Graphs of Life Project Portfolio

Link to Course

Introduction

This mini-course would occur in a 9th grade mathematics class after some basics of graphing have been learned such as how to graph points on Cartesian Coordinates. Students will find real graphs on the internet and explain the graphs. They will then collect their own data and make their own graphs, and conclude by describing the trend in their graphs and drawing a line of best fit. Their graphs could be the number of times an event happens in a given time frame, or the amount of time they spend on a given activity each day of the week. This incorporates aspects of authentic learning and teaching for understanding.

Needs Assessment

Nature of What is to be learned: Students will learn to analyze graphs that they find in the real world or that are created by themselves. Nature of Students: Students completing this unit are in 9th grade Algebra. They have learned how to graph points since sixth grade, but no not know how to graph equations or the different kinds of graphs. They do, however, know relations of graphs. They have had previous experience with graphing points on the Cartesian Coordinate system. Prerequisites:

Ability to graph points on a Cartesian grid.
Knowledge of X and Y coordinates
Ability to identify relations (direct, inverse, cyclic constant)

Accessing prior knowledge: A short pretest will be given which contains a question to graph given sets of points and identify the kind of relation each data set has. Students will then briefly discuss how to graph points.

General Outcomes

Purpose of course:Students will be able to graph functions, identify graphs that they see or create and describe the behavior of those graphs. This is useful in understanding what might happen to certain trends that are graphed (i.e. to predict future occurrences). It also helps in understanding how different variables relate, whether a trend remains constant or changes, and how fast changes occurs. Students will be able to understand graphs in real world contexts, both from outside sources and graphs of their own creation.

Performance Objectives

PO1: Students will be able to produce the graphs of certain equations.
PO2: Students will be able to understand which functions generate which kinds of graphs.
PO3: Students will learn how to find key features of linear and parabolic graphs. For linear graphs, students will identify slope and roots. For parabolic graphs, students will be able to identify roots and axis as symmetry.
PO4: Students will be able to identify kinds of graphs (parabola, line, hyperbola).
PO4S: Students will be able to identify kinds of graphs of outside sources.
PO4C: Students will be able to identify kinds of graphs in graphs they create.
PO5S: Students will be able to identify relations of graphs in graphs from outside sources.
PO5C: Students will be able to identify relations of graphs in graphs they create.
PO6: Students will be able to create graphs based on data they have created, identify the kind of graph and the relation of the graph.
PO7: Students will be able to draw a line of best fit for their graphs.

Target Objectives for Understanding and Authenticity: PO4C, PO4S, PO5C, PO5S, PO6, PO7 (the products of units 2 and 3, which are based on unit 1 PO1, PO2, PO3 and the course prerequisites)

Task Analysis

Instructional Curriculum Map

Unit 1: Graphing Functions

Unit 2: Identifying Graphs

Unit 3: Analyzing Graphs of Own Creation

Authenticity and Understanding

According to Alan H. Schoenfeld in Chapter 3: Mathematics for Understanding of "Powerful Learning", mathematics is understood through going beyond the usual rote memorization of a set of rules which characterizes so much of mathematics education today. In my course "Welcome to the Graphs of Life", I've attempted to go beyond simply telling students the "facts". I've opted for activities in which students actively explore concepts and mathematical structures and in which students discuss patterns they observe. This is in keeping with Schoenfeld's model. The course as a whole is designed to get students to realize the applications of math - which also develops in-depth analysis of how functions and graphs relate to the real world. This culminates in students creating their own graphs and being able to identify familiar structures (the functions upon which graphs are based) in the new and unfamiliar context of their own data. Schoenfeld also speaks of authenticity - encountering meaningful applications. I believe each day of every unit of my course contains meaningful applications, but also that the final project in unit 3 entitled "To Graph Oneself" allows students to directly take events from their own lives and make sense of them using mathematics. Also, Unit 2 is heavilly based on the idea of analyzing various applications that I show students and for students to find examples of applications from outside sources. In general, both a constructivist-style approach to understanding and authenticity are woven throughout the course, as well as following from a natural progression through the units.