The phrase Common Core Standards gets a loud reaction when brought up in political conversation. It shouldn’t, education issues have little to do with politics.
In my last column we discussed the timely demise of No Child Left Behind and the advent of the Every Student Succeeds Act. One point made was that state governments and local school boards are best suited to meet the needs of students within their jurisdictions. That is true for assessments, accountability, classroom structures, and student placements. However, the task of providing the standards from which school departments and classroom teachers organize their curricula is best served by a larger group of educators working together to determine learning specifics.
A national project to provide basic standards of learning is the most efficient way to make sure all American students are getting instruction that flows seamlessly and logically from skill to skill during the learning cycle.
Basic math facts, great literature, historical events, and scientific findings are not regional, and do not need to be interpreted. Simply, the logic of addition and subtraction being taught before multiplication and division does not depend upon in which state one lives.
Common Core Standards are sometimes misrepresented as the whole of education. Common Core attempts to ease the burden of local educators by providing a framework for instruction. Common Core does not and should not delve into teaching methods or suggest specific assessments. Common Core forms a triad with assessment/accountability and pedagogy; the art teachers apply in their classrooms.
Restated, states use Common Core as a base for creating assessments and rating accountability. Local schools use Common Core as a springboard for developing expectations and lessons that cater to the needs of their individual students.
The Department of Education is best suited to oversee and manage the experts in each curricular field developing a national set of standards available for use in every state, school district, and classroom in America. Common Core needs to be a living, breathing document that is constantly in flux to keep up with discoveries; developing history; and new, innovative methods of turning curricular data into useful skills in the hands of our national student population.
One more restate: Federal government provides the base data; states organize, assess, rate, and rank; and local school districts deliver the best instruction they can.
How many out there bemoan a lack of mathematical skills? Part of the reason may be that you were never taught to understand what math is all about. When social media posts pooh-pooh New Math and wed it to Common Core, it is because of a lack of understanding, not a lack of value for math standards.
I taught “new math” in my classrooms for over 30 years and have been out of the classroom for nearly 15, so “new math” isn’t really new. Let’s call it “set theory”.
The basis for math instruction is often the rote memorization of counting, math facts, and a chain of isolated steps to get a “correct” answer for basic math functions. We memorize addition and subtraction facts and then use them to follow a series of tasks to get answers to multiplication and division …set up the bracket; put the dividend inside and the divider on the outside; use multiplication facts to see how many times the divider gozinta (goes into–we called it “gozinta math” because that is what it sounds like to kids trying to follow along in class) the dividend from left to right–even though we usually start with the ones column–and go from there using multiplication and subtraction facts until we finally reach the ones column and find out if the problem comes out even or has a remainder.
365 divided by 17 equals 21 with a remainder of 8. Now, pray tell, what did we do? In substandard classrooms we got an A on our paper because we got the right answer, but in a set theory classroom the learning has just begun. The object of the lesson and the challenge of Common Core are to be sure students know when to apply division to solve, not just math problems, but legitimate, real world posers.
Set theory is based on understanding. It incorporates much more than rote learning. By using our base ten system and set theory, we learn such tid-bits as “addition puts together and subtraction takes apart what addition has done.” Same relation with multiplication putting together, not individuals like addition, rather equal sets into a larger group, which division can undo. 3×5 is putting together three sets of five items or 15 items in all. 15 divided by 5 is the undoing of multiplication by repeatedly subtracting sets of five from 15 to see how many sets there were originally–15 grapes with five grapes repeatedly taken away three times shows that three kids could get five grapes each to share evenly. 3×5=15, 5×3=15, 15÷3=5, and 15÷5=3. They are all related and if we know the theory, learning one is sufficient to learn all four. Easier!
Many, many students are successful at learning the rote skills of math facts and then applying the system to solve the problem in a school setting, but many are not. So, teachers need more tools than merely the more abstract version of math instruction. Set theory provides a more tangible way to direct students at sea. There is no rule stating one must use the division grid. If one understands base 10 and that division is repeated subtraction one can solve the problem with another method. What is wrong with that?
In the problem above, 365 items in a group can render at least 10 groups of 17 or 170 items taken away leaving 195 items in the original group. 10 more groups of 17 can be removed, or 170 more leaving only 25 items in our original group. We see that one more set of 17 can be subtracted leaving 8 items that will not fit into a complete set of 17, ergo, 10 groups plus 10 more groups, plus one more makes 21 groups of 17 taken from the original 365 with 8 stray items remaining as a partial set. 21 remainder 8–same answer. If that seems awkward and more time consuming than the “traditional” way, it isn’t if you practice. Plus you now have the added understanding of what division is all about and can generalize the skill when division is needed in a life situation.
Teachers need a large tool kit to help all students with many different learning styles attain proficiency. A national set of Common Core standards that offer extensive varieties of approaches to thinking and problem solving, from which teachers can pick and choose, is the best way to start.