Oct 6, 2013

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


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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
and:
http://www.whohub.com/marsigit
Thank's

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

William 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
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.

Thank

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

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

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
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
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
Marsigit Dr MAThank Elias Gourtsoyannis for the information
Elias Gourtsoyannis
Elias GourtsoyannisΔεαρ Marsigit. You can call me Elias!
Behnaz Herbst, MSc.OCT
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
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
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.
http://static02.linkedin.com/scds/common/u/img/icon/icon_no_photo_80x80.png
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
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
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
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
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
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
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
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
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 MA
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.

Thank's
Elias Gourtsoyannis
Elias Gourtsoyannis@Marsigit. Thank you for your kind comments.

A noted worker in the field of ancient mathematics is Serafina Cuomo. Her
main concern is to determine the self-image of ancient mathematicians from
the professional point of view. In other words, how did these ancient
mathematicians see themselves? As practical advisers, as
researchers-scholars, or what? Daily bills had still to be paid,
presumably!
A well known book of hers can be found in
http://www.amazon.com/Ancient-Mathematics-Sciences-Antiquity-Series/dp/0415164958
<http://www.amazon.com/Ancient-Mathematics-Sciences-Antiquity-Series/dp/0415164958>

She has also written on Pappus, the Alexandrian mathematician.


Yogyakarta, 25 Agustus 2012

34 comments:

  1. Rindang Maaris Aadzaar
    18709251024
    S2 Pendidikan Matematika 2018

    Assalamualaikum warahmatullahi wabarakatuh
    Menurut saya mengapa kemampuan matematika seseorang buruk adalah karena matematika seakan-akan berbentuk seperti tangga dimana setiap prinsip merupakan penguatan dari konsep-konsep yang ada. Matematika seperti suatu proses kehidupan dimana hal-hal yang mendasar harus bisa dipelajari terlebih dahulu sebelum ingin mempelajari hal yang lebih kompleks lagi.
    Wassalamualaikum warahmatullahi wabarakatuh

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  2. Dini Arrum Putri
    18709251003
    S2 P Math A 2018

    Matematika adalah suatu aspek pelajaran yang penting untuk diajarkan, oleh karenanya matematika sudah dibekali sejak sekolah dasar, namun nyatanya pada pembelajaran sekolah dasar masih banyak siswa yang belum memahami konsep dasar matematika itu sendiri, seharusnya dalam mengenalkan matematika seseorang perlu tahu bagaimana konsepnya, struktur serta pola-pola dalam matematika, tidak semata-mata hanya diberikan terus masalah dan diminta untuk menyelesaikannya. Pembelajaran pun juga perlu disuguhkan semenarik mungkin agar adanya minat belajar dalam diri anak karena persepsi matematika sendiri selalu dianggap sulit oleh mereka. Hal ini pula yang dapat menghambat seseorang gagal untuk membangun pengetahuannya trhdap matematika.

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  3. Diana Prastiwi
    18709251003
    S2 P Mat A 2018

    Lemah belajar matematika. Belajar matematika lemah karena siswa selama ini hanya belajar matematika saja hanya dengan mneghafal, tidak menemukan ide atau konsep matematika dalam diri mereka sehingga masalah yang akan menjadi buntu siswa dalam menjawabnya, tidah hanya itu dalam proses pendidikan sedang siswa membutuhkan bantuan dari guru yang sebagai fasilitator. Bantuan guru adalah menciptakan pembelajaran yang menarik dengan cara atau model tertentu sehingga siswa dalam diri mereka muncul motivasi untuk menambah matematika dan kemampuan mengkontruksikan konsep matematika, sehingga akan membekas dalam benak siswa. Prosesnya bukan lah proses yang mudah untuk guru.Untuk dapat memiliki pemahaman matematika yang baik, maka diperlukan latihan yang berulang, motedo dan trategi yang dipilih guru secara tepat.

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  4. This comment has been removed by the author.

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  5. Rosi anista
    18709251040
    S2 Pendidikan Matematika B

    Assalamualaikum wr wb
    Matematika dianggap sebagai pelajaran yang sulit karena para pelajar sudah menjudge bahwa matematika itu sulit dan rumit karena selalu berhubungan dengan angka, rumus dan hitung-menghitung. Mereka pun tidak berniat untuk mempelajarinya, kecuali karena tuntutan materi. Pemikiran awal seseorang yang seperti itu jelas akan memengaruhi terhadap penguasaan matematika seseorang karena sebelumnya sudah ada rasa takut tidak bisa memahami pelajaran matematika dan malas. Mereka sudah terlebih dahulu tidak tertarik dengan matematika sebelum mencobanya. Matematika dianggap sebagai pelajaran yang sulit karena para pelajar sudah menjudge bahwa matematika itu sulit dan rumit karena selalu berhubungan dengan angka, rumus dan hitung-menghitung. Mereka pun tidak berniat untuk mempelajarinya, kecuali karena tuntutan materi. Pemikiran awal seseorang yang seperti itu jelas akan memengaruhi terhadap penguasaan matematika seseorang karena sebelumnya sudah ada rasa takut tidak bisa memahami pelajaran matematika dan malas. Mereka sudah terlebih dahulu tidak tertarik dengan matematika sebelum mencobanya. Para guru juga harus memikirkan bagaimana cara mengajar yang menyenangkan dan mudah dipahami para pelajar. Para guru harus memikirkan bagaimana metode belajar yang bisa membuat setiap pelajar merasa senang dan menyukai guru tersebut.

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  6. Ibrohim Aji Kusuma
    18709251018
    S2 PMA 2018

    Seseorang lemah dalam belajar matematika jika matematika itu sendiri didefinisikan sebagai matematika formal dan abstrak. Akan berbeda tentunya jika matematika (learning dan teaching) didefinisikan sebagai creativity, process of thinking dan social activity. Setiap siswa pasti akan memiliki kemampuan matematika yang baik jika kita dapat mengimplementasikan yang demikian.

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  7. Bayuk Nusantara Kr.J.T
    18701261006
    PEP S3

    Saya sepakat bahwa persepsi terkadang tidak baik untuk siswa. Persepsi cenderung untuk memberikan judgement saja tanpa memikirkan bagaimana solusiny. Guru, sebaiknya tidak memberikan persepsi kepada siswa. Guru harus dalam posisi senetral mungkin sehingga lebih mudah untuk mencari solusi dari pada meberikan judgement terhadap siswa.

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  8. Aji Joko Budi Pramono
    PEP-S3-2018
    18701261003

    Pemahaman konsep merupakan unsur penting dalam belajar matematika di sekolah dasar. Penguasaan terhadap banyak konsep, memungkinkan seseorang dapat memecahkan masalah dengan lebih baik, sebab untuk memecahkan masalah perlu aturan-aturan, dan aturan-aturan tersebut didasarkan pada konsep-konsep yang dimiliki. Konsep adalah ide abstrak yang memungkinkan seseorang untuk dapat mengelompokkan objek atau kejadian dan menerangkan apakah objek atau kejadian itu merupakan contoh atau bukan contoh dari ide tersebut. Dalam pendekatan matematika realistik guru dipandang sebagai fasilitator, moderator, dan evaluator yang menciptakan situasi dan menyediakan kesempatan bagi siswa untuk menemukan kembali ide dan kosep matematika dengan cara mereka sendiri. Oleh karena itu, guru harus mampu menciptakan dan mengembangkan pengalaman belajar yang mendorong siswa untuk memiliki aktivitas baik untuk dirinya sendiri maupun bersama siswa lain.

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  9. SUHERMI
    18709251007
    S2 PENDIDIKAN MATEMATIKA A

    Bagaimana pembelajaran terbaik untuk matematika selalu diperbincangkan. Dimulai dari metode, bahan ajar, media selalu dilakukan perbaikan untuk menciptakan proses pembelajaran yang maksimal yang dapat meningkatkan hasil belajar siswa. Di Indonesia, pembelajaran matematika harus mengacu pada kurikulum yang sudah di tetapkan, dan guru dalam proses pembelajarannya harus mempertimbangkan kemampuan peserta didiknya.dan pembelajaran matematika yang baik, adalah ketika siswa dapat memahami konsep dari materi yang di sampaikan, sehingga pemahaman tersebut dapat digunakan menjadi bekal dalam memahami materi berikutnya.

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  10. Totok Victor Didik Saputro
    18709251002
    S2 Pendidikan Matematika A 2018

    Selamat sore Prof.
    Hal ini dapat terjadi karena matematika tidak dikenalkan secara menyeluruh sejak dini. Bagian umum dari matematika yang biasanya hanya dikenalkan pada usia dini. Selain itu, ketika diberikan materi matematika siswa ataupun guru tidak mengulang kembali apa yang sudah didapatkan. Alasan lainnya adalah siswa atau guru belum mampu mengaplikasikan pengetahuan matematika yang dimiliki dalam kehidupan sehari-hari. Hal ini diperlukan agar menciptakan pengalaman yang berkesan bagi pembelajar. Terima kasih.

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  11. Umi Arismawati
    18709251037
    S2 Pendidikan Matematika B 2018

    Assalamu'alaikum, wr, wb.
    Kemampuan matematika lemah karena siswa lebih ditekankan menghafal rumus daripada penanamkan konsepnya. Guru hanya memberikan rumus dan menerapkannya dalam persoalan sehingga dalam benak siswa kurang tertatam konsep dari materi tersebut.

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  12. Umi Arismawati
    18709251037
    S2 Pendidikan Matematika B 2018

    Assalamu'alaikum, wr, wb.
    Setiap siswa pada dasarnya memiliki kemampuan yang berbeda-beda. Ada yang memiliki kemampuan matematika tinggi ada juga yang memiliki kemampuan matematika yang lemah. Untuk itu hendaknya guru dapat memfasilitasi siswa dengan berbagai kemampuan. Memfasilitasi dapat dilakukan dengan berbagai hal salah satunya dengan memberikan berbagai pembelajaran yang bervariasi.

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  13. Fany Isti Bigo
    18709251020
    PMA PPs UNY 2018

    Tujuan utama dari belajar adalah memperoleh hal baru yang berguna untuk kelanjutan hidup ke depan. Begitu juga tujuan dalam mempelajari matematika. Namun tidak semua orang dapat memahami matematika dengan baik dikarenakan pengalaman dengan pembelajaran matematika yang kurang menyenangkan. Oleh karena pengalaman yang kurang menyenangkan tersebut ditambah dengan konstruksi matematika yang kurang lengkap menyebabkan seorang anak hingga mencapai usia dewasa tetap tidak memiliki kemampuan matematika yang baik. Untuk memperbaiki hal ini salah satu caranya adalah dengan melakukan perubahan pada cara mengajar guru dengan membawa strategi-strategi mengajar yang baru yang dapat membantu siswa mengkonstruk pengetahuan dengan lebih baik.

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  14. Herlingga Putuwita Nanmumpuni
    18709251033
    S2 Pendidikan Matematika B 2018

    Kemampuan matematika seseorang baik kuat maupun lemah, keduanya dipengaruhi oleh beragam faktor. Begitupula dengan siswa di kelas, dalam satu kelas ada siswa yang memiliki kemampuan matematika yang baik dan ada pula memiliki kemampuan matematika yang lemah. Kemampuan matematika yang lemah itu bisa saja disebabkan karena kurangnya motivasi siswa dalam belajar, tingginya tingkat kecemasan siswa terhadap matematika, kurangnya pemahaman konsep, maupun adanya miskonsepsi pada benak siswa. Oleh karena diperlukan kepekaan guru untuk dapat mengenali kendala yang dimiliki siswa dalam pembelajaran dan berupaya untuk mencarikan solusinya baik melalui inovai metode pembelajaran ataupun alternatif solusi lainnya.

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  15. Nur Afni
    18709251027
    S2 Pendidikan Matematika B 2018

    Assalamualaikum warahmatullahi wabarakatuh.
    Menurut Bradford Hansen-Smith Cara terbaik untuk mengatasi pergumulan adalah mulai memiliki rasa ingin tahu tentang apa yang kita lakukan sampai taraf bahwa disiplin diri dan tanggung jawab menjadi hasil dari usaha tanpa usaha dalam belajar untuk mencintai melalui pengalaman melakukan. Persaingan membunuh rasa ingin tahu dan cinta untuk apa yang kita lakukan dengan berfokus pada diri sendiri terhadap orang lain. Mungkin dengan membuka di luar kepentingan pribadi kita dapat menemukan rasa ingin tahu yang cukup untuk mencintai dan bekerja sama, langkah pertama menuju kolaborasi. Belajar didasarkan pada rasa ingin tahu, namun kami masih menyukai kompetisi, pergi berperang satu sama lain untuk membuktikan diri. Sulit bagi siswa untuk belajar ketika mereka berada di zona perang pendidikan. terimakasih

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  16. Deden Hidayat
    18709251032
    S2 Pendidikan Matematika B 2018

    Matematika merupakan salah satu pelajaran yang dianggap sulit menurut beberapa siswa. Lemahnya keterampilan matematika siswa sendiri karena kurangnya minat dari siswa untuk belajar matematika. Siswa beranggapan bahwa matematika hanya sebagai mata pelajaran yang mempelajari mengenai angka-angka dan operasinya. Ditambah lagi seorang guru dalam memberikan pembelajaran langsung memberikan rumus kepada siswa, tidak memberitahu mengenai asal mula kenapa hal tersebut bisa terjadi. Oleh karena itu, kedua hal tersebut merupakan penyebab keterampilan yang dimiliki oleh seorang siswa dalam matematika lemah.

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  17. Deden Hidayat
    18709251032
    S2 Pendidikan Matematika B 2018

    Menurut saya lemahnya keterampilan matematika siswa dipengaruhi oleh proses pembelajaran di dalam kelas. Pembelajaran yang baik yaitu pembelajaran yang mampu memahamkan siswa akan materi yang dipelajari. Tentunya pembelajaran yang seperti itu dapat terbentuk jika seorang siswa mampu mengkonstruksi pengetahuan yang dimilikinya sendiri. Mengkonstruksi pengetahuan yang dimilikinya sendiri akan membuat siswa menjadi selalu ingat mengenai apa yang telah dipelajarinya. Tugas seorang guru yaitu mempersiapkan atau merencanakan suatu proses pembelajaran yang dapat memfasilitasi siswa untuk membangun pengetahuan yang dimiliknya.

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  18. Yoga Prasetya
    18709251011
    S2 Pendidikan Matematika UNY 2018 A
    Matematika yang dianggap sebagai pelajaran yang sulit menjadi sifat yang ditakuti. Menurut Paul matematika itu dianggap sebagai konstruktivisme sosial, seperti halnya dalam proses pembelajaran di kelas seorang guru harus memberikan kesempatan kepada siswanya untuk melakukan dalam kelompok diskusi. Sehingga dalam hal ini aktivitas sosial mulai terbentuk dengan sendirinya, karena para siswa secara tidak langsung saling berinteraksi dan komunikasi satu sama lain.

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  19. Cahya Mar'a Saliha Sumantri
    18709251034
    S2 Pendidikan Matematika B

    Assalamualaikum wr.wb.
    Penilaian terhadap kemampuan matematika orang lain adalah diri mereka sendiri karena mereka yang membatasi dan mengembangkan sendiri bakat dalam mempelajari suatu hal. Bila orang lain yang menilai bisa jadi hanya penilaian luarnya saja, padahal orang tersebut bisa melebihi ekspektasi orang lain atas penilaian terhadap dirinya dan bila diharuskan untuk menilai kelemahan kemampuan matematika orang lain yang bisa dikatakan adalah mungkin orang tersebut sedang dalam kondisi tidak bisa fokus dalam memahami permasalahan matematika atau bisa jadi karena seperti pada umumnya orang tersebut kurang menyukai pelajaran matematika sehingga terdorong dari pikirannya untuk berhenti berpikir lebih jauh tentang matematika.

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  20. Hasmiwati
    18709251023
    S2 Pend.Matematika B 2018

    Assalamualaikum Warahmatullahi Wabarakatuh.
    Beberapa kali saya pernah "ngobrol" dengan anak yang kemampuan matematikanya masih rendah. Mereka mengungkapkan bahwa matematika itu sulit, bikin pusing, isinya rumus semua, gurunya galak, menjenuhkan, dan hal-hal negatif lainnya. Saya rasa tidak hanya satu atau dua anak yang mengalami atau merasakan hal yang sama. Oleh karena itu, diperlukan pendidik yang mampu mengubah pikiran negatif anak tersebut menjadi sebuah pandangan positif terhadap matematika sehingga anak bisa belajar dengan menyenangkan dan sesuai dengan dunianya. Dengan demikian, kemampuan matematika akan meningkat karena proses pembelajarannya sesuai dengan alur berpikir anak.

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  21. Aizza Zakkiyatul Fathin
    18709251014
    Pps Pendidikan Matematika A

    Dari postingan ini, dapat diketahui bahwa banyak faktor yang menyebabkan siswa lemah dalam kemampuan matematikanya. Lingkungan rumah dan keluarga ternyata juga berpengaruh terhadap prestasi matematika. Meraka yang menerima tantangan dan harapan tinggi dari para orang tuanya cenderung tinggi skor matematikanya. Sebaliknya, juga terjadi. Para siswa Indonesia sangat jarang menerima tantangan dan harapan yang tinggi dari para orang tua mereka dibandingkan para siswa dari Negara lain. Jadi faktor dari luar siswa juga perlu diperhatikan dalam rangka meningkatkan prestasi matematika siswa.

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  22. Aizza Zakkiyatul Fathin
    18709251014
    Pps Pendidikan Matematika A

    Faktor lain yang menyebabkan siswa lemah matematikanya bisa terjadi karena guru. Guru yang tidak mampu mengantarkan siswa dalam membangun konsep matematikanya sudah barang tentu berdampak pada siswa. Guru yang sudah merancang sedemikian rupa perencanaan pembelajaran tetapi tidak semua guru dapat menerapkan. Oleh karena itu, disamping faktor internal siswa, faktor eksternal juga harus diperhatikan. Terlebih jika itu berasal dari guru, maka guru tersebut harus memperbaiki kualitasnya dalam mengajar.

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  23. Cahya Mar'a Saliha Sumantri
    18709251034
    S2 Pendidikan Matematika B

    Assalamualaikum wr.wb.
    Tidak bisa menyalahkan siapapun bila berbicara tentang lemahnya keahlian diri. Kecuali memang diri sendiri menyadari mengapa itu bisa terjadi dan akhirnya berani untuk membuka diri, pikiran, untuk memperbaiki dan mencoba untuk mengasah kemampuannya lagi. Untuk kemampuan matematika yang lemah bisa jadi mereka sudah berniat untuk tidak terlalu mendalami ilmu tersebut dan akhirnya enggan untuk menerima pelajaran meskipun wajib. Bisa jadi karena kurangnya rangsangan dari luar untuk mengajak lebih ikut aktif dalam pelajaran matematika.

    ReplyDelete
  24. Sintha Sih Dewanti
    18701261013
    PPs S3 PEP UNY

    Menanggapi pendapat 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.” Iya memang benar, terutama di bimbingan belajar. Banyak menggunakan trik-trik dalam penyelesaian soal. Mungkin cocok untuk menghadapi soal-soal UN atau ujian masuk perguruan tinggi. Namun ini berdampak negatif untuk jangka panjang. Kenyataannya sering siswa mampu memecahkan masalah yang sangat mirip dengan yang diajarkan di kelas, tetapi begitu tata letak berubah, mereka tidak dapat melihat pola, atau fakta bahwa mereka perlu menerapkan konsep yang sama dalam suatu bentuk yang berbeda. Pembelajaran seperti ini menjadi dangkal dan lebih didasarkan pada menghafal daripada pada logika.

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  25. kamhar ngado
    18709251048
    no one perfect on the earth. the only perfect is Allah almighty. when our students cannot figure out math it doesn't mean the are weak in math because study is different with study another subjects, which means study math need teachers' special attention. firstly, we have to know what are our students math's problem? if their weakness in basic analysis or counting, maybe geometry we don't know yet. the best methods is giving them many math examples as much as we can and how to solve it. it's better rather than theory because theory they only remind and forget about it tomorrow. i think we have to use the suitable methods for applying in our math class. there are many methods we can try consisting of PBL, contextual, Jigsaw, scientific inquiry maybe it will be the best choice. just try good luck

    ReplyDelete
  26. Assalamu'alaykum wr wb
    Dwi Kawuryani
    19709251061
    Pendidikan Matematika S2 D
    Sesuai yang Bapak tulis, bahwa keberhasilan seorang guru dalam mengajarkan matematika dikatakan berhasil jika siswa dapat merasakan "mathematics is belong to them"
    Suatu pendefinisian yang sangat sulit dicapat, dikaitkan dengan pendapat dari William Galinaitis, bahwa pemahaman matematika tergantung dari beberapa faktor eksternal yang salah satunya adalah lingkungan. Seperti yang kita tau bahwa tidak semua siswa memiliki lingkungan yang kondusif untuk belajar matematika, sehingga keberhasilan pembelajaran Matematika tidak hanya diperankan oleh guru disekolah tetapi harus diambil peran oleh semua pihak yang ada di lingkungan siswa. Menilik hal itu, di lingkungan Indonesia, matematika menjadi salah satu mata pelajaran yang sulit dan menjadi momok bagi siswa, sehingga adanya faktor eksternal yang disebutkan William akan sangat menghambat proses belajar siswa.
    Wassalamu'alaikum wr wb

    ReplyDelete
  27. Ngaenun Nangim
    19709251058
    S2 Pendidikan Matematika D 2019

    Berdasarkan artikel di atas, saya sependapat bahwa kurangnya penilaian tidak selalu dapat dimaknai kurang kompetisi. Hal ini disebabkan bahwasannya dalam kompetisi tidak hanya terjadi dalam penilaian. Kompetisi yang baik terjadi dalam suatu proses dan penilaian atas kompetisi itu cukuplah kiranya jika dilakukan di awal kompetisi untuk mengetahui hasil dari kompetisi tersebut. Sehingga, tidak tepat kiranya jika kompetisi yang banyak hanya dapat terjadi saat penilaian yang banyak dilakukan. Kompetisi dapat diciptakan dalam proses dengan memanipulasikan ruang dan waktu untuk menghasilkan kompetisi yang sehat dengan penilain yang jujur dan akurat.

    ReplyDelete
  28. Vera Yuli Erviana
    NIM 19706261005
    S3 Pendidikan Dasar 2019

    Assalamualaikum Wr. Wb.
    Belajar matematika lemah karena siswa selama ini hanya belajar matematika saja hanya dengan mneghafal, tidak menemukan ide atau konsep matematika dalam diri mereka sehingga masalah yang akan menjadi buntu siswa dalam menjawabnya, tidah hanya itu dalam proses pendidikan sedang siswa membutuhkan bantuan dari guru yang sebagai fasilitator. Pembelajaran pun juga perlu disuguhkan semenarik mungkin agar adanya minat belajar dalam diri anak karena persepsi matematika sendiri selalu dianggap sulit oleh mereka. Dalam pendekatan matematika realistik guru dipandang sebagai fasilitator, moderator, dan evaluator yang menciptakan situasi dan menyediakan kesempatan bagi siswa untuk menemukan kembali ide dan kosep matematika dengan cara mereka sendiri. Oleh karena itu, guru harus mampu menciptakan dan mengembangkan pengalaman belajar yang mendorong siswa untuk memiliki aktivitas baik untuk dirinya sendiri maupun bersama siswa lain.

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  29. Assalamu'alaykum wr wb
    Dwi Kawuryani
    19709251061
    Pendidikan Matematika S2 D
    Dalam pemahaman matematika terdiri dari metode matematika dan konten matematika serta sikap matematika. Disiplin diri / tanggung jawab dapat berkontribusi pada sikap matematika; tetapi mereka masih jauh dari metode matematika, konsep matematika dan sistem logis. Dengan demikian kemampuan matematika seseorang dikatakan masih rendah. Salah satu yang menjadi penyebab rendahnya kemampuan matematika adalah tingkat stress siswa didalam kelas dan juga kurangnya kemampuan siswa dalam menggunakan fokus belajarnya didalam kelas. Matematika sekolah diajarkan menggunakan menghafal dan pengulangan mekanis, daripada pemahaman tentang mekanika dan logika. Sangat sering para siswa mampu memecahkan masalah yang sangat mirip dengan yang diajarkan di kelas, tetapi begitu tata letak berubah, mereka tidak dapat melihat pola, atau fakta bahwa mereka perlu menerapkan konsep yang sama dalam suatu bentuk yang berbeda. Hal ini berarti pembelajaran yang dangkal, lebih didasarkan pada menghafal daripada pada logika.
    Wassalamu'alaikum wr wb

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  30. Tiara Wahyu Anggraini
    19709251065
    S2 Pendidikan Matematika D 2019

    Rendahnya kemampuan dasar matematika dapat disebabkan oleh faktor internal (dari dalam) misalnya seperti motivasi, kepercayaan diri dll, kemudian faktor eksternal misalnya pengalaman belajar. Kemampuan dasar matematika sangatlah penting untuk dikuasai karena merupakan basic untuk pembelajaran di tingkatan yang lebih tinggi. Oleh karena itu, dalam penyampaiaannya sangat diperlukan kesan yang baik bagi siswa dan inilah merupakan tugas untuk seorang guru yaitu bagaimana menyelenggarakan pembelajaran yang menyenangkan dan bermakna.

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  31. Rona Happy Mumpuni
    19709251059
    S2 Pendidikan Matematika D 2019


    Ada beberapa hal yang mempengaruhi kemampuan matematika dasar seseorang lemah, diantaranya: matematika dianggap momok oleh sebagian orang, beberapa orang malas mencoba karena takut salah ketika melakukan penyelesaian matematika, matematika dianggap pelajaran yang kurang menyenangkan, tidak ada minat untuk belajar matematika, dll

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  32. Yufida Afkarina Nizar Isyam
    19709251073
    S2 Pendidikan Matematika D 2019

    Menurut saya kemampuan belajar matematika rendah dikarenakan kurangnya pemahaman siswa terhadap matematika sehingga siswa hanya menghafal rumus yang diberikan guru dan tidak dapat menyelesaikan masalah yang belum pernah diberikan sebelumnya. Padahal materi dalam pembelajaran matematika saling berkaitan satu sama lain. kemampuan dasar matematika sesungguhnya sangatlah penting agar siswa dapat memahami matematika yang lebih kompleks lagi.

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  33. Latifa Krisna Ayu
    19709251060
    S2 Pendidikan Matematika D

    Menurut saya, bagaimana cara pengenalan konsep dasar matematika akan bepengaruh pada kuat atau tidaknya konsep tersebut tertanam pada siswa. Jika siswa hanya menghafal konsep atau rumus yang ada tanpa memahami dasar dari konsep tersebut, maka siswa hanya dapat menggunakan konsep tersebut pada bentuk-bentuk permasalahan yang ia hafal atau yang ia pernah pelajari. Namun jika siswa menemui bentuk lain yang baru, maka siswa akan kesulitan menerapkan konsep tersebut walaupun ia mampu menyelesaikannya dengan baik pada bentuk lain. Oleh karena itu proses pengenalan konsep dasar matematika kepada siswa haruslah diperhatikan dengan baik, karena konsep dasar matematika tersebut akan berpengaruh pada konsep-konsep matematika berikutnya yang lebih kompleks yang akan dipelajari oleh siswa.
    Terima kasih

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