Lesson Play: The Importance of Anticipating Student Response

Many teachers do not recognize the importance of anticipating students’ reactions to instruction and questioning.  However, this is a very important part of planning a lesson.  Teachers will often think about the questions they would like to ask, as well as the ideal answer they want, but will neglect to think about the responses that students may actually have.  This is vital for lesson planning because teachers should be aware of what students may struggle with and how to bring students to the desired answer without just telling the students.  This week in my course on Teaching Mathematics at the Intermediate/Senior level, we were required to make a Lesson Play.  What this entails is making a script that would align with your lesson plan and trying to anticipate the types of responses students would have.  This can assist us in determining how we would respond to certain responses or difficulties students may have.  The following is the script co-created with Laura Gravina that aligns with our lesson plan on linear relations and points of intersection.

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Teacher: Now that everyone has presented their information to the class, we are going to discuss as a group.  So would you still choose your payment method, now that you have done some mathematical research? And why? Billy.

Billy: I originally chose option 1 but now I think I would choose option 3.

Teacher: What made you change your mind?

Billy: Well I was thinking that the first one had the most money that I could get.  But after making the graphs I realized that I could make more money using option 3.

Teacher: What aspect of the graph led you to the conclusion that option 3 was the best?

Billy: Well once we found the point of intersection I realized that as long as I sold 9 hats I would make more than $16. And I could do that no problem at a Jays game!

Teacher:  Okay great.  Did someone have a different answer? Sarah.

Sarah: I chose option one too but I decided to stick with it because I wouldn’t have to sell any hats in order to get paid. No matter what I’d get paid $16.

Teacher: That is true. Ok so what did you notice about the steepness of the lines? Jessica.

Jessica: They all had different slopes.

Teacher: How does this relate to how much money you would earn?

Jessica: Uh I don’t know.

Teacher:  That’s okay. Can anyone help Jessica out? Bryan

Bryan: If the slope was greater, then if I sold more hats I could make more money.

Teacher: Right! So because the slope is steeper for option 3, for example, if you sell tons of hats you can make more money.  The amount of money you make increases more quickly with a steeper slope. Therefore, how hard you work will affect how much you make.  How is this different for option 1? Joseph.

Joseph: Option one doesn’t have a slope.

Teacher: So the slope is not increasing or decreasing but that doesn’t mean there is no slope.  What would the slope be in this case? Rachel.

Rachel: Zero

Teacher: Great.  So the slope of option 1 is zero.  Therefore, in option one, the number of hats you sell doesn’t change the amount of money you make.  You will always get $16.  Okay so you all discussed in your groups what the meaning of the points of intersection are.  What do these mean for our real-world problem? Trish.

Trish: It’s where the two lines overlap.

Teacher: Okay good, so that is what it means mathematically.  But we want to know the real world meaning.  What does the lines overlapping mean in terms of money?

Trish: That when you sell that many hats you make the same amount of money no matter which payment method you choose.

Teacher: So I could choose any one of the three payment methods?

Trish: No, I think it is only the two lines that are intersecting.

Teacher: Awesome! So the intersection point of two lines means that if you sell x amount of hats, you will make the same amount of money for those two payment methods.  Great job class! So now we are going to move on to our final activity.

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As evident in this script, Laura and I tried to anticipate the types of responses students would have, the specific mistakes students might make, as well as how we would respond and get students to the correct answer.  Through creating this script, I am even more convinced of the importance of anticipating student responses.  Since we know the desired answers to the questions, it can be very difficult to guess what mistakes students might make.  However, this part of lesson planning is vital for being prepared and organized in your classroom.  It is important to keep in mind what you want the final takeaway to be, while still making sure you lead students to the correct answer rather than tell them the answer.  This will likely contribute to students better understanding the content.