LinkedIn Groups Group: Math, Math Education, Math Culture Discussion: Why do you think people's basic math skills are weak? Guckin, Alice Mae :I agree with David Elm. We need to have mathematics taught by competent elementary teachers who like mathematics and have much more mathematics content background than is usually required in an elementary education curriculum. If all elementary teachers are not required to have the sufficient mathematics content, than we need to have the mathematics taught only by those who do have the sufficient mathematics knowledge as well as the pedagogical skills needed.Marsigit Dr MA:@Guckin: Your comment have a problem with accountability and sustainability.Bradford Hansen-Smith:@Marsigit, Not knowing the work of Ebbutt and Straker, my observation about the points you mentioned1-4 are as follows. This is not about math per say, it is about learning and education. I see no NATURE OF SCHOOL MATH. What math is we make to our liking as we teach it. The diversity of ideas and viewpoints in these discussions give some indication of this. Your four points: 1. Pattern recognition is a skill for greater understanding about the universe. We seem to teach patterns as an end as they relate to math. Relationships can only be understood to have value in larger context than themselves. 2, To identify problems means we have some idea of what is comprehensibly appropriate, to know when something is out of alignment, to know the adjustments and changes necessary. Prior to solving a problem we must observe where we are and our place towards purpose that presents a problem. Math problems rarely relate to social, economic, philosophical, ethical, and moral issues that urgently need our attention. This is problem solving 101 and math with a sense of responsibility could serve towards a greater purpose if desired. 3. Even infants are investigating where they are, which is pretty much arrested by formal education because there are no formulas for investigation, curiosity is always personal. 4. If math is a means of communication then let’s approach it as such and stop teaching as it it were separate as the only elevated capacity to human understanding. What kind of reconstruction is needed is beyond my knowing. I am communicating my observations with hope that in our view of math being about relationships between unit parts, we will come to realize what is missing is an understanding that parts are first in relationship to unity of the whole, which determines the relationships between those parts.Marsigit Dr MA:@Bradford: That's it. You have elaborated the four points of the nature of school math very succinctly. As to compare directly with what the origin, herewith I expose what Ebbutt and Straker (1995) said : As a search for pattern and relationship, mathematics can be perceived as a network of interrelated ideas. Mathematics activities help the students to form the connections in this network. It implies that the teacher can help students learn mathematics by giving them opportunities to discover and investigate patterns, and to describe and record the relationships they find; encouraging exploration and experiment by trying things out in as many different ways as possible; urging the students to look for consistencies or inconsistencies, similarities or differences, for ways of ordering or arranging, for ways of combining or separating; helping the students to generalize from their discoveries; and helping them to understand and see connections between mathematics ideas. Creativity in mathematics lies in producing a geometric design, in making up computer programs, in pursuing investigations, in considering infinity, and in many other activities. The variety and individuality of children mathematical activity needs to be catered for in the classroom. The teacher may help the students by fostering initiative, originality and divergent thinking; stimulating curiosity, encouraging questions, conjecture and predictions; valuing and allowing time for trial-and-adjustment approaches; viewing unexpected results as a source for further inquiry; rather than as mistakes; encouraging the students to create mathematical structure and designs; and helping children to examine others’ results Mathematics can provide an important set of tools for problems- in the main, on paper and in real situations. Students of all ages can develop the skills and processes of problem solving and can initiate their own mathematical problems. Hence, the teacher may help the students learn mathematics by: providing an interesting and stimulating environment in which mathematical problems are likely to occur; suggesting problems themselves and helping students discover and invent their own; helping students to identify what information they need to solve a problem and how to obtain it; encouraging the students to reason logically, to be consistent, to works systematically and to develop recording system; making sure that the students develop and can use mathematical skills and knowledge necessary for solving problems; helping them to know how and when to use different mathematical tools. Language and graphical communication are important aspects of mathematics learning. By talking, recording, and drawing graphs and diagrams, children can come to see that mathematics can be used to communicate ideas and information and can gain confidence in using it in this way. Hence, the teacher may help the students learn mathematics by: creating opportunities for describing properties; making time for both informal conversation and more formal discussion about mathematical ideas; encouraging students to read and write about mathematics; and valuing and supporting the diverse cultural and linguistic backgrounds of all students. You may look at my work containing the work of them in the following: http://staff.uny.ac.id/system/files/pengabdian/marsigit-dr-ma/marsigitmateri-workshop-qitepphilosophymatheduclesson-study-teamfinal.pdf ThankBurçin Yildiz:@Marsigit, unfortunately, people have lots of problem about math.Some reasons of this are opportunities, the system of education and especially bias...fırstly, people sould learn how to solve problem... ıf you cant solve a problem you should try easer one, easer and easer one. and the most important idea is that ' ı can do it' . ı am a math student and my professor always says that '' it is not necessary to have so much intelligence. if you have a little bit intelligence idae is easy : if you study you can do, if you dont study you can not.'' ı wasnt like this before entered the university. but know ı blieve that it is enoug to have ambitions, discipline, positive opinion and of coursely LABOR.Marsigit Dr MA:@Burçin Yildiz: You look critically on how the students are to manage math problems. From the side of teachers, it is not just about managing them but also developing and implementing. As we know that managing math problems is inside the area of math thinking. According to Katagiri (2004) there are three aspects of Math Thinking: mathematical attitude, mathematical method, and mathematical content. So, you have elaborated about math method. Again, Katagiri's notions indicated that math method consist of : 1.Inductive thinking, 2.Analogical thinking, 3.Deductive thinking4.Integrative thinking (including expansive thinking), 5.Developmental thinking,6.Abstract thinking (thinking that abstracts, concretizes, idealizes, and thinking that clarifies conditions), 7.Thinking that simplifies, 8.Thinking that generalizes8.Thinking that specializes, 9.Thinking that symbolize, 10.Thinking that express with numbers, quantifies, and figures. Bay saying "'' it is not necessary to have so much intelligence. if you have a little bit intelligence idae is easy : if you study you can do, if you dont study you can not.'', your Professor strives to motivate you; and it can be related to the area or math attitude. As for Katagiri, math attitude consists of : (1) Attempting to have questions (2)Attempting to maintain a problem consciousness, (3)Attempting to discover mathematical problems in phenomena, (4) Attempting to take actions that match the objectives. (5) Attempting to establish a perspective, (6)Attempting to think based on the data that can be used, previously learned items, and assumptions, (7)Attempting to record and communicate problems and results clearly and succinctly (8)Attempting to sort and organize objects when expressing them, (9) Attempting to raise thinking from the concrete level to the abstract level, (10)Attempting to evaluate thinking both objectively and subjectively, and to refine thinking, (11) Attempting to economize thought and effort. You may read Shigeo Katagiri (2004) on his "Mathematical Thinking and How to Teach It".Bon Crowder:250 comments in this thread and comment #5 is the one that got it right. Notice that literacy doesn't have near the problems that numeracy does? Notice that people FREAKING READ TO THEIR KIDS IN EUTERO?! Megan Willingham is dead on - it's the culture. It's called "social modeling." If you scream when you see a roach your kids will know that roaches are scream worthy. If you cringe when they mention math homework, they'll see it and learn from it. Practice, teachers, schools, systems - regardless of all the rhetoric and action, if you don't get parents talking some positive things to their toddlers about math we'll never turn this tide.Marsigit Dr MA:@Bon Crowder: I am rather not convenient with the notions " If you scream when you see a roach your kids will know that roaches are scream worthy. If you cringe when they mention math homework, they'll see it and learn from it.". Besides that these notions reflect authoritarian way, they also indicate the very strong and dominant character of parent in his interaction with his kids. As you know that, in fact, our kids have various resources in learning things. They learn not only from parent but also from TV, internet, and other media. In my point of view, nowadays, there is no alternative for parent except that they should be more democratic and not force everything to our kids. I agree that learning math is as a part of culture. It is not as easy as Megan Willingham said that if our culture shifted the way we think and talk about math then the learning and skills would follow. The first big problem is of course about how to en-culture math learning. Some countries may need to learn from other country. As a parent, whenever my kid was at 5th grade, I also had a unique experience on how he should learn math (and other subjects of course). I had two alternatives; first forcing my kids to learn math by solving much problem, drill, and tightly supervise. Second, using indirect ways e.g by making the stories related to math, informal communication before going to bed, and making some jokes. I then chose the second alternative, and surprisingly my kid had the highest rank in the national examination. So I do agree that the parents have important and strategic role in their kids learning. Thank'sMarsigit Dr MA:@Everybody: It is the time to deliver the questions to the (Pure) Mathematicians on how they teach math? If they are not willing to speak, their accountability as lectures, teachers, supervisors has a problem. If they can not perform their accountability, then their positions in each area of math educ are illegitimate and needs to be questioned.Art DiVito:@Marsigit. Hi, Marsigit. I am sorry I've been away for a number of days, and I see that there's been quite a bit of activity. Apparently, you had asked me some questions, but now they are buried behind too many posts. If you can recall them, I'd be happy to address them now. ... I was away with my senior (50+) tennis team at a five state Sectional playoff. While I am now too old to be a force on this team (I only played in one match and it was a close loss!) we have a cadre of outstanding 50-52 year-olds who carried the weekend and earned us a trip to the National Championships in a couple of months! ... It's a beautiful example of that great aspect of competition, ... a team effort! : )Bradford Hansen-Smith:@Marsigit, thank you for making your work available. You bring up many important questions that need discussion and clarification in pursuing meaningful changes in math education, in all education. There are too many important ideas to make any limited comments about, nor am I educationally qualified to do so. It appears in the right direction and I encourage all that are following this discussion to take the time to read it, if you have not done so. http://staff.uny.ac.id/system/files/pengabdian/marsigit-dr-ma/marsigitmateri-workshop-qitepphilosophymatheduclesson-study-teamfinal.pdf There are serious questions that need serious clarification before any choices can be made. Change is inevitable and it is our responsibility to make clear and informed choices for ourselves. We have a duty to our students and future generations to give them the best and highest value of what we know, with enough room and support to discover those things we do not know. This means individual choices have to be made because we do not have control over the larger situation. The changes that need to be made will happen classroom by classroom, student by student, and teacher by teacher. By going deeply into some of the questions Marsigit poses you will have a good idea of why people's basic math skills are weak.Marsigit Dr MA:@Art Divito: I am pleased to hear your nice competition. It's difficult to be a great mathematicians and great Tennis player simultaneously. I perceive that education will guarantee you not to be too old to do so. It may be can be one of the different between education and competition. Though it may be a very small notion, your explanation or elaboration of math educ. will be very important not only for others but also for you as a pure mathematician; because, again, everything need accountability in order that outside agents trust to what we will do and we have done.Marsigit Dr MA:@Bradford: Thank's Bradford. What a unique from me is that I am a new comer and outsider of your society (usa). So my idea is still pure and I has no any certain agenda except that for the basic needs of human life universally. This is really my potentiality so that to a certain degree I feel I am proper enough to be your counterpart in this business. I found we have similar perceptions, understanding, challenging and vision. So it is always inspirational to have a sharing ides with you. Thank

## Mar 25, 2013

### Dialog Internasional 2 Pendidikan Matematika

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Fatmawati

ReplyDelete16709251071

PM.D 2016

Ketika siswa dapat memecahkan sebuah persoalan matematika, yang diharapkan guru setelah itu adalah bagaimana siswa dapat mengembangkannya dan dapat mengimplementasikannya. Seperti yang kita ketahui bahwa memecahkan masalah matematika merupakan bagian dari berpikir matematis. Menurut Katagiri (2004) ada tiga aspek berpikir matematis, yaitu mathematical attitude,

mathematical method, and mathematical content. Tugas guru adalah bagaimana menggabungkan aspek-aspek tersebut dalam sebuah proses pembelajaran yang menarik.

Sehar Trihatun

ReplyDelete16709251043

S2 Pend. Mat Kelas C – 2016

Guru memiliki peran penting dalam memajukan pendidikan bagi para generasi penerus bangsa. Peran guru yang penting inilah yang menjadikan guru tidak dapat dipandang sebelah mata. Guru harus terus dapat meningkakan kompetensi-kompetensi yang dimiliki nya agar dapat mendidik generasi-generasi muda untuk dapat menjadi generasi-generasi yang unggul dan berguna bagi bangsa Indonesia. Mencerdaskan siswa dalam berbagai bidang disiplin ilmu agar nantinya para siswa memiliki bekal untuk dapat menjawab tantangan nasional maupun global. Untuk dapat menjalankan tugas dan tanggung jawabnya tersebut guru harus dituntut untuk memiliki kemampuan pedagogis yang baik, guru harus akuntabilitas yaitu dapat dipercaya oleh siswanya dan guru juga harus sustainbilitas yaitu konsisten dalam segala hal.

Angga Kristiyajati

ReplyDelete17709251001

Pps UNY P.Mat A 2017

Terima kasih Banyak Pak Prof. Marsigit.

Yang kami pelajari dari dialog ini adalah dalam membelajarkan matematika kepada anak haruslah bijaksana dalam memilih cara. Pada dasarnya adalah ada dua cara, cara pembelajaran langsung: memberikan penjelasan materi matematis, latihan drill soal dengan cara yang serius, yang kedua adalah dengan cara pembelajaran tidak langsung: bisa dengan dongeng, permainan, bahkan mungkin dengan sedikit bercanda. Pemilihan cara yang baik tentulah harus sesuai dengan waktu dan kondisinya.

Dimas candra saputra, S.Pd.

ReplyDeletePPs PMA 2017

17709251005

Assalamualaikum prof,

Dalam dialog tersebut, Bradford Hansen-Smith menyatakan bahwa terdapat pertanyaan yang serius yang perlu diklarifikasi sebelum membuat beberapa pilihan. Perubahan tidak dapat dihindari dan hal tersebut merupakan kewajiban kita untuk membuat pilihan yang jelas. Kita memiliki kewajiban pada siswa dan generasi penerus untuk memberikan yang terbaik dari yang kita punya, dengan cukup ruang dan dorongan untuk menutupi apa yang tidak kita ketahui. Ini berarti pilihan individual dibuat karena kita tidak memiliki kontrol pada situasi yang lebih besar. Saya setuju dengan pendapat tersebut, seperti halnya tentang anggapan guru bahwa kemampuan dasar lemah ialah hal yang perlu didiskusikan.

Auliaul Fitrah Samsuddin

ReplyDelete17709251013

PPs P.Mat A 2017

Thank you for sharing this, Sir. If we read what Ebbut and Straker (1995) said about four points on the nature of school mathematics, we can notice that all teachers do in class should be "motivating", "facilitating", "giving opportunities", "encouraging", etc. All the process in constructing ideas and concept must be done by students themselves with the sufficient amount of assistance from teachers.

I Nyoman Indhi Wiradika

ReplyDelete17701251023

PEP B

Terima kasih banyak Prof, atas dialog yang sangat menarik ini. Saya memahami bahwa sudah seharusnya sejak sekolah dasar anak-anak diajarkan oleh guru yang benar-benar paham matematika dasar dan karakteristik anak sekolah dasar. Permasalahan yang kerap muncul di sekolah dasar adalah pembelajaran matematika semakin tahun terkesan semakin kompleks dan para guru tidak memiliki pendekatan yang ampuh dan update untuk dapat membawa pengalaman matematis ke dunia anak-anak. Kita, orang dewasa sering terjebak pada matematika yang sekedar memecahkan soal bukan soal konsep berpikir.

Nama : Habibullah

ReplyDeleteNIM : 17709251030

Kelas : PM B (S2)

Assalamualaikum wr.wb

Guru matematika yang memiliki kompetensi yang baik sangat diperlukan di sekolah SD - SMA. Hal ini bertujuan agar guru matematika bisa membangun iklim belajar yang bersifat akti, kreatif, inovatif, kritis, dan kolaboratif baik dengan siswa maupun tehadap sumber belajar dalam pengajaran matematika. Selain itu guru yang kompeten tau apa yang harus dilakukan dalam mengajar dan paham dengan pendekatan atau metode apa yang sebaiknya digunakan agar terjadi hubungan timbal balik yang kondusif antara guru – siswa, siswa – siswa, siswa – sumber belajar. Dengan mengacu pada hal tersebut maka pembelajaran yang dilaksanakan akan lebih bermakna terhadap diri siswa.

Nama: Hendrawansyah

ReplyDeleteNIM: 17701251030

S2 PEP 2017 Kelas B

Assalamualaikum wr wb

Dialog yang menggugah dan berkesan.Yang dapat saya tangkap dari dialog tersebut bagaimana mengokohkan fondasi matematika anak dengan membiarkan ia mencari atau menemukan masalahnya sendiri.Membiarkan anak lebih melibatkan dirinya dan lebih leluasa berpikir sehingga anak dapat berkembang.Sistem belajar mestinya harus berpusat pada siswa .Penerapan pembelajaran mungkin dapat dialih fungsikan dari yang tradisional menuju ke yang modern.Saya sangat setuju bahwa belajar matematika tidak hanya sekedar mengenal pola tetapi juga harus mengembangkan dan mnerapkannya sehingga kita tidak terlihat kaku dalam menghadapi perkembangan zaman.Sebab teori,pendekatan, dan metode pembelajaran akan berkembang sesuai dengan perubahan waktu.