TEACHING CHANNEL
INTERVIEW WITH JENNIFER GIUDICE

JENNIFER GIUDICE:
We are gonna start today by simply having you guys take out your homework from last night. You had a few problems that you were finishing up with factoring on page 260.
(interview)
My name's Jennifer Giudice. I am a math teacher at Staples High School in Westport, Connecticut. Today’s lesson really serves two purposes. The mathematical purpose is we were reviewing quadratics. We’ve been looking at the graphs and changing the forms. Also sort of considering domain and range and dealing with interval notation. I also wanted in today's lesson for the students to get some exposure to how to prepare for a math test. I get a lot of feedback of kids saying, I don't really know how to study. How do I study for this?
(class)
You guys are sitting the way you're sitting today for a reason. You are going to work in groups today based on your homework from last night. So, by 10 p.m. last night, all of you had to email me your two possible test questions, which I must say, some of you were really good and some of you were pretty hard on your peers.
(interview)
Yesterday in class I gave them a relatively traditional assignment, to factor some problems, but then with that, they were also assigned to go home and come up with two questions for their peers around the topics that we've been doing, to assist in the review. And they knew that I would be compiling them. Some students really did ask those conceptual questions, to really get at, do you understand exactly what we're doing with quadratics. Obviously those are the ones that I selected. When they write a problem, they're thinking about it differently. They're putting it together -- hopefully it's challenging -- and they have to think about not only what am I asking, but how am I going to solve it, how are other students going to approach it. Everyone has three questions, and they are all different. Each group is different. OK? You’re gonna complete all three of them, but I want you to do it a little less traditionally. I want you to solve them according to the directions, but then, amongst your small group, I want you to discuss how you might study for this type of question on a test or a quiz. And then the first question in every group is starred, and we're gonna go through each of the first questions as a whole group, and each group will present their question and sort of their findings.
STUDENT 1:
OK, so, what the answer should have been is three, and then in parentheses, X-comp, plus 5x plus...
STUDENT 2:
You know, you could do the -B/2A to find it if you wanted, but that's even too much work.
JENNIFER GIUDICE:
I have them work in groups because I want them to hear other people's opinions and other students' ideas, and I want them to see that other students aren't sure how to approach it as well. They’re not alone.
STUDENT 3:
I just got confused. Like remember that first worksheet we had, where it was like, is it vertex or intercept. I got every single one wrong.
JENNIFER GIUDICE:
I’ve always told me students that the right answer is great, but so is the wrong answer, because oftentimes, if a student gives a wrong answer, the richness of the class conversation is unbelievable.
(class)
Even if you are not quite done, I want you to turn your attention up to the front.
STUDENT 4:
So we were looking at the error, and I’ll admit at first I was really confused, but then they pointed out that his foiling wasn't correct.
JENNIFER GIUDICE:
They were concerned about their ability to foil correctly and to deal with the power with the binomial and things like that. So I had a number of students write, do a question where, OK, here's a student response, this is what they gave the teacher. What went wrong?
(class)
So ultimately you guys ended up with -3x-squared + 12x - 4, correct? Good, so they found basically an arithmetic error in that you really have to be careful when you're changing forms that you follow your order of operations. Good job. Thanks, ladies.
(interview)
That really caused them to have to reflect on what was happening. It was more than just doing it. They had to identify what went wrong, had to explain why it went wrong, and then correct it. So it really does sort of push them beyond just a traditional complete-the-following.
STUDENT 5:
So we sensed the second x equals two. We decided that four, negative two would be the best answer. So...that's what we got.
JENNIFER GIUDICE:
Good. And just set that. Do y-equals for that one. Perfect. So they went from vertex to intercept one. OK?
(interview)
When they do get into a test situation, if there's a question that they're not as familiar with, they will have the confidence to step back from it and think, wait, I know a lot about quadratics, I don't know exactly the answer to this, but what can I put together and piece together to get where I’m going. This is the first experience they've had writing questions. I will do this sort of activity again throughout the year, and it's always interesting to see how the questions change as time goes on.
(class)
All right you guys. I’m going to give you about two more minutes to wrap these up.

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