We are doing the right thing. That is the most important message I can give you at this time. When we teach for greater understanding of mathematical concepts, and coach our young people into becoming better problem solvers, we are doing the best thing we can for them. So the questions we need to be asking ourselves when we are faced with how to teach a lesson, a unit, or a concept, is: Will this help my students become better problem solvers? This is one of the reasons we went with Everyday Math 4-- The emphasis is on problem solving and deeper understanding of mathematical concepts.
Common Core math is constantly under scrutiny in social media and even in the news, mostly because teaching for deeper understanding is not how previous generations were taught, as a rule. We were primarily given instructions to follow, rather than a puzzle to work at, take risks with, and eventually solve, perhaps with some help from a neighbor or two. Puzzles aren't always easy to understand, and they often involve making mistakes before a solution is found. For some puzzles, it helps to look at them from multiple perspectives, which is why we often have our students problem solve with partners and small groups. Other puzzles are best approached independently (have you ever tried to solve one of those nine-square puzzles with birds or reptiles or another such scene on them, with a group? Unless one member is a very dominant type, it is almost impossible!*).
Let us remember that Common Core is merely a set of standards, and not entirely different than standards we've had in the past. The major difference is within the eight Standards for Mathematical Practice and the content standards, there is greater emphasis on deeper understanding and problem solving. This is not understood by some parents and other vocal critics, who see what looks like strange and unusual homework assignments coming home (and others, with questionable authenticity, posted on Facebook) they have trouble helping their children with, let alone understanding themselves. While the Common Core math standards are the same in 42 states, how they are implemented is not always the same. Different districts in these 42 states have different math programs, and within those districts there is a varying degree of fidelity to those supposedly Common Core aligned math programs. As someone who has studied the Common Core math standards since before they were released, while still in draft form, my opinion is that EM4 has done an impressive job aligning to the standards and capturing the emphasis on understanding and problem solving. As with any mass-published resource, we each will find the occasional weirdly worded problem, or curiously designed activity, but the mathematical content and instructional shifts that are the focus of EM4 are its major strengths, and teachers in RSU5 are doing a fabulous job in the inaugural years of using these resources.
I want to share a NY Times article that was published recently which attempts to address some concerns about Common Core math, just to help celebrate and acknowledge what we are doing. I think you will read this short article and say to yourself, "I'm doing that," or, "that's already happening in my classroom." So congratulations, you are doing the right thing. I am confident that as the next couple years progress, we will see more and more great things coming out of the work our students produce, because I see the difference one year makes every day in the classrooms I visit. Imagine what will happen when we all really get good at this.
Thank you for taking risks in your work, for allowing opportunities for your students to problem solve together, for shifting your instruction, and for putting so much love and hard work into your math lessons.
Here's the link:
NY Times Common Core Math piece
* There's a story that goes with this puzzle thing... I worked at the Spurwink School, among other intense alternative education environments, prior to getting my teaching certificate, and one day I pulled out one of those nine-piece square puzzles for a boy that was dealing with a lot of emotional issues and had recently gotten himself in some serious trouble at school (that would eventually involve charges being brought against him). I brought in the puzzle because my wife and I had been working on it at home periodically, and it took almost two weeks for us to stumble upon the solution. Intuition led me to believe this particular child might really focus on such a thing, and he was obsessed with songbirds. This puzzle had songbirds all over it. The first thing he did was correctly name each bird species, and then he went to town on the puzzle, quietly mumbling to himself as he rapidly swung cards around in different positions. He solved it in less than 60 seconds. Now one could come to a number of conclusions from such a phenomenon, one being that my wife and I are perhaps not all that sharp... but I prefer to use this as an example of not just a special kid (I have never seen anyone else solve the puzzle so fast), but of one of those situations where other perspectives actually complicate the problem solving process. When my wife sat beside me at the table, she was looking at the puzzle from a different angle. Every time she moved a piece in or out of place, it completely messed with what I was seeing, and I had to switch gears in my thinking. When I would adjust the puzzle, my wife would let out a displeased sigh. For the child I gave the puzzle to, it was just a matter of rapid-fire trial and error, in total quietude, without disruption, and bam. Puzzle solved. It didn't end up being a very lengthy distraction for him, but he did get to feel good about himself for a few minutes.
It just goes to show that while problem solving is a process most often benefitted from collaborative work environments, we should continue to still provide opportunities for our students to do some work independently. Sometimes that is where their strengths manifest themselves.