I’ m reading Steve Leinwand’s Accessible Mathematics and he poses this question as a bell-ringer or review question for a chapter that was covered a month ago. He points out that making sure that students understand place value is critical but it’s not about one question and then moving on; it’s about asking multiple questions about one problem and letting students explore the topic. The answer to the question is easy 17,294 and students can likely answer the question without having great number sense. Students can line up digits and figure out that the 1 (from 1,000) and the 8 (from 18,294) line up and use the procedure to subtract, but that doesn’t mean they have good number sense. If you read his explanation he proposes to ask several follow-up questions:
What digit did you change? Why?
Or what number is 100 more than 18,294?
Or what is 100 more than 2,954?
It’s not about this question as much as it about pushing students to be able to expand on a specific problem to create deeper understanding beyond recognition of the tens place. Another reason why I like this kind of questioning to begin a class, is that it’s accomplishing the goals most bell-ringers have in mind (reviewing concepts studied previous in a routine and intentional manner) but it’s not just about posting 5 questions that are ACT like. This approach treats the students as learners capable of adding to the conversation and adding to the learning and it treats teachers like professional who can make instructional decisions beyond which multiple choice questions to ask today.
In this example, the teacher is asking a great question, but is basing the next series of questions on what she is observing and what students are doing in class. Is it more important to ask another unrelated question about place value or to ask students who explained their answers to the first question very easily a question like, “what is 100 more than 2,954?” This question is a natural extension of the previous question, but is asked once the teacher is sure the students understand the initial premise (place value) and she wants to test whether the students are capable of regrouping easily.
If however, students struggled with the initial question, the teacher backs up and asks a related question like, “what number is 100 less than 18,294?” Note in this question we aren’t asking students to regroup. This question stays with the idea of place value understanding, and offers students opportunity to clarify their thinking immediately and provides students opportunity to end the interaction positively.
Making sense in a mathematics class isn’t about getting the right answer every time, but it is about knowing why and how you get the right answer and what makes the answer correct. I wish more administrators and instructional specialists would read Steve’s book because for my money, his questions make a lot more sense than some random 5 multiple choice questions done at the beginning of class that aren’t discussed because there isn’t time to review that many questions and teach new material.