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.
As a tech geek and a math nut from the time I was in 5th grade, I was astonished when my daughter gave me the following problem and my wife questioned my answer based on what Camille was taught last year in Kindergarten.
It is not a Triangle, it is not a rectangle, what is it?
You should color in the circle under the proper answer. What do you think the answer is? There is only one answer to the question and I feel that it is rather easy if you have been taught the proper definitions to all the shapes above.
Let’s Solve It
The first part of the question “It is not a Triangle” obviously removes the triangle from being the right answer. That leaves us with the other three shapes, so the second part of the question states “it is not a Rectangle” which eliminates the rectangle next to the triangle. We are now left with two other shapes, a circle and a square, but there can only be 1 answer to the question. Of course here is where the proper definitions come into play, which is where the teaching at the Kindergarten level left some things to be desired. A Square is a special type of rectangle under the definition of a rectangle which is:
A rectangle is a parallelogram whose sides intersect at 90° angles. Now, since a rectangle is a parallelogram, its opposite sides must be congruent.
A Square is also a parallelogram whose sides intersect at 90° angles. Like a rectangle its opposite sides are congruent. However, a square is also a rhombus. and all of its sides are congruent. A rectangle is a square when both pairs of opposite sides are the same length. This means that a square is a specialized case of the rectangle and is indeed a rectangle. So, that means that we can eliminate the square as one of the answers, leaving us with just the circle let to choose as the proper answer.
Kindergarten Taught What?
What they didn’t teach is that a square is a special rectangle. Because the teaching in kindergarten is so new to a lot of children I believe that everything is simplified and this part is left off. I don’t think that is right, because if they are going to get this type of question in 1st grade then they need to at least be exposed to it in Kindergarten. By no means do I think my daughter got a bad education in Kindergarten, on the contrary I feel that she had an extremely good teacher and one that let Camille be the best she could be.
Unfortunately, in the first week of 1st grade my daughter is taught a new definition, in a homework question. She isn’t going to know the proper answer when she didn’t get all of the definition the year before. Maybe this is supposed to be a teaching moment for the children, but my wife was following what she had been taught the year before and I was contradicting that answer based on the correct answer. My daughter is questioning my answer because she learned something else and we have taught her to listen to your teacher. I did not work with my daughter on rectangles and squares in Kindergarten, but I will spend more time looking at every piece of work she does this year. I want her to get a better foundation, one that I know my wife and I can help give her in addition to what she is learning in school.
Success is more a function of consistent common sense than it is of genius. – An Wang
Tonight I went to watch a district presentation on the new math standards that we have been using since the beginning of this school year. While it is a different way of teaching, it isn’t “New Math”.
There is no such thing, just different methods of teaching the same thing. What these new standards and benchmarks teach are visual, reasoning and justifying your work. I believe it is a good way to teach because math teaches how to think things out, how to look at things step by step. Instead of being taught 5 + 5 = 10, do it 10 times, kids go through a visual progression of seeing 5 ducks plus 5 frogs equals 10 water animals. The steps go on and on, all of which are good sound common sense progressions.
This brings me to another point that learning the common sense and reasoning of math make for good decisions. This weekend my family went to the mall to shop for jeans for me and for some small things for the kids, including some sale sandals for our daughter. We got a pretty good deal on the sandals, but I knew we wouldn’t find jeans that were any kind of deal. We went to Sears, the lowest priced of the anchor stores in the mall and found jeans “On Sale” for $39.99 ($40 for those who get lost in the penny marketing). Of course I did not buy those “Sale” jeans, opting instead to drive around the corner to the nearby Target where I was able to find jeans that I liked for $19.99 ($20 to be consistent). I ended up with 2 pair for $40, which in any type of math, reasoning and common sense is 2 pair for the price of 1 of the more expensive jeans. If this was money savings in the bank, I would have just doubled my money.
New Math? No, it’s just common sense.