I Beat Subtraction With Regrouping

Oh, subtraction…how it can be a thorn in my side! This year subtraction has been a difficult battle for me. I have been an advocate for student invented strategies for years now and have used them in my classroom. I mainly used them for multiplication and long division when I taught third grade under GPS. Now I teach second so they are mastering addition and subtraction. Subtraction with regrouping is always a battle. In first grade they learn basic subtraction and therefore come to second knowing to count backwards. When they get to a problem like 32 – 27, most students (all but 2) just made it 37 – 22 and subtracted. They did this when writing numbers horizontally as well. The rest of my grade level teaches the traditional algorithm explicitly and that’s what the students learn. Through all of my research, I just couldn’t do it. Last year I started with strategies and then conformed to my peers and taught the algorithm…feeling pure guilt the whole time. This year I was determined to stick with it and prove that it works. Through lots of investigation with numbers and manipulatives my students were able to come up with 4 different ways to subtract that will work every single time and are efficient for those that understand them. Trying to get all 49 students that I teach to invent a strategy is unrealistic, but many students did. There were hard days where I wanted to give up. Days where they just went out to recess early and I prayed through tears (and a Twix) for direction. Days where I left uncertain if I was doing them wrong by not standing up and teaching the steps. On those days I would read my Van de Walle books and read the blogs of my math minded friends. I would pray and regroup my thoughts and start fresh the next day. Our curriculum guide for our county gave us 3 weeks to teach 2 digit addition and subtraction (yeah right)….I took 3 ½ months. I did our other skills along with it…we did measurement, coin recognition, graphing, etc, but would do at least 2 addition and subtraction problems every day. I made slides for each of the four strategies my students came up with and the whole class had to try each one a few times before deciding on the one or more than one strategy that they wanted to adopt as their own. One of the strategies was the traditional algorithm. Two students showed it to the class (one is a repeater and one is from China and learned it there). They were able to explain it with manipulatives, so it could be used. We called it the “old way” since it’s the way I did it in school and they think I’m old. I sent a letter home to parents explaining the importance of invented strategies and pleading to let their child use the strategy that made sense to them. I also sent a “how-to guide” for the 4 strategies we came up with in class so that parents could help their children with homework. We are finally taking our test this week. I’ve been testing in small groups and so far they have done a phenomenal job! I am so incredibly pleased. My low students are performing way beyond what I thought they could do. I am now so thankful that I stuck through the hard times and persevered. It was worth every stressful day to see my students to not just subtract with regrouping, but to subtract with UNDERSTANDING!

Student Invented Subtraction Strategies

Student using counting up (Gordon’s Way) on a test

Student using equal distance (Vincent & Michael’s Way) on a test