My general observation on our students has been Maths is the
most difficult study area. How can i remove this syndrome in our students?
13 days ago
•
Warren
Wolff • You cannot overcome all their reluctance. Frequently, this is because
of poor preparation in the earlier years. For boys, it is easier than girls.
Creata a scenario in which there is some problem that needs fixing, but you are
not sure how. So, you go to the tool box, and meditate over which sequence of
which tools should be "attempted". Sometimes, I relate about an
engineer I knew who was making a healthy salary to solve several problems. One
of them, he had been working on for over 3 years and still had no solution.
12 days ago
Jonathan
Young-Scaggs • Teddy,
Could you be a bit more specific? What math
course are you most challenged by in terms of delivering content in a
accessible manner? Are the students "invested?" Math can be difficult
because we have always told students that it is a difficult subject, but those
of us teaching math ... I guess we never really had that tough a time. Why must
our students hear anything negative about the material? We need to say just
what we know. With some hard work and a little practice ... math is fun!! In
fact it gets even more intriguing as we add complexity. Who would argue??
Calculus is easy ... its the algebra that makes the subject complex. Teach what
needs to be done, and make space for the creative elements of student
initiative.
Yeah, I know ... I have oversimplified the problem. But "the
machine" must be moved forward by any means necessary. What are we to do?
I wish our education system would place a much emphasis on math literacy that
it places on reading and writing. Then we might not have to start sooo far
behind. Catching up is where the real problem resides.
Your thoughts?
12 days ago
David
Ball • Maths is a challenge. And it is achievable. A good Maths lesson is a
good lesson in any subject, not so different. Maths has the virtue of right,
wrong and quirky. People refer to how easy Maths is without considering why
people become phobic. Intimidation cows students. But rising to the challenge
.. and possessing the arrogance to say to ones self "I don't understand
what you mean but I will do this thing that others have" is helpful. I
have dealt with students who were so low they couldn't follow simple
instructions to solve routine algebra. Their knowledge is poor regarding mental
arithmetic. Their problem is not to do with following an algorithm. There is a
low percentage of students who by year 10 (15 years old) don't gain anything
beneficial from further Math study. Most 'weak' students can benefit from
remediation which targets basic 'skills' building their confidence. Online material
is available for such remediation. I have run a battery of tests and
assignments for building mid range students which has been successful from
years 7 to 10.
12 days ago
Marie
Kielty • We begin at the earliest years with well trained
teachers. There is research published in 2008 in Developmental Psychology,
"School Readiness and Later Achievement" by thirteen researchers at
nine universities in three countries. (The principal researcher was Greg Duncan
from Northwestern who is now at one of the universities in California.) The
research showed that it is the math more than the reading that children know at
the beginning of kindergarten that is the greater predictor of success by the
middle grades. This was referenced in Mathematics Learning in Early Childhood:
Paths Toward Excellence and Equity, a publication of the National Research
Council.
Teachers of young children typically do not have a good background
in math and how to teach it. The National Reserach Council publication
mentioned above has listed the trajectories, the sequence, for learning number.
Because young children can count, parents and sometimes teachers assume that
the children have the same understanding as we adults. They may or they may
not.
This is especially true of understanding cardinality. In my work of
training teachers I use several phrases in other languages. One of them is
"isa dalawa tatlo apat". I ask the group what the phrase means to
them, how does it makes them feel and then I ask them to share with those
around them. It is eye-opening! The phrase has no meaning! The phrase is
"1, 2,3 4" in Tagalog, one of the languages of the Philipines. If
children do not understand cardinality, they need to begin counting at one when
they add, instead of beginning with the last number and adding on. And the
solution is counting on one's fingers into third, fourth, fifth grades and
beyond.This has major implications in the children moving toward mental math.
When
teachers typically teach addition to young children, they begin with the math
terminology "plus", "minus", "equals" without
teaching the concept of equality. Again this has inplications into second and
third grade when children deal with problems such as, 8 +5 = _____ + 3. The
blank means that is where the answer is put. So the problem becomes 8 +5 = 13
+3, in which students ignore the "+3".
Illinois has no endorsement
in the teaching of mathematics below the middle grades!
The whole foundation
for math has been laid by then!
11 days ago
Richard
Catterall • One: Mathematics IS the most difficult area of study
because it involves language at one further level of abstraction. There is
nothing wrong with noticing that! and
Two: Mathematics can be made enjoyable
and therefore students will want to learn even when it is difficult - in fact
students thrive on challenge. There is so much richness in the study of
mathematics that when the teacher is enthusiastic (and preferably knows plenty
of mathematics) the students will want to know what there is to know.
Three:
much of the learning in mathematics is sequential, so that if a student has a
gap in knowledge, or understanding, or both, the gap needs to be filled before
further learning past that point can take place - rather like trying to build a
taller building on a weak foundation - and often students are very reluctant to
do work that they perceive as "beneath their level". Explaining this
and fixing the problem are probably the most difficult parts of teaching
mathematics.
Four: New Zealand mathematics education has tried to address some
of these challenges recently (in the last 7 or 8 years), and although there are
still problems and difficulties the improvement in attitude of students towards
mathematics has been significant. Get hold of a copy of the Numeracy Project
booklets and encourage your local, regional and national governments to get
something similar working there. And good luck! Remember that the probability
of success is directly proportional to the amount of inspired work of dedicated
teachers!
11 days ago
Richard
Catterall • PS Something I have found useful in explaining to
students why they need to practise exercises once they have grasped a new
concept is the parallel between learning mathematics and learning to ride a
bicycle (or learning anything actually). There are five distinct stages and
many people become stuck at one of those stages and never get to the next: One:
When you know you cannot - I cannot ride because I am too small/I cannot do
mathematics because my parents tell me they couldn't, so I won't be able to
either. Two: When you know you can - I have not tried the bicycle yet but I see
my brother riding and he is a person just like me so I know I will be able to
learn/I haven't tried this mathematics yet but all those other students learned
so I can too. Three: When you try, and fail - I got on the bicycle then fell
off and hurt my knees/I tried that problem but got it wrong. Four: When you try,
and succeed - I got balance/I got a problem correct on my own. Because this is
such a happy time, many people stop there and do not proceed to the fifth
stage, which means that if a difficulty arises they fall off/fail again and
sometimes drop straight back to stage one! Five: When you "overlearn"
- I have done so much practice that now riding is automatic and I can
concentrate on the traffic around me/I have done so much practice that now I
can tackle new and different problems that are unfamiliar. :)
11 days ago
Seong
Kim • Math can be as easy as 1, 2, 3, 4, 5, ... or easier, and it can be as
hard as 2, 3, 1, 4, 5, ... or harder.
The same is true, too, for any other
area in school discipline as language arts, science, history, etc. And the same
is true, also, for any work that needs to be done.
If something is worth it,
it is probably not easy, and is usually not free.
$50 can be a big money for
many people, but can be a petty cash for many other people.
It is for sure
though, no money is easy if it is earned.
And the same is true for math, too.
What
matters in education is sincerity, and not efficiency.
11 days ago
Dixie
Donovan • I teach the students (secondary level) that struggle in
math. The number one issue is integers--dealing with the negative numbers. If
they can't do that it doesn't matter what we try to teach them as it always
falls back on dealing with the negatives. I've put together a research project
on this that I will be implementing over the next two months. Hopefully I can
find a way to help them understand this very basic but critical concept.
When
I started teaching high school I didn't understand why integers was an area
being taught. It's taken me eight years to realize that is the crux of the
problem in understanding. If you don't believe that, look at your students and
try to remove the various issues and get to the core issue. When you do, I bet
it's the negative numbers.
11 days ago
David
Ball • Good luck Dixie but I think you will find it is more than that.
Addressing individual needs is the imperative in classwork because if an
individual won't be part of the lesson, you can have no end to dividing the
class to achieve the lesson's end. As for dealing with negative integer
operations, I find the visual aid of the creation of a table .. 3 +1 = 4, 3 + 2
= 5, 3 + 3 = 6 .. then reverse the table and continue .. 3 + 0 = 3, 3 - 1 = 2
.. etc by doing the table with the class you can illustrate the abstract rules.
Some drill work to reinforce it. Make put together jigsaw puzzles out of
student made problems .. get the students to make and do them. Paper exercises
are still effective.
11 days ago
Seong
Kim • As we all know, example is the best teacher.
So teaching negative
numbers, too, we may want to begin with examples as the ones David showed above,
or the ones below:
1 + (-1) = 0, 2 + (-2) = 0, 3 + (-3) = (-3) + 3 = 4 + (-4)
= ... = 123 + (-123) = 0, etc.
-7 = (-1) + (-6) = (-2) + (-5) = (-3) + (-4) =
(-4) + (-3) = (-5) + (-2) = (-6) + (-1) = 0 + (-7)
Then, for instance, move
on to: 2 - 1 = 2 + (-1) = 1 + 1 + (-1) = 1 + 0 = 1.
And then, ask the students
to come up with their examples, and then, ask them to say what they mean by a
negative number. And if necessary, help them keep refining the definition they
come up with until it is close enough or appropriate enough within the
knowledge or understanding of the object they have now or at the moment.
Then,
move on to the other operations in arithmetic, together with examples, of
course.
Experiencing examples, and producing examples, along with correcting
the mistakes and discussions on their findings, the students will approach the
idea they need to get, and they will get it themselves.
And during the
examples and discussions, we can add some spices to their cooking, and the
spices are the theoretical facts, terminologies, notations, etc.
Adding those
spices, we want to consider, of course, timing and the amount, and should be
able to modify the spice in accordance with the students responses or feedback.
11 days ago
Rajinikanth
Dhakshanamurthi • Build and maintain good relationships with students and
Planning regular maths classes to be key skill to remove this syndrome. i
believe this will work if only if the teacher is expert in the subject.
10 days ago
Jan
Olivas • Making Math lessons and practice assignments as connected
to real life as possible often pulls students back into the "teachable
moment". When they see the relevance of what they are doing in the
classroom to their lives, the light bulb goes off!
10 days ago
Teresa
Katuska • I liked the bicycle analogy- it seems that our struggling
students don't actually get to stage two. I think many students (at least in
the United States) are influenced by parents and others who are readily willing
(and even proud) to say "I can't do math" in a way that they would
never say about another subject. I get very upset when I hear a colleague in
the English department say this. My math students know that I read a lot, both
for pleasure and to learn new things. We talk a good talk about learning "across
the curriculum" and yet we tolerate a culture in which people brag about
poor math skills. Math IS hard, but so is learning to read, playing the piano,
hitting a baseball, or beating a video game. We need, at least from the early
grades, to make sure that kids believe they can be "good at math".
10 days ago
David
Ball • (in answer to a message) .. Yes, but there is a diminution in the
analogy which is counter to reality. How the brain grows to pick up and acquire
grammar is not perfectly understood. I have met better teachers than I who
assure me there are some concepts some students don't get. There are a myriad
of possible reasons for it and only some are addressed through basics mastery.
A counter example is how the greatest math minds sometimes develop without
mastering basics .. eg Ramanujan whose mistakes were as elegant as his proven
theories. In some ways, slowing down learning to accommodate a few translates
to slowing down everyone and promoting no one. I focus on the middle in big
schools because there are always those willing to help the top and bottom. But
also systemic resources are best allocated when the middle is the target.
10 days ago
Joseph
Ventola • When I was a leave replacement and a substitute the way I
had them enjoy and learn was make it realistic to them. Find out their likes
and apply the lessons to that. Also, integrate the other subjects to math
showing how important math is because it is in pretty much everything.
9 days ago
Kathryn
Kozak • I teach mathematics at a community college. Most semesters I teach a
developmental mathematics class. One thing I have noticed over the years is
that students give up if they don't understand the problem right away. I, and
my colleagues, believe this may stem from timed tests of math facts in
Elementary School. I am now seeing this with my son. He says he is not good at
math, because he cannot get his skills done fast. However, the other night he
divided 120 in half correctly without even thinking about it. He is actually
quite good at math. This may be why we see a gender difference in math, though
I have no empirical evidence of this, or my other theory. But we do see
students in college give up on a concept very shortly after they try it, if
they don't get it right away. I would like to see a reduction in the emphasis
in the speed of knowing the math facts, and more of an emphasis in the beauty,
excitement, use, and fun of mathematics.
9 days ago
Cliff
Cohen • Possibly if we paid math teachers more, more people with a real
talent for mathematics would pursue a teaching mathematics. Math is undervalued
and math teachers more so, therefore why teach math when there are so many
careers that reward talented mathematicians.
9 days ago
Warren
Wolff • Sadly, Kathryn, this all a result of the overall concept of a
"throw away " and "instant gratification" society. Not sure
significant improvement is on the horizon, BUT we just keep working at it.
9 days ago
Lucinda
French • The use of calculators and computers has made this a very
technologically dependent generation of young minds. Challenging to teachers as
well as Grand-parents, is the pre-shcooler who is computer dependent. Laying
the foundation for advanced thinking in a classroom for children using software
technology that was only recently developed is the biggest challenge that I've
encountered. Yet the principals taught in mathmatics dated back to ancient
times and do not change. My experience has been to excite the student with the
history of each topic and link the theory to the applied use. Kids need to see
and feel the bicycle before even conceptualizing actually riding it!
9 days ago
Dixie
Donovan • Kathryn--Interesting you should talk about the timed
tests. My son is brilliant in math but his mind works faster than his hands.
Orally he could do lots of math. When it came to the timed tests he was not
completing them because he was being careful with his penmanship. Once I
realized the test was the same each time, I taught him to memorize the 100
answers so he could concentrate on writing the answers and not doing the math.
What did I learn? The timed tests were a load of hooey!
Don't get me wrong,
learning by rote can be a good thing. I work with a girl with a very low IQ who
can give me the answers to simple multiplication without the calculator. When
she gets frustrated or unsure she then relies on the calculator. The point is,
she's learned the basics and it had to me memorization and practice. But again,
it's when I work with her orally. We don't allow for the students that work
better that way. My son could do his math homework faster by dictating it to
me.
Writing is good, but I believe knowledge is better. We seem to be willing
to forego real learning in order to do things the way they've always been done.
It means we as teachers have to be willing to decide what is important and
change our methods. But even if we do and the students actually learn, there is
a paper and pencil test waiting for them at the end to determine their fate.
9 days ago
Richard
Catterall • Dixie - Yes paper and pencil tests are always there
waiting; One thing I do with my senior students is to emphasize at the start of
the year that my aim for them is for them to learn to think for themselves, and
that results in examinations are a bonus, a usual by-product of being able to
think mathematcally. After a year with me most of the students "buy
in" to this aim, and are more relaxed about the final examination than
many of their schoolmates. Many do well; but, more importantly, they mostly
take away a confidence in themselves as mathematical problem solvers that
serves them well later. I was fortunate to be able to teach my son in 2011 and
he gave me feedback that these teaching methods have worked well for him.
One
other thing I do, with every class, is to survey at least two (relatively)
randomly chosen students (different each time) at the end of every lesson to
ask: did you learn something? what? did you enjoy something? what? If I get
less than three "yes" answers out of four I know to amend my
teaching.
8 days ago
A
Cron • Teddy, when can you get the parent to say "Math is easy for
me" and I will help you, and they do. The problem has been ingrained into
the psyche of your students...it will probably take a few generations of savvy
teachers and parents to change the overall attitude...oops this sounds like a
downer attitude, but there is no easy solution...
My mother was an educator
and my father had a masters in economics, my parents never stated any thing
about any subject being difficult for them...so I did not have this ingrained
into me, my students do...I had a brilliant math student once, but since the
mother and father had trouble with math they discouraged her abilities...this
is a problem...
8 days ago
Richard
Galbraith • Just a short comment, Cliff. Talented mathematicians
don't always make talented mathematics teachers.
8 days ago
A
Cron • I can verify that my first calculus teacher was an honor graduate
with a master's from Rice University, very talented...could not connect with
students and could not teach at all. Even math majors were failing...
8 days ago
David
Ball • I love the antecedent belief that many express here that students are
blank canvasses on which knowledge is placed. Research doesn't show that.
Parents can be helpful. Teachers can be constructive. Students can be
proactive. Some don't get it. Delivery can be improved. Instruction can be made
more explicit. algorithms can be shortened to a few steps. There is a danger
that good students get bored by pre-digested material. Getting back to the
original post, my advice is to target the middle bands. Schools that
effectively work with the middle tend to have happier, more productive top and
bottom ends too .. and better public results.
8 days ago
Seong
Kim • By the way, good math teachers are talented mathematicians, too,
aren't they?
It's simply because good math teachers know very well how math
works as well as how to teach.
8 days ago
A
Cron • But not all talented mathematicians can teach, this does not say a
talented math teacher is not a talented mathematician...most of my math
instructors were teachers talented in teaching mathematics...
7 days ago
Jonathan
Young-Scaggs • @A Cron -- Right talented teaching of the subject of
mathematics does not require one to be a "mathematician." But a
talented math teacher must pass the passion of math on to their students. When
that is achieved then success as gauged by student achievement will silence the
critics. Mr Kim (above) understand that the challenge is the inner workings of
math. Most of us have seen YouTube videos or late night commercials about
tricks to improve children's mathematics knowledge. These are just tricks and
memorization techniques. Nothing against memorization, but who needs to know
how to multiply 4-digit numbers in their head?
7 days ago
Warren
Wolff • If you can learn the tricks as a student, it actually develops
confidence and reveals that math CAN be fun. We engineers make decent math
teachers too. I think my HS students would agree. Sadly, we math teachers are
waaaay misunderstood by many administrators who are the very ones who hate
math.
7 days ago
Seong
Kim • If you know very well how math works and how to teach, together with
the passion of math, you can make a good math teacher, no matter what field you
may be in.
What's more important is though, the fact that the students learn
from you, so you want to be a good example yourself. Show and Do yourself
first, what the students need to do to see how math works and what they can do
with it.
And in teaching, what matters is sincerity, and not efficiency.
7 days ago
Ilirjan
Cane • The fact that mathematics is the most challenging subject in school
is not a syndrome; it is a reality. There are, of course, individual variations
with regard to time and effort a student spend on studying it, but for each
subject such variations exist, and other factors, such as motivation, genetic
predisposition, and learning environment also influence these variations. So my
question is: Do you really think that math is not the most difficult subject
for students? I am afraid that you will have a hard time convincing them about
it.
7 days ago
Richard
Galbraith • Too general a statement. There are many students for whom
math is not the most difficult subject, and, for example, English is.
7 days ago
Cliff
Cohen • Actually, the problem is that many parents tell their children that
mathematics is hard, worse, some teachers do as well, and worse of all, many
students believe them. We who know better need to tell students how exciting
mathematics is, and the exciting things that can be done with just a little
mathematics. Mathematics part of our lives. Most people can shoot a gun or
rifle and hit a target with a little skill and practice; not even thinking
about the math involved, but with just a little math, you can hit a target with
a cannon or launch a missile hit an unseen target.
7 days ago
Richard
Sippel • I agree with Cliff, my parents tell their kids they were
not good at math and instill in them that they will not be good at math either.
Before they ever step in my room they have decided they will not do well. It is
difficult but doable task to get some confidence built up in my students.
7 days ago
Deborah
Crichlow • I think the answer to this question is complicated. There
is no one answer to this question since there are so many reasons to ask it.
For example, is the math hard because students have poor math (including
problem-solving,visual literacy, and critical thinking skills), is it hard (for
us and them) because they are not motivated, is it hard because the pace is too
fast, is it hard because of our style of teaching for the students we have is
not effective, or is the math hard because there is no support for students who
need remediation? There is no magic bullet. Teachers need to gain experience,
continuing education in their subject, and mentors to help them be the best
that they can be. If mentors are not possible, then they should work with each
other in professional learning communities to discuss their problems, which
might be school-wide, rather than just in your classroom.
I don't need to say
that the student of today is very different than those of ten years ago. We are
in the computer age and with that comes changes in our social culture. As
teachers, we must adjust to these changes to get students to buy into what we
are offering them. They must see education as relevant to their lives.
7 days ago
Richard
Catterall • Ilirjan - Yes. Richard G. - No; all other things being
equal Mathematics is one abstraction more difficult than a person's first
language (though parts of it may be easier than parts of subjects as taught in
schools), Incidentally it is the same part of the brain that processes language
as the part that processes mathematical abstractions, so anyone who can read,
write and speak their own language CAN learn Mathematics, it is just hard work.
That does mean that the person who can do Mathematics can do anything else too,
which is why researchers are finding mathematical ability a good predictor of
future success in learning. Cliff - Yes; Mathematics is fun, exciting and
incidentally useful. I try to emphasise the first two as parents, employers and
the whole wide world put plenty of energy into telling students how important
Mathematics is for jobs (compare the reasons people learn Art!). Richard S -
Yes; teaching Mathematics is mostly about building confidence - it's a con
game! We take the students through all those five stages of learning and get
them to give themselves so much evidence that they can do Mathematics that they
never drop back to stage one again, and then they can do the rest for the rest
of their lives. That's an exciting business to work in. Deborah - Yes, it is
complicated, so we need to use every available strategy and piece of research
to assist us. A wise old teacher once said to me that, knowing that you can
lead a horse to water but not make it drink, our job is to give it salt! We
strive to continuously learn ways to be salt for our students so that they
drink deep of the mysteries of Mathematics.
One tactic I have been using
lately (a couple of years) is to invite "intelligent questions" about
Mathematics from my students, and accept all questions as
"intelligent" and find ways to answer them that lead to more
mathematical learning. This does sometimes mean that I introduce advanced ideas
to junior classes; but I usually only give them a taste then return to the
spiral of learning they need to advance on to gain a complete understanding.
Thank you folks for all these answers to Teddy's question. They have helped
inspire me to keep learning more and teaching more Mathematics.
7 days ago
Pamela
Kranz • Great thread. Sadly, I've found in elementary school that teachers
are more comfortable teaching reading and writing than math. I taught 6th,
still in elementary, and spent a lot of time showing kids that they understood
more than they thought they did. "I don't get it" was met with,
"OK, but what do you understand about the problem-we have to have a
starting point so I can help you". It took awhile to build their math
confidence, but we always made growth. Oh, and not a fan of timed tests.
6 days ago
Paul
Sinjani • I struggled with math in my school days, in fact, I
failed. I tarted learning maths when I went college. This was so because I was
always thinking math was tough and everyone said so. In college I met a
lecturer who had a different attitude and approach to math. She made fun when
teaching it and she assured me that I was a smart student. That boosted my
interest for math and I have been learning it. In fact I have taught grade 8
and 9 math and all my student passed.
We need to make the teaching of math
very practical, applicable and relevant to life. Math is all around us and is
with us. We need to help students realize this. Get students engaged.
6 days ago
Seong
Kim • If you are a math teacher, and your students like you, your students
will probably do math pretty well or very well, and more importantly, at least,
will not grow objection against math or study of math.
You don't have to look
beautiful or attractive to get liked by the students.
And you don't have to
please your students, either. You are a friend of theirs.
All you have to do
is to be sincere and considerate, and always listen to them.
Listen to them,
and see what they need, and then, do it.
Ask questions so that they can reveal
what they need, and then, do it.
So don't just see it or say it. Just do it.
If
it doesn't work, revise it, and do it again.
6 days ago
Brian
przybylski • I have read some tintilating comments on this thread.
comes down to: Be excited about teaching it and get the students on your side.
I sing and dance(poorly) and generally act the fool in class, but my students
show up, and some times they get the picture.
5 days ago
Richard
Galbraith • Brian, I agree, up to a point. Some of us are not
effective singing or dancing. I also did weird things to get their attention
and it worked most of the time. However, all students do not react favorably to
that sort of thing. You must find what works for you (most of the time) and
"hope for the best."
5 days ago
Louise
Berman • This is from an article I read and thought to publish it
in the school newsletter to parents.
. "The frequency of number talk in
the children’s homes had a big impact on how well the youngsters understood
basic mathematical concepts such as the cardinal number principle, which holds
that the last number reached when counting a set of objects determines the size
of the set (“One, two,
three—three apples in the bowl!”). A subsequent study
by Levine found that the kind of number talk that most strongly predicted later
knowledge of numbers involved counting or labeling sets of objects that are
right there in front of parent and child–especially large sets, containing
between four and ten objects.
Though it may not come naturally at first,
parents can develop the habit of talking about numbers as often as they talk
about letters and words. Some simple ways to work numbers into the
conversation:
• Note numbers on signs when you’re walking or driving with
children: speed limits and exit numbers, building addresses, sale prices in
store windows.
• Ask children to count how many toys they’re playing with, how
many books they’ve pulled out to read, or how many pieces of food are on their
plate.
• Use numbers when you refer to time, dates, and temperatures: how many
hours and minutes until bedtime, how many weeks and days until a holiday, the
high and low the weatherman predicts for that day.
• With older children, math
can become a part of talking about sports, science, history, video games, or
whatever else they’re interested in.
With practice, parents and children alike
will find that math makes a very satisfying second language"
5 days ago
Marie
Kielty • Excellent ideas, Louise!
5 days ago
Tamara
McAnelly • Why do you want to? Something has to be difficult...
challenging. Math is a discipline. Nothing worth anything comes without struggle
or trial. I can not tell you how many times I have cried over the frustration
of math... but I LOVE IT!! It's part of the game.
4 days ago
Warren
Wolff • Judicious application of disequilibration!
4 days ago
Seong
Kim • If students can build strong foundation of algebra, they can reduce
the syndrome.
Doing algebra, they need to know not only numbers, expressions,
etc., but how they work and how they mingle with the arithmetic operations.
Algebra
matters, together with geometry.
What actually connects problems to solutions
is algebra.
3 days ago
David
Ball • Seong, that sounds reasonable. In the US, following Sputnick, the
Bourbakist math movement emphasised set theory for similar reasons. It became a
fad and was largely felt to have failed as abstracting concepts doesn't help
most learners. It was followed by concrete materials to introduce concepts. Now
computers allow us to pursue individualised mastery. My preference for mass
instruction is "introduce a concept. Practice it. Drill it. Use the time
to set its place among the scheme of things and allow homework/improvement"
There will always be a performance band from good to bad. The idea being to
pitch to the middle. Let school process handle the rest. The idea that we can
teach all equally and get equal outcomes is not observed in research.
3 days ago
Louise
Berman • I did not reference my quote above so here it is now:
Why
It’s Important to Talk Math With Kids
March 2, 2012 | 8:27 AM | By Annie
Murphy Paul
http://blogs.kqed.org/mindshift/2012/03/why-its-important-to-talk-math-with-kids/
I
am not sure about copyright on this stuff and don't want to break any laws or
offend people.
3 days ago
Cecilia
Villabona • I am fascinated by this thread started by Teddy with
"......Math is the most difficult study area..." to which we have
many responses from " ....for boys, it is easier than girls" (did you
mean Math, Warren?) with ideas like to be entertaining, be liked, be a
mathematician, make sure students know Algebra, use the right
sequence,introduce Math early, and more to remove the syndrome that math is
hard.
No mention made to curriculum and methodology, it seems. Or to ability,
except by Richard who says that anyone who can learn a language can learn
mathematics.
Then Paul shared with us that only when a college lecturer "
made fun when teaching and assure me that I was smart" was he able to
learn it.
Here is what I believe: Mathematics learning required using our
ability to think abstractly, and in general about 5% of us are naturally
abstract thinkers. Some of us in that category become math teachers. If when we
do we approach our students with the viewpoint that they should get it as
easily as we do, we might become misunderstood by administrators and parents
who would like to see more students get it that just 5%, understandably so. Our
challenge is to reach the 95% who in most cases speak a language or two but
loose confidence in themselves and end up believing they are not smart.
In
this moment all of the suggestions given come in handy, but often the
curriculum is our enemy, taught to students in the order in which mathematics
was discovered, for no other reason that it has been so, with the pressure to
put our students through the high states test mill when at times they are not
even abstractly ready. No wonder they end up thinking they are not smart!
To
the risk of making this too long, now on methodology. When elementary teachers
are math anxious, they are not capable of building confidence in their
students, when we as teachers assume that it is hard to learn math and only
some can do it that is what happens.
When we make students feel insecure and
unsafe because they do not have the right answer, they go to a safe place to
not think and not say anything for fear of being wrong, when we choose easy
tasks for them since we believe that is all they can handle, we prevent them
from doing the hard work, when we give them the answer too soon we encourage
them to give up, oh I could go on forever....
2 days ago
Richard
Galbraith • Cecelia, You almost did go on forever!!!(just kidding) I
think we all would like a simple answer but, as you have described, there is no
one answer and it certainly is not simple. Those of us who have taught for a
lot of years have seen curriculum, method, and just about everything else cycle
several times.
2 days ago
David
Ball • Well put Cecilia. I only wish more math teachers were abstract
thinkers. I'll settle for the ones who use abstract thoughts .. which is
probably most .. but which .. (I'll stop that line) ..I think the issue of
anxiety is more closely related to the failure of authorities to specify what
is required .. they fail because they want more and accept less .. which is
confusing. Then add math phobia. Thing is, we want a lot because some can
handle it. I love the "Joy of Mathematics" and its sequel. But they
aren't books you simply hand to children. They need to be read and understood
and applied when the time is right. That takes someone special. I think what we
are seeing is more a lack of leadership confusing junior initiate instructors.
2 days ago
Richard
Catterall • So, David, (and Richard, and Cecilia, ...) here is the
challenge: take some leadership in the USA and begin programmes like the
Numeracy Project we have used here. You have the opportunity to do some
important work for your country. It will cost you the time and energy and
effort involved in lobbying local and state and national administrators, and
you will very likely (two sigma probability I'd say) get no financial reward
nor any recognition for doing it; but the result will be a numerate population
in the next generation - a noble goal. What do you say?
1 day ago
David
Ball • Love it Richard. I live and work (?) in Sydney Australia. Cecilia is
doing exactly what you suggest with a wonderful program crossing Finland and
the US ( http://app.pathstomath.com
). I have developed a program which lifts the middle band performance of a
suburban multiethnic HS in Sydney. I have a stumbling block which I could use
international help with related to death of school child Hamidur Rahman (I'm
not at fault). I am unemployed yet working full time .. but I can't help myself
.. I am a teacher, born and bred ..
1 day ago
Cecilia
Villabona • Richard my life mission in my entire teaching career has
been to teach my 95 % non-abstract thinkers and to help them experience Aha!
moments as they learn mathematics. Have I changed the status-quo in either
Colombia or the USA? Not really but I have worked with over 10,000 learners and
have experience a lot of rewards (non-monetary) which are very valuable to me.
Thanks
for the endorsement David, I appreciate it. Yes, we are combining expertise
from my teaching years with Finnish materials to create what we consider a
necessary change agent.
1 day ago
Wallner
Alina • First course as a student, our dean told us that we should get
prepare for one of the most difficult Faculty and won't be 4 easy years. And he
was right, in the first year we start in a number of 220 students and we
graduated unless than 60%.
12 hours ago
Cliff
Cohen • Responding to Wallner Alina: When I start college as a Math major, I
was informed that I was in the top 2% of entering freshman majors. Thirty-five
of us so designated began an "by permission of the professor" two
year program of mathematics courses, and at the end of two years only 17 of us
were left. I am not sure what happened to the other 18, but personally I found
it challenging to not be the one of the top two or three students in my math
class.
12 hours ago
Teddy
Kafwanka • I am really being inspired with a lot of ideas on how to
influence children positively on this study area. It is good to learn beautiful
ideas on this link. You have been giving me excellent strategies and
applications. My approach in my presentation has changed. My expectation for
the year 2013 are better placed with much confidence.
11 hours ago
Merden
Bryant • I used to teach in a public science high school for
intelligent but underprivileged students. Students who get to enroll in that
school have to pass a qualifying examination in English, Math, and Science.
Despite
being on the honor roll upon elementary graduation, many of my students before
did not have proficiency in performing operations on fractions, integers,
decimals, exponents. The most surprising thing was they shun problem solving
even if the problems are procedural, algorithmic, and simple translational
problems. Not only that, I also found their speed in performing math exercises
alarming. Moreover, they believe that it is okay to perform low in Maths
because according to them, Math is the most difficult subject anyway, like what
they'd been told from their previous teachers and from the people in their
circle.
To address their weaknesses, I dedicated a month of my time budget for
the school year in giving remedial instruction. I promised them in the
beginning that with their cooperation, I would be able to help them realize
that contrary to what they believe, math is the easiest subject. However, they
had to go through a great overhaul of everything about mathematics. Firstly, I
discussed place values then mental addition and subtraction by separately
dealing with thousands, hundreds, tens, and ones. They never thought that
addition can be easy and fun. Slowly, their speed improves because our practice
exercises were like this: For 10 items of mental arithmetic, I would state
number 1 exercise and check right away. It's like a quiz bee. I'd say right
away, "Exchange with your seatmate!". They would shout and tremble.
During the checking I would model the mental computation necessary to compute
the answer. However, even if some could not answer no. 1, I'd say, " If you
get no. 2, I'd give you a bonus to cover up your mistake in no. 1. I kept doing
that for every number. As a result, their speed improved. Some quick and
accurate thinkers would get double the item score. However, I kept reminding
them this: Would scores in tests matter after finishing school? I underscored
that it's learning that matters and what matters most is that everyone is
learning and all of them would become mathematically literate which would be
good for the country so all of them would be able to help the country prosper.
I made it a point that the vision is for them to become great math thinkers to
be able to contribute to society in the future. I made it clear that they
should have a uniform score in each quiz. Their grades would only differ in
Oral Participation and in the Quarter Exams. Basically, all exercises have to
be answered by group, by pair or individually. A student can choose. For those
who choose by group, they had to tutor each member so that a validation
question/s would be answered by one or two of them because I had to call
randomly member/s to represent the group.
2. Before I discussed fractions, I
had to make sure that students master these concepts: even number, odd number,
composite number, prime number, Least Common Multiple, and Greatest Common
Factor. I exposed them with common sense problems related to LCM and GCF. I
emphasized prime numbers because prime numbers are the keys for tackling
fractions, fractional exponents or radicals, and logarithms. I introduced the continuous/progressive
division as an algorithm after presenting them a paper-folding activity where
Least Common Denominator can be derived concretely resulting to conceptual
understanding. Because of these, they realize that mathematics is an
interesting subject.
There are many things a teacher can do to make abstract
concepts in math concrete. However, it takes a teacher with a heart--full of
patience and understanding.
I wish I could relate everything I used to do when
I was a teacher. But I don't think I have the time in the world to tell it.
This group rocks!
11 hours ago
Clifton
Ellis • don't give them home work. Make them do the work in class under your
supervision. Make them study in groups for each test (complete a study guide).
Peace,
1 hour ago
Warren
Wolff • Typical socialist solution. An idle mind is bad. Load 'em down in
class and give them a wad more to do at home. Turned out a bunch of outstanding
products, despite their complaining. Some refused to cooperate and flunked.
Many have come back and said, "You had the right idea, Mr. Wolff. I have
since grown up and made something out of myself. You taught me more than you
will ever know." Guess I have a good report card!
1 hour ago
David
Ball • I have been to dysfunctional schools and outstanding schools. You
can't do homework at dysfunctional schools, although homework isn't the problem.
At outstanding schools the homework wasn't dull drill work. It may well be the
case homework is impossible at some schools .. but that suggests they are
failing in their mission. There is a pathway out of such a bad situation .. and
that pathway includes homework at the end. Looking to the future where learning
is more individualised homework will still exist. Te simple reason for it is
that to raise a student to the end of year 10 requires about 1000 hours of math
instruction (not consecutive!) and that is not sufficient to cover the material
and have the student internalise the material. Home time should ideally allow
that time to expand to 2000 hours. Which illustrates why dysfunctional schools
where homework is not done fare so badly in public performance.
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