When my daughter was in 5th Grade, she brought home a worksheet that featured a series of multiplication problems she had to solve using this graphic.
I am an educator. My experience has primarily been in teaching English and language arts at the middle and high school level. However, I did a stint of middle school mathematics during my first year of teaching due to the school needing a math teacher and since I was the last hired ... well, you know how that goes. While I don't consider myself to be a "math person", I have become skilled and proficient in mathematics mostly out of necessity and my own frustration with the concept. However, I had never seen this graphic before.
When I showed this to my wife, who is an elementary teacher, she informed me that this is "one of those methods Khan Academy uses". I went on Khan Academy's website and sure enough, there it was - the Lattice Box, the name of this foreign graphic my daughter brought home and was required to use to multiply multi-digit numbers. I studied how to use the method and found it to be highly confusing, which surprised me because I am a visual learner but could not figure out how the pieces of this cube fit together.
I asked my daughter if she could just multiply the numbers using more conventional and traditional methods, and she said, "No, I have to do multiplication this way!"
I said, "Wait a minute. What's more important here - that you understand what is multiplication and how and why it can be used to determine amount or that you use this method?"
She said, "Daddy, this is the way I have to do multiplication now."
That made this assignment much clearer to me - and also why there's such misconception and misinformation about this notion of "Common Core Math" and "Common Core English".
Interestingly, a week later after working on this assignment with my daughter (which we completed using the Lattice Box even though we both disliked the method), this story and the accompanying image was making the rounds on social media.
Perhaps some of you may remember this story about the father whose rant about the "Common Core Math" homework their child brought home became the viral sensation and caught the attention of magazines such as Time Magazine and even a featured spot on an episode of THE GLENN BECK SHOW. The misinterpreted message became, "This is now how our children need to do math!" No more could our children just borrow the one, regroup, perform long division, or use algorithmic formulas. This was now the "New Math" our children needed to learn.
I became curious about what exactly what was this method students were now "required" to learn and use to subtract numbers, and I discovered through research and investigation that this graphic or tool featured in the homework assignment is the empty number line, which is a model for addition and subtraction by researchers from the Netherlands in the 1980s. I read about this methodology, how it was developed, and how it should be used, and it was fascinating. I took one of my wife's elementary level math texts and worksheets and experimented with this methodology. Sure enough, I attained the same differences I did when I subtracted using the more conventional and traditional method I was taught. Still, I was fascinated to learn about the history and development of this tool and experience how it could be used.
After this experience, I decided to do some research and investigation into Lattice multiplication, and I found that Asian and European cultures have been using this strategy to multiply numbers as far back as the 13th Century. I learned the history and development of the Lattice box and experimented with how it could be used to multiply multi-digit numbers. Personally, I found the method to be confusing and even cumbersome, and I would not choose to use it. However, again, I was fascinated by its history and development.
Both my daughter's homework and the Facebook father's viral posting piqued my interest to learn about the different methodologies that can be used not only to perform the four operations of arithmetic - addition, subtraction, multiplication, and division - but also help deepen conceptual and procedural understanding about mathematical practices, principles, and processes. I learned that with math there is usually only one possible answer (which is what I already knew), but I discovered so many different methods and ways that the correct answer can be achieved and attained. I did not find all of these methods and strategies and methods to be helpful or even useful, but I did enjoy experimenting with these practices and procedures and deciding which method would work best for me.
This experience reminded me of how I much I disliked not only instructing but also evaluating my students on how effectively they can use specific methodologies and strategies in English language arts. I disliked teaching and grading my students on how to diagram sentences because I did not like using the method.
I also disliked requiring my students to use the Jane Schaeffer Writing Method because that was the writing program and process the district and school where I was working adopted. While some of my students benefit from these methods, the majority of them did not, and I found myself frustrated teaching them not only because my students were struggling but I also struggled to use these methods and strategies that did not meet my learning style. It actually caused me to have one of the worst teaching experiences in my career - and this was in an AP English Language class! These kids hated writing style analyses for me not because they were frustrated in determining the tone and effect of the craft, structure, and language of the texts they were reading but because they had to use THE JANE SCHAEFER METHOD! In fact, that became the name of the pain they felt from writing.
This is where teaching becomes a miserable experience for both the students and the teacher - when we are FORCED to use a prescriptive method, strategy, or technique to answer questions, address problems, and accomplish tasks. We have to use THIS READING PROGRAM because that's what the school adopted. We have to use THIS MATHEMATICAL PROCEDURE because that's what the district or charter has decided to use. While these methods, strategies, and techniques are proven effective, they're not for everybody, and the mere mention of their names can cause both kids and adults to cringe. Try it. Mention Singapore Math or whole language and see the reaction and response you get.
Now we have a new name for our pain in education: Common Core. "Common Core Math", "Common Core Reading", and "Common Core Writing" - the very name strike dread and disgust in the hears of many! They are characterized to be as evile and vile as Darth Vader, The Joker, Freddy Krueger, or Hannibal Lecter. Their names are spoked with a sneer or a tone of disdain and even fear and hatred The parents and even the kids have said, "Can't we just use the old way to do math or read text?" and they are being told, "NO! This is the way you must now read, write, and do math!"
According to whom?
I have reviewed the questions on the PARCC and SBAC exams extensively, and I have yet to see anything that resembles the practices and procedures provided in the textbooks, presented on the worksheets, or featured on Khan Academy. I would presume this is not the intention of the textbook publishers or even Saul Khan. However, the message has been grossly misinterpreted to state, "This is NOW HOW you must demonstrate and communicate your learning!"
So my question to consider is this - when we teach, are we teaching for cognition or compliance?
Are we requiring students to answer questions correctly by following directions as explicitly and prescriptively as they are taught or are we encouraging them to think deeply and express and share how and why they can achieve and attain correct answers, desired outcomes, or specific results in different ways?
Are we challenging students students to think deeply and express and share how they could transfer and use what they are learning to answer a question, address a problem, or accomplish a task, or are we directing them to understand there is only one way to answer a question, solve a problem, and complete a task, and you must do it this certain way just as you were taught?
Perhaps you're saying, "But the curriculum features all these different methods and strategies the students must use to demonstrate and communicate deeper knowledge and thinking." True, but what if we approached these different methodologies, strategies, and techniques not as a mandated assignment they must complete but rather as a hands-on learning experience in which they experiment with using these practices and processes and decide whether they want to use this particular method or another strategy? Would they not only become familiar with these different processes but also realize there may be more than one way to answer a question, address a problem, and accomplish a task and they have the freedom to choose the method that would work best given the circumstances, the context, or even their own personal preference?
If you truly want to understand how our children are expected to learn math and why they should experiment with these different methodologies, I recommend you watch this video by Dr. Raj Shah, who explains perfectly how we should teach math for cognition, not compliance: https://www.youtube.com/watch?v=X_CK1e0Lmxw
I ask you educators to consider when you send your students home with those homework sheets that feature the Lattice Box or the empty number line or require them to identify the parts of a sentence through diagramming or write an essay using the Jane Schaeffer writing method, are you teaching for cognition or compliance?
Erik M. Francis, M.Ed., M.S., is the lead professional education specialist and owner of Maverik Education LLC, providing professional development and consultation on teaching and learning for cognitive rigor. His book Now THAT'S a Good Question! How to Promote Cognitive Rigor Through Classroom Questioning will be published by ASCD in February 2016. For more information on this topic or how to receive professional development at your site, please visit www.maverikeducation.com.