mathematical education

Mark Taylor Nice summary. As an educational psychologist, I have a strong interest in this topic. Since the 1990s we have known definitively what causes dyslexia and we know clearly how to treat it (not that it is easy), but we still know little about math disabilities. 

I used to organize the major annual training institute for the Montana Association of School Psychologists. Our institutes last for two-and-a-half days, all on a single topic, and all presented by just one speaker. I tried to get David Geary to come to present to us, having had a chance to visit with him at a major conference in Chicago in the late 1990s, but he declined, on the grounds that no one in the entire world knew enough about math disabilities to present for that much time. Finally, in 2011, after calling a bunch of top researchers, I was able to bring Michele Mazzocco from Johns Hopkins to talk to us. We still do not know much, but we are finally getting some good research. 

David Geary was lead author on the National Panel report on math learning processes in - I think - 2009, and that is available for free on line. A book that I like a lot is Dehaene, S. The Number Sense: How the Mind Creates Mathematics. (OUP - not sure what the current edition is). He is working in France but writes brilliantly in English and for a geek like me the book is laugh-out-loud funny in parts. He also had a terrific article in Science on sources of mathematical thinking. It is a little bit older information but it is solid. If you are a member of AAAS you can find it on line.


http://www.newyorker.com/magazine/2008/03/03/numbers-guy

Russian Empress Alexandra Fedorovna on children

Our children naturally bring along with them a multitude of cares and concerns, and for this reason there are people who look upon the appearance of children as a misfortune. But it is only cold egotists who can look upon children in such a manner.

It is a momentous thing to take upon oneself the responsibility for these tender young lives, which can enrich the world with beauty, joy, and power, but which can also easily perish; it is a momentous thing to nurture them, form their character, – this is what one should think about when establishing a home. It should be a home in which children will grow up to a sincere and noble life, grow up for God.

No treasures in the world can replace for man the loss of truly incomparable treasures – his own children.

There are things which God gives often, and others that are given only once. The seasons of the year pass and return again, new flowers bloom, but youth never comes twice. Childhood and all its possibilities are given only once in a lifetime. Whatever you can do to adorn it, do it quickly.

Parents should be what they wish their children to be – not in words, but in deed. They should teach their children by the example of their own life. The greatest treasure that parents can leave their children is a happy childhood, with tender memories of father and mother. It will lighten the forthcoming days, it will preserve them from temptation, and it will help them face the harsh realities of life after they leave the parental roof.

May God help each mother understand the majesty and glory of her forth-coming endeavor, when she holds at her breast her infant, whom she must nurture and bring up. As far as children are concerned, the parents’ duty is to prepare them for life, for any trials that God may send them. While the parents are alive, the child will always remain a child for them and should treat his parents with love and respect. The children’s love for their parents is expressed in complete trust in them. A real mother finds importance in everything in which her child is interested. She listens just as willingly to his adventures, joys, disappointments, achievements, plans, and dreams as other people listen to a romantic narrative.

vision problems in elementary school aged children

There are vision problems which can impair a child's ability to read which are not easily caught by general eye exams. There is a special field called "developmental optometry".

What areas of vision are assessed by developmental optometrists?

Binocularity: the ability of the eyes to work together to transmit information to the brain

Ocular Motility (tracking): the ability to smoothly and accurately move the eyes, which is especially important for reading

Accommodation: the ability to rapidly re-focus the eyes when looking at something up close, then from a distance, and back again

Doubles Plus and other shortcuts

One of the things that we must help children do is recognize when to use a particular strategy. For the Doubles Plus One strategy, tell the children "when the numbers are next door neighbors (the numbers are consecutive like 6 and 7) then we can use the doubles plus one strategy."

Doubles Plus Two
If a child is faced with a problem like 5 + 7, think through the same steps as Doubles Plus One except add 2 instead of one. This works for facts that have number that are separated by two.

When helping a child to recognize when to use this strategy tell them to use it "when the numbers are NOT next door neighbors, but two doors down from each other."

Plus 9 Shortcut
If your child is learning a fact like 9 + 5 these are the steps to think through:
* Think 10 + 5 = (which is much easier to add)
* Now minus 1 (Think 15 - 1 + 14)
* Now say the fact: 9 + 5 = 14
* Remind your child that you added 10 + 5 instead of 9 + 5. That's one more than you started with, so you have to take that one away to get to the correct answer.

Minus 9 Shortcut
If your child is trying 17 - 9, these are the steps to think through:
* Change the 9 to 10 ( Think 17 - 10 = 7, which is much easier to subtract)
* Now add 1 ( Think 7 + 1 = 8)
* Now say the fact: 17 - 9 = 8
* Now remind your child that you subtracted 17 - 10 instead of 17 - 9 . That's taking one more away then you started with, so you have to add that one back to get the right answer.

Minus 8 shortcut
If your child is learning 15 - 8, these are the steps to think through:
* Change the 8 to 10 (Think 15 - 10, which is much easier to subtract)
* Now add 2 (Think 5 + 2 =7)
* Say the whole fact now: 15 - 8 = 7
* Remind your child that you took two extra away when you changed to 8 to 10 in the first step, and you must add it back to get the right answer.

What is Multiplication?

Keith Devlin claims

“Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.”

http://letsplaymath.net/2008/07/28/whats-wrong-with-repeated-addition/

Addition requires identical units.

The sum must always have the same units as the addends.

Multiplication requires different units.

The product does not have the same units as either the multiplier or the multiplicand.

    .

Multiplication: multiplier X multiplicand = product. 

The multiplier and multiplicand have different names, even though many of us have trouble remembering which is which.

• multiplier= “how many or how much”
• multiplicand= the size of the “unit” or “group”

classroom management

A good article about "classroom management".
Some of these ideas may help volunteers at their child's school.

http://blogs.edweek.org/teachers/classroom_qa_with_larry_ferlazzo/2015/01/response_goal_of_classroom_management_is_to_have_power_with_not_over_kids.html

Common Core resources

http://commoncoretools.files.wordpress.com