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Introductory Scenario

Rewind the clock

Let’s travel back to when Jessica and Sam were in seventh grade—before Algebra I, Geometry, and long before they started dating. In seventh grade, they were both in Mr. Samson’s math class.  

He was a language arts teacher, but the school was having a hard time finding licensed math teachers. He had agreed to teach a couple periods of math that year. As he prepped for his first week of class, Mr. Samson was relieved to find that the math came back to him quite easily. In fact, his first few classes went quite smoothly. Here’s a snippet from the third day of class:  

Mr. Samson: Who remembers what a proportion is? (Three students raise their hands.) Sam?  

Sam: It’s when you have two numbers on top of each other. Like a fraction.  

Mr. Samson: Good, Sam. That’s part of it. What kind of numbers? (Pauses for a second.)  

Class:Silence 

Mr. Samson: Anyone? (Pauses for another second.)  

Class:Silence 

Mr. Samson: Well, they should be integers, right? (A few nods.) Okay. And we should have an equation and an unknown somewhere, right? (Some more nods.) And then we multiply the numerator of the fraction on the right side and the denominator of the fraction on the left. Then, we divide by the other denominator, right? Well, let’s try one out. Let’s say we have 2 over 3 on this side and something over 6 on this side. We’ll use a question mark to represent the something. Who knows what this question mark should equal? (Only Sam’s hand goes up.) Okay, Sam?  

Sam: 4  

Mr. Samson: Nice work, Sam. Now, let’s say we have 2 over 3 on this side like before, but now we have question mark over 9 on the other side. What would the question mark equal? (Only Sam’s hand goes up.) Let’s get someone else this time. Anyone other than Sam? (Pauses for a second.) Jessica, what about you?  

Jessica: I’m not sure.  

Mr. Samson: Just take a guess.  

Jessica: Uh… 5?  

Mr. Samson: Not quite. Okay, Sam, help her out.  

Sam: 6. 

Mr. Samson: That’s right. You almost had it Jessica. Any questions, class?  

Class: (Silence.)  

This is how it went in class from day to day. Most of the class seemed to follow along fairly well. So, it shocked Mr. Samson to discover that half the class failed the first exam. This is what he said after he had passed the tests back:  

Mr. Samson:  Listen up everyone! These grades are not acceptable. You need to be putting in more time outside of class. You also need to be asking questions if there is something you don’t understand, okay? So, do you have any questions from the first four weeks?  

Class: Silence 

Take Notes

(to be answered by yourself or in a group)  

  1. Put yourself in the students’ place. What effect would Mr. Samson’s questions have on you?  
  2. Did you ever have a teacher who asked questions in the way Mr. Samson did? What was it like?  
  3. If you were taking a class where you weren’t really confident about the material, what kind of questions would make you feel comfortable about sharing your thoughts?  

Module: Helping Students Do Math

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