Bemidji State University
M3066/ GEOMETRY AND TECHNOLOGY
IN THE MIDDLE SCHOOL MATHEMATICS CLASSROOM(4)
Fall
MTWR,
811:30 am
Instructor: Dr.
Glen Richgels
Email: 
grichgels@bemidjistate.edu
Office Phone:
755 2824
Professional Education
Department Mission Statement:
ŇThe Bemidji State University
Professional Education program is preparing today's teachers for tomorrow,
through effective, inquisitive, and reflective practice. Our students are
proficient, selfreliant, and thoughtful practitioners, developed in a viable
and growing program, who can teach effectively in various settings with diverse
learners."
Course Description
This course helps meet the
licensure rule with respect to concepts of patterns, shape and space; spatial
sense; plane, solid, and coordinate geometry systems; generalizing geometric
principals; limits, derivatives and integrals; and appropriate use of
technology in the classroom.
Prerequisites
MATH 1011 and MATH 1100 or MATH 1110 or
equivalent
Required Text
No text required – course taught with handouts
Resources: 
This course is taught with
handouts from a variety of sources and using several computer application /
instructional programs. Richgels, G.W., Frauenholtz, T., Hansen, H.,
Severson, A.R., Rypkema, C. Computer Activities for Teachers, Bemidji State University. Mathematics for Elementary Teachers a Contempory
Approach, Papert, S. MINDSTORMS Children,
Computers, and Powerful Ideas. Basic Books, Inc., Publishers, 1980. Software: á
Cinderella á
CoreLite
FTP á
FUGU á
GeometerŐs
Sketchpad 5 á
Macromedia
Dreamweaver á
Microsoft
Excel á
Microsoft
Word á
Microworlds EX Robotics (LOGO) á
Mindstorms NXT Internet Browsers: á
Internet
Explorer á
Mozilla
FireFox á
Safari 
Technology: 
A computer or calculator 
STANDARDS OF EFFECTIVE PRACTICE FOR TEACHERS
"K"
indicates standard is taught at the KNOWLEDGE level. "A" indicates
standard is taught and ASSESSED.
Board of Teaching Standards
8710.3320 MIDDLE
LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.
Department of Mathematics and Computer Science




8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS 

In this syllabus you will find the word TEACH. This will mean
to:


Standard 
K/A 
Activity 
Assessment 
(1) concepts
of patterns, relations, and functions: 



(e) apply
properties of boundedness and limits to investigate
problems involving sequences and series; and 
K A 
TEACH: Limit or bound as a number from
a sequence  fibonacci/lucas
numbers; seq/ratios; n/n+1, n+1/n, golden ratio Limit or bound as a point or
asymptote in the graph of functions Limit or bound as a number from
a series – Area and lower Riemann sum series, upper Riemann sum series,
other Riemann sum series. The integral is the limit of a
Riemann sum. Assignment: 22, 24 
Assessment: Teacher observation Students will construct a
spreadsheet to find a bound or limit of a sequence. Students will find the area
between the xaxis and a function. They will use the limit of sequences and
series that bound the area above and below to find the area as a limit of a
Riemann sequence or series. 
(f) apply
concepts of derivatives to investigate problems involving rates of change; 
K A 
TEACH: Derive the concept of rate of
change, derivative of a curve from the concept of slope of a line.
Demonstrate that the derivative is the limit of a difference quotient. Find
the derivative of a function at a point, find the equation of the tangent
line, graph the function and equation of the tangent line. Prove the power rule for
polynomial functions. Use the power rule to find the derivative of a function
at a point, find the equation of the tangent line, graph the function and
equation of the tangent line. Assignment: 23 
Assessment: Teacher observation Students will calculate the
derivative or rate of change of a polynomial function at a point using the
difference quotient. They will then write the equation of the tangent line,
then graph the function and the tangent line to verify their calculations. Students will calculate the
derivative, or rate of change,
of a polynomial function at a point using the power rule for polynomials.
They will then write the equation of the tangent line, then graph the
function and the tangent line to verify their calculations. They
will check their equations visually and use Geometers Sketchpad to confirm their calculation. 
(4) concepts
of shape and space: 



(a) shapes and
the ways in which shape and space can be derived and described in terms of
dimension, direction, orientation, perspective, and relationships among these
properties; 
K A 
TEACH: Locate a point in different
dimensions with different reference systems; What are the applications of
different dimensions and different reference systems. Assignment: 14 TEACH: What is a fractal? Definition
includes self similarity, simple rule, iterative / recursive growth Investigate fractals, fractal
structures and fractal dimension. Fractals as a more ŇrealÓ model for the
ŇrealÓ world than Euclidean and Platonic structures. Fractals in nature and
fractals as link between mathematics and biology. Assignment: 14 TEACH: Tessellations are a covering /
tiling of a plane surface. Triangles and quadrilaterals tessellate all
planes. Regular and semiregular
tessellations are finite – > 3 and 8. Escher merged art and
mathematics into examples of orientation, perspective, and dynamic
tessellations. Mathematical rules, geometric transformations or the geometry
of motion consists of translations, rotations, and reflections. Escher used
translations, translation reflections, midpoint rotations, and vertex
rotations to create his art and tessellations. Look at the polygons that
allow for the use of single or multiple transformations in a tessellation. Assignment: 20 
Assessment:  Teacher observation will
verify that students can specify locations in space using different reference
systems that include, dimension, direction, orientation and relationships
between these properties.
Students will construct
fractals in a computer / Microworlds environment
using logo. Students will construct fractals with different fractal
dimensions. Assessment: Students will create at least
two tessellations of a plane utilizing at least two different
transformations. The tessellations will be
derived from shapes whose
relationships can be described in terms of direction, orientation,
perspective, and relationships among these properties; 
(b) spatial
sense and the ways in which shapes can be visualized, combined, subdivided,
and changed to illustrate concepts, properties, and relationships; 
K A 
TEACH:  LOGO fundamentals of turtle
movement, turtle orientation, heading and programming procedures. Use graph
paper to model construction of twodimensional shapes that can be scaled
using sliders to assign parametervalues. Construct circle and arc procedures
by approximation with ngon, n>=30. Help
students visualize a linear geometric object as a combination of simple
geometric shapes. Students should decompose the geometric object into simple
shapes that can be combined to create the whole object. Make project
constructions using simple component tools such as square, triangle, right
triangle, rectangle, É to create a two dimensional linear object. Assignment: 7 TEACH:  LOGO fundamentals of turtle
movement, turtle orientation, heading and programming procedures. Use graph
paper to model construction of twodimensional shapes that can be scaled
using sliders to assign parameter values. Construct circle and arc procedures
by approximation with ngon, n>=30. Demonstrate
how to visualize a set of movements within a background. Animate the ŇturtleÓ
to carry out the movements through geometric commands. Assignment: 7 TEACH:  LOGO fundamentals of turtle
movement, turtle orientation, heading and programming procedures. Use graph
paper to model construction of twodimensional shapes that can be scaled
using sliders to assign parameter values. Construct circle and arc procedures
by approximation with ngon, n>=30. Help
students visualize geometric objects as a combination of simple geometric
shapes including circles or arcs. They should decompose the geometric object
into simple shapes that can be combined to create the whole object. Make
project constructions using simple component tools such as square, triangle,
right triangle, rectangle, circles, arcs É to create a two dimensional
object. Assignment: 7 TEACH: Regular polygons have
properties including number of sides, central angles, interior and exterior
angles, side length of sides and perimeter. Assignment: 7 TEACH: Standard form of families of
mathematical functions includes parameters such as this quadratic form: Assignments: 11 
Assessment: Students will create a
changeable, scalable, linear twodimensional figure construction. The figure will be one that can be
subdivided into simpler figures and constructed as the combination of these
figures. Students will use a turtle and component tools or computer
procedures. Assessment: Students will animate at least
one turtle to carry out a student designed path. This project should be
posted to the WWW.
Students will create a
changeable, scalable, twodimensional construction with a turtle and using
component tools. This object must contain circles or arcs as components in
the object. Assessment: Students will create procedures
that will make regular polygonal shapes. The number of sides and side length
will be changeable and dynamic to illustrate concepts, properties, and
relationships of the parts of the geometric shapes polygons and to connect
polygons to circles and its parts, radius, diameter, and circumference.
Students will graph the
standard forms of families of functions and be able to use sliders to
dynamically change the value of parameters and to illustrate concepts,
properties, and relationships of the parameters. 
(c) spatial
reasoning and the use of geometric models to represent, visualize, and solve
problems; 
K A 
TEACH: Review linear equations and
slope as a way to characterize the shape and orientation of a line. Utilize
spatial reasoning to conclude that the slope of a nonlinear function is
constantly changing. Use the geometric model of a tangent line to model the
slope of a curve at a point. Use spatial reasoning to view that the limit of
a chord through A and B, as B approaches A, is the line tangent to the
function at A. Formulate the derivative definition and derive the power rule
for polynomials. Students will practice finding the derivative of a
polynomial, writing the equation of the tangent line, and graphing the
function and tangent line to check their work. Review area formulas for simple
polygonal shapes: cube, rectangle, triangle, parallelogram, trapezoid.
Develop notation for finding the area between a function and the xaxis in an
interval. Use the mean value theorem to derive the fundamental theorem of
calculus. Students will find the area of simple polygons and polynomial
functions using the antiderivative. Develop the Riemann sum
approach to visualizing the area of a region. Use the geometric model of
rectangles, trapezoids, or parabolas to approximate the area under the
function. Demonstrate that the limit as n approaches of a Riemann sum model
for a two dimensional region is the area and is equal to the value for the
area that can be calculated through the antiderivative (integral) approach. Model a geometric solid of
revolution as the sum of many, thinly sliced pieces of the whole. Each slice
can be modeled as a thin or short cylinder. Model the volume of a solid of
revolution, sphere, cylinder, cone, as a Riemann sum of many thin cylinders
and calculate the volume formula. Assignment: 2225 
Assessment: Teacher observation Students will calculate the
derivative or rate of change of a polynomial function at a point using the
difference quotient. They will then write the equation of the tangent line.
They will then graph the function and tangent line to verify their
calculations. Students will calculate the
derivative or rate of change of a polynomial function at a point using the
power rule for polynomials. They will then write the equation of the tangent
line. They will then graph the function and tangent line to verify their
calculations. Students will calculate the
area between a function and the xaxis on an interval for elementary
geometric shapes and for polynomial functions. 
(d) motion and
the ways in which rotation, reflection, and translation of shapes can
illustrate concepts, properties, and relationships; 
K A 
TEACH: Tessellations are a covering /
tiling of a plane surface. Triangles and quadrilaterals tessellate all
planes. Regular and semiregular
tessellations are finite –>
3 and 8. Escher merged art and
mathematics into examples of orientation, perspective, and dynamic
tessellations. Mathematical rules, geometric transformations or the geometry
of motion consists of translations, rotations, and reflections. Escher used
translations, translation reflections, midpoint rotations, and vertex
rotations to create his art and tessellations. Look at the polygons that
allow for the use of single or multiple transformations in a tessellation. Assignment: 20 
Assessment: Students will create at least
two tessellations of a plane utilizing at least two different transformations
from: á
translation, á
rotation, á
reflection, á
translation and rotation, á
translation and reflection, á
and rotation and reflection. 
(e) formal and informal argument,
including the processes of making assumptions; formulating, testing, and
reformulating conjectures; justifying arguments based on geometric figures;
and evaluating the arguments of others; 
K A 
TEACH: Demonstrate the creation of a
model mathematical system. A mathematical system consists of undefined terms,
defined terms, assumptions, axioms or postulates, lemmas, theorems, and
corollaries. Study the system used to find
the measure of arcs and angles with respect to circles: central, inscribed,
interior, and exterior angles. Begin with the undefined terms,
point and line. Review the definintion of angle,
circle, and major and minor arcs. Begin with the definition of a central
angle and its intercepted arc. Begin with an inscribed angle
definition. Use geometric figures to model the three cases for an inscribed
angle. Have students utilize the given conditions, their assumptions and a
dynamic geometry tool to formulate hypotheses or conjectures about the
relationship between an inscribed angle and its intercepted arc. Use the
geometric figure constructed in the dynamic geometry environment to
investigate their conjecture and to establish an informal proof or conclusion
about their conjecture. Then construct the formal arguments necessary to
justify the conjecture to prove a lemma and the first theorem of the
mathematical system. Next define an interior angle.
Model an interior angle with static and dynamic geometric figures. Utilize
previous knowledge to augment the existing geometric figure, utilize the
figure to formulate a conjecture, make informal arguments and finally prove
an interior angle measurement theorem. Finally define an exterior
angle. Model an exterior angle with static and dynamic geometric figures. Utilize
previous knowledge to augment the existing geometric figure, utilize the
figure to formulate a conjecture, make informal arguments and finally prove
an interior angle measurement theorem. Assignment: 12 
Assessment: Students will solve a puzzle
involving unknown central, interior, inscribed, and exterior angles and their
associated arcs. They will use the properties that were derived from formal
arguments. The formal arguments are the culmination of the process that
includes the processes of making assumptions; formulating, testing, and
reformulating conjectures; justifying arguments based on geometric figures;
and evaluating the arguments of others. Informal arguments can be made based
upon dynamic investigation of the objects that lead to the formal arguments.
All answers need to be correct before proceeding. Instructor corrected. Students will construct a
puzzle to apply the results of the informal and formal arguments. The puzzle
will have at least one unknown central, interior, inscribed and exterior
angle and associated arcs. 
(f) plane,
solid, and coordinate geometry systems, including relations between
coordinate and synthetic geometry and generalizing geometric principles from
a twodimensional system to a threedimensional system; 
K A 
TEACH: Construct a table of the 8
measurement concepts to be taught in grades K8: length, area, volume,
capacity, mass, time, temperature, angle measure. These measurements would be
in column 1, column 2 would contain English system examples of the concept,
column 3 would contain metric or SI system examples of the concept. Include
the defining relationship in metric between volume, mass, and capacity.
Discuss the evolution or design of the two systems. Assignment: 17 TEACH: Students will be introduced to
different geometric systems during the examination of the van Heile levels. The different geometries occur at level
four. Assignment: 8 TEACH: The students will investigate
the theorem: the lengths of the diagonals of a rectangle are equal. The
students will develop a sketch that demonstrates the theorem dynamically
using geometerŐs sketchpad. This approach supports student learning at level
two of the van Hiele levels. Students at this level
need to see informal proofs through dynamic examples. The students will then
construct coordinate and synthetic proofs of the theorem. These approaches
will help students see what is needed to help public school learners in
middle school transition to high school. Assignment: 10 TEACH: Students will be asked to locate
a point in different referent systems. One dimensional system: label,
number line coordinate Two dimensional system: label,
Cartesian coordinates, polar coordinates. Three dimensional system:
label, Cartesian coordinates, spherical coordinates, cylindrical coordinates. Cartesian coordinates : most
people use this system Spherical coordinates :
physicists and astronomers use this system Cylindrical coordinates :
computer scientists use this Conversion between coordinate
systems. Distance formula between points
p and q in n dimensions is: Assignment: 14, 15, 16 
Assessment: Students will construct a
table showing the eight measurement concepts and examples from the SI and
English measurement systems. Assessment: Students will investigate the
following problem: What is the sum of the angles in a triangle? They will use
the software Cinderella to investigate the problem in plane,
hyperbolic, and spherical geometries. They will show triangles
that support their answer to the instructor.
Instructor observation of the
sketch, the synthetic and coordinate geometry proofs. Assessment: Students will identify points
in the different reference systems and will calculate the distance between
two points in each system. Student work will be checked by instructor
observation. 
(g) attributes
of shapes and objects that can be measured, including length, area, volume,
capacity, size of angles, weight, and mass; 
K A 
TEACH: Students will order geometric
solids consisting of cylinders, spheres, hemispheres, cones, prisms, and
pyramids based upon volume. They will use conservation of volume as they
compare volumes using a medium such as rice or water. Students will be able to use
standard naming conventions to name the different solids as they order them
from least volume to greatest volume. Assignment: 18 TEACH: Construct a table of the 8
measurement concepts to be taught in grades K8: length, area, volume,
capacity, mass, time, temperature, angle measure. These measurements would be
in column 1, column 2 would contain English system examples of the concept,
column 3 would contain metric or SI system examples of the concept. Include
the defining relationship in metric between volume, mass, and capacity.
Discuss the evolution or design of the two systems. Assignment: 17 TEACH: Examine the formula that are
used for computation of different geometric objects. Two dimensional geometric
objects: square, rectangle, triangle, parallelogram, trapezoid, regular ngon. Formula to compute perimeter and area. Three dimensional geometric
objects: prism, pyramid, cylinder, cone, sphere. Formula to compute surface
area and volume. Assignment: 19 
Assessment:  Students will put their
orderings of geometric solids on a common
display and then resolve all differences until an ordering has been agreed
upon. Assessment: Students will construct a
table showing the eight measurement concepts, length, area, volume, capacity,
size of angles, weight, degree measure and mass, and examples from the SI and
English measurement systems. This table will be posted on their homepage. Assessment: Students will construct a
table of the formula used to calculate perimeter, area, surface area,
and volume and post the table on their homepage. 
(h) the
structure of systems of measurement, including the development and use of
measurement systems and the relationships among different systems; 
K A 
TEACH: Construct a table of the 8
measurement concepts to be taught in grades K8: length, area, volume,
capacity, mass, time, temperature, angle measure. These measurements would be
in column 1, column 2 would contain English system examples of the concept,
column 3 would contain metric or SI system examples of the concept. Include
the defining relationship in metric between volume, mass, and capacity.
Discuss the evolution or design of the two systems. Assignment: 17 
Assessment: Students will construct a
table showing the eight measurement concepts, length, area, volume, capacity,
size of angles, weight, degree measure and mass, and examples from the SI and
English measurement systems. This table will be posted on their homepage. 
(i) measuring,
estimating, and using measurements to describe and compare geometric
phenomena; 
K A 
TEACH: Students will construct an
inclinometer from simple classroom materials: straws, folders, paper,
centimeter graph paper, string, paper clips, and tape. Students will measure /
determine their stride length in English or metric units – instructor
choice. Students will gather data on at
least two tall objects outside of the classroom, e.g. trees, flag poles,
light poles, multiple story buildings, etc. The class will develop how to
take the data and use it to measure / estimate the heights of the objects
that they measured. Assignment: 21 
Assessment:  Students
will construct an inclinometer from simple classroom materials: straws, folders,
paper, centimeter graph paper, string, paper clips, and tape, measure
different geometric phenomena, post their measurements to the board, make an
oral presentation given to the class and instructor for comparison with the
all of the class. 




Technology Requirements and
Expectations
Students
will use internet browsers to access information and answer questions posed in
class. Students will may use graphing calculators, GeometerŐs Sketchpad, or
data programs such as Excel, Tinkerplots, Fathom 2,
or Minitab as needed. Written assignments for class will be composed using a
word processor such as Microsoft Word.
Students
in M3066 will be expected to construct a homepage and post it to the WWW.
Teaching Methodology
PolyaŐs problem solving steps
1.
Understand
the problem
Lesson Sequencing
Intuitions
Þ Concrete ó SemiConcrete ó Abstract
GlenŐs Teaching/Learning Principles
1.
Teach the
way students learn
2.
Use group
work, heterogeneous, 34, change monthly
3.
Communication
student ó student
4.
Communication
teacher ó student
5.
Multiple
solution paths
6.
Use
contextual settings / problem solving
7.
Assessment
University Policies and Procedures
http://www.bemidjistate.edu/students/handbook/policies/
Academic Integrity
BSU students are expected to practice the
highest standards of ethics, honesty and integrity in all of their academic
work. Any form of academic dishonesty (e.g., plagiarism, cheating and
misrepresentation) may result in disciplinary action. Possible disciplinary
actions may include failure for part of all of a course as well as suspension
from the University.
Students with Special Needs
Upon request this document can be made
available in alternate formats. Please contact Kathi
Hagen at Disabilities Services at (218) 7553883 for assistance or the AUC
Office at 2626753 or (800) 3694970.
Student Rights and Responsibilities
Student
Code of Ethics
http://www.bemidjistate.edu/academics/catalog/10catalog/GradCatalog/Frontpages/sectionIV/rights.html
Student
Academic Rights and Responsibilities
http://www.bemidjistate.edu/students/handbook/policies/academic_integrity/rights_responsibilities.cfm
Instructor Rights and Responsibilities
 I work with
all students and expect success from all students. It is my expectation for
those students who attend class regularly and complete assignments that they
will earn an A or B.
 I am available for help whenever I am in my
office. I encourage students to do homework at a table outside of my office so
that I can help them whenever they have difficulties. Help is also available
through email and at my home, if prior arrangements have been made.
 I will try to give grade status reports at
least every three weeks.
Course Grades
A: 100
– 90% B: 89 – 80% C: 79 – 70% D: 69 – 60%
Course Policies
Attendance:
Daily attendance is expected
Participation: Class participation and group work is expected
Tentative Course Calendar
Assign 1 
Conceptual compuer; Evolution of
von Neuman machine and current state of computer
architecture and devices. Two computers review Features and prices 
Assign 2 
Instructional software. Software review 
Assign 3 
Internet resources for the classroom. WWW Review 
Assign 4 
Internet resources for computers. Java Applets 
Assign 5 
Internet communication Email game 
Assign 6 
WWW Homepage construction. Home Page 
Assign 7 
The use of LOGO for learning geometric fundamentals. Microworlds EX project / LOGO 
Assign 8 
Van Hiele levels and geometric
learning. 
Assign 9 
The relationships between different types of triangles and
different types of quadrilaterals. Use GSP to construct Venn diagrams.
Geometer's Sketchpad  Geometry relationships 
Assign 10

Develop geometric theorems from observation. Geometric
plausibility through dynamic examples. Geometer's Sketchpad  Geometry
theorem 
Assign 11

Geometric visualization of standardized equations. The use
of dynamic parameters for exploration of standard forms. Geometer's Sketchpad

Assign 12

The development of a mathematical system: undefined terms,
defined terms, axioms, postulates, lemmas, theorems, corollaries. Proof,
application, and synthesis. Circles and angles 
Assign 13

Construct and program a simple robotic car to follow a
predetermined course. Lego robotics 
Assign 14 
Reference systems: Number Line, Cartesian, Polar,
Spherical, Cylindrical. What are they and who uses them. Fractals: dust,
lines, area. Point, logo fractals, Euclidean and Fractal Dimension 
Assign 15 
Distance between two points in different reference systems. Distance between two points in 2,3,n Euclidean dimensions 
Assign 16 
Synthetic, Coordinate and dynamic geometry proofs. Prove diagonals of a rectangle are equal, bisect each other

Assign 17 
Measurement systems: evolution, design, units. English and
metric (SI) systems 
Assign 18 
Conservation of volume, analyze and compare geometric
solids 
Assign 19 
Geomeric measurment of polygons and solids, perimeter, area,
surface area, and volume. Platonic and Archimedean Solids 
Assign 20 
Reflections (Flips), Translations (Slides), Rotations
(Turns), Escher tessellations 
Assign 21 
Similarity, congruence, constant of proportionality. Construct an inclinometer. Apply similar triangles (trigonometry) to find unknown
heights / distances. 
Assign 22 
Examine limits: movement, sequences, functions Characterize a function by slope, rate of change or
derivative. The derivative is the slope of the line tangent to a curve
at a point. Calculate the derivative of polynomials from the difference
quotient. 
Assign 23 
Derive the power rule for the derivative of a polynomial
function. Calculate the derivative rule for a function, find the
derivative at a specified point, write the equation the tangent line at the
point, and demonstrate that the line is tangent to the function at the point
with a graphing tool. 
Assign 24 
List area formulae for elementary polygonal shapes. Consider the area between a function and the xaxis between
two points. Derive the fundamental theorem of the Calculus, i.e.
integral. Compare polygonal formulae to integration to find the area. Use integral to find area under curves. 
Assign 25 
Develop Riemann sums as a model to find area. Demonstrate that an npartition model yields the area under
a curve as n increases without bound. Model a sphere, cylinder, cone as a volume of revolution. Derive the formula for a sphere, cylinder, or cone. 
Assign 26 
Examine Euclidean, Spherical and Hyperbolic geometries with
Cinderella. Explore the sum of the measure of the angles in a triangle
using a dynamic geometry tool such as Cinderella. 
Assign 27 
Explore the nonEuclidean geometry – Taxicab
geometry. Investigate segments, perpendicular bisectors, midpoints, and
circles in Euclidean and Taxicab geometry. 






Assign GS 
Instructional Lesson and Task (Graduate Students only)
– Improve at least 10 days of instruction by including technology and
concepts from class. Include assessment to evaluate students and the
effectiveness of the changes in the instructional unit. 
Assign
Final 
Final Paper – synthesize the information, concepts
and technology from class into a proposal for technology for your classroom. 