Oct 6, 2013

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

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Group: Math, Math Education, Math Culture

 Marsigit Dr MAOutside 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
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 WintersIs 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 NistoranI'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 MAThe 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
Marsigit Dr MAOur further perceptions on how to educate (mathematics) can be read at the following:http://www.whohub.com/drmarsigitma

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 GalinaitisAgree 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 NorthridgeI 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 PattersonI 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, MBAMy 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@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.

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.

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 MillsYes 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-SmithThe 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 DiVitoArgh. 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 MAArt 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.OCTWe 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 GalinaitisPeople 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 FreyBecause 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 MAThank Elias Gourtsoyannis for the information

Elias GourtsoyannisΔεαρ Marsigit. You can call me Elias!

Behnaz Herbst, MSc.OCTElias, 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-SmithArt, 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-SmithArt, 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 "....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.

Marsigit Dr MAMarsigit 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. Hajarul Masi Hanifatur Rohman
    S2 Pendidikan Matematika C 2016

    Menurut saya, kemampuan dasar matematika seseorang itu lemah karena pembentukan konsep mereka sejak kecil kurang baik dan benar. Kita semua mengetahui bahwa matematika itu full konsep dan skema. Ketika salah satu konsep tidak dipahami betul oleh anak, maka skema yang terbentuk akan cacat atau rusak. Sehingga agar kemampuan dasar kuat, maka yang harus diperhatikan adalah bagaimana cara membentuk konsep pada anak dengan baik dan benar. Konsep terbentuk dalam benak anak melalui beberapa tahapan. Pertama yakni abstraksi dan klasifikasi, kedua penamaan dan pendefinisian, dan ketiga pengkomunikasian. Di samping itu, dalam pembentukan konsep, siswa juga memerlukan bantuan atau scaffolding sebagaimana dalam teori belajar Vigotsky. Matematika sekolah juga mengedepankan interaksi sosial dalam pembelajaran matematika untuk anak. Dengan memperhatikan hal-hal tersebut, guru dapat membantu anak dalam membentuk konsep matematika yang benar, sehingga kemampuan dasar matematika anak tidak akan lemah.

  2. Ahmad Wafa Nizami
    PPs Pendidikan Matematika D 2016

    Assalamualaikum. Wr.Wb
    Mungkin karena kita memang mempunya basic yang lemah dalam hal konsep matematika itu juga dikarena bahwa pembelajarn waktu kita kecil itu hanya sepertiitu saja, guru yang menjelaskan tidak seperti sekarang sehingga kemmapuan konsep dna pemahaman konsep kita lemah. Maka dari itu kita sebagai guru apalagi yang mengajar di SD seharusnya siswa nya ditekankan pada pemehaman konsep yang kuat sehingga kedepannya konsep mereka dan kemampaun matematika mereka akan lebih baik.

  3. Syaifulloh Bakhri
    S2 Pendidikan Matematika C 2016

    Assalamu’alaikum wr.wb.
    Kemampuan seseorang itu ada yang berasal dari luar dan ada yang berasal dari dalam. Kemampuan yang berasal dari dalam karena faktor keturunan, sedangkan kemampuan dari luar berasal dari alam. Kemampuan matematika seseorang dimulai sejak dini dalam hal pembentukan konsep dan dasar/konsep yang dibentuk haruslah kuat. Jika tidak memiliki pondasi yang kuat, maka untuk membangun konsep baru diperlukan penguatan (scaffolding) pada konsep yang lemah yang sebelumnya telah ada. Matematika dengan segala kompleksitasnya harus dipahami meski paham saja tidaklah cukup. Oleh karena itu, membentuk konsep itu adalah penting dalam hal belajar karena konsep baru dibangun atas konsep-konsep yang telah ada sebelumnya.

  4. Syahlan Romadon
    PM C 2016 / 16709251047

    Matematika adalah aktivitas. Ketika seorang guru memegang teguh prinsip tersebut maka guru tidak akan memberikan matematikanya terhadap siswa. Guru tersebut akan menjadi fasilitator sedemikian sehingga siswa dapat mengkonstruksi matematikanya sendiri. Banyak siswa yang memiliki keterampilan dasar matematika yang rendah. Hal ini bisa disebabkan oleh guru tidak memfasilitasi siswa namun malah memberikan matematika kepada siswa sehingga siswa hanya menghafal materi matematika tanpa memahaminya. Oleh karena itu, seorang guru seharusnya tidak hanya fokus pada hasil belajar namun juga pada proses pembelajaran agar siswa dapat mengkonstruksi matematikanya sendiri. Selain itu, menurut saya, guru perlu memberikan pengalaman sukses agar siswa menjadi lebih percaya diri pada kemampuan matematikanya. Dengan pengalaman sukses, siswa akan lebih tertarik kepada matematika sehingga siswa mau berusaha untuk membangun matematikanya.

  5. Sylviyani Hardiarti
    S2 Pendidikan Matematika Kelas D 2016

    Seorang guru tidak hanya harus mngutamakan bagaimana mengajar siswa, namun bagaimana agar siswa mau belajar matematika. Dengan kata lain siswa belajar matematika karena keinginannya sendiri dan karena ia mengetahui peran penting matematika untuk kehidupannya. Oleh karena itu, seorang guru dituntut untuk mampu menciptakan pembelajaran yang menyenangkan, bermakna dan mampu memfasilitasi siswa membangun pengetahuannya. Di sini peran guru dalam menggunakan metode, sumber, media dan interaksi pembelajaran yang bervariasi dan menyenangkan sangat diperlukan bagi siswa. Sebab, pada dasarnya setiap siswa berbeda kemampuannya dalam belajar. Lalu mengapa kemampuan matematika seseorang bisa lemah ? Ada banyak faktor yang mempengaruhi kemampuan matematika seseorang. Salah satu alasannya karena ia tidak memahami konsep matematika yang telah ia pelajari, ia tidak belajar matematika dengan membangun sendiri pengetahuannya, atau bisa dikatakan pembelajaran matematika yang ia dapatkan hanyalah suatu kegiatan menghafal rumus tanpa pembentukan pemahamannya tentang konsep tersebut.

  6. Heni Lilia Dewi
    PPS Pendidikan Matematika Kelas C 2016

    Lemahnya kemampuan dasar matematika seseorang lemah disebabkan oleh beberapa faktor. Kasus ini juga terjadi dalam elegi di blog ini ketika seorang anak kelas 4 SD belum memahami konsep dasar perkalian. Menjadi sangat miris jika hal seperti ini terus terjadisehingga kelanjutan materi oleh siswa tidak berjalan dengan baik. SOlusi yang perlu dilakukan yaitu pembelajaran matematika misalnya tidak dimulai dari definisi atau rumus. Siswa harus dilibatkan dalam proses konstruksi konsep sehingga pemahaman lebih mendalam. Selain itu siswa juga harus berinteraksi dengan cara diskusi sehingga kemampuan komunikasi dan koneksi matematika nya berkembang.

  7. Annisa Hasanah
    PPs Pendidikan Matematika C 2016

    @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.
    Karena belajar matematika mencakup bagaimana siswa bisa menerima pembelajaran matematika, dan itulah tujuan pembelajaran. Sedangkan jika kita focus dgn bagaimana mengajar matematika kita seolah mengabaikan siswa yang menerima, mungkin saja siswa masih belum bisa walaupun pemberi materi sudah sangat ahli.

  8. Rahayu Pratiwi
    PPS PM-D 2016
    Practice is key and I find that my hardest working students (not necessarily the most brilliant ones) are the most successful.
    Dari pernyataan yang dikemukakan oleh Susan Northidge dapat dipahami bahwa dalam bermatematika perlu praktik, aktivitas maka ia akan dapat dikatakan paling sukses. Hal ini karena ilmu perlu diterapkan dan digunakan dalam kegiatan yang sebenar-benarnya.

  9. Ratih Eka Safitri
    PPs Pendidikan Matematika C 2016

    Setiap orang memiliki kemampuan belajar matematika yang berbeda, tergantung gaya belajar yang mereka sepakati masing-masing. kemampuan dasar matematika seseorang akan lemah jika belajar dengan metode konvensional, hanya menerima tanpa ada pengembangan akan konsep-konsep yang di berikan. Lemahnya kemampuan matematika juga disebabkan karena siswa menggunakan sistem menghafal dalam belajar, matematika adalah ilmu melakukan jadi tidak bisa jika dihafalkan.

  10. Saepul Watan
    S2 P.Mat Kelas C 2016

    Bismilahir rahmaanir rahiim..
    Assalamualaikum wr..wb...

    Mengapa dasar matematika lemah? Ada yang mengatakan hal ini disebabkan dengan adanya berbagai fakor yang dapat dipengaruhi oleh pikiran siswa itu sendiri. 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 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. Penyebab lain yang menjadi alasan mengapa keterampilan matematika dasar matematika lemah yaitu karena biasanya matematika diajarkan dengan cara menghafal dan pengulangan mekanis, bukan pemahaman mekanik dan logika.

  11. Listia Palupi Wisnu Aji
    S1 Pendidikan Matematika I 2014

    Kemampuan matematika dasar siswa yang masih lemah bisa juga dikarenakan kurangnya berlatih soal secara mandiri. Padahal berlatih soal-soal secara mandiri dapat membantu meningkatan daya kreativitas, membangun pengalaman belajar, dan meningkatkan pemahaman siswa terhadap konsep matematika.

  12. Listia Palupi Wisnu Aji
    S1 Pendidikan Matematika I 2014

    Kemampuan matematika dasar masih lemah karena mereka belum menguasai konsep dengan benar sehingga terkadang bisa salah pemahaman ketika menyelesaikan suatu permasalahan. Hal tersebut bisa saja terjadi ketika seorang guru di sekolah kurang memperhatikan peserta didiknya, mereka hanya mengejar materi tanpa memberi kesempatan bagi peserta didik untuk bertanya.

  13. 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. 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.

  14. Desy Dwi Frimadani
    PPs Pendidikan Matematika Kelas C 2016

    Lemhanya kemampuan dasar matematika seorang siswa dalampembelajaran disebabkan beberapa faktor. Faktor pertama dari siswa sendiri, faktor dari guru yang bersangkutan dalam pembelajaran, atau faktor lingkungannya. Misalnya faktor yang berasal dari guru, guru belum dapat membantu siswa mengkonstruksi pengetahuan siswa dengan baik. Mungkin guru hanya memberikan siswa rumus dan meminta menghafalkannya, tidak membantu siswa dalam mengkonstruksi konsep untuk memperoleh pengetahuan yang baru.

  15. Operasi aritematika tentang bilangan negatif dan pecahan yang belum dipahami dan tidak dikuasai maka materi selanjutnya akan sulit untuk dipahami. Materi aljabar yang harus kuat aritmetikanya menjadi gagal untuk dikuasai kemudian kalkulus dan materi lainnya. Menurut hemat saya maka dasar aritmetikanya harus dikuasai atau diperbaiki agar dapat menguasai materi berikutnya. Dalam setiap kesempatan ketika pembelajaran disetiap jenjang perlu diberi penguatan tentang dasar aritemetika. Pembelajaran dasar aritmetika diselipkan dalam pembelajaran pada materi apapun.

    S1 Pendidikan Matematika I 2014

    Lemahnya kemampuan dasar matematika siswa bisa dikarenakan pemahaman siswa terhadap materi masih kurang, materi itu berkelanjutan dan berkesinambungan , sehingga pada setiap materi perlu diperkuat kembali pemahaman siswa sebagai bekal untuk mempelajari materi berikutnya.

  17. Eka Dina Kamalina
    S1 Pendidikan Matematika A 2014

    Lemahnya kemampuan dasar matematika anak disebabkan oleh kurangnya penanaman konsep sejak dini. Sejak anak mulai belajar matematika, konsep dasar dalam matematika kurang begitu ditanamkan sehingga dalam materi yang lebih tinggi, anakpun kurang paham dengan konsep penyusunnya.

  18. Loviga Denny Pratama
    S2 P.Mat D

    Dari sini saya memperoleh pemahaman bahwa pengajaran Matematika tidak berbeda dengan pengajaran menggambar, melukis, atau memahat. Ini adalah salah satu dari 'tujuh seni liberal' era Helenistik. Terutama pada ujian dan penilaian. Penilaian pada matematika bisa melalui lisan dan bisa juga melalui Portofolio. Selain itu agar siswa antusias dalam mendapatkan nilai, guru berhak memberikan stimulus bagi siswa. di artikel ini menyarankan dengan pujian yang paling berharga adalah persetujuan antusias dari teman sebayanya.

  19. Ahmad Bahauddin
    PPs P.Mat C 2016

    Assalamualaikum warohmatullahi wabarokatuh.
    Menurut saya kemampuan dasar matematika adalah logika dan bahasa. Setiap orang punya intensitas yang berbeda kemampuan tersebut. Adapun kemampuan dasar matematika yang lemah, itu dikarenakan yang bersangkutan tidak mengerti bahasa dan logika matematika. Seorang anak mungkin ada yang cenderung lambat apabila disuruh menjumlahkan 48 dan 9. Namun apabila dia disuruh menghitung total uang 48 ribu dan 9 ribu, anak tersebut dapat dengan cepat mengetahui jumlahnya. Kenapa seperti itu? Karena di dalam benak anak, bahasa uang dan bahasa matematika berbeda. Bahasa matematika masih sangat umum, sedangkan bahasa uang ada properties khusus. Seperti satuan seribu, 2 ribu, 5 ribu, 10rb, dan 50rb. Sehingga apabila ditanya jumlah 48 ribu dan 9 ribu, anak bisa dengan cepat menjumlahkannya. 48 ribu, adalah 50 ribu kurang 2 ribu, sedangkan 9 ribu adalah 10 ribu kurang seribu. Sehingga apabila dijumlahkan pasti jumlahnya adalah 60 ribu kurang 3 ribu. Padahal hal ini juga bisa dipraktekkan ke dalam penjumlahan 48 dan 9 tadi. Hanya saja, anak belum terbiasa dengan bahasa matematika dan tidak ada properties satuan seperti pada uang. Berbeda dengan uang.

  20. Resvita Febrima
    P-Mat D 2016
    Matematika sekolah mempunyai peranan yang sangat penting baik bagi siswa. Adapun fungsinya adalah sebagai media atau sarana siswa dalam mencapai kompetensi. Dengan mempelajari materi matematika diharapkan siswa akan dapat menguasai seperangkat kompetensi yang telah ditetapkan. Oleh karena itu, penguasaan materi matematika bukanlah tujuan akhir dari pembelajaran matematika, akan tetapi penguasaan materi matematika hanyalah jalan mencapai penguasaan kompetensi. Fungsi lain mata pelajaran matematika sebagai: alat, pola pikir, dan ilmu atau pengetahuan. Dengan mengetahui fungsi-fungsi matematika tersebut diharapkan kita sebagai guru atau pengelola pendidikan matematika dapat memahami adanya hubungan antara matematika dengan berbagai ilmu lain atau kehidupan. Sebagai tindaklanjutnya sangat diharapkan agar para siswa diberikan penjelasan untuk melihat berbagai contoh penggunaan matematika sebagai alat untuk memecahkan masalah dalam mata pelajaran lain, dalam kehidupan kerja atau dalam kehidupan sehari-hari. Namun tentunya harus disesuaikan dengan tingkat perkembangan siswa, sehingga diharapkan dapat membantu proses pembelajaran matematika di sekolah.

  21. Primaningtyas Nur Arifah
    Pend. Matematika S2 kelas C 2016
    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.

  22. Tahtalia
    S1 Pendidikan Matematika A 2014
    Kebanyakan dari siswa yang memiliki kemampuan matematika rendah merasa bahwa matematika itu sulit, bikin pusing, terlalu banyak rumus, tidak aplikatif dalam kehidupan sehari-hari, dan hal-hal negatif lainnya. Oleh karena itu, diperlukan pendidik yang mampu mengubah pemikiran negatif mereka menjadi sebuah pandangan positif sehingga mereka dapat belajar dengan menyenangkan. Dengan demikian kemampuan matematika mereka akan meningkat.

  23. 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.

  24. Hening Carrysa
    S1 Pendidikan Matematika A 2014

    Faktor lain yang menjadikan Kemampuan dasar matematika siswa lemah adalah dari metode/strategi/model pembelajaran yang digunakan guru dalam proses pembelejaran matematika dikelas. karena jika guru tidak mengunakan berbagai metode/strategi/model pembelajaran tidak dapat mengembangan potensi-potensi siswa yang setiap individu memiliki ciri khas masing masing dalam proses belajarnya.

  25. Wahyu Berti Rahmantiwi
    PPs Pendidikan Matematika Kelas C 2016

    Kendala yang terjadi ketika siswa tidak memahami konsep sebelumnya merupakan permasalahan yang serius karena banyak siswa yang motivasinya kurang kuat sehingga ia sudah tidak mau belajar lagi ketika materi awal merasa tertinggal. Tetapi ini tidak terjadi pada semua siswa hanya beberapa siswa saja. Sebagai guru kita harus benar-benar menerapkan proses dan hasil belajar siswa bukan hanya pada hasil. Karea melakukan hal yang sedikit tetapi secara berkesinambungan itu lebih ringan daripada melaksanakan pekerjaan yang berat dan itu hanya sekali. Guru harus menghindari pemberian konsep di awal pembelajaran karena hanya akan membuat siswa menjadi penghafal bukan pembelajar.

  26. Hening Carrysa
    S1 Pendidikan Matematika A 2014

    Faktor yang menjadikan kemampuan dasar matematika siswa rendah adalah penerapan pembelajaran yang hanya pemberian rumus dan menghafal rumus, terutama ketika jenjang pendidikan SD. Pada masa itu, anak sedang membentuk konsep matematika. Untuk itu pembelajarn ketika di SD harus mengedepankan pembelajaran yang bermakna bagi siswa agar terbentuk kemampuan dasar yang mumpuni untuk jenjang pendidikan selanjutnya.

    16709251056_PMC 2016
    Pendidikan Matematika-S2

    Pendapat saya, orang-orang yang menganut matematika murni itu lebih kepada matematikanya, dan jika mereka diminta untuk mengajar, tentu pembelajaran yang terjadi adalah pembelajaran tradisional. Mereka akan fokus pada penemuan hasil daripada proses penanaman konsep.

  28. Luki Slamet Purwoko
    S1 Pendidikan Matematika I 2014

    Di Indonessia sendiri menurut saya basic mathnya kurang bagus atau disini kurang kuat. Pandangan tentang pendidikan dipandang dari hasilk nya saja. Sehingga matematika pun terkena dampaknya yaitu lebih mementingkan hasil. Padahal matematika itu lebih keprosesnya unutk menciptakan pola pikir mnatematis yang terstruktur. Lain hal pemikiran bahwa matematika hanyalah tentang menghafal rumus sehingga pengetahuan tentang pembuktian rumus yang merupakan basic mathe yang penting yaitu pembuktian terhilangkan oleh anggapan tersebut.

  29. Hyldha Wafda Mufida
    S1 Pendidikan Matematika A 2014

    Defiisi pengetahuan sangat beragam. Ilmu pengetahuan juga dapat dicapai melalui beragam cara. Dapat berupa kreativitas, proses berpikir, ataupun kegiatan sosial. Pada saat pembelajaran, siswa biasanya dilatih untuk membuat kelompok diskusi untuk mempermudah penyampaian ilmu pengetahuan, selain itu juga untuk variasi metode pembelajaran.

    S1 Pendidikan Matematika 2014

    Lemahnya kemapuan matematika yang dimiliki siswa dapat disebabkan karena kurangnya inovasi pembelajaran, dahulu sebelum k13 ini muncul pembelajaran cenderung berpusat pada guru, siswa hanya mendengarkan dan menghafalkan rumus tanpa diketahui konsep nya , itu yang saya alami dulu waktu saya masih sekolah SMP dan SMA, jadi disekolah itu orientasinya pada hasil nilainya, padahal tanpa diketahui beberapa siswa cenderung melakukan perbuatan kecurangan untuk mendapatkan hasil nilai yang bagus, itu akibatnya jika pembelajaran hanya berorientasi pada nilai, sebaiknya pembelajaran itu berorientasi pada proses, proeses dimana siswa dapat mengkonstruk pengetahuannya sendiri. Proses dimana siswa mendapatkan pemahamannya, dimana paham itu menajadi salah satu tujuan pendidikan , menajadikan siswa paham mengenai konsep matematis nya.

    S1 Pendidikan Matematika 2014

    Kemampuan basic dalam matematika itu sangat penting, karena basic itu adalah modal awal untuk mempelajari materi materi selanjutnya, kita ketahui bahwa materi matematika sangat berkaitan satu sama lain, sehingga basic itu sanagt penting, maka dari itu pembelajaran waktu SD harus benar benar memahamkan siswa, seperti operasi hitung dll. Karena jika basic nya belum dapat maka siswa akan sangat kesulitan dalam mempelajari materi materi selanjutnya. Kemudian juga jika kemampuan dasar nya sudah baik maka intuisi siswa juga akan bagus, dan intuisi ini sangat diperlukan dalam penyelesaian masalah. Intuisi bisa dikatakan hipotesis awal siswa dan ini dapat membantu siswa dalam menyelesaiakan masalah yang ada.

  32. Yuni Astuti
    S1 Pendidikan Matematika A 2014
    Matematika memang ilmu pengetahuan yang sulit dipelajari hampir semua orang. Namun bagi orang yang menyukai atau bisa matematika, pasti tidak menganggap matematika itu sulit. Meskipun sulit tetap ada penyelesaiannya. kemampuan dasar dalam matematika sangat lah perlu khusunya untuk mempelajari materi-materi selanjutnya, karena beberapa materi matematika yang saling berhubungan.

  33. Ika Agustina Fitriani
    S1 Pendidikan Matematika I 2014

    Dasar mempelajari sesuatu adalah ketika kita sedang berada dalam proses pemkembangan. Disini siswa SD menempati posisi terpenting dalam membangun karakteristik dan minat belajar, termasuk dalam mempelajari matematika. Pembelajaran yang dirancang sedemikan rupa akan membuat siswa merasa nyaman dan senang dalam mempelajari matematia, sehingga materi dasar yang disampaikan pun akan mudah diterima oleh siswa

  34. 'Azzanie Karima Arroida
    S1 Pendidikan Matematika I 2014

    Kemampuan dasar matematika anak lemah? Ya, bagi sebagian besar orang memanglah seperti itu, hal itu dikarenakan tidak dibentuk sejak kecil. Sangat jarang orang tua akan menstimulus anak 1 tahun dengan angka-angka, yang dilakukan orang tua pertama kali adalah mengenalkannya dengan verbal. Anak diajari untuk memanggil kedua orang tuanya, diajari berbicara sedikit demi sedikit, baru ketika beranjak besar dikenalkan dengan angka. Maka dari itu, kemampuan dasar matematika itu lemah. Tetapi, jika terus diasah maka kemampuan tersebut akan meningkat, bahkan meningkat pesat.

  35. Nita Lathifah Islamiyah
    S1 Pendidikan Matematika A 2014

    Menurut saya kenapa matematika dasar yang dimiliki masih lemah? salah satunya adalah karena ketika usia anak atau SD, penanaman matematika dasar belum sepenuhnya ditanamkan secara baik. karena pada usia anak itu tidak hanya mengajarkan saja, tetapi juga harus melalui aktivitas sehingga siswa paham terhadap apa yang diajarkan.

  36. Assalamu’alaikum wr wb
    Dwi Kawuryani
    14301241049 (S1 Pendidikan Matematika I 2014)
    Membaca artikel tersebut saya jadi tertarik untuk mengutarakan kesulitan saya dalam matematika. Dalam matematika saya kesulitan mengutarakan aksioma-aksioma untuk membangun suatu pengetahuan baru, atau membuat pembuktian matematika secara sistematis. Seperti yang saya tau, hal itu menjadi sangat penting dalam proses bermatematika, sehingga say harus meingkatkan kemampuan saya dalam hal itu.
    Terima kasih.
    Wassalamu’alaikum wr wb

  37. Suci Renita Sari
    S1 Pendidikan Matematika I 2014

    Lemahnya kemampuan dasar seseorang dalam matematika disebabkan karena cara belajar ataupun proses pembelajaran yang kurang tepat. Pembelajaran dengan metode konvensional yang mengandalkan papan dan kapur tulis adalah salah satu metode yang kurang tepat diterapkan dalam rangka meningkatkan kemampuan dasar matematika. Matematika adalah sesuatu yang mudah dipahami ketika kita terbiasa. Artinya dengan kita membiasakan diri mempelajari, mendefinisikan, memahami model dan pola matematika, maka kita akan mempunyai kemampuan yang tinggi di bidang matematika.