Mar 15, 2013

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



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Group: Math, Math Education, Math Culture

Marsigit Dr MA 
Outside perception is sometime not good to the students, because they tend to judge rather than to facilitate. Further read my web http://powermathematics.blogspot.com
And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

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

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

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

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

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

Marsigit Dr MA
 The architectonic of Kant teach us that mathematics is the business of the students' architectonic. So, for me, whatever the external criteria to measure students mathematics is always mislead. The genesis competence of mathematics is really their architectonic. So, the problem for the teachers is how to uncover mathematics depth inside of the students. Until then you get the criteria of the success of your teaching mathematics after you hear the students' claim that mathematics really belong to them.
Further read my web http://powermathematics.blogspot.com
And also my works on http://staff.uny.ac.id, click FMIPA, click Pendidikan Matematika, click APPLY and chose Marsigit. Thanks

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thank

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

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

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

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

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

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

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

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

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

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

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

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

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

Elias Gourtsoyannis
 @Art. I agree. Perhaps not with the tone. But, you're right.
I once participated in a Mathematics competition in California. At the
time, I did not even know trig identities. I revised until late night from
the textbook. Next day, I took part. Several schools. It was a big
multiple-choice test. Together with some additional questions. The top
prize was an aluminium state of the art log-log type slide rule. In the
test, I did not even make the top 50%. But, I had an idea. The competition
was sponsored by the slide rule makers. The top prize was for sale for $32.
Now, I had some pocket money I had not spent. Given to me by the AFS,
monthly. So, I promptly bought it. It had a beautiful leather case!

Perhaps one of the reasons I eventually studied math?

Marsigit Dr MA

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

@Pat. I agree with you. Mathematics should always be taught by Maths
graduates. However, the reality is that, until this happens, most primary
mathematics teachers would be trained practitioners. Increasingly, however,
in some countries, teacher training includes basic mathematical skills.
With the right trainer, student teachers can, and do, experience something
of the flavor of true mathematical thinking and processes. And, later, they
can pass it on to their pupils!

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

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

Marsigit Dr MA
Thank Elias Gourtsoyannis for the information

Elias Gourtsoyannis
 Δεαρ Marsigit. You can call me Elias!

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

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

Bradford Hansen-Smith
Art, you state “Education has its problems today. Competition is not one of them.”
Teaching to the test is certainly competitive when the results are used to determine who gets the prize, from individual students, to teachers, to school board, to country ratings.

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

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

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

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

Marsigit Dr MA 
@Art DiVito: Assessment is the most crucial problem in education. I totally agree with the assessment if it means to collect or record students' activities and achievements. However, it can be a big problem if it means to evaluate, because the next important question is who has the authority to evaluate? It will also no problem if the teacher himself evaluate his/her students, because the teacher is the people who knows the best about his students. The problems arise when evaluation is carried out externally or by external institution/board.
If it does so, philosophically there will be a huge reductions or simplification. Reduction or simplification is a kind of psychologically unhealthy partially dimension of life. If education from time to time always produce a simplified generation, then we will have a problematic generation. Look at directly to the phenomena in the society not only in the certain country but also in each country all over the world. So, according to my point of view, the best assessment should be supported by keeping-record (portfolio) both by the teacher and by the students themselves. The form of it can be authentic assessment or classroom-based assessment. Thank you

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

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

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

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

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

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

Elias Gourtsoyannis
 @Marsigit @ Bradford@Art

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

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

40 comments:

  1. Wahyu Lestari
    16709251074
    PPS P.Mat D

    Siswa tidak bisa dipaksa belajar matematika murni karena dapat mempengaruhi emosional siswa yang berakibat stress kepada siswa. siswa perlu berlatih bukan diberi teori. otak siswa dari sekolah dasar untuk berlatih saja. jika siswa dipaksa belajar matematika hanya dengan teori, hanya mengakibatkan siswa merasa tidak nyaman dalam belajar maematika. Oleh karenanya guru sebagai fasilitator harus kreatif, mereka harus kreatif dengan lingkungan mereka. siswa tidak lemah dalam setiap pelajaran, masalahnya hanya ajaran kreativitas guru.

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  2. Yosepha Patricia Wua Laja
    16709251080
    S2 Pendidikan Matematika D 2016

    Saya setuju dengan pernyataan Pak Prof bahwa “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”
    Pendidikan itu untuk semua orang. Sebagai pelaksana pendidikan, banyak yang perlu dipertimbangkan oleh para guru sebagai pelaksana pendidikan. Jangan jadikan pendidikan sebagai sebuah kompetisi yang akan menghasilkan seorang yang menang dan seorang yang kalah, tapi jadikan pendidikan sebagai bentuk kerja sama dimana semua anak adalah pemenangnya. Jika guru menjadikan pendidikan sebagai sebuah kompetisi maka kemungkinan akan berdampak pada kondisi psikologis anak, baik anak yang dianggap memenangkan kompetisi maupun anak yang tidak memenangkan kompeteisi. Jika pendidikan sebagai sebuah kerja sama maka anak-anak diberi kesempatan untuk berinteraksi secara sosial bersama teman-temannya, belajar bahwa masih ada orang lain selain diri sendiri, bersikap terbuka terhadap perubahan dan tentunya anak-anak dapat saling membantu. Dengan begitu angan-angan pendidikan yang demokratispun dapat terwujud.

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  3. Supriadi / 16709251048
    Kelas C 2016 Pendidikan matematika – S2

    Melihat kajian pembelajaran matematika sehinga diangap senbagai mata pelajaran sulit bagi siswa yang mengakibatkan rendahnya partisipasi siswa dalam pembelajaran matematika. Hal ini memang tidak sepenuhnya bisa disalahkan karena pertama kemampuan anak berbeda-beda di setiap bidang, kedua objek matematika yang abstrak dan begitu kompleks, sehingga untuk mengabstraksasikan suatu fenomena ke model matematika sangat sulit, ketiga anggapan siswa bahwa matematika hanyalah mata pelajaran dengan sekumpulan angka dan rumus-rumus yang harus dihafalkan. Maka dari itu peran matematika sekolah sangat dibutuhkan dalam hal ini, di mana guru tidak hanya menguasai materi yang akan disampaikan tetapi juga menuntut guru dapat menyampaikan materi tersebut dengan bahasa atau komunikasi yang mudah dipahami siswa. Dari tulisan di atas juga dibahas bahwa pendidikan untuk semua orang. Dalam hal ini guru harus memperlakukan setiap siswa secara adil. Artinya guru tidak boleh hanya memprioritaskan kepada siswa yang memiliki prestasi yang baik saja namun juga guru harus dapat merangkul siswa-siswa yang memiliki prestasi kurang baik. Serta guru juga harus memperhatikan semua dari aspek kognitif, psikomotorik dan afektif siswa.

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  4. Orang menganggap matematika sebagai bilangan dan operasinya, ilmu tentang berhitung. Ketika matematika bergeser kearah aljabar, kalkulus, peluang maka orang mengalami keterasingan karena tidak sesuai dengan pandangannya tentang matematika. padahal matematika dasar tentang bilangan negatif dan pecahan saja penguasaannya masih rendah karena kesulitan memahami arti bilangan negatif dan pecahan. Ditambah materi lain yang tidak sesuai persepsinya maka orang-orang mulai kehilangan motivasi untuk belajar matematika

    ReplyDelete
  5. Hajarul Masi Hanifatur Rohman
    S2 Pendidikan Matematika C 2016
    16709251052

    Bismillaah...
    Saya kurang setuju dengan pernyataan “Why do you think people's basic math skills are weak”. Hal itu bergantung pada bakat dan minat seseorang. Memang terdapat beberapa orang lemah dalam matenatika, hal ini karena itu memang bukan bakat ataupun minatnya. Mungkin ia minat di hal yang lainnya misal ilmu sosial atau seni. Jarang dijumpai orang-orang yang menyukai keduanya, meskipun pasti ada. Nah, terdapat pula yang menyukai matematika, sehingga “basic math skills”-nya pun baik. Hal ini karena matematika dirasa adalah bakat dan minat. Sesungguhnya basic math skills dapat diwujudkan, meskipun matematika bukanlah bakat atau minatnya, yaitu dengan cara sering berlatih. Lama-lama seseorang akan terbiasa dan terbentuk basic math skills.

    ReplyDelete
  6. Sylviyani Hardiarti
    16709251069
    S2 Pendidikan Matematika Kelas D 2016

    Salah satu penyebab mengapa kemampuan matematika dasar seseorang lemah karena dipengaruhi cara belajar matematikanya. Matematika yang biasanya diajarkan dengan cara menghafal dan pengulangan mekanis, bukan pemahaman mekanik dan logika. Sehingga seringkali ditemukan para siswa dapat menyelesaikan masalah yang sangat mirip dengan apa yang diajarkan di kelas, tetapi segera setelah perubahan tata letak, mereka tidak dapat melihat pola, atau fakta bahwa mereka perlu untuk menerapkan konsep yang sama dalam berbeda bentuk. Ini akan menjadikan pendidikan matematika menjadi sia-sia atau percuma, padahal matematika itu merupakan kegiatan mencari pola. Solusi akan kasus ini adalah dengan memperbanyak praktek, di mana siswa diberikan pengetahuan yang akan menjadi dasar penyelesaian masalah lalu siswa dihadapkan pada masalah sejenis namun dalam bentuk yang berbeda-beda, hal ini akan melatih siswa dalam menelusuri pola, memahami kasus untuk dapat diselesaikan dengan cara yang bervariasi. Dengan begitu, siswa akan lebih mengerti bagaimana harus menerapkan matematika dalam berbagai kasus, tidak hanya mengandalkan apa yang telah ia hafalkan di kelas. Dan poin penting lainnya yaitu matematika perlu dibudayakan. Belajar matematika tidak dapat dipaksakan, seseorang belajar matematika karena keinginan sendiri dan karena kebutuhan yang mengharuskan mereka bersungguh-sungguh dalam belajar matematika. Belajar adalah membangun pengetahuan di mana saja dan kapan saja.

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  7. Syaifulloh Bakhri
    16709251049
    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.

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  8. Rahayu Pratiwi
    16709251077
    PPS PM-D 2016

    Saya setuju dengan pendapat Ginetta Nistoran yang menyatakan matematika diajarkan dengan menggunakan hafalan dan pengulangan mekanis, daripada pemahaman tentang mekanika dan logika. Tidak jarang guru memberikan soal rutin kepada siswa. Akibatnya adalah siswa hanya mampu memecahkan masalah yang sangat mirip dengan yang diajarkan di kelas, tapi begitu tata letaknya berubah mereka akan mandapatkan kesulitan di dalamnya dan mudah menyerah untuk menyelesaikan untuk memecahkan masalah tersebut.

    ReplyDelete
  9. Muh Ferry Irwansyah
    15709251062
    Pendidikan Matematika PPS UNY
    Kelas D
    Belajar tidak bergantung dengan ada atau tidaknya guru sebagai fasilitator dan belajar tidak hanya dilakukan bila di sekolah saja. Untuk membangun konsep dan kehidupan siswa sendiri (matematika) maka sangat dibutuhkan peran guru sebagai fasilitator. Peran guru tersebut dapat berupa pememilihan metode pembelajaran. Metode yang dipilih haruslah metode yang menyenangkan sangat diperlukan bagi siswa untuk menuntun siswa kearah berfikir kritis dan kreatif serta dapat memahami konsep-konsep matematika atas penemuan atau pengalamannya sendiri. Sehingga dalam mengevaluasi siswa dapat dilakukan secara terus-menerus dan menggunakan berbagai pendekatan, misalnya portofolio. Dalam hal ini ditekankan pada proses bukan hasil.

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  10. Annisa Hasanah
    16709251051
    PPs Pendidikan Matematika C 2016

    Saya setuju bahwa dalam mengembangkan matematika jangan hanya mengutamakan bagaimana mengajar siswa, namun bagaimana agar siswa mau belajar metematika. Dengan kata lain siswa mau dengan sendirinya untuk belajar matematika bukannya memaksa siswa untuk belajar matematika. Di sini peran guru dalam manciptakan metode yang menyenangkan sangat diperlukan bagi siswa. Sebab, pada dasarnya setiap siswa berbeda kemampuannya dalam belajar. Dan terdapat beberapa hal yang menyebabkan siswa lemah dalam belajar matematika salah satunya karena guru dalam mengajar belum memberikan pemahaman secara konsep kepada anak. Sehingga jika mengerjakan soal sering kali mengalami kesulitan.

    ReplyDelete
  11. Kunny Kunhertanti
    16709251060
    PPs Pendidikan Matematika kelas C 2016

    Matematika adalah salah satu hal yang penting dalam kehidupan, dalam kehidupan selalu ada perhitungan, menggunakan logika matematika, dan banyak hal yang lainnya. Saat seseorang yang memiliki kemampuan baik dalam matematika akan cenderung dalam pelajaran eksak lainnya, dan tidak menutup kemungkinan baik pula dalam pelajaran sosial. Sehingga tidak ada alasan orang yang hanya memiliki kemampuan dasar matematika itu lemah.

    ReplyDelete
  12. Lana Sugiarti
    16709251062
    PPs Pendidikan Matematika D 2016

    Beberapa siswa dalam suatu kelas tentu akan ada yang mengalami kesulitan daam belajar matematika. keterampilan dalam matematika pun dapat dikatakan lemah. Hal ini disebabkan oleh banyak faktor. Mungkin ia kurang semangat dalam mempelajari matematika, atau mungkin juga karena gurunya kurang tepat dalam pemilihan metode mengajar. Namun mungkin juga karena siswa tersebut lebih menyukai mata pelajaran lain dari pada matematika dan minatnya terhadap mata pelajaran lain lebh besar dari pada minat terhadap matematika. Jadi orang yang lemah dalam matematika belum tentu lemah juga dalam pelajaran lain. Mungkin malah lebih menonjol dalam pelajaran lainnya.

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

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  14. Ratih Eka Safitri
    16709251059
    PPs Pendidikan Matematika C 2016

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

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  15. Ahmad Wafa Nizami
    16709251065
    PPs Pendidikan Matematika D 2016

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

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  16. Heni Lilia Dewi
    16709251054
    PPs Pendidikan Matematika Kelas C 2016

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

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  17. Dessy Rasihen
    16709251063
    S2 P.MAT D

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

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  18. Lihar Raudina Izzati
    16709251046
    P. Mat C 2016 PPs UNY

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

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  19. Primaningtyas Nur Arifah
    16709251042
    Pend. Matematika S2 kelas C 2016
    Assalamu’alaikum. tema yang diambil dalam diskusi di atas ialah mengapa dasar ketrampilan matematika siswa itu lemah. Siswa berada di lingkungannya lebih lama dari pada di sekolah. Di lingkungan siswa mengalami berbagai permasalahan yang melibatkan matematika, maka untuk mempeajari matematika hendaknya melibatkan permasalahan-permasalahan di sekitar siswa. Dengan begitu siswa akan merasa tertantang untuk belajar.

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  20. Munaya Nikma Rosyada
    14301241002
    S1 Pendidikan Matematika I 2014

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

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  21. Munaya Nikma Rosyada
    14301241002
    S1 Pendidikan Matematika I 2014

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

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  22. Munaya Nikma Rosyada
    14301241002
    S1 Pendidikan Matematika I 2014

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

    ReplyDelete
  23. Munaya Nikma Rosyada
    14301241002
    S1 Pendidikan Matematika I 2014

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

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  25. Ahmad Bahauddin
    16709251058
    PPs P.Mat C 2016

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

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  26. Hening Carrysa
    14301241012
    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.

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  27. ARNY HADA INDA
    16709251079
    PPS-MAT D 2016
    Ada empat kelemahan yang dimiliki oleh siswa sebagai penyebab rendahnya hasil belajar siswa antara lain, kurang memiliki pengetahuan materi prasyarat yang baik, kurang memiliki kemampuan untuk memahami srta mengenali konsep-konsep dasar matematika (seperti definisi, teorema, aksioma, dalil, kaidah) yang berkaitan dengan pokok bahasan yang sedang dibicarakan, kurang memiliki ketelitiaan dalam menyimak dan mengenali persoalan matematika yang berkaitan dengan pokok bahasan tertentu, kurang memiliki kemampuan untuk menyimak kembali sebuah jawaban yang diperoleh (apakah jawaban tersebut mungkin atau tidak), dan kurang memiliki kemampuan nalar yang logis dalam menyelesaikan persoalan matematika. Keempat kelemahan ini akan menghambat proses belajar bermakna, di mana belajar bermakna maksudnya, di samping materi yang disajikan harus disesuaikan dengan kemampuan siswa, juga harus relevan dengan struktur kognitif siswa, sehingga materi harus dikaitkan dengan konsep-konsep (pengetahuan) yang telah dimiliki siswa dan dikaitkan dengan bidang lain atau kehidupan sehari-hari siswa.

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  28. ARNY HADA INDA
    16709251079
    PPS-MAT D 2016
    Rendahnya prestasi belajar siswa tidak hanya disebabkan oleh kelemahan belajar peserta didik, tetapi dapat disebabkan oleh faktor lain yaitu sistem pengajaran yang kurang membangkitkan gairah belajar pada peserta didik, dan rencana pengajaran yang kurang menarik minat peserta didik dalam belajar. Faktor kecil yang dapat mempengaruhi rendahnya hasil belajar siswa adalah karena pengajaran disajikan masih dalam bentuk yang kurang menarik, sehingga terkesan angker, sulit, dan menakutkan sehingga siswa sering tidak menguasai konsep dasar yang terkandung dalam materi pelajaran matematika yang dapat menghambat kreativitas siswa dalam menjawab soal, yang akhirnya hasil belajar siswa menjadi rendah.

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  29. Wahyu Berti Rahmantiwi
    PPs Pendidikan Matematika Kelas C 2016
    16709251045

    Sebagai guru salah satu hal yang harus dihindari pada saat berlangsungnya pembelajaran di dalam kelas ialah membanding-bandingkan siswa satu dengan yang lainnya. Hal ini dilarang karena kaan berakibat pada psikis siswa dan dapet menimbulkan kecemasan semakin meningkat saat pembelajaran. Gruu harusnya memberikan reward untuk siswa yang berprestasi bukan membanggakan didepan kelas. Dari percakapan diatas, salah satu ada yang menyebutkan bahwa anak didiknya mengalami stres karena dipengaruhi oleh aktivitas tunggal yang hanya bisa dilakukan siswa. Salah satu hal yang mengurangi stres yang akan dialami siswa ialah tidak memberikan pembelajaran yang mengandung hafalan.

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  30. Nita Lathifah Islamiyah
    14301244011
    S1 Pendidikan MAtematika A 2014

    Lemahnya kemampuan dasar matematika, kemungkinan disebabkan dari dua faktor, faktor siswa dan guru. Tapi menurut saya faktor guru memang lebih dominan karena peran yang paling penting saat menanamkan dasar matematika itu sendiri adalah dari cara penyampaian oleh guru tersebut.

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  31. Nita Lathifah Islamiyah
    14301244011
    S1 Pendidikan Matematika A 2014

    Maka sebaiknya ini merupakan evaluasi bagi guru dan menjadi catatan bagi calon guru. Sehingga kedepannya dapat diperbaiki lagi. Jangan sampai terjadi kekecewaan dia akhir karena mengabaikan evaluasi evaluasi yang terlihat, yang dianggap biasa saja, padahal sangat berpengaruh terhadap perkembangan siswa tersebut.

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  32. Nita Lathifah Islamiyah
    14301244011
    S1 Pendidikan Matematika A 2014

    Sebagai guru salah satu hal yang harus dihindari pada saat berlangsungnya pembelajaran di dalam kelas ialah membanding-bandingkan siswa satu dengan yang lainnya. Hal ini tidak boleh diterapkan karena akan mempengaruhi psikologis siswa tersebut dan nantinya akan berdampak pula ke hasil belajar siswa tersebut.

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  33. Nita Lathifah Islamiyah
    14301244011
    S1 Pendidikan Matematika A 2014

    Menurut saya, matematika merupakan salah satu ilmu yang begitu penting dalam dunia pendidikan. karena matematika dipelajari di semua jenjang pendidikan. Namun, karena masih banyak yang menanamkan bahwa matematika itu sulit, abstrak dan sebagainya, maka yang terjadi adalah kemampuan dasar matematika semakin melemah karena tidak ada usaha untuk mencari tau makna dari pembelajaran matematika itu sendiri.

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  34. Ujang Herlan Permana
    14301249001
    S1 Pendidikan Matematika I 2014

    Kurangnya motivasi mengakibatkan lemahnya tingkat kemampuan dasar matematika siswa. Pembelajaran menjadi tidak bermakna dan partisipasi siswa tidak tinggi akibat dari guru yang tidak memberikan motivasi pembelajaran yang berhubungan dengan kehidupan sehari-hari terkait dengan materi yang diberikan

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  35. Ujang Herlan Permana
    14301249001
    S1 Pendidikan Matematika I 2014

    Sejak kecil siswa langsung diajarkan dengan sesuatu yang abstrak sehingga ilmu matematika yang didapat tidak akan melekat pada long term memory siswa akibatnya siswa akan cepat lupa. Maka dari itu, pendekatan matematika realistik dari sejak kecil sangat baik untuk kematangan pondasi awal siswa, sehingga setelah dewasa tidak kesulitan belajar secara abstrak.

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  36. Hyldha Wafda Mufida
    14301241026
    S1 Pendidikan Matematika A 2014

    Pada proses penyelesaian masalah matematika, setiap orang membutuhkan ilmu untuk melakukan proses penyelesaiannya. Akan tetapi, sebagian besar siswa menyelesaikan masalah matematika hanya berdasarkan hafalan bukan karena penanaman konsep. Hal ini tentu perlu menjadi bahan perbaikan dalam perkembangan ilmu pengetahuan. Karena dengan memahami konsep akan menghasilkan pembelajara yang bermakna.

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  37. Fatmawati
    16709251071
    PM.D 2016
    Ada berbagai macam metode pembelajaran yang dapat dilakukan oleh guru dalam proses pembelajaran. Metode pembelajaran yang akan digunakan harus disesuaikan dengan tujuan pembelajaran dan kemampuan apa yang akan dicapai. Berbagai kemampuan awal siswa yang ada dapat dimanfaatkan untuk merencanakan kegiatan pembelajaran yang akan dilaksanakan.

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  39. Yuni Astuti
    14301241035
    S1 Pendidikan Matematika A 2014
    Dalam proses pembelajaran matematika sangat dibutuhkan strategi atau model pembelajaran yang inovatif. Dengan demikian dapat mencapai tujuan dari pendidikan matematika. selain itu juga bisa meningkatkan motivasi siswa untuk belajar matematika.

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  40. Sehar Trihatun
    16709251043
    S2 Pend. Mat Kelas C – 2016

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

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