So today a friend tagged me in a FB post regarding the “frightening” method that students MUST solve subtraction problems. I have posted the link below, and I believe the link is at the bottom of this post as well! Take a look.
So let’s summarize the tutor’s concerns. 1. That we are writing problems horizontally rather than vertically. 2. That students are using a strategy of “adding up” rather than “stack and subtract”. 3. They MUST use this strategy and no other.
I would like to address each of these and provide some comments.
- Most of us are used to seeing math problems vertically. Why? Well, for one, it makes the problem ready to go for the algorithm of “stack and subtract” (which is not the ONLY algorithm in the world, mind you). I would contend it also saves space for publishing companies in their workbooks. If the problem is already written for the algorithm, publishers do not have to provide additional space and therefore can fit more problems on a page, and save money. (Yeah, I went there. Bring on the comments!) However, when you write a subtraction problem vertically, you lose the essence of the numbers. Here I only see single digit subtracted by single digit. I do not see 40 – 20, but 4 – 2 and 5 – 1. This is okay for problems where we do not have regrouping. However, some students get so stuck in the process of regrouping that they no longer see the value of the places and just write a very ‘random’ value as the difference. When I write the problem horizontally (45-21), it allows me to view it from a place value perspective. My eyes look first at the tens and then the ones, versus the horizontal example where I start with the ones and then look at the tens. Also, writing it horizontally does not constrict me to a “stack and subtract” method. (See prior blog for more info on great subtraction strategies to help kiddos.) Really, both are fine; no need to get all uppity about it. And if a teacher says they HAVE to write it that way, it is not true, but what is true is that they learn to think about relationships and different strategies using place value and properties of numbers BEFORE learning the standard algorithm. In fact, the standard algorithm for multi-digit subtraction should not be mastered until grade 3: CCSS.Math.Content.3.NBT.A.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. So students have lots and lots of time to process what it means to subtract and its relationship to addition.
- (and 3.) Adding up is one strategy students can use. Makes sense to me! If I already know how to add, I can simply use that to help me figure out the missing addend. This is all a subtraction problem really is: a missing addend problem! Consider the following: 43 – 16. This is really finding out 16 + ____ = 43. Now typically, students do not need to go to the next five as the tutor suggests. And really a number line is FABULOUS for modeling adding up. Here is one way to get the value. Notice this is a great strategy for students who struggle with regrouping, because there IS NO REGROUPING!!! I went up 4 to the nearest ten (20), added 20 more (40), and ‘hopped’ 3 more to get to my end point (43). 4 + 20 + 3 is 27. Therefore, 43 -16 = 27. Using the tutor’s problem (43-13), I think adding up is efficient, if you move up by tens. I can simply add by tens until I reach 43. 3-tens is 30. Not sure why it is so convoluted in her explanation and NO! Students do not have to add up the same way the tutor did. In fact, that is the wonderful thing about Common Core. CCSS.Math.Content.2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. Notice that students can use any method, with or without drawings or concrete models!!! Super awesome! Hooray for creativity! I no longer have to use one method (that I don’t really get and just memorized because my teacher told me to); I can use any method so long as I keep in mind place value and my rules (properties).
“Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules. The teaching of mathematics has been viewed as a discrete set of rules and procedures to be implemented with speed and accuracy but without necessarily understanding mathematical logic. For the majority of our nation, knowledge of mathematical rules has not allowed them to use math confidently in their daily lives. With almost two-thirds of the nation’s adult population fearful of mathematics, they have simply said “NO” to math and closed the doors to careers that require higher math” (Burns, 1998; Parrish, 2010).
Let’s allow students to make sense of number relationships, what the operations MEAN, and figure out what makes sense and how to approach the mathematics based on the numbers given.
4 thoughts on “Response to Confusion 43-13”
Love this Jen! You explain it so well. As a result of past teaching, both my sons in their 20’s refuse further learning that requires Math. So sad. They had A’s and B’s in math throughout elementary and middle school years,but failed to understand it. Therefore hit roadblocks in high school. So wish they had common core and teachers like you!
Thanks, Sally. I wish others were able to see what kids can do when given their power to manipulate numbers and reason!
I can believe it. I truly believe in the CCSS standards for mathematics. They are cohesive and allow students creativity in solving problems. However, the implementation of the standards is horrible in most cases. Teachers were expected (in many cases-not all) to put away the programs and curricula one day and start teaching CCSS-M the next, without any professional development not understanding why we had the change.