If you are on Facebook, you have seen this (or one similar to it), usually followed by stating that a certain set of standards are evil and we should be teaching the kids drill and kill through the “right way”. So let’s clear the air (Or let me fill it with hot air and you can comment below. Bring it on!).
To start, “our way” is not the way of all. The step and structure with which we add, subtract, multiply and divide are not used by all countries. In fact, these methods are just some of the many ways students can simplify problems using these four operations. The ones we traditionally use are examples of “algorithms”. If used correctly, each will work for different number types and you can get “the right answer” pretty quickly if you have had lots of practice with them.
BUT THEY ARE NOT THE ONLY ONES! And I would fight the good fight that there are MUCH easier ways to get to the value using other strategies. I will even throw myself under the bus and tell you that I do not use the traditional multiplication algorithm. I make too many mistakes when I use it. I know it, but there is another method that works just as fast for me, and I get the correct value using it. And long division? Ugh. Why not just start with something I know, chunk it out, and get to easier numbers??? May look a bit odd, but still it is faster than sitting there trying to find out how many times one value goes into another (More on this division idea in an upcoming post for all you 4-6th grade parents!).
So think back to your elementary days. How many days were spent drilling the algorithms you now know (or pretend to know since you use a calculator instead)? How many hours? For me, it was a nightmare. I didn’t get them. I didn’t know when to move a little 1 (And why was it so tiny if it meant a bigger number???) in addition, why we crossed out stuff on top and not only moved it over, but made a double digit number in subtraction (What happened to my little 1 friend in addition? Where did she go???), when to put an “X” and why the heck were we even using an X in multiplication when it isn’t even a number, and so on. I was confused, and I covered it up by checking with a calculator and fixing each line to pretend I knew what I was doing. It was horrible, and I felt stupid, slow and sad.
I had my a-ha moment in seventh grade. (So it took EIGHT YEARS to finally figure it out.) My math teacher took me out of science, my favorite class mind you, to have a double dose of math. (Great. Now I get to hate it twice as long.) However, he started showing me other ways to do the math. What other countries and cultures were using to figure out the exact same problems, but with visuals and graphic organizers and all kinds of craziness. It was wonderful. It was a breath of fresh air. It was my lifeline to true mathematics.
You see, math isn’t just about calculating. I think of mathematics as finding patterns and relationships in and among quantitative items, and using those patterns and relationships to create rules, strategies and “algorithms”, prove or disprove others (And my own!) rules and algorithms, and figure out how the world works on a quantitative scale. It is beautiful. It is elegant. It makes life make sense.
Keep in mind, the standards DO say for students to eventually use our traditional algorithms as ONE STRATEGY for finding the values. But it is at the end of their journey of understanding. It is the final step of a long walk through discovery; using manipulatives, moving to visual representations, conjecturing student-strategies (whether they work all the time or not), and finally moving into the algorithm you all claim to know and love.
Think of a puzzle. My husband starts with the border. I start with the middle and the pieces that have the same color or object. Yet we will both finish the puzzle, even though we went at putting it together differently. Some of the representations will be easy for your child, others a bit more difficult until they understand how they are relating to the operation. Yet, they will get to the end and finish the puzzle, even if his struggles are different than another’s. That is why working together is so important. We can help each other make sense and persevere to the end!
So, at the beginning of another school year, take a deep breath. Give different models and strategies a chance. Ask for help in understanding how the strategies or models work and their significance to understanding an operation (Send ME questions and problems!!!!). Encourage your child to try something new, and be supportive. As the child who needed something different, I thank you. 🙂
Mine (as I am on the lazy side) typically look like a rectangle with an opening at the top (for the input) and an opening at the bottom (for the output). They are just very boring and sad. The one to the right is super cute and soooo not me.
Geogebra: 
Math Learning Center: 
moffett4understandingmath 