So, thanks to David Wees- this train began rolling…
The problem: CCSS formally addresses Angles in 4th grade here, but expects 2nd graders to identify polygons here. Clearly a bit of lateral alignment needs to be done on CCSS, and Mr. Wees was surprised it wasn’t caught earlier. Looking strictly at the scope of what CCSS is trying to do and what it stands for, I understand the concern. This should have been addressed before now. Enter me, I guess I am a bit more laid back on such matters- that or the fact that I have done essential standards far too long. Here is how I approach essential standards
1) Look for commonality within Substrands.
Read the standards and envision the tasks you will ask students to do. Band standards that make sense. I would band these two standards together because I see a task where I ask students to create pictures of polygons, lines, points, rays and angles. Read through all of the standards for a substrand, think on what rich activities or tasks you have students experience and use them. Creating connectivity between standards and helping students see the overarching picture of why they are learning them will create critical thinkers in mathematics. Students will begin asking themselves about connectivity and will look for mathematics in other activities from non-mathematics classes.
2) Look for commonality between Substrands.
Just because you are working on an Algebra strand doesn’t mean that students can’t also explore Statistics and Probability. In fact, one activity I like students to perform for me in 8th grade is constructing graphs of positive and negative association, constructing a line of best fit and equation of that line. Once again, this will build a connectivity of mathematics that students will see, understand and start to investigate on their own. Students should not think that every day of math class is a new skill they need to perform, independent of all the other skills they know in mathematics.
3) Look for the lateral progression of the strand.
You are a teacher, preparing students for their future. One question students always ask is why/when are they going to use the math. The best way to not have to address this question is to have a good understanding how the concept progresses throughout a student’s education. Knowing where it is introduced and how it is developed in previous grades gives you a baseline to ask refresher questions and introduction point. Knowing where they will use the concept in later years provides you an outline for mastery that students will need, beyond their current grade. It allows you to use vocabulary they currently know and transition them into vocabulary they will need now and later. Elementary students should know when they are doing Algebra, don’t make it such a big mystery and surprise to them in 8th grade. Vertical PLC’s are very important for this step. At the minimum, talk with the teachers 2-3 grade levels above you and let them know how you present topics and what vocabulary you use. Creating this channel for professional talk with go a long way to ensure students are successful in their latter years.
4) Know the testing benchmarks of the strands.
Every high-stakes test should has a reference for teachers outlining the sample size of questions for each substrand. Some call it benchmarks, some performance standards- but the bottom line is they tell you how many questions each student will receive on a topic. This should come into play in your planning, make sure that you give students ample time with those concepts most tested. I am not saying to teach to the test, but to realize that just because you spend two weeks on probability students may not have mastered the skills to answer 15 test questions in an end of year, high pressure situation.
5) Make your Essential Standards manageable.
You aren’t just rewording each substrand and making it your own. You are doing this for a purpose, to make a guideline for your year that is manageable. Students can handle around 8 big ideas throughout the school year, don’t make your Essential Standards such that they are presented with 20 different ideas/topics. Essential Standards need to be big, broad statements that encompass the mathematical concept, not breaking it down into individual parts. Contrary to some beliefs, students are not great at “assembly line” learning in math, they need to build the whole car, not just the seats. Structure your standards and year so that your students become the managers of the math factory, not specialized implementers.
6) Be flexible.
You are the professional, you know what students will need to accomplish the lesson- make sure that you provide it. Don’t blindly follow pre-made lessons from the publishing company, don’t feel you have to start at chapter one and progress through chapter fifteen. Provide your students with the tools they need to be successful, realizing that those tool change with each class, and with each individual. Don’t create barriers, students are ready for more than you realize- provide the nurturing scaffolding they require to help them accomplish great things.