If you were to take a look at the curriculum maps for any mathematics subject at the secondary level for my school district, or any school other district, you will notice 10 – 12 neat little units outlined within a pacing guide to fit precisely within the allotted weeks for the school year. You will see objectives for each unit, vocabulary students should know, as well as priority standards highlighted as the must know concepts for each course. Many districts are even moving so far as to create proficiency scales and proficiency tests to keep track of how well students are mastering the priority concepts.
I am in full favor of curriculum maps, as without them people seem to think they are allowed to interpret what material makes it into their teaching and what material is left out. This is often times based on the teacher’s likes, dislikes and view of what their current students will be able to handle. Curriculum should have teacher input but shouldn’t be that open to interpretation. I believe that curriculum maps help to ensure that every student in a particular course receives the same instructional topics no matter what school they are attending within a school district. I personally am excited to see the data from the proficiency scale tests of my students so that I can better help them reach mastery level on the priority standards as well as reflect on my own teaching of these priority concepts. Proficiency scale data used correctly can strengthen a course as well as student achievement.
When the curriculum maps were first created it was to ensure that all of the standards for a course could be taught within a school year. We have always had lists of standards and objectives, but they weren’t always organized. Plus, we had to make sure that our courses aligned with the state standards. During the creation process, time needed to teach topics was looked at as well as what standards appeared in more than one mathematics course. Once everything was settled pacing guides were created to keep instruction consistent across the district. I agree with keeping the instructional pace moving to ensure that too much time isn’t spent on one unit or concept. It can be much too easy to spend time on a favorite topic, thus causing other units to get shortchanged in both time and emphasis. Keeping a pacing guide in mind can keep your instruction focused on what students really need to know and help you emphasize those priority standards.
What you will not see in any of these neat colored-coded standards aligned curriculum maps is review and reteaching time. The objective of the curriculum map is to plan out all of the standards that will fit within a course within a given school year. Time is allowed for the week of finals, but nothing else. This fast-paced schedule of teaching works for the high-achievers who are able to take in lots of information with little need to practice it in order to retain it. Most students are not built this way – in fact the fast-paced schedule allows students to think they know something because they have ‘seen it’ regardless of how well the material is actually mastered.
Proficiency scales built around priority standards are supposed to help with ensuring that students are able to master the big ideas from a course. What students really need to master the material is the time to truly learn the material. It takes several encounters with a topic for most students to even begin to reach the first levels of mastery. Students have to have processing time, time to make mistakes and then time to correct those mistakes. Students have to have time to learn – which is often not accounted for in instructional pacing.
Instructional pacing has not really changed much over the course of time; at least in mathematics. If you look at mathematics textbooks from past decades compared to more recent editions, they all have around 11 or 12 chapters with a stringent built-in pacing guide. The curriculum maps seem to mirror these pacing guides from years ago. Eleven or twelve chapters or units is quite a bit of material to be taught in a school year, let alone absorbed. It is shocking to me that we are still stuck in this antiquated system given how much is known about how the brain works and how students learn.
Students are not little machines that remember everything they see the first time, and this is how education has existed and how it continues to exist. Students need the time to process their learning and practice with the material. Students need time to embrace their mistakes and see them for the learning tool that they can be. Our current pacing doesn’t appear to allow mistakes to be a part of the learning process. We teach a lesson, give homework and repeat this the next day. If a student gets behind or struggles one day then they will have less of a chance of learning everything in the curriculum map because inevitably frustration will set in and take over.
How can teachers help their students have the time they need to master a concept? We need to build cyclical and intentional review into our units. We need to revisit concepts repeatedly and directly throughout the unit. We need to be intentional with our planning to make sure all students have ample time to learn what we need them to.
A colleague of mine teaches in a manner that builds continuous review into every lesson and every test. At first I was hesitant to try this method as it is much different than I am used to teaching and much different than I was taught. The need for my students to show more proficiency has me contemplating why more of us don’t teach this way. She teaches a small piece of a new concept each class and continues to review older ideas each class as well. She still meets all of her curricular objectives for each unit and while it might look like it takes longer, she ends up in the same place that the rest of us do at the end of the semester. She structures her course so that students have ample time to practice mathematical concepts and ample time to correct mistakes that happen as they are learning. It is a huge change in mindset, but one that I am hoping to implement more into my teaching practice.
I have started to revise my teaching process to allow for more review with my students and I am loving the results. I had numerous students score quite well on their semester finals – more than in past years! I have continued to expand my activities and change up my questioning approaches, but the number one thing I can credit this success of my students to is the better job I have done with building review into my class structure. My bellwork exercises have been more intentional with reviewing troublesome ideas from each lesson throughout the unit. I have started putting problems from previous sections at the end of each worksheet – while still keeping the problem number to below twenty. It does a student no good to receive twenty problems over new material when they are still trying to understand the lesson. Also, they need to practice the new material multiple times over multiple days and one set of practice problems is not enough to accomplish this learning need.
My students are receiving fewer new problems and more review over other concepts in a unit and they are finding this a better approach to learning. They are able to ask questions on the material over the course of several days instead of once right after a lesson and then once before the test. They have even told me that while they still don’t like the idea of homework, it doesn’t seem quite as daunting as they can practice an idea many times before a test or quiz.
The struggle for me is to now is to ensure that I stay on track to complete all of my curricular objectives. At times this seems absolutely daunting as there are so many things to teach and not nearly enough time. In math, we can’t simply skip concepts as this is truly a subject area that builds upon itself. I really want to be able to spend the time each student needs to learn the material, but this is not a possibility as I really do have to make sure all the standards are taught. To miss a standard completely would be an even bigger disservice to my students.
For now, I will continue working on increasing the cyclical nature of review. It is taking a lot of thought readjustment and extra time revising perfecting good assignments, but I am keeping my fingers crossed that the longer I explore and expand my cyclical review methods, the more they will become like second nature. My students are doing better and at the end of the day, their success is what is most important.
Musing of a Motivated Math Teacher 