32-12 my opinions

Standard

I usually don’t post on things as ridiculous as this.  The comments and posts made me cringe. These attitudes are from people who are uneducated about common core…  It makes me sad to think so many are mis-educated and truly believe this is what CCSS is all about.

image

CCSS is not about making math more difficult.

I agree this example looks longer than most of us learned the traditional way but CCSS is about allowing students to develop number sense.  IF a student solved a problem this “longer way” -I agree it is not how I would have approached it, but is it incorrect? Is their thinking wrong?  I would like to have a conversation to really hear/see their thinking.  It seems they started at 12 and counted up to 32.  For a student who struggles with subtraction, yet excels in addition, I think this is a perfectly legit approach.

I never remember being allowed to explore different strategies but told how to do the problem and what to think about it.  When students are required to do it “the teacher’s way” many do not think/process the same way, they get frustrated, feel like a failure, hence the reason so many dispise math nowadays.

At some point in my career, I complained I taught something but don’t know why students didn’t get it. So, I retaught it, the same way I did the first time, just more examples and spoke more slowly and expected different results.  Sheesh.

I have complained that “they knew it” on the unit test yet not on a cumulative exam at the end of the year.  Did I spiral review throughout the year?  Did I teach isolated skills?  Did I let them approach it a way that made sense to them?  Did I allow them to work, sharing their strategies with classmates?  Seriously, if you are very traditional in your teaching, watch a struggling student trying to use a procedure, they never really understood, to solve a problem.

I am not saying get rid of good instruction but listen to your students.  If they don’t understand your method/procedure, let them make sense of it in their own way.  Number talks are an amazing way to start listening to student thinking.  Insidemathematics.org has some nice examples to consider.

IF you are posting statements to #boycottcommoncore please learn more.  Find out what its really about.

Advertisements

20 responses

  1. I’m with you on the frustration surrounding this type of misinformation. Cheez! The whole point of CCSS is that there isn’t a “new way” of doing things. We aren’t changing all of the “standard algorithms” into “new & improved standard algorithms.” We are having students MAKE SENSE of math. Wow! What a revolutionary concept–that math should make sense to the people doing it.

  2. My issue with it is that my son who is in 4th grade answered his multiplication homework the traditional way and was told to re-do it using the ladder method. These new algorithms are not just being introduced and given as an option they are telling my kids that he is wrong is he answers the “old way”

    • Hi Anonymous. It sounds to me the issue is not with CCSS but with the feedback your 4th grade son is receiving.

      Speak with the teacher. Kindly ask what standard the algorithm is addressing. I may be wrong, because I have only skimmed elemntary level standards, but its my interpretation of the Standards of Mathematical Practices that students offer different approaches, be able to defend their reasoning and critique that of others…does it work? Will it always work? Why does it work? Not work?

      I am not familiar with ladder method. Is it similar to lattice method? Would like to know more. I have a 4th grader myself and yes, it can be frustrating when they voice they need to do it the way they were shown in class, to see new strategies, especially when I was often taught a single way of viewing the math and never encouraged to make sense with my own thinking. Talk with them, do they understand the procedure? Ask the teacher, again without accusing them, their rationale with sticking to one method.

      In my experience, usually only a certain % can do it one way, so by allowing students to see different ways, they can pick which one is best for their thinking.

      I attempt to let my students struggle a bit, providing probing questions that will move their thinking forward. When they offer a strategy that I think will not work, I voice that I am unsure- I had never looked at it that way. If I see a counterexample, I offer it and ask them to try their method. But I don’t stop there, I like to have a discussion as to why it works for some situations, but why not with the counterexample. This takes time, to really allow students to talk it through. Some teachers still feel pressured to get their content covered and are afraid to use classtime in this way.

      Can I offer you a few resources I have found to be valuable to me…

      Jo Boaler offers a course for parents and teachers through Stanford University. There may actually be a cost for the course this term. But its well worth it, imo. She also has a book What’s Math Got to Do With It that is worth the read!

      Phil Daro – Against “Answer Getting” https://vimeo.com/79916037 this is worth 17 minutes of your time to better understand ideas intended by CCSS.

      Christopher Danielson has research and suggestions for different ages http://talkingmathwithkids.com/
      He also has it in eBook format at amazon.

      When we make math procedural, we take away its intuitiveness. We have to allow students to see it their way.

      I am sorry parents and students are having these experiences you shared. My hope is you will consider the opportunities CCSS can offer for improvements in education when implemented correctly.

      • What about asking your student to compare “the old way” and the new method? Simply, how are they alike? How are they different?

        When I use number talks in my classroom, I ask students who quickly use a traditional algorithm to find 2 other ways of presenting their work. Then we try to connect the varied approaches.

    • I’m guessing that’s the Lattice Method and your son uses Everyday Math. I doubt he was told the older method was wrong but that the assignment was to use Lattice multiplication, not the traditional US algorithm. I question whether anyone should really use Lattice because I can’t really find much value other than it’s another way. If your son is using Everyday Math, this site can be helpful to parents who were taught in the traditional way. http://everydaymath.uchicago.edu/parents/

  3. I have to say, I was truly flabbergasted by this post that I saw on FB today and I literally debated it most of the day . I mean what was the problem with teaching it the old way ? And then as I figured out the logic behind it, I realized that it is actually quite clever to teach a 2nd or 3rd grader this way. It teaches addition and multiplication in one small subtraction problem. It’s brilliant. Mind you, I am totally against the common core because I don’t believe in standardized testing whatsoever.. but this particular math methodology is brilliant for a 7 yr old. Not for anyone older than maybe 8 or 9 but for grades 2-5, it’s pretty cool. It strengthens math facts in 3 different areas..

  4. I have 32 apples. I ate 12. How many do I have left? Well let’s see. I ate 12, however, If I would have eaten 3 more, I would have eaten 15, another 5, that’s 20, maybe 10 more, that’s 30, what the hell, an extra 2, that’s 32. Then I would have none left, however, if I count the ones that I might have had eaten after I have eaten the first 12, that would be 20 extra that if I add them to the 12 eaten would be 32! So the answer is….What’s the question again?

    • Thank you for your comment. Yes, we sometimes get so lost in the problem we have to ask ourselves-what was the question again? Does my answer make sense? Am I answering the question asked?

      Several times in wrong answer analysis, students realize they gave a related answer but didn’t actually answer the question given.

    • Who said anything about taking away apples? Removal of objects is one meaning of subtraction. Can you think of another? One in which this way makes sense? I can: comparison of two quantities, a/k/a “the difference”.

      You have 32 apples. I have 12. How many more than me do you have? Simple: 32 – 12 = 20. A subtraction question, right? But it is not unreasonable — in fact it is natural — for children to think addition given this context. How many more apples do I need to get before we have the same?

      Now, I agree with you that this is not a very efficient (or likely) strategy given the (cherry-picked) numbers. But this would be a lovely way of thinking about 32 – 17: 3 more to get 20, 10 more to get 30, and 2 more to get 32, so 15.

  5. Thank you! I’ve been trying to explain this as well online, after seeing this example pop up, using my twin 7 year olds who have been learning different math methods for 2 years now, as examples… they can do math in their heads that most adults need a calculator for… and they do it with ease. They’re not any different than the rest of the kids in their classes either… and my oldest son, 4th grade, can do the same thing… they have these math competitions in the car, in restaurants, in the middle of Target, where they try to stump one another… and people comment on how smart they are to which I try to humbly explain that it’s how they’re teaching math these days; it’s making it easier for kids to find solutions in real time and to enjoy it!
    I wish this example would stop circulating though… it’s not what they’re actually learning and it’s been intentionally set up to display a biased example in order to confuse and engage people in a negative debate about something they obviously don’t understand?
    Aside from which, my 7 year olds say the example is wrong anyway

  6. I love this approach. What a refreshing way to think around this problem. I bet the student who did this can do a better job of explaining the answer than the student who took the ‘traditional’ path.

  7. copied this from comments on another post concerning this post…
    My general thought — not being a math teacher — is that the bottom part isn’t really supposed to be a way of deriving the answer to the problem “32-12,” but rather, simply a way of getting students to explore the relationships between the various numbers, showing how the student can add three to get a multiple of five, then add five, then 10, and so forth. An exercise to develop mathematical dexterity, so to speak.Instead of just learning that “20″ is the answer to “32-12,” the student learns to see that the number “32″ is composed of different groupings of numbers that can be combined in various ways.

    It seems to me that many don’t want to take the time to consider all the cool ways you can actually do to solve a math problem.

  8. Thank you for commenting. I agree some methods are more time efficient than others for me as well. I would also like to see/hear more of the student’s thinking with the example . As someone else commented, this student likely views 32 as being composed of several numbers.

    • Hi Scarlet. All of this has made me wonder – is there some type of Parents (Grandparents) Guide to Common Core? I don’t know – but it seems it may be something that could benefit both students & their families who are trying to help them. Is this something you would like to see available? What suggestions / ideas would be helpful if this type of online resource did exist? I am not here to cause an argument. Only help.

    • Be open to learning new ways of doing elementary mathematics and support the student in learning the “new” way. Many folks confronted with a different way to solve a solution simply revert back to the way they know and then ridicule the different way. Resist that urge. The student should not have been told the “old” way was wrong, but they should still master the “new” or different way.

  9. I disagree with you on this. Here’s my problem:

    Most kids seem to be able to grasp the top version just fine with enough practice. Drill them enough on it and it will start to make sense and it’ll become second nature. And this is how I was taught in the olden days of the 1980s. There were always some “alternate” ways to think about or solve the problem though and those were brought out just for the kids that weren’t grasping the regular method, either in a side session with the teacher or a tutoring session after school. And from time to time a kid that could do the “traditional” method on other things would have something in math that would require looking at it from one of the alternate points of view.

    But now, schools are requiring all of the students to learn all of these methods and what it does is create confusion. Some teachers are good about it in that they’ll teach all the methods to the kids then on the test, they will allow them to choose whichever method makes sense to them to solve the problems. But others decide that the kids have to demonstrate that they understand ALL the methods and have to use each of them on the test. This is nonsense. My kid understands how to put 32 on top of 12 and subtract 2-2, then 3-1. There isn’t even any regrouping involved for crying out loud. Don’t make her have to learn all these convoluted methods that make it harder to hold on to the regular method that works well for her. As if they don’t have enough things to remember already, we’re going to give them 3 to 5 ways to work every kind of math problem? Sheesh.

    • I may agree with you that most kids would be fine with this type of problem where regrouping is not required. However, as problems progress in difficulty, several students tend to fall away in their deep understanding. And without a discussion – asking them for their reasoning, I may miss the fact that they can do a procedure but have no understanding.
      I don’t teach at the elementary level and I have such respect for those teachers developing foundational learning/ understanding of important concepts.
      I cannot speak for other teachers – but when students are remembering procedures without conceptual understanding – that’s when I notice gaps forming. Its up to me to address those gaps and its up to me to find ways to help students see math as something they can be successful at and truly understand.
      Thank you for being so involved and supportive in your child’s education. There are many students who aren’t so blessed.