivitas siswa sebagai media yang dapat membantu siswa dalam mencari suatu pemecahan masalah.

  2. Ratih Eka Safitri
    PPs Pendidikan Matematika C 2016

    Mengatakan bahwa siswa A pintar dan siswa B lemah adalah kecenderungan yang dilakukan guru dalam pembelejaran. Walaupun hal tersebut sebenarnya salah tapi kadang kala guru melakukannya, karena memang terdapat perbedaan kemampuan siswa dalam belajar dengan segala karakteristik nya masing masing. Namun yang paling ditekankan adalah siswa harus memiliki kesempatan belajar yang sama tanpa membeda-bedakannya.

  3. Ahmad Wafa Nizami
    PPs Pendidikan Matematika D 2016

    Kalau berbicara lembahanya kemampuan orang-orang dalam matematika itu banyak faktor, bisa karena kurangnya latihan menjawab soal atau kurangnya mengerjakan soal yang bermacam jenis tingkat kesulitan siswa itu. Kurang dasar pengetahuan mereka tentang matematika.

  4. Heni Lilia Dewi
    PPs Pendidikan Matematika Kelas C 2016

    Pendapat dari Ginetta Nistoran yang mengatakan bahwa guru masih menggunakan metode hafalan dan pengulangan dalam pembelajaran. Rumus dihafalkan, contoh dihafalkan, soal serupa dan rutin, inilah masalah besar yang dihadapi pembelajaran matematika termasuk di Indonesia. Ini juga menjadi salah satu penyebab lemahnya kemampuan dasar matematika siswa menjadi lemah, karena siswa tidak dilibatkan dalam penemuan konsep sehingga seringkali lupa akan konsep yang sudah pernah dipelajari. Kecemasan dalam belajar matematika juga menjadi pemicu lemahnya kemampuan dasar matematika siswa, diantaranya anggapan matematika sebagai "momok", kecemasan terhadap guru yang otoriter, dan lain sebagainya. Ini menajdi tantangan guru untuk lebih memperdalam pemahaman konsep matematika siswa.

  5. Dessy Rasihen
    S2 P.MAT D

    Hal ini mungkin dapat disebabkan oleh berbagai faktor. Selain dipengaruhi oleh faktor genetik dan lingkungan, pengalaman anak juga dapat mempengaruhi kemampuan mereka. Alasan lain yang mengakibatkan keterampilan matematika dasar siswa lemah dikarenakan oleh pembelajaran matematika yang biasanya diajarkan dengan cara menghafal serta pengulangan berlatih soal. Sehingga seringkali para siswa mampu memecahkan masalah mirip dengan contoh soal yang diajarkan di kelas, tetapi setelah perubahan soal maka kebanyakan siswa tidak mampu menyelesaikan soalnya dikarenakan tidak memahami konsep sebenarnya dan hanya bekerja sesuai urutan langkah berdasarkan contoh soal yang ada.

  6. Lihar Raudina Izzati
    P. Mat C 2016 PPs UNY

    Belajar matematika tidak hanya belajar tentang rumus-rumus. Kita harus benar-benar memahami konsep yang ada dalam matematika. Kemampuan matematika dasar seseorang lemah karena dia hanya mengingat-ingat rumusnya saja, dia tidak memahami konsepnya sehingga rumus dasar yang akan dipakai cepat dilupakan. Matematika dasar bukan berarti hal yang mudah untuk dipelajari, karena apabila kita tidak memahami dasarnya, kita akan kesusahan untuk menaikkan dimensi ilmu matematika kita. Oleh karenanya, matematika dasar pun harus benar-benar dipahami bagaimana konsepnya.

  7. Primaningtyas Nur Arifah
    Pend. Matematika S2 kelas C 2016
    Assalamu’alaikum. tema yang diambil dalam diskusi di atas ialah mengapa dasar ketrampilan matematika siswa itu lemah. Siswa berada di lingkungannya lebih lama dari pada di sekolah. Di lingkungan siswa mengalami berbagai permasalahan yang melibatkan matematika, maka untuk mempeajari matematika hendaknya melibatkan permasalahan-permasalahan di sekitar siswa. Dengan begitu siswa akan merasa tertantang untuk belajar.

  8. Munaya Nikma Rosyada
    S1 Pendidikan Matematika I 2014

    Kondisi siswa dalam belajar (aktivitas berfikir siswa) ternyata dipengaruhi oleh genetik dan lingkungan, seperti faktor budaya, keluarga, kimiawi, dll. Tingkat kecemasan yang dialami siswa juga mempengaruhi kemampuan dirinya mengontrol kebiasaannya di dalam kelas

  9. Munaya Nikma Rosyada
    S1 Pendidikan Matematika I 2014

    Matematika sekarang ini lebih banyak diajarkan dengan hafalan dan pengulangan, bukan dengan langkah pemahaman dan logika. Hasilnya, siswa akan bisa menyelesaikan masalah yang hampir sama dengan yang diajarkan di sekolah, namun akan tidak dapat menyelesaikan masalah yang diganti layout nya. Itu berarti matematika sebagai mencari pola belum mereka pahami, karena memang pembelajarannya ternyata menerapkan hafalan dibandingkan logika

  10. Munaya Nikma Rosyada
    S1 Pendidikan Matematika I 2014

    Salah satu kunci memahami matematika yaitu berlatih/practice. Seperti nasihat, orang pandai akan kalah dengan orang yang tekun. Dari diskusi diatas juga disebutkan bahwa latihan tanpa teori adalah buta, dan teori tanpa latihan adalah kosong. Jadi asalkan terus berlatih matematika, akan lebih cepat paham dan akan mendapatkan kesuksesannya . Dalam pembelajaran hal tersebut dihitung sebagai ketahanannya dalam belajar

  11. Munaya Nikma Rosyada
    S1 Pendidikan Matematika I 2014

    Pembelajaran adalah milik semua. Guru sebagai fasilitator harus mampu memfasilitasi semua siswa, dengan beragam kemampuan dan karakter. Pembelajaran yang disusun juga harus mampu mengcover semua kebutuhan siswa. Sehingga diharapkan seluruh siswa mampu bersama-sama mencapai tujuan pembelajaran dan mampu menjadi siswa aktif dan kolaboratif

  12. Ahmad Bahauddin
    PPs P.Mat C 2016

    Assalamualaikum warohmatullahi wabarokatuh.
    Sebetulnya kita tidak dapat menentukan apakah kemampuan dasar matematika seseorang itu lemah atau kuat. Kita hanya bisa menentukan, kemampuan dasar matematika seseorang jika diukur dengan suatu alat, rendah atau tinggi berdasarkan alat tersebut. Karena matematika ada dunianya sendiri. Dan masing-masing dunia matematika setiap orang adalah berbeda. Dunia matematika antar orang tersebut menjadi terhubung dan terjadi sinkronisasi apabila menggunakan bahasa yang sama. Sehingga, ada kemungkinan, orang yang dikira memiliki dasar matematika rendah, sebetulnya hanya tidak dapat melakukan sinkronisasi dunia matematikanya dengan matematika kita.

  13. Hening Carrysa
    S1 Pendidikan Matematika A 2014

    Matematika merupakan salah satu ilmu pengetahuan yang penting dalam dunia pendidikan, untuk itu matematika diberikan di semua jenjang pendidikan. Tetapi karena pola pikir yang turun temunun yang menyatakan matematika itu sulit, membosankan, penuh dengan angka-angka, rumus dan hanya menghitung. Hal tersebutlah yang menjadikan kemampuan dasar matematika siswa menjadi lemah karena sudah tidak ada rasa keingin tahuan, dan berusaha belajar.

    PPS-MAT D 2016
    Ada empat kelemahan yang dimiliki oleh siswa sebagai penyebab rendahnya hasil belajar siswa antara lain, kurang memiliki pengetahuan materi prasyarat yang baik, kurang memiliki kemampuan untuk memahami srta mengenali konsep-konsep dasar matematika (seperti definisi, teorema, aksioma, dalil, kaidah) yang berkaitan dengan pokok bahasan yang sedang dibicarakan, kurang memiliki ketelitiaan dalam menyimak dan mengenali persoalan matematika yang berkaitan dengan pokok bahasan tertentu, kurang memiliki kemampuan untuk menyimak kembali sebuah jawaban yang diperoleh (apakah jawaban tersebut mungkin atau tidak), dan kurang memiliki kemampuan nalar yang logis dalam menyelesaikan persoalan matematika. Keempat kelemahan ini akan menghambat proses belajar bermakna, di mana belajar bermakna maksudnya, di samping materi yang disajikan harus disesuaikan dengan kemampuan siswa, juga harus relevan dengan struktur kognitif siswa, sehingga materi harus dikaitkan dengan konsep-konsep (pengetahuan) yang telah dimiliki siswa dan dikaitkan dengan bidang lain atau kehidupan sehari-hari siswa.

    PPS-MAT D 2016
    Rendahnya prestasi belajar siswa tidak hanya disebabkan oleh kelemahan belajar peserta didik, tetapi dapat disebabkan oleh faktor lain yaitu sistem pengajaran yang kurang membangkitkan gairah belajar pada peserta didik, dan rencana pengajaran yang kurang menarik minat peserta didik dalam belajar. Faktor kecil yang dapat mempengaruhi rendahnya hasil belajar siswa adalah karena pengajaran disajikan masih dalam bentuk yang kurang menarik, sehingga terkesan angker, sulit, dan menakutkan sehingga siswa sering tidak menguasai konsep dasar yang terkandung dalam materi pelajaran matematika yang dapat menghambat kreativitas siswa dalam menjawab soal, yang akhirnya hasil belajar siswa menjadi rendah.

  16. Sehar Trihatun
    S2 Pend. Mat Kelas C – 2016

    Dalam mengajarkan matematika kepada siswa, guru tidak seharusnya menutupi karakter siswanya dengan hanya menentukan benar atau salahnaya jawaban mereka. Apa yang harus guru lakukan sebenarnya haruslah leboih menekankan kepada prosesnya. Biarkan siswa untuk dapat mengekspresikan dirinya dalam belajar matematika selama apa yang dilakukan siswa tersebut memang benar-benar menunjang dirinya untuk lebih mengembangkan potensinya dalam bermatematika. Hasil akhir siswa juga penting,sebagai tolak ukur bagaimana proses yang telah dilakukan oleh siswa dalam menyelesaikan permasalahan matematika, tetapi tidak seharusnya guru hanya menjudge siswa ini benar dan itu salah, hal itu akan menimbulkan siswa berpikiran sempit tidak terbuka terhadapa segala kemungkinan-kemungkinan yang harusnya dapat mgereka pelajari

  17. Alfiramita Hertanti
    S2- Pendidikan Matematika kelas A 2017

    Assalamualaikum wr.wb
    The post above talks about mathematics learning, in learning one's mathematics factors (environment, culture, teachers, absorption, etc.). The most important factor in learning mathematics is the teacher, because the teacher is responsible for the smoothness of the learning process, in this case mental, emotional, moral and spiritual, and creativity of students.

  18. Dimas Candra Saputra, S.Pd.
    PPs PMA 2017

    Assalamualaikum prof,
    Kemampuan matematika siswa dapat dikembangkan melalui pembelajaran yang sesuai. Pembelajaran yang dapat benar-benar membelajarkan siswa ialah pembelajaran yang berdasarkan pada pandangan konstruktivisme sosial. Pembelajaran matematika dalam pandangan tersebut merupakan kreativitas atau proses berfikir. Kemampuan matematika dapat berkembang baik melalui aktivitas sosial siswa di dalam pembelajaran. Maka panting bagi siswa untuk dapat terlibat aktif di dalam pembelajaran melalui diskusi kelompok. Di dalam diskusi tersebut, siswa dengan masing-masing kemampuannya saling bekerja sama membangun pengetahuannya. Kegiatan ini biasa disebut sebagai kolaborasi.

  19. I Nyoman Indhi Wiradika
    PEP B

    Kemampuan dasar matematik sangat dipengaruhi oleh bagaimana cara siswa mengenal matematika. Apakah dengan cara yang rumit atau dengan cara yang konstruk. Pada penerapannya matematika bagi siswa yang diterapkan oleh guru kerap abai dengan proses bagaimana cara siswa mengkonstruk pemikiran mereka. Saya sangat sependapat dengan pernyataan Pak Marsigit terkait soal 6x7 para ahli selalu mengharapkan hasil 42 bukan pada bagaimana perjuangan siswa menggapai hasil tersebut.

  20. Latifah Pertamawati
    S2 PM B

    I would like to share my opinion regarding this matter sir, why I think people basic maths skill are weak.

    Well, it has been known that mathematical skill is identical with solving problems. If it is delivered correctly, the pattern of solving problems in mathematics can help us solve different problems in other fields or even in our daily life. Thus, in my opinion, mathematical skill is said to be weak if someone couldn't apply what he/ she has gotten while studying mathematics and while solving the problems in his/ her mathematical activities. The failure of him/ her is caused by (perhaps) the weak grasp of concept in the beginning of learning mathematics (in her childhood, perhaps). In order to overcome this problem, we, as a (future) teacher and educator, must understand that students can't learn mathematics simultaneously. We have to motivate them, we need to deliver the concept first until the students understand clearly what they are going to learn so that they feel safe in learning mathematics. It doesn't matter whether some students are slower at learning mathematics (compared to their friends), as long as they understands the concept first, I think it is better than directly giving formulas to them. After they understand the concept, it is time to give the definition and engage the students in finding what (general) formulas that can be applied for the concept.

    The most important thing is applying the process of solving mathematical problems in the future; how the students solve the problems, how enthusiastic they are and how much they are willing to solve that problem.

  21. Nama : Habibullah
    NIM : 17709251030
    Kelas : PM B (S2)

    Assalamualaikum wr.wb

    In my opinion, one's mathematical ability is generally the same. which distinguishes it is the type of keceradasan that everyone has or in this case is the student. intelligence is divided into two namely intuitive and reflective intelligence. Intelligence is the intelligence of spontaneity means that students understand a problem without having to learn a problem. while reflective intelligence is the intelligence in understanding a problem but must first go through the process of learning first. besides the difference in the intelligence of the teacher's role in inculcating mathematical concepts is also very influential, because most teachers only transfer knowledge alone, so it does not pay much attention to cognitive students, whether the concept of mathematics can really be understood or vice versa. then the teacher must follow every development of students in the classroom so that the mathematical foundations of students can be formed with a solid.

  22. Nama: Hendrawansyah
    NIM: 17701251030
    S2 PEP 2017 Kelas B

    Assalamualaikum wr wb.

    Yang menyebabkan kemampuan dasar matematika anak lemah karena guru lebih menekankan pada penilaian bukan pada sebuah proses.Mangabaikan atau melupakan bagaimana mengkonstrukifkan pemahaman siwa merupakan suatu tindakan yang dapat melumpuhkan perkembangan matematika anak.Anak- anak harus telibat aktif dan bukan menjadi pendengar yang setia.Guru memiliki peran untuk memberikan kesempatan kepada anak untuk bertanya serta bagaiamana siswa dapat menemukan dunianya sendiri dengan tidak memaksa siswanya sehingga anak-anak merasa senang dan nyaman terhadap pembelajaran matematika.

  23. Anisa Safitri

    Mindset atau pola pikir adalah hal penting dalam kehidupan. Tidak terlepas pula, mindset matematika. Banyak yang mengatakan matematika itu sulit dan pada akhirnya membuat malas untuk mempelajari matematika. Padahal mindset berperan penting dalam mempelajari sesuatu.Sehingga pola pikir tersebut harus diubah agar ke depannya dapat berproses dan belajar dengan lebih baik. Pola pikir atau sudut pandang serta minset perlu diubah jika ingin meruah suaru peradaban atau suatu keadaan. genaerasi yang selalu birfikir tentang suatu perubahan yang baik adalah generasi yang diharapkan di kondisi yang saat ini melanda generasi sekarang yang mencari jalan cepat, perjuangan dan daya juang yang mulai turun harus segera di ubah.

  24. Junianto
    PM C

    Terkadang karena tuntutan kurikulum dan nilai yang bagus, siswa diajarkan metode hafalan karena diaggap lebih cepat untuk menyelesaikan soal/ permasalahan. Hal ini membuat siswa sekedar hafal saja tanpa memahami materi yang dipelajari sehingga pembelajaran menjadi tidak bermakna di benak siswa. Selain itu, tuntutan bagi siswa juga terlalu banyak, sehingga mereka tidak bisa fokus kepada satu hal. Kalau dalam matematika, materi yang diberikan terlalu melebar tetapi kurang mendalam.

  25. Shelly Lubis
    S2 P.Mat B

    indeed what pure mathematicians mean about mathematics, may be limited to the scope of fellow scientists, or the scope of the college. because they also had studied mathematics in school, of course they understand. so the point depends on the scope they are referring to

  26. Nur Dwi Laili Kurniawati
    PPs Pendidikan Matematika C

    Pendidikan di Indonesia selama ini merupakan ambisi orang dewasa. Hal ini membuat anak-anak lebih terbuasa dengan persaingan dibandingkan kolaborasi. Hal ini dapat kita lihat dari adanya sistem ranking, sekolah internasional, kelas internasional, yang menjadikan siswa saling bersaing untuk mencapainya. Dan kebiasaan ini terbawa hingga mereka dewasa dan bekerja. Mereka menjadi merasa bersaing dengan rekan kerjanya dibandingkan bekerja sama, mereka malah saling menjegal antar rekannya. Hal ini lah yang perlu diperbaiki, yakni bagaimana membuat pendidikan bukanlah ajang persaingan tetapi menajadi tempat untuk berkolaborasi sesuai bakat siswa masing- masing karena setiap siswa adalah unik dan memiliki kelebihan masing-masing.

  27. Arung Mega Ratna
    PPs PMC 2017

    Saya tidak berfikir bahwasanya orang yang berfikir sederhana adalah lemah akan tetapi sebaliknya berfikir seperti itu justru malah meningkatkan kualitas berfikir matematika yang akan dijalaninya.

  28. Gina Sasmita Pratama
    S2 P.Mat A 2017

    One of the causes of students' weak mathematical abilities is that mathematics is taught by rote and repetition, not understanding and logic. It often happens that students are able to solve problems very similar to those taught in the classroom, but once the layout changes, they can not see a pattern, or the fact that they need to apply the same concept in different forms. Whereas it should be, mathematics is taught by conditioned that the student is an architect who builds his own knowledge. That way, mathematics is not just rote, it builds.

  29. Rahma Dewi Indrayanti
    PPS Pendidikan Matematika Kelas B

    Pelajaran matematika hingga saat ini masih memberikan data nilai yang rendah adalah suatu fenomena yang perlu terus kita gali penyebabnya. Mengapa matematika menjadi pelajaran yang mencetak nilai merah? Kita harus mengkaji dari berbagai macam sudut pandang. Kalau kita lihat dari sudut pandang metode pembelajaran yang dilakukan oleh guru di sekolah maka akan dapat di ambil kesimpulan bahwa sebagian besar guru melakukan pengajaran bukan pembelajaran. Mengapa pengajaran? Karena yang aktif dan mendominasi kelas adalah guru. Padahal pembelajaran yang baik adalah ketika siswa menjadi subyek utama dalam pembelajaran tersebut ( Student Center ).

  30. Gamarina Isti R
    Pendidkan Matematika Kelas B (Pascasarjana)

    Saya setuju dengan pernyataan bahwa hal yang idiot apabila belajar matematika tanpa memahami dan mementingkan proses. Hal ini masih sering ditemukan dalam pembelajaran matematika apalagi guru yang masih menerapkan teacher center. Alasan yang diberikan mereka adalah karena materi yang terlalu banyak sedangkan waktu yang diberikan untuk belajar sangat sedikit. Padahal pemahaman dan proses lebih penting dari pada sekedar menghafalkan. Saat siswa hanya sekedar menghafalkan maka akan ada kemungkinan dia akan lupa apabila hafalan tersebut jarang digunakan. Namun dengan adanya pemahaman dan proses siswa akan lebih mudah mengingat karena siswa memiliki pengalaman-pengalaman yang akan mengingatkan mereka.

  31. Putri Solekhah
    S2 Pend. Matematika A

    Assalamu'alaikum wr wb,

    Saya berpikir memang benar bahwa kemampuan matematika dasar masyarakat masih lemah. Bahkan kemampuan dasar guru matematikapun masih lemah. Seperti yang telah disampaikan oleh beberapa pendapat di atas bahwa materi pecahan masih sangat lemah. Pada penelitian yang saya baca di jurnal internasional mengemukakan beberapa guru sekolah dasar mengalami miskonsepsi terhadap pengertian dan penyelesaian masalah pecahan. Padahal dasar materi pecahan sangat penting bagi siswa, khususnya siswa sekolah dasar, karena ana terus digunakan hingga jenjang sekolah berikutnya. Hal tersebut menjadi seperti lingkaran setan yang berulang dari tahun ketahun hingga siswa akhirnya menjadi guru serta melaukan hal yang sama dan seterusnya.

  32. Arina Husna Zaini
    PEP S2 B
    Assalamualaikum Wr.Wb
    Permasalah yang tertuliskan dalam judul diatas “Why do you think people’s basic math skills are weak? “ Mungkin salah satunya disebabkan oleh apa yang disampaikan oleh Ginetta Nistoran bahwa pemebalajarn matematika masih berpusat pada menghafal dan formula rumus yang cenderung abstrak untuk ditelaan melalui pikiran. Walaupun diberikan soal pemecahan masalah, terkadang siswa bingung jika soal pemecahan masalah tersebut diubah dalam konteks yang berbenda tetapi pada intinya sama. Oleh karena itu, sebagai salah satu solusi mengatasi hal ini perlu ditekankan pada pembelajaran yang berpusat pada siswa dan mengkontekstualkan dalam kehidupan siswa. Terima Kasih

  33. Novita Ayu Dewanti
    S2 PMat C 2017

    Kemampuan matematika seseorng itu lemah bisa jadi disebabkan oleh banyak faktor. Bisa jadi dikarenakan faktor dari guru, sekolah, atau siswanya sendiri. untuk faktor dari siswa, bisa jadi dikarenakan siswa tersebu kurang akan pengetahuan awalnya mengenai kemapuan matematika dasarnya, sedangkan untuk kemampuan guru yang menjadi penghambat adalah, kurangnya kompetensi guru akan apa yang menjadi tanggung jawabnya. Guru kurang memahami konsep matematika.

  34. Isoka Amanah Kurnia
    PPs Pendidikan Matematika 2017 Kelas C

    This may be caused by various factors. In addition to being influenced by genetic and environmental factors, the child's experience may also affect their abilities. Another reason that leads to basic mathematics skills of students is weak due to the learning of mathematics that is usually taught by memorizing and repetition practice questions. Students are only able to solve problems that are similar to the example of the questions taught in the classroom, but after a change of structure questions most students are unable to solve them. This happens because they do not understand the real concept and only work in the order of steps based on the examples of problems.

  35. Nama: Dian Andarwati
    NIM: 17709251063
    Kelas: Pendidikan Matematika (S2) Kelas C

    Assalamu’alaikum. tema yang diambil dalam diskusi di atas ialah mengapa dasar ketrampilan matematika siswa itu lemah. Siswa berada di lingkungannya lebih lama dari pada di sekolah. Di lingkungan siswa mengalami berbagai permasalahan yang melibatkan matematika, maka untuk mempeajari matematika hendaknya melibatkan permasalahan-permasalahan di sekitar siswa. Dengan begitu siswa akan merasa tertantang untuk belajar.

  36. Metia Novianti
    PPs P.Mat A

    Ada beberapa faktor yang mempengaruhi kemampuan basic matematika seseorang, entah itu internal ataupun eksternal. Faktor internalnya berupa hal-hal yang berasal dari dalam dirinya sendiri, seperti kemampuan dalam dirinya sendiri, motivasi, intelegensi dan seterusnya. Faktor eksternal adalah yang berasal dari luar dirinya, seperti lingkungan atau sekolah. Proses pembelajaran di sekolah dapat menjadi salah satu faktor yang mempengaruhi kemampuan matematis siswa. Dengan pembelajaran yang baik dan sesuai, siswa dapat mengembangkan kemampuannya dengan baik. Sebaliknya, apabila pembelajaran yang dilakukan kurang baik dan tidak bermakna bagi siswa, kemampuannya akan sulit untuk berkembang.

  37. This comment has been removed by the author.

  38. Nama: Dian Andarwati
    NIM: 17709251063
    Kelas: Pendidikan Matematika (S2) Kelas C

    Assalamu’alaikum. pengetahuan matematika seseorang rendah salah satu kemungkinan penyebabnya karena matematika diajarkan dengan langsung memebrikan rumus dan abstraksi. Matematika tidak diajarkan dengan hal-hal realistik yang dekat dengan siswa. Matematika cenderung diiingat bukan dipahami. Hal-hal tersebut dapat menyebabkan pengetahuan dasar matematika siswa rendah.

  39. Ramayanti Agustianingsih
    PPs PMat C 2017

    Assalamualaikum, wr.wb.
    Kemampuan dasar matematika siswa masih lemah disebabkan oleh penanaman konsep mengenai kemampuan dasar tersebut di SD tidak kuat. Pembelajaran hanya dibasiskan pada menghapal agar bisa mengingatnya saja, padahal ingatan manusia itu terbatas, lama kelamaan pun akan menghilang. Oleh karena itu dalam pbm yang diutamakan tidak boleh hasilnya namun prosesnya. Proses siswa menemukan serta membangun kemampuan dasar tersebut.
    Wassalamualaikum, wr.wb.

  40. Pbm pada siswa jika hanya berdasarkan hapalan maka tidak akan berarti. Karena pbm seperti hanyalah ambisi guru atau orang dewasa yaitu ambisi agar siswa-siswanya hapal akan perkalian, kemudian materi yang diajarkan cepat selesai. Padahal jika siswa belajar hanya melalui hapalan, maka siswa akan menemukan kesulitan dalam menyelesaikan soal baru, yang berbeda dengan yang ia hapalkan.

  41. Fitri Ni'matul Maslahah
    PPs PM C

    mengukur peningkatan atau sekedar pencapaian siswa dalam matematika secara leksiklal mungkin lebih mudah dibandingkan dengan mengukur performa siswa secara kontekstual. Hal ini dikarenakan dalam pembelajaran kontekstual disyaratkan adanya pembelajaran dengan penilaian yang otentik yakni penilaian yang bernar-benar mengukur keadaan siswa, sedngkan kita tahu hal tersebut sangatlah sulit dilakukan. Wallahu a'lam

  42. Fitri Ni'matul Maslahah
    PPs PM C

    Terlepas dari penilaian siswa yang harus benar-benar mencerminkan kadaan siswa, penilaian dalam pembelajaran dapat disiasati guru dengan melakukan kegiatan pengukuran atau penilaian menggunakan lebih dari satu teknik, seperti pengukuran atau penilaian siswa dilakukan dengan observasi dan penilaian rekan sebaya, sehingga data penilaian yang diperoleh akan lebih mencerminkan keadaan siswa yang sebenarnya. Wallahu a'lam

  43. Aristiawan
    S2 PEP 2017 B

    Banyak alasan atau factor yang membuat kemampuan siswa atau seseorang dipandang lemah atau siswa mengalami kesulitan dalam belajar matematika. Factor atau alasan tersebut sudah diulas dalam diskusi panjang diatas. Hanya saja, kita perlu menggaris bawahi bahwa kecerdasan matematika hanyalah satu dari sekian banyak kecerdasan. Bila seorang siswa tidak unggul dalam matematika, atau bahkan mengalami kesulitan di bidang matematika, mungkin dia memang bukan ahlinya disitu dan dia memiliki kecerdasan di bidang lain seperti music atau mungkin olahraga.

  44. Alman Kresna Aji
    S1 Pendidikan Matematika 2015
    Dari pandangan saya, ada beberapa faktor yang mungkin mempengaruhi kemampuan basik matematika yang dimiliki oleh peserta didik. Entah itu faktor eksternal maupun internal. Selain didasarkan pada kemampuan individu, cara guru dalam memfasilitasi siswa pun menjadi tolak ukur terkait penguasaan basik matematika yang baik. Bagaimana metode yang diajarkan dan bagaimana kegiatan pembelajaran dilaskanakan sekiranya perlu dikembangkan dan senantiasa di evaluasi supaya penguasaan basik matematika siswa bisa lebih baik lagi, serta ilmu yang didapatkan oleh siswa mampu mencerminkan sifat-sifat serta apa yang sebenarnya ingin diraih dalam pembelajaran matematika, misalkan dalam matematika tidak hanya mengedepankan jawaban melainkan juga proses dalam mendapatkan jawaban tersebut.

  45. Norma Galih Sumadi
    S1 Pendidikan Matematika I 2015

    Menurut pandangan saya, ada banyak sekali faktor yang menyebabkan kemampuan dasar matematika seseorang dikatakan rendah, baik itu faktor internal maupun eksternal. Faktor-faktor internal seperti gen maupun IQ memang faktor yang sudah menjadi bawaan seseorang sejak lahir. Selain itu faktor-faktor eksternal seperti pembelajaran yang diterimanya baik dalam lingkungan keluarga maupun pendidikan formal juga berpengaruh besar dalam menentukan kemampuan dasar matematika seseorang. Oleh karena itu, disinilah peran guru untuk memfasilitasi siswa dalam pembelajaran agar dapat mengembangkan kemampuan dasar matematika dari sedini mungkin.