Dialog Internasional 2 Pendidikan Matematika

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

Thank


Burçin 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's


Marsigit 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