Reflection: Discourse and Questioning The Remainder Theorem, Day 1 of 2 - Section 3: Individual Classwork


The individual time that I provide for my students when problems are first introduced is very important.

First of all, it's good for the students.  They need time to come to terms with the problem before they can have a chance of understanding or appreciating its solution.  Too often, problems are solved for the class before they even have a chance to recognize them as problems.  By asking seemingly simple questions, and insisting that students try to solve them independently, I'm setting up a situation in which each and every student will confront the problem face to face.  They'll have use their wits to try to find a solution, and they'll have a chance to discover it for themselves. 

Best of all, this individual time levels the playing field for my "slower" thinkers.  These students are often deep thinkers, but they take more time to come to conclusions, and it can leave them feeling inferior.  Nothing is more discouraging than to watch day after day as "quick" thinkers shout out the answer before you've even had time to ponder the question, and nothing is more encouraging than to solve those problems completely on your own.

Individual time is good for the teacher, too.  It gives me an ideal opportunity to observe my students at work.  Like a quiz, it allows me to assess the progress of each student, but unlike a quiz, it also gives me the chance to provide immediate individual instruction.  Often, this instruction simply takes the form of one or two questions.  I'll lean over, point to something on the student's paper, and ask, "Can you tell me what you did here?"  As the student explains her work and her thought process, I can quickly assess the depth of her understanding.  If there was a mistake, she will usually see it for herself after just one more pointed question.  If there was no mistake, she will enjoy a little boost of confidence and continue working with increased motivation.

  Formative Assessment
  Discourse and Questioning: Formative Assessment
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The Remainder Theorem, Day 1 of 2

Unit 4: Higher-Degree Polynomials
Lesson 3 of 8

Objective: SWBAT use the remainder theorem to identify roots of polynomial equations. SWBAT explain the relationship between factors and zeros of a polynomial equation.

Big Idea: Students make sense of the many connections between polynomial factors, zeros, and remainders from polynomial long division.

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3 teachers like this lesson
Math, Polynomial and Rational Functions, Algebra 2, master teacher project, Polynomial Long Division, Remainder Theorem, Polynomial, Polynomial Operations and Functions
  45 minutes
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