From LinkedIn:

**Do you think that students find difficulties for the imagination in mathematics especially in geometry? If you think so,what's the technics used for solving this situation?**

Salim Mchennec Professeur
de l'enseignement secondaire qualifiant de Mathématiques chez Ministère de
l'éducation nationale Top Contributor

Lecturer at Yogyakarta State
University

Imagination lies in Intuitions,
however teaching activities frequently have not developed intuitions yet or
even have eliminated them.

Mehtamatics = mathematics with a
difference

I am inclined to agree with Dr
Marsigit. But I do think that there is a distinction to be made between
geometrical visualisation and mathematical problem-solving in multi-dimensional
space. I certainly cannot visualise 5-dimensional space but mathematically, I
am perfectly comfortable working with 15 or even 500 dimensional spaces.

I have found that some of my pupils have good 3-d imagination and others don't. There appears to be no systematic difference between them otherwise. At first I had thought that people who were also interested in or studying art may have a better understanding of perspective and projections - from higher to lower dimensions. But that has not been the case.

I regret that I have no answers to Salim's second question, though.

I have found that some of my pupils have good 3-d imagination and others don't. There appears to be no systematic difference between them otherwise. At first I had thought that people who were also interested in or studying art may have a better understanding of perspective and projections - from higher to lower dimensions. But that has not been the case.

I regret that I have no answers to Salim's second question, though.

3D Innovator / Educator / Computer
Industry Veteran

Yes they do, however using tools
like 3d visualization to graphically depict numerical constructs provides a
trifecta of visual, audio, and tactile sensory experience for learners. The
millennials learn different lyrics and it is up to educators to adapt their
teaching styles to accommodate these new approach in the process of educating.

Professeur de l'enseignement
secondaire qualifiant de Mathématiques chez Ministère de l'éducation nationale

Top Contributor

Thank you for your contribution to
this subject.I think intuition plays a crucial role in mathematical work, it
can be regarded as a form of intelligence. As stated by Mr James we may use
tracking software or geometrical forms .But beyond the 3rd dimension it becomes
more complicated, arriving to the infinite dimension where all notions of
ordinary geometry changes completely

Lecturer at Yogyakarta State
University

Imagination lies in Intuitions, and
intuitions emerge through experiences. Experiences composes of spirit,
motivation, activity, interaction, knowledge, skill, and minor experiences. So
imagination and intuitions work not only for youngster but also for elders. For
elders, mathematics is both formal mathematics and intuitive mathematics; but
for youngsters (early childhood) mathematics is mainly intuitive mathematics.
Intuitive mathematics is mathematics that you understand but you need not to
define. The youngster understand well about the concept of big, small, close,
tall, high,...without needed to define them. They emerge from their interaction
both at home (family), school, and society. Most teachers behave arrogantly by
introducing formal mathematics to the youngsters. It is bad!.

Research Guide Mathematics
JJTUniversity

I agree to you Dr. Experiance in
Maths is another form of practice which we lag behind. it needs constant
struggle and time which youngesters dont have. Mathematics itself is
intuitive.What do you mean by formal. please explain

3D Innovator / Educator / Computer
Industry Veteran

Hi, To clarify, I was not proposing
we (necessarily) teach linear algwbra, actually use the visual depth of 3d as a
teaching medium for introducing concepts and providing spacial representation
to math topics.

Lecturer at Yogyakarta State
University

@Dr Prabha: I mean Formal
Mathematics is Pure Mathematics/Axiomatic Mathematics in which mathematicians
always perceive as a body of knowledge/structure of truth/logic. While for the
younger learner it is better mathematics to be introduced as School
Mathematics, in which mainly mathematics can be perceive as activities to find
the pattern and relationship and to communicate their findings. However, we
need intuitive knowledge to accomplish both of them.

Research Guide Mathematics
JJTUniversity

@ Dr. Understood pure maths is too
tough even teachers also find difficult to adjust it but there are fast
developments day to day it is difficult to cope up and maths has become too
vast to handle at school level also. We have to bring down Axiomatic approach
to school level. To develop intitutional approach you need to absorb yourself
in the subject where is the time. can we have any solution.

@James maths is a subject requires personal touch. It is very abstract yes 3D will help as a teaching medium but teacher should be good enough to representthe concepts in a friendly way otherwise maths is too hostile.

@James maths is a subject requires personal touch. It is very abstract yes 3D will help as a teaching medium but teacher should be good enough to representthe concepts in a friendly way otherwise maths is too hostile.

Mehtamatics = mathematics with a
difference

Dr Rastogi, what you say at the end
is true of any subject. There is beauty in mathematics and there is tedium. A
good teacher is one who can inspire pupils with the first and help pupils deal
with the second. I was lucky: I had two such teachers - one when I was around 9
years old and the other when I was 18. I am now in pay-back mode: using what
inspired me to inspire others.

Lecturer at Yogyakarta State
University

@Dr.Prabha: There is a huge gap
between the ideas of pure mathematicians (the "first") and school
math educators (the "second") in perceiving how the younger may learn
mathematics. Your idea " We have to bring down Axiomatic approach to
school level", is no problem for you and for pure mathematicians; however,
it can be very big problem, strange, odd and absurd in sense of younger
psychology of learning. The "first" strive to force their own math
concepts to the youngster; while the "second" strive to communicate
mathematics with the younger based on studying and understanding about
"the way of the younger learner think". So the "second" try
to creatively build a bridge e.g. by creating School Math in order to approach
the younger learner gently. If you and the "first" try to force your
method and are not willing to uncover the younger psychology of learning, there
will be no solution. However, please note that for many centuries your method
of teaching math can be perceived as fail and producing most of the youngster
dislike math. Anand Mehta is only a few example of the success student, but all
youngster have their right to learn mathematics based on their backgrounds.

Department Head -
Communications/Mathematics

How can students use their
imagination in mathematics when they aren't taught the fundamentals of problem
solving correctly? Once they master topics and generalized solutions to
problems, then they can move on to creating their own problems and becoming
more imaginative.

Research Guide Mathematics
JJTUniversity

@ Dr Marsigit. I understand the
problem but do we have the solution.To teach addition and subtraction at tender
age is very difficult. unless they have to byheart it . this tender age is very
difficult to handle. So you cant bring down more to lower level but pressure at
higher level increases the problems. That stage you feel helpless. Maths is not
only for mathematician but applicable every where wether you likt the subject
or not. May be we should use calculators or Ipads for calculations and abstract
concepts should be taught thoroughly in schools but teachers should be trained
enough.

@ Anand I agree to you good teacher makes an impact on the life of students. I was not lucky .I had to struggle thats why I became maths teacher but problem is when you get more of the students sitting in the class without interest. Your real test is to make concept simple and reach to them but time is detterent. You have to finish a lot in limited time

@ Anand I agree to you good teacher makes an impact on the life of students. I was not lucky .I had to struggle thats why I became maths teacher but problem is when you get more of the students sitting in the class without interest. Your real test is to make concept simple and reach to them but time is detterent. You have to finish a lot in limited time

3D Innovator / Educator / Computer
Industry Veteran

Dr. Prabha Rastogi,

Agreed a good instructor is required. that said, using 3d to illustrate concepts, I have seen pretest to post test increases of up to 30% regardless of class type. that includes visual learners, ADHD, ASD, and both average and a students. isn't the same 30% of course but is repeatable and measurable. key is the development of teaching materials by master teachers, and not by programmers. "Content is king" in that arena. 3d tech gets a bad name from poor implementations. does work well with good production team behind it.

Agreed a good instructor is required. that said, using 3d to illustrate concepts, I have seen pretest to post test increases of up to 30% regardless of class type. that includes visual learners, ADHD, ASD, and both average and a students. isn't the same 30% of course but is repeatable and measurable. key is the development of teaching materials by master teachers, and not by programmers. "Content is king" in that arena. 3d tech gets a bad name from poor implementations. does work well with good production team behind it.

Research Guide Mathematics
JJTUniversity

@James I have the knowledge of maths
but not much idea of programming. I am associated with educational publications
as a writer but want to do somthing on e learning so that I can reach to more
people. You are right when you say Content is King. I have seen the effects of
visual learning on kids.If concepts are made simple student friendly you can
reach easily to students

Lecturer at Yogyakarta State
University

Dr Prabha and others: In the sense
of Psychology and Pedagogy of learning mathematics the worst thing happened
when Pure Mathematician strive to deal with education/teaching. Pure
Mathematicians are frequently soliloquy express their own subjective perception
about their experience in dealing with mathematics as a science, e.g.
mathematics is beautiful (Anand), Content is King (Nord), bring down axiomatic
approach (Prabha), absorb mathematics (Anand), introducing concepts (Nord),
finish a lot in a limited time (Prabha)...All you have produced of your own
notions without considering what happened to the younger learner of math.
Again, all of those are about you (ambition of the adults), and not about your
younger generation. Unluckily, your younger generations have not equal chances
and right to express their own world. So all your claims and judgements about
good teaching practice of math are unfair and meaningless for them. To solve
the problems, please ask them how really to learn mathematics. I challenge you
all to make your younger generations to be your real teacher!.

Research Guide Mathematics
JJTUniversity

Dr I accept that I am not much
related to younger generation but I would like to understand the mind of
younger generation because even grown up students have same biockage for maths.
How you deal with students.At college level also students have same hate to
maths how much you simplify the concept

Research Guide Mathematics
JJTUniversity

Need your sugesstions

Lecturer at Yogyakarta State
University

Dear Dr Prabha, it is not an utopia
or fiction that we need to ask to young learners on the way they think (math).
Too much to be able to be indicated about the younger knowledge/concept in
which they understand well but they can not define, e.g. the concept of big,
small, long, short, high, short, near, far away, few, many, one, two, some,
sad, happy, love...etc. Those all I call as Intuitive Knowledge. In fact, it is
not only younger learner who employ Intuitive Knowledge but also the adults and
even the elders. So our live really consists full of Intuitive Knowledge. The
characteristics of Intuitive Knowledge i.e. when we understand something but we
do not remember when and how we did so. Intuitive Knowledge emerge from the
Context of life (family, society, and schools) through Interaction/activities.
So that why mathematics for younger learner should be defined as Social
Activities (Paul Ernest, 1995) and Activities to Search the Pattern, Problem
Solving, Investigation and Communication (Ebbut and Straker, 1994). From social
activities there will emerge a differentiation pattern of concepts in such a
way that we get our Categories of Knowledge (math) in our Mind (Aristoteles and
Immanuel Kant). Those categories make us be ready to think all new analytic, a
priori, a posteriori and synthetic knowledge. Mathematics is said to be a
Science if it is Synthetical a Priori. Thank

Angga Kristiyajati

ReplyDelete17709251001

Pps UNY P.Mat A 2017

Thank you very much, Mr. Prof. Marsigit.

This is another inspiring script of debate. This debate between pure mathematics mindset and educational mathematics mindset. I do agree with Paul Ernest that Mathematics education should be have:

a. Provision of a well structured environment and experience for mathematics learning;

b. Counseling children in active and autonomous inquiry in mathematics;

c. Attention to feelings, motivations, attitudes, and behavior from negative aspects.

(Ernest, 2004)

Auliaul Fitrah Samsuddin

ReplyDelete17709251013

PPs P.Mat A 2017

Thank you for your sharing your brilliant idea through this script, sir. I cannot help but agreeing with you on we should separate between formal and educational mathematics. Eventhough both are mathematics, but the way we deliver them to children should be different with that to college students for example. I also noticed your concern related to spacial ability which needed intuition and imagination. Fortunately we have mathematics-based application which can ease us to deal with three or more dimension related problems.

Junianto

ReplyDeletePM C

17709251065

One of the problems in learning mathematics, especially in geometry is student cannot imagine the object because they can learn well if the object can be seen or can be hold by them. When teacher study together with student in the classroom, teacher must fasilitate student so it can help student to imagine the object of geometry. For example, teacher use object in daily life that can represent one of the object in geometry like cube, triangle, etc. After that, new students are able to imagine when one day do not use concrete objects. For example, when the test took place, students are able to imagine because at the time of learning students have been given examples several object in geometry.