I was playing a game with my soon to be 5th grader when he asked me to pick a number between 0 and 10. Being the math teaching mom I am, I obviously selected 1/2 much to his dismay.
Jackson: “Mom, I said to pick a number.”
Me: “I did. I picked 1/2.”
Jackson: “Mom, that’s not a number. 1/2 is a fraction not a number.”
Me: “Jackson, fractions are numbers.”
Jackson: “I thought you taught math, fractions totally aren’t numbers.”
It was a super fun morning at my house! However, it really made me reflect on exactly why I am so very passionate about the work at Open Up Resources. Jackson is a great math student, he has had wonderful teachers, he scores well ahead of his grade level on standardized testing and yet somehow he has missed the beauty that is the cohesiveness of mathematics.
I am not going to lie, I never truly stopped and thought about the importance of coherence until my first Core Advocates Convening and from that moment on I made it my mission to start finding the connections between each and every standard I taught. In Kentucky, when the Common Core Standards came out we, like many other states, immediately started deconstructing and removing the coherence by turning them into a check list of skills to be mastered rather than focusing on the connections as intended by the authors. I decided after that first Convening that I was going to bring that coherence back. There was one problem…building in coherence is HARD. Managing 120 students a day, lesson planning, grading, communicating with parents, and then adding to that trying to make connections to previous grade levels, previous units, and upcoming units was more than this teacher could do successfully. There were times when I really hit the mark and did some really cool lessons that were conceptual and coherent but I am going to be honest, most of the time coherence took the back burner. I started every year with the plan that I was going to teach all of 7th grade math through the lens of proportional reasoning and then the year would start, I would get bogged down and would revert right back to my old faithful standards checklist.
Enter Open Up Resources Math 6-8 Curriculum into my life and what I thought I knew about doing coherence well was blown out of the water. Those lessons I occasionally did well, that were coherent, and brought in major work of the grade were nothing compared to a year-long curriculum that was spiraled, coherent, and truly finally taught 7th grade math through the proportional reasoning lens that I had always dreamed of. I began to see what a truly coherent curriculum could do for struggling learners. It took math from a list of skills, rules, and procedures that were done to them to something they could own and make sense of. My most struggling learners started looking for proportional relationships in all types of problems in order to make sense of them before just trying to “solve” them. They looked at equations for a constant to see if it was proportional, they made tables to check for a constant of proportionality, they found tax by first finding the unit rate or k. I know it probably sounds crazy or that I am over simplifying it but truly for the first time in 13 years when I posed kids with a difficult problem before just saying “I don’t know what to do” they would at least first try to make a table and look for a relationship.
Then we came to the rational numbers unit and for the first time in my teaching career I discovered a way to make subtracting integers make sense for struggling learners. I had tried every manipulative in the world; integer chips, algebra tiles, army men, thermometers and more, and when that didn’t work and the kids still struggled I cracked and taught terrible tricks that I am ashamed to even admit here (I am not proud but we’ve all done it). Then Open Up taught the topic by simply posing the question “how far apart are the two numbers on the number line?”. Are you kidding me? It was that simple! My kids were subtracting integers like pros! I have a first grader at home that was working on subtracting in math also so I began to notice that she subtracts the same way…using a number line. I can’t wait to see her subtract integers with Open Up in a few years. It’ll be coherent to her. I wish I had done that for the first 12 years of kids I taught.
So back to Jackson and his fraction his problem. I believe whole heartedly that it all goes back to this concept of coherence. He has wonderful hardworking teachers but again coherence is hard to build in as teacher if you don’t have a curriculum that has planned for it. They are forced to revert to the checklist just like I was. We are done with multiplying and dividing whole numbers kids…guess what we are going to learn about next…fractions! It seems innocent enough but without coherence fractions aren’t numbers to my 5th grader.