One of the things I love about teaching is that I feel I am always in the midst of the this ever-changing shift in philosophy. I always feel challenged, and I never feel apathetic, for there is always something new I can figure out. Such is the case with the current Common Core standards and my philosophy on teaching, specifically in math.
I have recently been able to participate in the curriculum mapping committee for our new math maps. Our charge is to deconstruct the Common Core math outcomes and help align them to our core program, Everyday Math. While this doesn’t seem like that grand of a task in isolation, it became a grander task when analyzing the philosophies underlying these two components of our curriculum.
Common Core Standards for Math
When analyzing these standards, it is tempting to look at them from a mastery perspective. In fact, it seems logical to make up a progression of the standards by going through them systematically, building on top of each other. For instance, geometry standard one paves the way for geometry standard two and so on. On the other hand, the intention behind the standards is to integrate them so that they become interdependent and cohesive, contributing to a more flexible and holistic knowledge of basic mathematics. While it would be nice and tidy to walk through the standards one-by-one, it really is not idea to approach it in this manner.
However, when I began, that was the way that I was trying to order the standards. I was trying to organize it so that kids would learn geometry standard 1 (4.G.1) and the learn the base-ten number sense standard (4.NBT.1) and then go to the second standards within each domain from there. In my mind, we could build units based on the each standard, create proficiency scales and assessments, and simply use resources from the Everyday Math Curriculum to help us. In fact, I found myself entering our mapping meeting the other day with my guard up, ready to defend my position that a program, especially Everyday math was not the best way to teach these standards. Our district teaches to mastery, and we need to do the same for math. Everyday Math will not help us to fulfill that.
Everyday Math (UCSMP)
Despite my initial feelings on integrating the Common Core Standards with the Everyday Math Program, I have always enjoyed teaching with the program. I like the idea of spiraling; I feel that it helps kids review content at sporadic but purposeful points throughout the year, and encourages kids to see math in a more holistic sense. However, some of the assessments and units lack focus, in my opinion, and the main essential outcome can be lost. In some units, the curriculum will cover many domains of math, including base-ten number sense, geometry, and measurement and data. This can be a lot for kids to handle!
In my (almost) three years of teaching, we have taught in the manner the curriculum asks, doing our best to honor the spiral, and testing using the pre-made assessments. I’ve noticed that it has helped them to make connections between domains in math, but I also feel that it lacks the structure that kids crave when learning. Of course, I don’t think it needs to be so structured that it is rigid, but they also have to be able to find their footing within a skill and not be constantly shifting.
This program does, on the other hand, allow for us to revisit skills that they were not able to pick up the first time. For instance, if they do not pick up fractions in Unit 7, then they can easily come back to it in Unit 9 and give it a try. Everyday Math, in essence, respects that idea that children learn at different rates and in different ways. After all, we don’t all learn to walk and talk at exactly the same time, do we?
Mastery Learning and Learning Targets
In recent years, my district has adopted the practice of posting learning targets and referring to them throughout the lesson. I think this is an excellent practice, and it is research-based. If learning targets are posted, children are more likely to be able to identify what they are learning; if they are more able to identify the learning target, they are more likely to be engaged and be metacognitive about their learning; if they are able to be more metacognitive, then they are able to reflect, and thus, learn more efficiently, and hopefully, make the material stick more permanently.
Posting learning targets, creating proficiency scales, and backwards designing units has, in effect, guided a great deal of our professional development and professional responsibilities. We’ve created tests aligned to our outcomes with test items outlining each descriptor in the 4/3/2 areas of the proficiency scale. Furthermore, we’ve made sure to focus their learning on one outcome at a time so that we provide structure and reteach if they are not learning what we’d like them to learn.
In addition, this also confines us to a rather rigid time frame in which we are able to teach the outcome. At the end of the time period, we are expected to assess that outcome using a common assessment so that we may compare them to their peers, and if they do not reach that, we either need to reteach again or move on.
Well, I know that I like both of these practices, and they seem to both be research-based, so which one do I utilize more? When I began my career with my district, I think I found solace in the structure that accompanies mastery learning and learning targets. It felt good to know that I was working on one outcome at one time, and that I was only working on assessing one outcome at a time.
However, as I matured as a teacher, I’ve realized that learning is anything but rigid and structured. In fact, outcomes can be so codependent that it is impossible to separate them and assess each of them separately without utilizing other knowledge along the way. I have begun to realize that the Common Core State Standards as well as the Everyday Math Program actually do share a similar philosophy: a philosophy of interdependent and deep standards that help to educate the whole child, and not just isolated pieces of them. While posting learning targets and only assessing certain outcomes might help us find the structure in our teaching, it does not necessarily mean we need to teach that way all the time. It is possible to begin exposing kids to concepts, even when we know we aren’t going to assess them; in fact, I think it will help them a great deal if we start “priming” them with skills that are coming up in the future.
Essentially, kids are not as one-dimensional as we are trying to make them. We are trying to funnel them through learning targets and essential outcomes holding them all to the same standard. While it is good to have high standards and to have general goals through which to gauge their ability levels, it is effort spent in vain if we continue to try and fit kids into a rigid mold. We’ve been saying for years that education cannot be “one size fits all,” and we need to truly uphold that philosophy when implementing some structure into our practice. Kids need structure, that’s for sure, but they also need enough wiggle room to master targets at a rate that suits their developmental level and the level of proficiency that is expected at their grade level. However, I am still left with a couple of enduring questions:
(1) Do we really need a “content” essential outcome? Could we have a limited number of essential outcomes (i.e., major standards and mathematical practices) that we can count on to permeate most of the domains in math? This could help us to still provide the structure or learning outcome (i.e., I can describe the relationship between visual representations and symbolic representations of a math problem.), but also provide the wiggle room to be working on many domains at a time.
(2) Is it necessary for students to master some outcomes only part-way through the year in order to be successful in their grade? If these standards are meant to be mastered by the end of fourth grade, isn’t it fair to give them all the time they need? Kids need context. Sometimes certain standards are strengthened by learning other domains. In fact, sometimes certain standards are so interdependent that each standard is necessary in order to truly understand both concepts. Maybe by not truly holding them to mastery until the end of year, we can provide the structure and the grade-level standards, but give them more differentiated time frames to reach these goals.
In essence, maybe we need to find structure in an overall lack of structure, and maybe a lack of clear structure or clear focus in one specific learning outcome becomes our one constant in our instruction. Or perhaps the commonality throughout each of the units, or the structure within our units, is not necessarily the learning outcomes or the content, but rather problem-solving and critical thinking strategies that we teach(which the mathematical practices encompass).
Regardless, I’m enjoying exploring my moratorium, and I look forward to finding clarity through this foggy patch.