1. Dates, Times and Location of Proposed Course:
(1 Semester Credit Equals 15 Professor Contact Hours plus an additional 30 Hours
Outside Work)
Online course - Time expectations for a 2 semester credit course as outlined
above. Course to be completed within
6 weeks of registration date.
2. Due Date for Completion of Course Requirements: Six weeks from start date.
Submit a reflection document
indicating what was learned and how it can be
incorporated into the educational setting to Dr. Mary Jones,
3. Learning Resources and Required Text: Technical
requirements: Word processor, Internet Service Provider, E-
mail
4. Evaluation Procedure: Pass/Fail
5. PBS TeacherLine Course Syllabus: MATH420 Seeing Math: Linear Equations
Prerequisites
To successfully participate and complete the as signments in this
course , the learner must:
Have an understanding that some functions have more
than one solution set.
Have practice transforming word problems into
functions.
Course Description
Most Algebra 1 curricula introduce linear
equations before linear functions. In this course, functions are discussed
in
order to lay the groundwork for learners to:
• View an equation as a function to
which a particular value has been assigned
• Gain a deeper understanding of
equivalence
• Make the connection between symbolic, graphic, and other
representations of equations
• Evaluate how this approach of teaching equations
under the umbrella of functions may help students
In this course learners use a
variety of approaches, including an interactive tool, to investigate the meaning
of
processes used to solve equations . They also come away with a tangible
benefit—interactive software and
activities to use with their students. Learners
can use these within the course, so they will be thoroughly familiar
with them.
(If they lack computer resources in their classroom, alternative activities that
do not require computers
are provided.)
Goals and Objectives
Understand the
rationale behind the rules of symbol manipulation that maintain an equality or
corresponding
inequality. The objectives for the participant are to be able to:
• Understand the relationship between variables by dynamically changing the
values of x and y
• Develop solution techniques (including techniques for
solving simultaneous equations ) by comparing standard
symbolic operations to
graphic and area representations of equations
Deepen the distinction between equivalence of function and equality of value.
The objectives for the participant
are to be able to:
• Interpret the "=" sign
in terms of equivalence, description of state, inviting a calculation, or
defining a quantity
• Distinguish x as a variable (in a function, where
different values of x result in different values of y) from x as an
unknown (in
an equation, to be solved for x)
Gain facility in moving easily between symbolic
and graphic techniques for solving equations and inequalities ,
whether presented
in symbolic or story (text) form. The objectives for the participant are to be
able to:
• Clarify what values change (or do not change) during standard
operations for solving equations, by using
graphic techniques to represent the
operations
• Solve word problems with greater skill through the use of graphs to
represent the problems
Outline of Content and Assignments
After previewing the
documents in the Course Information area, learners will proceed to Course
Content to
complete the five sessions, working through each session in order.
Throughout the sessions, learners are asked
to articulate their ideas in various
forms: they are encouraged to reflect on their ideas and experiences in their
online journal, and they take part in online discussions designed to al low them
to glean information from other
learners’ experiences.
This five-week course is
taken entirely over the Internet. Learners should expect to spend 4-6 hours per
week
completing assignments and discussions, and to log in to class and submit
work or join discussions at least three
times a week. Each week learners will
complete assignments such as solving problems, observing videos,
reading,
adapting problems for the classroom, and taking part in online discussions. In
the last week of the course
learners will focus on creating and completing a
final project.
Learners will also come away with a tangible benefit—interactive
software and activities to use with students.
These tools will be used within
the course, such that learners are thoroughly familiar with them. In addition,
learners are provided with alternative activities that do not require computers
in case computer resources are not
available for classroom use.
Session 1:
Orientation
Much of the Orientation session is spent getting to know the course
and meeting colleagues online. Learners also
read about the approach to learning
and teaching algebra implemented in this course.
Learners will:
Read
..
Information about the syllabus, facilitator, rubrics and how work will be
evaluated, and tips for successful online
discussions.
.. A summary of the goals
and objectives for the course
. .. The Landscape of Learning - A discussion on
the underlying principles behind the learning in this course and
what they
should expect.
.. The Landscape of Algebra – A discussion about the structure of
functions that underlies algebra, and how this
structure can help students make
connections
.. Nouns, Verbs and Mathematics - A discussion about the importance
of being able to view mathematical
expressions in more than one way.
.. Let’s
Discuss Approaches to Algebra – Discussion questions related to the three
primary reading assignments.
.. Journal – About the value of keeping a record of
one's own thoughts and problem solving during the course.
Write in journal
(Note: Keeping a journal record is an ongoing assignment referred to within
course activities, but
the journal is not handed in or evaluated by the
facilitator):
• Reflect on insights and ideas related to the three readings: The
Landscape of Learning, The Landscape of
Algebra and Nouns, Verbs and
Mathematics.
Participate in online discussion
• Post messages in the Discussion
Board, Session 1: Introductions
• After reading the questions in Let’s Discuss Approaches
to Algebra, share thoughts on The Landscape of
Learning, The Landscape of
Algebra, and Nouns, Verbs and Mathematics in the Discussion Board, Week 1,
Nouns, Verbs, and Landscapes.
Session 2: Math Focus
This week learners will look
at various aspects of equations and functions, including differences between the
two.
They will focus on ways to give students a better understanding of the
process of solving single and simultaneous
equations using a variety of methods
and representations.
Among the elements learners will investigate are:
• Solving
for unknowns using interactive tools and graphical representations
• Finding the
point where two linear functions share the same solution set
• Evaluating why
the traditional operations used to solve equations maintain the necessary
equivalence
Learners will:
Read:
.. Snapshots from the Curriculum – An article
that sets the stage for a different approach to teaching linear
equations
..
Observing Your Processes – Guidelines on observing personal problem solving.
..
Problem Solving Approaches – Exploring new ways to look at an old problem
..
Solving Systems of Linear Equations – Discussion about the intersection of
functions seen in a new light
Complete activities and assignments:
.. Function
Analyzer Warm-up – Activities to acquaint learners with the Function Analyzer
interactive
.. Diving In : Solving Equations from Different Perspectives Write in
journal
.. Reflect on approaches used to solve the Diving In challenges using
the Function Analyzer:
.. Reflect on the ways that intersections of functions
can come into play in the solving of systems of linear
equations
-
Participate
in an online discussion:
.. Share solutions, comments and challenges in the
Discussion Board, Session 2, Diving In: Solving Equations
from Different
Perspectives.
.. Discussion Board, Session 2, Solving Systems of Linear
Equations.
