The following picture has been going around Facebook as an example of how crazy the new Common Core Standards must be:
The argument is that in the “old fashioned” way, we can get the answer in just a very few steps. In the “new” way, it take many more steps and is more confusing. This superficial view and example of the common core standards misses the point entirely. Please consider the context by which either method might arise in the thinking of a student. For example, suppose the situation was that Ken had $32 and spent $12. Ken took away $12 from $32 and one might be thinking in the so called “old fashion” way. This is the “take away” model for subtraction. Suppose the situation was that Ken has $32 and Scott has $12. How much more money does Ken have than Scott? We are making a comparison (comparison model of subtraction). To make the comparison…to find the difference between how much Ken has and how much Scott has, one might start with Scott’s amount ($12) and add up to your amount: 8 more than $12 gets me to $20…another $12 gets me to $32…a total of $20 more. There are misconceptions that we are teaching new ways over old ways…not true! We are recognizing how one might think about the solution to a problem and that, depending on the situation, we might think in different ways.
People sometimes look at this example and make comments like, “no wonder our kids are confused when it comes to math!”
Actually, the issue is this: if the problem says (as in my second example) “how much more money does Ken have than Scott?” students see the word “more” and want to add 32 + 12! They are taught to look for “key words” like “more” which means to add. What I am saying is that we want students to think and make sense of the situation and solve the problem accordingly. My thinking in the “how much more” question might be to start with my $12 and add up to Ken’s $32. In the “Ken spent $12” question, I am thinking about subtraction because I am thinking about taking away $12 from the original $32. We are not showing new ways to subtract…we are solving problems in ways that might make sense.
By the way, in the given example, a young learner might count up to $32 from $12 in more or less sophisticated ways. In this case, it appears that that the student first counted up to $15 so that she could then count by 5’s (which may be more comfortable than counting by 8’s or 12’s). Once they counted up to $30, she only needed to count 2 more to get to $32 for a total of $20 more. This is great reasoning that respects that particular child’s thinking process!
For those that think that the common core is all about teaching “new” and confusing ways to “do math”, don’t worry…we are still teaching “old fashioned” subtraction! But, we are also teaching students to think, reason, make sense, solve problems, etc. You might consider the Common Core Standards for Mathematical Practices. This is the “core” of the Common Core:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Scott
getrealmath 
nice deceiving Scott , but u fail to point out not learning ur times tables to count by 5 is going to hinder there ability to do algebra witch is going to put kids 2 yrs behind college math .
I am not trying to be deceiving…quite the contrary! I am trying to help people to understand how young children come to be fluent in mathematical computations. I didn’t fail to point out anything about times tables…this post was not about multiplication but about subtraction. I believe strongly (by the way…so do the proponents of the common core standards) that children should be fluent in multiplication. I agree with you that it is important for students to learn their times tables as it is helpful in subsequent mathematics coursework.
PS – your message reminds me of why the common core standards are so important. One of the standards is focused on “critiquing the reasoning of others” and I don’t believe that you have learned this well. You are critiquing my failure to point out the importance of “times tables to count by 5” specifically when the post is focused on subtraction. Furthermore, your use of the English language is poor (you say, “there ability” instead of “their ability” and “witch is” instead of “which is”).
Scott
From what I can see, Common Core is like what we intuitively used to do before computers became prevalent. We used to do a lot more math “in our heads,” and techniques like these became second nature.