Are You Teaching Branching? Make Sure You Do This First…
Several years ago I worked at a charter school the first year it opened. The school implemented Singapore math, so that was my first year to test the waters of Singapore math. Our trainer instructed the 3rd grade teachers to go ahead and teach branching even though it was a skill the students should have learned in second grade. To teach children the procedure of branching, it took about four weeks total, and then not all of the students perfected the ‘procedure’ of addition and subtraction branching. The students had more success learning addition than subtraction branching. With the mandates of testing, we weren’t able to solely use Singapore math, but I had to supplement with other materials. Then as you are all familiar with, testing approached and likewise the pressure along with it. Then we didn’t have ‘time’ to teach number sense SO deeply since other skills are tested. Unsurprisingly, the teaching of Singapore Math somewhat fell apart midyear. Please don’t take this wrong I LOVE Singapore math because it works, but the conditions of testing hindered us from teaching it wholly.
Fast forward to four years later. After teaching small groups today, I have reflected on the year that I taught branching and its effectiveness. Yesterday I pulled small groups of average math students to teach them regrouping for the second day in a row, I had them build double digit numbers with base ten blocks blocks. I repeated this process today with the same group of students. After that I started notating their thinking with branching representation on a small white board. Students intently watched and helped me notate the thinking they had done with the blocks in (abstract) numbers . They began to understand grouping with tens and how to decompose numbers to build more tens or hundreds. Then I told them that they couldn’t use paper or blocks, but could only look at the addends I was about to write on the board. I asked them to whisper the answer in my ear so that others could still think. I was amazed! Half of them could answer the question correctly doing mental math. The other half were only 1 away from the correct answer. I was so proud.
I shared the above to really say the kids taught me something in just two days because of their adept ability to add mentally. Teaching branching worked so much better four years later–all I had to do was provide an experience with branching directly after building with base ten blocks. Why didn’t I start out with the concrete blocks first before I threw abstract numbers at them…duh me! Branching made so much more sense to them after building a concrete foundation. Reflection is priceless!