Let’s Talk Addition


I’ve been watching my 4th grade daughters homework since the school year started with the new Common Core Standards being taught. Camille brought home some math homework the other day that was really basic addition with some other division problems that I will talk about in another post. Since I have a math background and have written on her learning what a rectangle was in Kindergarten I thought that this would be an interesting post. Turning 55 this year it has been interesting to see how she is being taught in the subjects that I love. Here is the problem and solution as it was taught:

9 + 6 = x

9 + (1 + 5) = x

(9 + 1 ) + 5 = x

10 + 5 = 15

While that is correct, to me it is an interesting way to factor to the answer. Now if we replace the non 9 number, which in this case was 6 with y this is how it was done when I was her age. Take 1 off y and add it to the first digit to the left of the 9 and replace the 9 with the new y. I am using 49 instead of 9 to show it with a bigger number below, but with the single digit 9 there is no number in front of it so you assume to add the 1 + 0 where I am using 49 instead of 09.

49 + y = x

49 + 6  = x

6 – 1 = 5

4 + 1 = 5

x = 55

It’s still 3 steps but the answer is the numbers from the two other equations. Lets try it with 3 digits

189 + 8 = x

8 – 1 = 7

8 +1 = 9

x = 197

or when you are in the 3 digits or more in the 90’s, 900’s, etc.

199 + 9 = x

9 – 1  = 8

9 + 1 = 10

Here is the extra step with the carry over 1 in 3 digits or above where you need to take the 1 and add it to the number in front of the second 9.

1 + 1 = 2

x = 208

Carry over is taught in 3rd grade, so students should know how to do that when taught larger numbers. Of course all of this is a matter of opinion, whose teaching and who is the supposed expert at knowing what is the best method. I don’t think there is a best method, but it was curious to me coming from a math background through college Calculus of the changes from when I was younger. The other big difference from when I was younger is that we memorized addition and multiplication tables so we could rattle and answer off without using a piece of paper, whereas I have not seen one flash card or memorization technique from Camille. Not that I’m worried about her because she got a perfect score on in math on the FCAT in 3rd grade last year.

Just some fun math and interesting differences from 1967.


4 Year Olds Do Not Belong in Kindergarten

Some research suggests that children who enter kindergarten later perform better on standardized tests, but critics contend that family background and preschool experience often have a bigger influence on academic success than age. In any case, they say, such benefits disappear by middle school. – New York Times

I read the article quoted above intently because I was a 4 year old that went to Kindergarten in Connecticut back in 1963. The article is set in Connecticut, but also talks about the whole United States age requirements for Kindergarten. The whole gist of the arguments one way or the other is the development of the children and the income level of the parents. The critics for the most part continue to beat the “low income can’t afford preschool” drum to get support, while at the same time trying to tell people that the gains of leaving students at home until they are emotionally ready for the rigors of today’s Kindergarten is wasted later in the k12 levels.

One major flaw in this theory is that parents feel that once in school the responsibility is off of them and completely on the school districts. While not all parents think this way, I see it a lot everyday to know that it is a problem that we need to look at. Parents need to spend time with their children, it’s their responsibility, it can’t be abdicated to the schools and expect your children to magically learn without your help when they are at home.

Speaking from the experience being a 4 year old in Kindergarten, I can tell you that the critics of holding children out until they are 5 are completely wrong. I was smaller than all my peers all the way through school and felt intimidated. I also was not ready for school emotionally, even though my parents worked with me to prepare me for school. What they were able to prepare me for was being able to tie my shoes, know my alphabet, know my counting and other basics. You can be on a first grade level for reading, writing and arithmetic but a 4 year old is not emotionally ready for the Kindergarten that is so much different from what I went through when I was 4. But I wasn’t really ready emotionally, because as a 4 year old you are not developed emotionally and you haven’t been in a school type setting for that amount of time away from your parents. You also have not had the amount of interaction with children other than family that they need to develop the skills needed to progress in Kindergarten.

What’s the solution? I don’t know, but I do believe that as we have in Florida, a free state Prekindergarten (PreK) would be a great help. I believe it should be a federal law or funded program that all children have the opportunity to go to a PreK, either private or public that is paid for by the state and/or Federal government. This would alleviate the critics income issue completely because there would be a free program that a parent without the ability to pay for would have. With the way the current testing standards are now, we need to have our children ready for the what we call Kindergarten in today’s world. It isn’t the playland of years past, it’s really school and our children need to be prepared.

College Out Of Reach For Most Americans?

According to a survey by Pew Research most Americans think that college is too expensive and out of reach for our children.

In the survey, 75 percent of U.S. adults said college was unaffordable for most Americans, and almost half said that student loans had made it harder to pay other bills. – Bloomberg

That is an outstanding number of people in our country. The problem is that having a college education is worth about $20,000 a year more than a high school education. So, we have a quandary here, do we continue to fork out outrageous costs or do we try to have our government try to help fix the skyrocketing costs? Honestly, I don’t think it is going to get any better, but we will need to try to find ways to save or work around the system to give our children the best education we can. That means not doing some things that we want to so that we can save that extra money for their future education costs.

Interestingly enough, the college presidents are passing blame to the high schools as not doing a good enough job of preparing our children.

Some 58 percent of college presidents said public high school students arrive at college less well prepared than their counterparts a decade ago, according to the survey. – Bloomberg

That’s just pass the buck and the standardized testing that the government thinks is the way to improve our children. Merit pay, No Child Left Behind, FCAT and other standardized testing is doing more damage than good to our children. Lets work on what we are teaching, funding education and helping the teachers instead of fighting against them. The state of Florida has declared war on teachers with our new Governor Mr. Scott. That is not the way to help, it’s just a way to make Florida the worst state in education. Add to this in that the legislature has for more years than I can count taken money away from the education system because they can’t find a better way to balance their budget deficit. Soon we will be 51st in the US:

Florida is 41st out of 50 states and Washington, D.C. when it comes to the amount of  ”public revenue per student”  it spends, according to annual rankings compiled by the National Education Association. – Orlando Sentinel