## Reflection: Developing a Conceptual Understanding Intercepts of Polynomial Functions - Section 4: Section 4: Using Intercepts to Find the Equation of a Polynomial Graph

There is a delicate balance between giving students the opportunity to struggle and discover mathematics, and the confidence to move forward and actually feel like they can persevere in mathematical tasks.  Too hard a task and the students will give up before they begin.  Not enough mastery of the prerequisite skills, and again they will give up.  On the other hand, tasks that are too easy won’t motivate students or properly develop their mathematical habits of mind.  This is why teachers are professionals. It is our job to provide tasks that fit our students’ ability and confidence level.  During the task, it is our job to continuously reassess to ensure that our students are progressing.  This seems huge when put into words, but the reality is that this is what we each do intuitively every day.

In this section, I had to be very mindful of the confidence level in my classroom.  We have just discussed several new skills that are now going to be put together in a graphical representation before the students have fully mastered them. Obviously my students are capable of this but my vigilance in catching conceptual holes in individual peaked here.

They all felt pretty capable with finding the intercepts, even with a multiplicity of two.  When they graphed the equation and saw that their graph was different from the graph on the PowerPoint, some got a bit frustrated.   I think this is because of a deficiency in numerical reasoning that some of my students struggle with.  Working through the remainder of the practice problems (Notes) and some individual scaffolding helped to catch many of those students who felt a little overwhelmed here.  I do think that we will need to readdress this idea tomorrow to ensure that they are all feeling confident.

Developing a Conceptual Understanding: Keeping Them All On Board

# Intercepts of Polynomial Functions

Unit 6: Polynomial Functions
Lesson 7 of 15

## Big Idea: The relationship between graphical and algebraic representations of polynomial functions, it all comes down to the roots!

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Standards:
Subject(s):
Math, polynomial functions, intercepts, Algebra 2, master teacher project
51 minutes

### Amelia Jamison

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