MATH 409

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Electronic Portfolio

• MATH 409
• MATHEMATICS THROUGH COMPUTERS
• ELAINE REED
• FALL 2007

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Table of Contents
About Me
Article Critique
Lesson Plans
WebQuest
Reflections
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About Me
Resume
Education Classes Taken
Philosophy of Education
Table of Contents
I am currently in my junior year at Central
Connecticut State University and in my second
semester in the Education Program. During this
semester I was enrolled in Mathematics through
Computers, MATH 409. In this class I was exposed
to different ways that technology could be
integrated with mathematics instruction.
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Resume
Elaine Reed 182
South Main St.
reedelm_at_ccsu.edu
Marlborough, CT
[phone]
Education
About Me
High School
RHAM High School, Hebron, CT
2000-2002
-Received honors each year
St Eskils Gymnasium, Eskilstuna, Sweden
2002-2003
-Exchange student for 10 months with AFS
Education Classes Taken
RHAM High School, Hebron, CT
2003-2004
-Graduated with honors
College
CCSU New Britain, CT
Spring 2005- present
Philosophy of Education
-Deans List Spring 2006 -Deans List Fall
2006 -Deans List Spring 2007 -Kappa Delta Pi
Honors Society Spring 2007-present -Golden Key
Honor Society Fall 2007-present
Table of Contents
Work Experience
Marlborough Country Bakery
Fall 2003-present
-Counter staff
Tutor for Sixth Grader
Fall 2005- Spring 2006
Marlborough Elementary Child Care Association
Summer 2006
-After school care and summer camp Volunteer
Marlborough Elementary Child Care Association
Fall 2006-present
-Before and after school care and summer camp
daycare provider
Special Skills
CPR Certified First Aid Certified Child Care
Certified
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Education Classes Taken
Mathematics Structures of Math I Number
Systems Structures of Math II Probability and
Geometry Structures of Math III Number
Patterns Structures of Math IV Development of
Geometry Topics in Elementary Math Proof and
Logic Psychology General Psychology Life Span
Development Childhood Development Educational
Psychology Technology Introduction to
Educational Technology Developing Educational
Materials Technology Through Computers Reading
Comprehensive Reading Instruction
I Comprehensive Reading instruction
2 Theoretical Introduction to Education and
Learner Exceptionalities Education and Teaching
Leadership- Diverse Learning Effective
Elementary Teaching Practicum DiLoreto Magnet
School, New Britain, CT Third Grade Webb
Elementary School, Wethersfield, CT Fifth
Grade Dwight School, Hartford, CT Fourth Grade
About Me
Resume
Philosophy of Education
Table of Contents
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Philosophy of Education
Through personal experience as well as my classes
at Central Connecticut State University I have
developed certain philosophies about how students
learn and foster their knowledge. These are just
some of the main points that I have noticed
though the semesters I have spent in the
education program. To start, I have recognized
that all students learn differently. Students
are like snowflakes, there are no too that are
alike. But, there is one thing that all of the
students have in common all students are capable
of learning. To have this learning occur,
material needs to be presented in a variety of
ways. There are eight multiple intelligences
according to Howard Gardner, and all eight of
these intelligences should be incorporated in to
learning. I also believe that students do not
always have to learn from the teacher. Students
can teach themselves and teach others. By having
the students work in cooperative groups, the
students are able to teach each other, as well as
learn and grow socially. Another belief of mine
is that students learn by doing. In order for
the majority of students to learn about the
Pythagorean theorem, they would have to be
actively engaged in the lesson. This could be
through drawing out the theorem, finding the
theorem in real world situations, or by
completing a WebQuest on the subject. My last
thought for now is that diversity in the
classroom plays a key part in classroom dynamics.
By having a diverse classroom there is a variety
of view points. These view points lead to better
learning and understanding about any topic. The
different view point and the diversity should be
fostered, and definitely not ignored. My
philosophy of education is always changing and
expanding as I learn more through my classes and
from the students that I see.
About Me
Resume
Classes Taken
Table of Contents
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Article Critique
Article Read
Critiquing this article was a positive experience
for me. It exposed me to a multitude of
different ways to incorporate technology into
lessons in the classroom. The technology that
this article focused on was the use of virtual
manipulatives in the classroom to enhance the
understanding of students.
PowerPoint Presentation
List of Links
Table of Contents
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List of Links
Article Critique
Virtual Manipulatives Examples of Static vs.
Dynamic Virtual Manipulatives Visual Fractions
Room 108 Manipula Math Useful Sites with
multiple Virtual Manipulatives Utah State
University National Library of Virtual
Manipulatives Arcytech
Article Read
PowerPoint Presentation
Table of Contents
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Lesson Plans
Data Analysis
As part of this course we were required to write
four lesson plans. Four each of these lesson
plans we focused on a different area of
mathematics. These areas were Data Analysis,
Number Systems, Geometry, and Algebra. For each
of the lessons we also incorporated technology
into the lesson. This was helpful in
understanding the importance technology to
learning. I was able to see how the different
technologies could be used to enhance a lesson,
not just be added to a lesson.
Number Systems
Geometry
Algebra
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Data Analysis
Topic Data analysis Technology use Environmental
learning Grade Level Second Grade Lesson
Objectives The students will demonstrate their
ability to make a column graph by using excel and
making a chart including 3-4 categories of
litter. Standards Record and analyze data using
charts and bar graphs Purpose Creating graphs
is a useful way to convey messages, enabling
visual representation as well as effectively
summarizing large amounts of data. In this
lesson the graphs are being used to show the
amount of litter that was found and collected at
a local park. Materials and Equipment Computer
s equipped with Microsoft Excel Group data that
was previously collected Printer Letters to
students Anticipatory Set Send all students a
call to duty letter to help save the planet by
spreading the word about the need to cut back
pollution, specifically littering. Bring in
newspaper and magazine clippings of bar graphs or
charts that relate to topics the students would
be interested in. Have the students look at the
clippings to get an idea of how graphs and charts
can be used to convey messages.
Lesson Plans
Number Systems
Geometry
Algebra
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Data Analysis
Time Estimate Receiving and reading letters 5
minutes Looking at clippings 10 minutes Break
into groups move to computer stations 2
minutes Organize data into charts 13
minutes Instruction and Make into bar graphs 10
minutes Print graphs and put into folders 5
minutes Total time 45 minutes Prior
Knowledge Students have previously visited a
park and collected litter. The litter was
recorded and recycled by the students. The
groups that are to be used for this lesson were
assigned at the park according to the area where
they were collecting the litter. Students have
already encountered graphs on a small scale and
they have created bar graphs using paper and
pencil. The students have had science lessons
that focused on the damage that pollution can
cause. Important Terms (Vocabulary) Column
graph (bar graph) Chart Litter Pollution Environme
ntalist EPA Environmental Protection Agency
Data Teaching Model/ Learning
Environment Working with cooperative groups of
about 3-4 students with one computer per group.
Computers are stationary, so the students will be
gathered around an assigned computer.
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Number Systems
Geometry
Algebra
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Data Analysis
Differentiated Instruction For the multiple
intelligence, we have addressed the following
intelligences in the following ways Visual-
Demonstration by teacher Logical- analyzing
graphs Spatial- creating graphs Bodily
Kinesthetic- Gallery tour Interpersonal- working
groups Intra personal- coming up with your own
ideas about graphs, looking at the
clippings Naturalistic- Environmental
concerns For Blooms taxonomy we are at the
Synthesis level of the cognitive scale. The
students are creating their own graphs. For the
affective domain our students will be
demonstrating internalizing values. This is
because they will be active members in a group
and demonstrating problem solving. Procedure 1.
Deliver the call of duty letters to the
students. Allow time for the students to read
the letters. a. What could we do to
help? 2. Come up with an idea of how they could
help the EPA solve the problem of pollution by
spreading the word of pollution. a. How can
we reach a large number of people quickly? 3.
Present the other graphs and discuss how a graph
is an effective way to deliver a large amount of
information very quickly. a. What do you
notice about all of these graphs? b. What
do they have in common? c. What are some
differences? d. What graphs are easier to
understand than others? 4. Break the students
into their groups and give out what their data
was that they have collected. Have the students
move to their computer station.
Lesson Plans
Number Systems
Geometry
Algebra
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Data Analysis
5. Show students how to use excel to organize
their data into 3-4 groups by combining the
categories they have previously made. Include on
every chart a title (where that group collected
the data), types of litter, and the amount of
each type of litter. a. What is a title?
b. Where are the types of litter? c.
Where are the amounts? d.What categories
could we make that would include what we found?
i. Think of recycling groups. 6.
Highlight all of the cells that have information
in them. 7. Click on insert, and then the icon
with the column graph. Allow students to select
what graph would best represent their data.
a.What would be the best representation of your
data? 8. Double check the graphs and make sure
that all of the components of a graph are there.
(Title, labeled axis, numbers are
correct.) Assessment We will know how the
students understood the concepts that were
presented by watching the students making their
graphs and charts. Also at the end of the lesson
there will be a gallery walk to look at all of
the different graphs that were made for the
different areas of the park. The students will
then discuss the graphs with their
groups. Closure After the gallery walk the
students will discuss what they have seen today
in a large group and how the graph can be used
to show other students in the school about the
problems of pollution. References and additional
Resources Parker, D L (March 2003). Take care of
mother earth technology and the
environment. Teaching Children Mathematics, 9, 7. 
p.414(6). Retrieved October 03,
2007, from General OneFile via Galehttp//0-find
.galegroup.com.csulib.ctstateu.edu80/itx/start.do
?prodIdITOF
Lesson Plans
Number Systems
Geometry
Algebra
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Number Systems
Topic Bases for Number Systems and creating
individual number systems Subject or Grade Level
Fourth Grade Mathematics Lesson Objective
Students will be able to understand numbers in
bases other than base 10 by creating another
number system using a different base. Standards
Understand numbers, ways of representing numbers,
relationships among numbers, number systems (NCTM
Standards of Number and Operations Standard for
Grades 3- 5). Purpose Learning about numbers in
different bases is useful because although in our
culture base ten is considered the norm, in other
cultures this is not always used. Understanding
this is important not just in mathematics, but in
all facets. Along with this, students should
make the connection that what we see as the
standard in our culture may be looked at by
different perspectives from other cultures and
vice versa. Children will realize that learning
from other cultures is beneficial. Materials and
Equipment Paper (poster sized) Pencil Colored
Pencils Computers with Internet Access (one per
student) Pictures of different tropical island
(one per group of four) Anticipatory Set Hand
out the images of different tropical islands.
Ask the students to imagine that they are
stranded there and they need to develop a number
system other than base 10. Since the island is
their habitat, brainstorm ideas of things that it
may be a good idea to keep track of i.e. bananas,
coconuts. These things may serve for the basis
of a new number system. For example, you could
say that since you usually find 3 coconuts per
tree that 3 is the new base number. While the
students are brainstorming there will be
background music of island music to help set the
mood of the brainstorming.
Lesson Plans
Data Analysis
Geometry
Algebra
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Number Systems
Time Estimate Split into Groups of Four 3
minutes Hand out images/ Anticipatory Set 7
minutes Explore link provided (individually) 10
minutes Hand out Colored Pencils and Paper 2
minutes Groups Collaborate and make Posters 15
minutes Present Posters 15 minutes Total Time
Estimate 52 minutes Prior Knowledge This
lesson should be a follow-up to a previous lesson
on numbers in different bases. It allows
children to explore, personalize, and enrich
their understanding of the previous lesson. The
students had a good understanding of how the
bases worked after the prior lesson. Important
Terms (vocabulary) Base numbers Culture Number
Systems Numerals Teaching Model/ Learning
Environment The children are going to be
working in groups for the value of collaboration.
Each group will represent their own island with
different number systems from the rest of the
class. The groups will be of about four
students. While the children are exploring the
provided website, however, they will be working
alone for the purpose of understanding the lesson
on their own terms.
Lesson Plans
Data Analysis
Geometry
Algebra
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Number Systems
Differentiated Instruction Gardners Multiple
Intelligences Linguistic- Presenting number
systems to the rest of the classroom. Students
will use words effectively to explain and defend
their ideas. Intrapersonal- Students work
independently at the computers, investigating the
website. Interpersonal- Working in the groups of
four, learning through interaction Musical- There
will be music playing in background while they
are brainstorming and working in their
groups Visual-Spatial- Creating the
poster Bodily-Kinesthetic- The groups will be
getting up to present in front of the
class Logical-Mathematical- Thinking abstractly
to devise a number system. The students will use
reason to choose an appropriate base
number. Naturalistic- Using nature to create a
number system Blooms taxonomy Cognitive- The
lesson is at the Evaluation Level. The students
will be presenting their uniquely created number
systems, explaining them, and making connections
to the meaning as a whole. Affective- The lesson
reaches the Organization Level. The students
will organize and prepare a poster. Then, the
students will present, explain, and defend their
ideas. Psychomotor- The lesson is aimed towards
the level of Adaption. The students will be
adapting new numerals and bases for the specific
task. Lesson Design/Procedure 1. Split the class
into groups with four students in a group. 2.
Hand out the pictures of the islands to the
groups and tell them that they are stranded on
this island and they do not know how to count.
In their groups they need to find a way to count
that is not in base ten. At this time the
students will think which base will work best for
their island. a. Who remembers what we
learned last class? b. What are some
other bases that we have learned about?
c. How would we go about picking a different
base? d. What is important to consider?
e. What do you see in your picture that
could help you decide what base might be most
useful to have?
Lesson Plans
Data Analysis
Geometry
Algebra
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Number Systems
Lesson Plans
3. The students will go to the computers and
explore the website http//nlvm.usu.edu/en/nav/fra
mes_asid_152_g_2_t_1.html. At this website the
students should be able to see how adding and
subtracting can work in the different bases as
well as how many different numerals would be
needed for each of the bases. a. How
are these bases different from the base ten that
we are used to? b. How many numerals
would be needed for base 5? 3? 7? 4.The students
will meet back up in their groups and come up
with their numerals and discuss how their number
system will work. a. Why did you choose
those numerals? 5. The groups will create their
posters. 6. The groups will present their posters
and explain why they chose the base that they did
as well as the numerals that they did. They will
then demonstrate how their number system would
work by adding and subtracting. Assessment The
students will make a poster of their numerals and
demonstrate to the class how their number system
works (what base they chose and why). The poster
will include all of their numerals for their
number system, a name for the number system, one
addition equation done out both in their numerals
and drawn with base blocks, and one subtraction
problem done out both in their number system and
in base blocks. Closure Refer back to the groups
the students were placed in. Note that each
groups work on number systems is unique. Make
the conclusion that cultures may be different in
how they do things, but this is not a bad thing.
Then ask question such as what makes a number
system, and are there some number systems that
are better than others? References and Additional
Resources http//nlvm.usu.edu/en/nav/frames_asid_
152_g_2_t_1.html Culture in the Curriculum
Enriching Numeration and Number Operations.
Teaching Children Mathematics 8.4
(2001) 238.
Data Analysis
Geometry
Algebra
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Geometry
Topic Geometry Subject Tessellations grade
4 Lesson Objective Students will be able
determine what is needed to make a tessellation.
They will explore a website about tessellations
that will guide the students in making
tessellations. After testing what they think is
needed, the students will be able to make their
own tessellations. Standards NCTM Math
curriculum scope and sequence standard 6.2 for
the fourth grade states that students will make
and test conjectures about geometric properties
and relationships involving shape, position,
movement, subdivision, tessellation, and
transformations. Purpose The purpose of this
lesson is to show that our whole environment is
made up of tessellations. There are
tessellations in architecture, nature, and art
work. Materials and Equipment Computers with
internet access Index cards Tape Scissors Colored
Pencils Pictures of tessellations Pencils Paper An
ticipatory Set Gather the children in a group
and have them seated. Tape pictures that youve
previously collected of tessellations found in
architecture, in nature, and in artwork (Try to
use interesting, and colorful examples. When
picking out artwork with tessellations, use at
least one piece by Escher). Ask the children
what they see in each picture or what it is a
picture of, and if they notice any type of
patterns. Recall what tessellations are and ask
if the pictures are also tessellations. This
discussion should guide children to discovering
that tessellations are all around us. Depending
on the classroom, ask the students to look up at
the ceiling (or on a wall, or at the tiling on
the floor) and ask them again what they see. End
the discussion by telling them that today they
are going to get the chance to explore
tessellations, and then create their own.
Lesson Plans
Data Analysis
Number Systems
Algebra
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Geometry
Time estimate Anticipatory set 5
minutes Transition to computers and get to
website 4 minutes Explore website 13 minutes Hand
out index cards, colored pencils, paper, tape,
and scissors 3 minutes Create tessellations
(guided) 8 minutes Create and begin coloring
tessellation on own 12 minutes Gallery tour of
tessellations 5 minutes Total Time 50
Minutes Prior Knowledge The students will have
already been introduced to identifying polygons
in various orientations including combining,
subdividing, sliding, rotating and reflecting In
the previous year (NCTM grade 3). Important
Terms Tessellation Rotation Sliding Tiling Plane
Learning Environment The learning environment
being created will be a combination of whole
class and individual work. The students will
collaborate as a whole class during the
Anticipatory Set. At this time the children will
listen to each others responses about the images
of tessellations as an aid to understanding the
bigger idea. After the anticipatory set the
students will work individually at the computers
and then independently at their desks to
construct the tessellations.
Lesson Plans
Data Analysis
Number Systems
Algebra
Table of Contents
Differentiated Instruction Gardners multiple
intelligences Linguistic- reading on the
website Logical mathematical- creating the
tessellation Spatial intelligence- planning out
the tessellation Bodily kinesthetic- gallery
tour Interpersonal- whole group questions
Intrapersonal- individual work
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Geometry
Blooms taxonomy This lesson allows the student
to synthesis their own meaning of what a
tessellation is, while they create their own
tessellation. It is also motivating to move
through the different stages of the tessellation
website. The students also have to use their
motor skills to operate the computers as well as
to cut, copy, and color their tessellations. Lesso
n Design 1. Gather students to the front of the
classroom where you have displayed the examples
of tessellations from architecture, from nature,
and from artwork. a. What are these
pictures of? b. What do you notice in
common in all these different pictures? 2.
Distinguish which tessellations are architecture,
which are from nature, and which are artwork.
Suggest that tessellations are a part of everyday
life and are all around us. a. Who can
tell me what other picture is from
nature/architecture/artwork? b. Ask the
children to look up at the ceiling (or walls or
floor). Ask if they recognize a pattern. Is
this also similar to the tiling of a
plane? We can see tessellations around us every
day if we look. 3. Tell the children that they
are going to individually explore a website to
see how building a tessellation would work, and
after this they will have a chance to create
their own original tessellation. 4. Break from
whole class to individual seats at computers with
internet access 5. Do a demo on an overhead
projector to guide them to the website
http//www.mathcats.com/explore/tessellationtown.h
tml 6. Explain how the website works,
highlighting the clouds that contain
information. 7. Children will explore the website
on their own. Be sure to walk around to assist
any students having difficulties and to be
certain that all students are on task. 8. After
the students have had some time to practice
creating tessellations on the internet, hand out
paper/index cards/tape/scissors/colored pencils.
Announce that now the students will create their
own original tessellations.
Lesson Plans
Data Analysis
Number Systems
Algebra
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Geometry
Do a demo on how to create a tessellation out of
an index card Choose one side of the index card
to begin with. Tell students to cut out some
type of design that begins and ends at the top
and bottom of that side Tape that side to its
corresponding parallel side Repeat these steps
for the remaining two sides Tell the children to
trace their new shape onto the paper, filling the
plane. You can relate it to a puzzle piece to
make a connection of what the children are doing.
Walk around to help any students who might
it. Color the tessellation after it is traced.
Note that some children may spend a very long
time on coloring, so stick to the amount of time
set aside for this and be aware that it is okay
if a few children do not finish coloring. 10. The
students leave their tessellations on their desks
and then move around the class to view all of the
other tessellations that were made in a gallery
presentation. 11. Hand in Tessellations Assessmen
t You will be able to tell if the students
understand the concept of tessellations by
assessing the tessellations that they create
individually. You also want to check that each
students tessellations is unique in order to
make sure that students were not just copying a
design they saw their neighbor create. Although
the finished project will look like a
tessellation, if it is not original then the
student did not understand the concept
expected. Closure After the gallery tour the
students will discuss what they saw and what
makes up a tessellation. To extend knowledge and
thinking about tessellations we will ask if there
are any reflections, rotations, or slides in the
tessellations that were made. Reference http//ww
w.mathcats.com/explore/tessellationtown.html
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Data Analysis
Number Systems
Algebra
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Algebra
Topic Algebraic Patterns Grade Level Second
Grade Lesson Objectives The students will be able
to see number patterns and expand a given number
pattern by making charts and seeing the
relationships. Standards Use tables and graphs
to display pattern data and explore a variety of
ways to describe and write rules for patterns.
Explore and describe number patterns. Model
situations that involve addition and subtraction
of whole numbers using objects, pictures, and
symbols, including open number sentences.
Analyze observable changes using qualitative and
quantitative descriptions. (NCTM Standards of
Algebra and Functions for Grade 2) Purpose This
lesson promotes real-world thinking and problem
solving. The students will learn that their
observations of patterns can lead to a greater
understanding of relationships around them.
Materials and Equipment 1 Laptop per pair
equipped with Microsoft Excel Pattern blocks
(equal number of trapezoids and squares, one
triangle per group) 1 T- Chart with columns of
Years Old and Number of Pattern Blocks as
headings per pair (on Microsoft Excel) Ancient
Ones The World of the Old-Growth Douglas Fir, a
book by Barbara Bash Printer Anticipatory
Set Explain to the students that today we are
going to read a story. The story that we are
reading is about tall trees that grow in forests,
and all of the animals that live in the forests.
Tie the lesson in with the science unit of
ecosystems. Explain that we are going to pay
close attention to how the trees in the story
grow into these tall trees. Time
Estimate Anticipatory Set- 5 Minutes Reading
story- 15 Minutes Going over what was read- 3
minutes Splitting into pairs- 2 minutes
Lesson Plans
Data Analysis
Number Systems
Geometry
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Algebra
Building trees and recording number of pattern
blocks used- 10 minutes Making chart into a
graph- 5 minutes Finding a pattern and closure- 5
minutes Total Time Estimate 45 minutes Prior
Knowledge The students have been learning about
ecosystems in their science unit. They have also
previously used Microsoft Excel for recording
data and making graphs. The students have had
little practice finding patterns in numbers, but
they have found patterns using objects
before. Important Terms Pattern Growth Ecosystem G
raph T-Chart Learning Environment The students
begin the lesson on the classroom rug to listen
to a story and for the anticipatory set. After
the story the students break up into pairs and
find a spot in the class where they are
comfortable to work. Each pair then receives a
laptop computer that they can use in the spot
that they chose. For finding the pattern and the
closure the class will come together in a central
area with their laptops to discuss what patterns
were found. Differentiated Instruction This
lesson is differentiated due to the number of
multiple intelligences that are being
used. Linguistic- The students are listening to a
story Bodily Kinesthetic- Building the trees out
of pattern blocks Interpersonal- Working with a
partner Intrapersonal- Listening to the story
and thinking about how the trees
grow Naturalistic- Learning about natural growth
and ecosystems Spatial- Making the graphs Logical
Mathematical- coming up with a pattern, making a
chart
Lesson Plans
Data Analysis
Number Systems
Geometry
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Algebra
This lesson is also differentiated because it
utilizes different aspects of Blooms
Taxonomy. Affectively- this lesson allows the
students to value the different ecosystems and
how patterns are found in different
places. Psychomotor- the students develop motor
skills by building with the pattern
blocks. Cognitive- The students analyze a pattern
to determine what the pattern is and then use the
pattern to see if it holds true in test
cases. Lesson Design 1. Anticipatory set, explain
what is going to be done and introduce the book
that is going to be read. a. What have we
been learning in Science class? b. Has
anyone ever noticed how a tree grows? 2. Read the
story to the students. Have them pay particular
attention to the size of the trees at different
stages in their lives. 3. Go over what was read.
a. Did anyone notice any patterns with how
the trees grow? 4. Have the students break into
pairs and explain what is going to be done. The
students will take turns growing the tree that
is made out of the pattern blocks. The first
year tree is made out of one square (for the
trunk), one trapezoid, and then a triangle on the
top of the trapezoid, forming a tree. For each
year the students will add one square to the
bottom and one trapezoid to the body of the tree.
This will make the tree grow each year. While
one student is making the tree grow, the other
student is recording how many pattern blocks are
being used for each year. The students will take
turns with these two tasks. a. What
patterns are you noticing? b. Each year,
how many more blocks are added? 5. Use the chart
that was made on Excel and make a line graph.
Look at the graphs that were made. a.
What do these graphs look like? b. Is the
line curved or straight? c. By how many
pattern blocks do the trees grow each year? 6.
Print off both the charts and the graphs.
Lesson Plans
Data Analysis
Number Systems
Geometry
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Algebra
Assessment The teacher assesses students by
collecting their charts and graphs. During the
lesson the teacher will also ask questions such
as, What patterns do you see in order to gain
some insight into which students are picking up
the lesson and which may need more help.
Closure Ask questions such as What patterns did
we find? How many blocks were added each year?
How many bocks would be used for a tree that was
25 years old? What would happen if the trees grew
by two trapezoids and one square each year? What
would this pattern look like? Would it look
similar or different?
Lesson Plans
Data Analysis
Number Systems
Geometry
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WebQuest
WebQuest
This WebQuest assignment was designed to show us
how easy it is to put together a motivating
lesson for students to take learning into their
own hands. The WebQuest is a good format for a
lesson such as this. It allows the students to
learn both on their own and with a group. This
WebQuest is on Pythagoras, his life and his
theorems.
Reflection
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Reflections
During this class we had the opportunity to
reflect on what we were doing. The two
assignments that we reflected on were our lesson
that were taught to the class and our WebQuest
that we created. Reflection is an important
aspect to teaching because it allows the teacher
to see what worked well during the lesson. This
will allow the teacher to see possible ways to
reconstruct the learning. Reflection also allows
the teacher to see areas that did not work so
well and areas that could be improved. This is
especial useful for a beginning teacher, but
should be continued throughout the career.
Data Analysis Lesson Reflection
WebQuest Reflection
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WebQuest Reflection
When starting this WebQuest I already knew what
it was all about. I have previously made a
WebQuest using Zunal.com. Previously I did not
enjoy making the WebQuest. I found it boring and
unimaginative. The way that the website had the
constructer build the WebQuest did not leave room
for any variation. This, I suppose, is a good
think for a first timer, but I did not enjoy the
experience. When we made the WebQuest for Math
409, we used Microsoft PowerPoint. There was no
template to use and there were hardly any
guidelines to follow. This made for a more
creative page that could engage the students
better. Working on this WebQuest was a group
effort. We all worked together to have this come
to fruition. There was not a member of the group
that did not participate equally. Ideas were
flowing between our group freely. There was also
not any animosity between the members and all of
the members were able to voice their
opinions. Looking back there would not be too
much that I would change. The topic was a bit
dull, and we tried spicing it up as much as we
could. I think if we put more effort into coming
up with a premise for the WebQuest we would have
been able to find a more realistic scenario for
the students to feel engaged. Over all I feel
that we did a good job making an engaging
WebQuest for our imaginary class to use to learn
more about Pythagoras.
Reflections
Data Analysis
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Data Analysis Reflection
The first area to look at was how we addressed
our lesson objectives. We did state what our
lesson objectives were, the only problem with
this was that we did not state our objectives at
the beginning of our lesson. There was reason
behind this decision though this reason was
because we wanted to student to come up with the
idea to make the graphs. If we were to state at
the beginning of the lesson that we were going to
make bar graphs to show why it was important not
to litter, then the students could not have
thought for themselves of the best way to show
what they wanted to show. This lesson was part
of a larger project and the project was one for
the students to take charge of. Another area to
look at was how we addressed the standards. This
area I believe we had them complete. There was
only one standard that applied to our lesson that
we could find and in this standard there was only
a portion of the standard that applied to our
lesson. Still another area to examine would be
our purpose. I think we did a good job showing
how graphs can be used in the real world and also
giving the students a reason to make the graphs.
I think that it is important to link graphs to
something that the students are interested in.
If I were to do this again I would not change how
we made the graphs meaningful for the
students. The next area to look at would be the
anticipatory set. This is the part of the lesson
that I liked the most. We got the attention of
the students by writing them a letter from the
EPA. This idea I believe would have worked
better if the students were actual second graders
instead of college students that were pretending
to be second graders. I would not change this if
I were to teach this lesson to a class. What I
might try to do would be to go to the local DEP
headquarters and ask if they could actually write
a letter about cleaning pollution. This I think
would be more realistic than a letter made up by
myself. If I were teaching this lesson in an
actual classroom I would ideally want laptops so
that the class could be spread out. I would
still want the students to be in groups. I think
it is important for the students to be in groups
and working together to learn a new technology.
I remember when I was in elementary school, the
teacher would have the whole class go to the
computer lab and each work individually on a
computer. I would not always know what to do,
when other people were jumping ahead of the
lesson. This would often frustrate me and I
would end up asking my peers for help. If the
students can start out in groups, then they are
already in a position to teach each other.
Reflections
WebQuest
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Data Analysis Reflection
An area that could use improvement would be our
directions and our procedures. I feel that we
were not as clear as we could have been when it
came to giving directions. We did not fully
think through all of the directions that we would
have to give. An example of what I am talking
about is when we were preparing the class to
begin the gallery tour. Here we did not
specifically say where to go to look at the
different graphs. Overlooking these details
leads to confusion in the classroom. Next time I
will try to map out exactly what will take place
and anticipate problems. I do not feel that our
transitions were smooth. Again, we did not plan
extensively on how we would deliver our
transitions. This I believe comes with more
practice and with watching what other people
do. I enjoyed our assessment. The gallery tour
allowed for each group to share what they came up
with for a graph and to show what they
accomplished at the park. It also allowed Joey
and myself an opportunity to see what groups had
an understanding of the bar graphs and all of the
aspects that went into the graph. A problem that
we were faced with was the difference in Excel
between the version that we are used to and the
version that is now on the computers at Central.
When we were planning and practicing our lesson
on our own computers, forgetting that the school
had a different Excel. If I were to teach this
lesson again, I would make sure I tried out the
lesson on the actual computers that will be used
to find out if there are any differences. We
used technology as a tool to make our graphs. Or
lesson was designed for a second grade class and
they most likely would not have the background to
make the graphs on their own. Some guidance by
the teacher would be needed. I do not see how
this lesson could be carried out with a group of
second graders without going through how to make
the graphs each time for at least the first few
times. This lesson was however intrinsically
motivating. Most students at this age that I
know feel passionately about pollution issues and
they want to help the environment. Throughout
the lesson we attempted to create discussion.
This did not work very well. The class did not
seem willing to participate in the discussions.
This seems to be typical of presenting lessons to
college age students. If I were to attempt this
again, I would attempt to facilitate discussion
by having the students first talk in small groups
and then ask them to share with the class. This
might work better to get some discussion
going. There were many areas in our presentation
that could use improvement, but there were also
some good areas. The areas that need the
improvement need to have a solution thought
about. It does not good to simply say I need
improvement, but then to give mo plan of action
to improve.
Reflections
WebQuest
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