If there`s one question that parents ask me just more than just about any other question it is why are they teaching math so much differently now than they did when we were growing up why don`t they just teach the standard algorithms why aren`t they helping kids just get to the answers and get them quickly and why I spend so much time with these things that seem so inefficient and I have an answer to that question.
I`ll start by saying you know we have decades of research that shows that teaching people just to memorize algorithms and execute procedures hasn`t worked it`s worked for a small group of people but for most people they don`t like that they don`t enjoy that they don`t think they`re good at math they have a really hard time with it because no one taught them to understand the concepts and why we`re doing what we`re doing we didn`t teach kids how to think we just taught them how to do and execute in this misguided idea that we just need them gets the answer as quickly as possible.
Let me start with a multiplication example two digit multiplication and as students we may have learned it or you`ve probably learned it to do the standard algorithm line your numbers up vertically and then start with a ones column we`ve got four times five is 20 we`re not allowed to read the whole 20 year we just write the zero and bring them two up there so that`s the first place where we`re doing something that is kind of weird then we do 4 times 4 which is 16 we have to remember to add in the 2 which is 18 and we place that there again we haven`t really told anyone exactly why we`re doing that but that`s how you I proceed you then you put in your what we call what I used to call the placeholder zeros to put 0 here and you move over to this number and you do 2 times 5 is 10 you only write the 0 and then we don`t need this anymore we carry a 1 and then 2 times 4 8 at adding that one 9 and then we add these all together zero zero zero there`s an eight and here`s 10 and it`s 1080 hopefully that`s right now these days before we teach kids the standard algorithm we might teach them let`s called partial products where we`re going to help then see what`s going on with place value in these problems so again we start with 4 times 5 which is 20 and we`ll just go ahead and write that whole thing right here cutting that`s the first part of the problem the next is we`re going to do four times this four but we`re teaching students that this is not a floor it is the digit 4 but when it lives in this column it`s actually represents 40 4 times 40 is a hundred and 60 and you`ll notice this is the 180 that was there so there`s nothing really different going on here just didn`t have it write it down then I have not two but 20 times 5 which is hungry and I have 20 times 40 which is being hundred and you`ll notice again.
These two here are 900 that`s just what we had there we`ll add them all up and we will get 1080 now just you might say well this is a very efficient look how many steps that was how many things ahead right now and you`re right but we now have a conceptual understanding of place value we`re not having to write numbers up here and scramble them out which is a bit confusing and we`re still getting the same result so we`ll teach this to students first so they understand what`s going on later we can teach them the shortcut so they can save a tiny bit of paper to get to this answer but there you go and then we might even give them a visual picture of what`s going on when you multiply two numbers you can think of that as the area of a rectangle and this rectangle would be 24 units on this side and 45 units on that side and if I break it up like this and I imagine this to be 40 and 5 and this side to be 20 and for then I can compute the area of these four little internal rectangles this one here is 20 by 40 which is 800 this one here is 40 by 4 which is 160 little one is 5 by 4 which is 20 and this other one brutal one here spy by Tony which is hungry and you`ll notice those are all the same numbers that we have over here ok this is the same thing but now I`m giving you a visual picture of what`s going on and it turns out that this picture B comes in really handy when we get to algebra because we could replace this with variables and still be able to figure things out but that`s probably an aside for another time.
But now I have different ways of conceptualizing what`s going on before I get to the standard algorithm this is why I were teaching math so much differently now and there is research that shows that when you give people a conceptual understanding of what`s going on it really helps them get answers that we want them to get and explain their thinking and also look for better ways to do things because the standard algorithms are not always the best way to do things.
I hope that hope that helps you as a parent see why math is so much different now the other thing that is a corollary to that first question is I don`t know how to help my students with the math because it`s so different and these homework assignments look so confusing because I`ve never seen anything like this before and I think that question kind of proves the point of if you learn math in a way where it was always this way always follow these steps this is how it works then you never learn to have flexible thinking how to take numbers apart and put it back together how to find shortcuts how to be creative in mathematics and that`s where some of the beauty most of it actually lies in mathematical thinking isn`t in executing algorithms that`s kind of boring but learning how to think and solve problems is a lot of fun and so teaching math this way also can bring back a lot of fun