Have We Damaged Our Children’s Ability to Reason by Teaching Procedures?
I have been working with many small groups of average leveled students to help build their number sense since there will be so many gaps in common core understanding with students moving up to 4th and 5th grades. Up until earlier this year I confidently thought that students in second grade needed to learn the traditional regrouping algorithms for addition and subtraction. After some common core training, I humbly realized that students aren’t necessarily expected to know how to complete this traditional procedure, but rather be able to make sense of a problem by decomposing and composing numbers using strategies that are comfortable for them. I said all of that to say that because of this thinking, I gave students in my small groups base ten blocks and NO paper. I gave a double digit addition problem that would give students the opportunity to regroup 73 + 48 (mind you they should have been able to handle larger numbers). I thought I would start with a really easy problem. Well, I was wrong! The students struggled to get an accurate answer with blocks to solve this problem. Of the four students I had in this particular small group, only one student was able to find the correct answer. Well, I changed my mind on the no paper and gave them a sticky note. I instructed them to write their answer on the sticky note just so I could do a quick assessment of who could accomplish finding the answer with the blocks without blurting it out. To my chagrin two of the students were trying to solve the problem on their sticky note with the procedural algorithm. I promptly reminded them while replacing their sticky notes that we were solving the problem with the blocks and not paper. When all students had finished thinking, I listed all of the students’ answers on the board and asked them who was correct. After having students count and recount their blocks, they finally came to a consensus of the correct answer …121. They struggled with counting past 100 especially by 10′s… 110, 130, 140… and they would correct one another to say 110, 120, 130, 140. Surprisingly enough to me, the students felt more comfortable lining up numbers in an algorithmic procedure with no understanding to obtain an answer than they did counting out blocks past 100 to obtain the correct answer.
Below is a picture of the students counting out their blocks. I had them place their addends onto small sheets of square paper to help keep them organized since they were getting their extra blocks confused with the ones they were counting. I wanted to use small paper plates to help them organize their blocks, but I didn’t have any. I happened to have some origami paper lying around, so I just used that instead.