Watching the Common Core State Standards in Action ~ Ruth BallingerApril 15, 2015
Teacher, pointing to a number on a large poster, says “Yesterday was our 114th day at school.” She paused before continuing. “Can anyone make a prediction of what that number will be tomorrow? What number will I write here tomorrow?”
She calls on the first student, a particularly squirmy little boy. “Um . . . Eleven . . . five.”
Teacher writes “11 5” on the whiteboard. “So, we have a prediction of “eleven five.” Thank you, Jarret. Who wants to make another prediction?”
Teacher calls on a girl. “Yeah . . . One hundred . . . One hundred . . . fifteen.”
Teacher writes “115” on the whiteboard. “So, we have another prediction. Kalia says the number will be 115. I am looking for one more prediction.”
Teacher calls on a second little girl, who is silent for a moment, then says “One hundred fifteen.”
Teacher writes another “115” on the whiteboard. Pointing, she says, “So, we have ‘eleven five’ and two predictions of 115. Now. What do the rest of you think? Talk to your neighbor.”
The sound level increases as the students turn to each other and, in pairs, begin talking.
After a minute, Teacher says, “OK. Now. How many of you like 11 5? I see three hands raised. How many of you like 115? It looks like the rest of you think it will be 115.”
Teacher says, “I see that in this one [pointing to the 11 5] the five is one more than the four in the number 114. And that makes sense. But, we don’t say ‘eleven five.’ In this one [pointing to the 115] 115 is one more than 114. ‘One hundred fifteen’ is how we say this number. Everyone say ‘one hundred fifteen.’ ”
The class continued, but I was lost in my own thoughts. On the surface this was a lesson in counting one up from a given number, 114. In traditional teaching, this lesson would have taken, perhaps, 15 seconds. The teacher would have asked her question, received the answer “eleven five,” corrected it with some statement about the fact that we don’t say “eleven five” but we say 115, and moved on. Instead, in this five-minute lesson I realized I was seeing the results of the Common Core State Standards. Specifically, I noted the first three of the eight Common Core Standards for Mathematical Practice in action.
Mathematical Practice 1: Make sense of problems and persevere in solving them. The teacher had presented the question as a “prediction,” an invitation for all her students—even those who were not sure—to make an effort to find the answer. She had given no indication that “eleven five” was incorrect, thus, providing no disincentive for students to continue to think and propose answers. She promoted even further deliberation when she had her students dialog with each other about the two different answers. All in all, the teacher was able to create a context in which her students persevered in thinking about the answer to one mathematical question for a full five minutes.
Mathematical Practice 2: Reason abstractly and quantitatively. The boy who gave the first answer was using logical reasoning based on his current understanding of mathematics. I can imagine his thinking went something like this. “I see a 4. I know a 5 comes right after 4. So the answer is 5. But I also see an 11. I can’t just forget the 11; I know the 11 is important. So I will put the 11 in front of the 5, because that is the way it was with the 4.” Throughout this brief lesson, the teacher placed as much regard on the reasoning behind his response as on the correct answer.
Mathematical Practice 3: Construct viable arguments and critique the reasoning of others. The teacher voiced the reasoning that the boy had used as a mathematical concept, specifically that five comes right after four. In this manner, she was modeling for her students how to construct a logical argument. In the end, she concluded the lesson by highlighting the correct answer for the whole class and giving a reason for that being the correct answer, which was that we say “one hundred fifteen” and not “eleven five.”
Kindergarteners are five and six years old. These children that I had briefly observed were evidencing a powerful confidence in their own ability to think mathematically and a fearlessness in taking the risk of answering. Most of us, brought up in a traditional teaching style, would never attempt to answer a question—especially a math question—unless we knew we were right. Moreover, we would see two different answers as right and wrong and not as two responses that both encompass logic and reasoning. In my five-minute observation of this kindergarten class, I saw the power of the Common Core in full force.