Saturday, September 22, 2018

New School Weeks 2 & 3: The More They Talk (Part 1)

Now that I am into weeks 2 and 3 at my new school I am in the grading avoidance mode.  Even first year teachers recognize this mode within a month or so of school.  You look at your bag with the pile of papers in it and think of other things you would rather do.  It's Saturday morning.  I have plenty of time to attack those papers.  Here's an idea. I'm going to blog instead!

          An Old Transcript: Teacher-Centered

Are you a teacher who is afraid to have your students talk?  Does your classroom dynamic go something like this?

Teacher: Who can tell me what is f(6) for this function?

A few hands go up and then a few more. Teacher calls on one of the students who raised a hand.

Student: Twenty-two.

Teacher: Good. What about this question.  What is x if f (x) is 12?

The teacher gives sufficient wait time for a few hands to go up, but notices that they are mostly the same students as before.  Teacher calls on another student.

Student: x is 8/3.

Teacher: That is correct.  Can you explain how you got your answer.

Student: I wrote 3x + 4 = 12.  Then subtracted 4 to get 3x = 8 and then divided by 3.

In my early years of teaching, I would have considered this a successful classroom discussion.  I wasn't telling students the answers.  I was asking questions and students were giving me correct answers.  I look at this transcript now and cringe.  This is my twenty-sixth year of teaching and even now my classroom looks different than it did five years ago.  What does this look like for me in my classroom this year?

          A New Transcript: Student-Centered

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: Let's say that I wanted a function to make the input of 4 become an output of 3.  We could do that by writing f(x) = x - 1.  I want you to work with your partner or trio to come up with a different function that would contain the point (4, 3).  Write your function somewhere on the board.

Students work together and talk in their groups for a minute or so with each group putting a function on the board.  Here are several of the functions that were created.

Teacher: What do you notice about the functions that are written here?

Many students are raising their hands. Teacher calls on one of the students.

Student: Several of the functions are the same.

Teacher: That's true.  Is there anything that all or most of the functions have in common?

Teacher gives time to think and then calls on a student who does not have her hand raised.

Student: They all had something multipled to the x and then either added or subtracted a number.

Teacher: Good observation.  Which ones had addition and which ones had subtraction.

Teacher calls on student with hand raised.

Student: When you multiply by a number bigger than 1, it made the result get larger. So you needed to subtract.  When you multiplied by 1/2, it made the result smaller and that meant that you needed to add a number.

Teacher sees some students nodding in agreement as she restates what the student just said.

Teacher: I would like each group to answer the following questions. (Points to the board.) What is f(6) and what value of x would make f(x) = 8?  Write your answers and work under the function you wrote on the board.

Students work together and show their work.  A few students finish quickly and the teacher asks those students to create a new function that is more complex, maybe involving exponents.  Those students add their function to the board.

Teacher: Talk in your trio or with your partner about the difference between how you answered these two quesions.

Students talk together for a minute or two.

Teacher: Who would like to share what you just discussed?

Teacher acknowledges a student near the windows.

Student: The first question gives us x and we plug it in to get the answer.  The second question gives us the answer and we have to use it to find x.

Teacher: That's true.  Would anyone like to add to what [student's name] just said.

Teacher acknowledges a student near the classroom door.

Student: The first question gives us an input, or x and we find the output, or y.  The second question is asking the opposite.  We are told an output and we find the input.

Teacher: That's a good observation.  I'd like everyone to take a minute to write that observation in their notes.

Teacher observes students writing and waits for almost all the students to be done.

Teacher: Does anyone else have observations to make about what we just did?

Student raises her hand and teacher calls on student.

Student: (Referencing the answers on the board.) Why don't we all have the same answer?

Teacher: That's a good question, [student's name]. Why don't we all have the same answer?  Can anyone clarify this.

A few students raise their hand and teacher calls on one of them.

Student: They all went through the point (4, 3), but that doesn't mean that they will all have the same answer for the other questions.  They are different equations and will go through different points.

Teacher: That's true.  You all created equations of lines, but they aren't the same line for everyone.  They have different slopes and different y-intercepts.  Think back to geoemtry.  If you have a single point, there can me many lines that go through it.

Teacher looks at student who originally asked the question to see if this makes sense to that student.  Student is nodding head in agreement.

          Compare and Contrast: Old vs New  

My blogs don't often invite comments, but for this one I definitely want to invite comments.  I can see the difference between the old transcript and the new transcript; can you?  Write what you notice in the comments below.  I'll be blogging my compare and contrast thoughts about this lesson in a week or so. I attack those papers, clean the bathrooms or mow the lawn?

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