Dgc

Instrumentation in
Teaching
Mathematics
(Teaching Tools and Instructional Materials in
Mathematics)
by Divine Grace Cabahug

Topic Outline
• Why Teach Math?
• Goals in Teaching Math
• Achieving the Goals in Teaching Math
• Underlying Principles and Theories in Teaching Math
• Definition, Uses, and Evaluation of Manipulatives
• Examples of Manipulatives and their Pedagogical Uses
• Sample Outputs of Manipulatives

Topic Outline
• Integrating Technology in Mathematics
Virtual Manipulatives (Mayend Dagunan)
Dynamic Geometry Software (Divine Grace Cabahug)
Computer Algebra System (Marie Christine Regis)
Presentation Software (Mary Alyssa Cacha)
Spreadsheet (Mayend Dagunan)
Internet and Java Applets; Nitiquttes (Angerica
Gellecania)
Movies and Videos in Mathematics Teaching (Miriam
Grace Ceprado)

Why Teach Math?
Because “Mathematics is one subject that
pervades life at any age and in any
circumstance. Thus, its values go
beyond the classroom and the
school.” (K to 12 Curriculum Guide in
Mathematics, 2010)

Goals in Teaching Math
 According to the K to 12 Curriculum in
Mathematics (2010), the main goal of
mathematics is to develop the CRITICAL
THINKING SKILLS and PROBLEM
SOLVING SKILLS of the learners in
Mathematics

Goals in Teaching Math
 CRITICAL THINKING SKILL
according to Scriven and Paul (1987), it is the
intellectually disciplined process of actively and
skillfully conceptualizing, applying, analyzing,
synthesizing, and/or evaluating information
gathered from, or generated by observation,
experience, reflection, reasoning, or
communication, as a guide to belief and action

Goal in Teaching Math
 PROBLEM SOLVING SKILL
according to Polya (1945 & 1962), it is
finding a way around a difficulty,
obstacle, and finding solution to a
problem that is unknown.

Achieving Goals in Teaching Math
1. Strengthening the Content;
***Taking into consideration the:
1. Skills and Processes;
2. Values and Attitudes;
3. Mathematical Tools; and
4. Context

1. Strengthening the Content:
a) Numbers and Number Sense
b) Measurement
c) Geometry
d) Patterns and Algebra
e) Statistics and Probability

2. Skills and Processes :
a) Knowing and Understanding;
b) Estimating, Computing, and Solving;
c) Visualizing and Modeling;
d) Representing and Communicating;
e) Conjecturing, Reasoning, Providing, and Decision-
Making; and
f) Applying and Connecting

3. Values and Attitudes
a) Accuracy
b) Creativity
c) Objectivity
d) Perseverance
e) Productivity

4. Mathematical Tools:
a) Manipulative Objects
b) Measuring Devices
c) Calculators and Computers
d) Smart Phones and Tablet PCs
e) Internet

5. Contexts:
a) Beliefs
b) Environment
c) Language
d) Culture
e) Learner’s Prior Knowledge and
Experiences

Underlying Principles and Theories
in Teaching Math
a) Constructivist Perspective
b) Cooperative Learning
c) Discovery and Inquiry Based
Learning
d) Experiential and Situated Learning
e) Reflective Learning

Definition of Manipulatives
These are concrete models
that involve mathematics
concepts appealing to several
senses

Uses of Manipulatives
It helps students learn to:
1. Relate real world situations to math
symbolisms
2. Work together cooperatively in solving
mathematics
3. Discuss mathematical ideas and concepts
4. Verbalize or communicate mathematics
thinking

Uses of Manipulatives
It helps students learn:
5. To make presentations in front of a
large group
6. That there are different ways to solve
problems
7. That math problems can be symbolized
in many ways
8. That they can solve math by exploring

Evaluation of Learning Using
Manipulatives
Assessing or evaluating student’s output
presentation through:
Concept understanding and development
should be valued more highly

Evaluation of Learning Using
Manipulatives
Assessing or evaluating student’s insights through:
1. Student’s sharing and interaction;
2. Observing student’s work in group activities
and individual works
3. Asking Why and How questions (HOTS-Higher
Order Thinking Skills)

Examples of
Manipulatives and
their Pedagogical
Uses

Geometry
Compass
A compass is a metal or plastic V-shaped
drawing tool with a clamp on one end to hold a
pencil and a sharp point on the other end that
keeps the tool steady on the drawing surface
while the pencil moves. A compass is used in
mathematics, drawing and drafting to create
arcs, circles or other geometric figures that can
be determined by measuring intersecting line
segments. A compass can be used to bisect lines,
find midpoints and help solve problems in
geometry.

Geometry
Geoboard
A Geoboard is a very useful device for
introducing children to important topics in
school geometry. It consists of an array of
nails or pegs which are placed at equal
distances on a square acrylic board making
up a grid.
Geoboards have many uses. One is teaching
perimeter and area. Here is a fun activity we
enjoy for teaching perimeter and area with
geoboards.

Geometry
Graphic Calculator
Graphing calculators are programmable
calculators with a large display screen that can
be used for graphing, solving equations, and
many other tasks that involve variables. These
gives students the opportunity to learn concepts
through experience with the use of the graphing
calculator and these enhances students’ learning
by allowing them to see a visual display of the
results on the calculator screen.

Geometry (13 Archimedean Solids)

Geometry
Platonic and Archimedean Solids
In schools the subject of geometry, whether
plane or solid, is often treated in a very abstract
way. Through the construction of these, students
will have hands-on experience and understanding
with nets and solid geometry concepts.

Geometry
Protractor
The protractor is an instrument used for
measuring angles. It is usually made of
transparent glass or transparent plastic.
Depending on the measurement system,
protractor can have radian scale or degrees
scale on it. The protractor is usually had
semi-circle size divided into one hundred
and eighty parts or full circle divided into
three hundred and sixty parts

Geometry
Ruler
Rulers are used for measuring a line, and
the straight edge allows them to be used for
drawing, scoring, or cutting. They are often
used in technical drawing, math &
geometry, engineering, carpentry, and print
fields. Rulers are relatively short measuring
instruments most commonly 12”, and are
most useful for measuring the length of
small objects.

Geometry
Tangrams
Tangrams "help students develop
mathematical concepts of fractions,
spatial awareness, geometry, area, and
perimeter" (Rigdon, D., et al., 2000, p.
304.305). Because tangrams involve
physical manipulatives as well as
virtual manipulatives, this caters to a
variety of learning styles.

Trigonometry
Clinometer
A clinometer is a tool that is used to
measure the angle of elevation, or angle
from the ground, in a right - angled
triangle. You can use a clinometer to
measure the height of tall things that you
can't possibly reach to the top of, flag
poles, buildings, trees. Follow the
directions below to create your own
clinometer.

Numbers and Number Sense
Fraction Bar or Strips
Fraction strips help students to visualize and
explore fraction relationships. They allow
students to develop a concrete understanding
of fractions and mixed numbers, investigate
equivalency, compare and order fractions and
explore number operations with fractions.
Fraction strips help students by allowing them
to manipulate parts of the same whole. By their
very nature they keep the whole consistent for
students.

Sample Outputs of
Manipulatives

Geometry
Booklet of Definitions, Postulates,
Corollaries, and Theorems

Geometry
Booklet of Mensuration

Geometry
Golden Ratio Scrapbook

Geometry
Platonic and Archimedean Solids

Trigonometry
Radian the Snowman

Linear Algebra
Application of Linear Regression: Story
Book

Numbers and Number Sense
Fraction Bar

Problem Solving
Compilation of Examples of the Strategies
in Problem Solving

Problem Solving
Compilation of Math Problems

Integrating Technology in
Mathematics?
Integrating technology into the classroom
is a great way to empower students to
stay connected in this technological era.
Technology-rich lessons have been
found to keep students motivated and
engaged longer.

Virtual Manipulatives
(Mayend Dagunan)
 “an interactive, Web-based visual representation of a
dynamic object that presents opportunities for
constructing mathematical knowledge”
allow teachers to allow for efficient use of multiple
representations and to provide concrete models of
abstract mathematical concepts for learners of
mathematics

(Mayend Dagunan)
Effective Use of Virtual Manipulatives
teachers must have an understanding of how to use
representations and how to structure a mathematics
lesson where students use technology
teachers must also be comfortable with technology and
be prepared

(Mayend Dagunan)
SAMPLE WEBSITES
SAL'S SUB SHOP
http://mrnussbaum.com/sal-play/#
Objectives:
•to give the correct measurement asked
•to familiarize the measurement indicated in the metric rules

(Mayend Dagunan)
SAMPLE WEBSITES
COMPUTATION CASTLE
http://mrnussbaum.com/castle/
Objectives
•to convert the given measurements
•to enhance the skills in covering units

(Mayend Dagunan)
SAMPLE WEBSITES
ARTIE OUNCES SODA JERK
http://mrnussbaum.com/soda-play/
Objectives:
•to convert the units in volume
•to produce the correct order of the customer

(Mayend Dagunan)
SAMPLE WEBSITES
MATTHEW METRIC GUM'S PARLOR
http://mrnussbaum.com/metric/
Objectives:
•to identify the correct value of gum
•to select the correct number of gums based on what is
asked

(Mayend Dagunan)
SAMPLE WEBSITES
METRIC MILLIONAIRE: MEASUREMENT
http://www.quia.com/rr/30535.html?AP
rand=1842435648
Objectives:
•to convert the given measurements correctly
•to develop accuracy in solving the word problems in
measurements

(Mayend Dagunan)
SAMPLE WEBSITES
INTEGER DRIVING TEST- INTEGER ADDITION
SUBTRACTION
http://www.xpmath.com/forums/arcade.php?do=play&gameid=
82
Objectives:
•to locate in the number line the correct spot for the given number
•to perform the operations of integers
•to practice speed in solving the operations of integers
•to develop accuracy in solving the operations of integers

(Mayend Dagunan)
SAMPLE WEBSITES
MATH GAMES ARCADE-SCIENTIFIC NOTATION
http://www.xpmath.com/forums/arcade.php?do=play&gam
eid=21
Objectives:
•to illustrate the right scientific notation
•to recognize the different parts of the scientific notation
•to develop speed in constructing the scientific notation
•to develop accuracy in formulating the scientific notation

(Mayend Dagunan)
SAMPLE WEBSITES
MATH MAN- OPERATIONS WITH INTEGERS
http://www.coolmath-games.com/0-math-man/aindex.html
Objectives:
to perform the steps in the basic operations of integers
to compute for the correct answer
to develop speed in solving the basic operations of integers

(Mayend Dagunan)
SAMPLE WEBSITES
MATH RACING- ADDING INTEGERS GAME
http://www.math-play.com/math-racing-adding-integers-
game/math-racing-adding-integers-game.html
Objectives:
•to compute the sum in adding integers
•to perform the steps in adding integers
•to develop accuracy in solving the addition in integers

SAMPLE WEBSITES
Base blocks
• illustrates addition and subtraction in variety of
bases
Circle 99
• a puzzle involving adding positive and negative
integers to sum to 99
(Mayend Dagunan)

SAMPLE WEBSITES
CIRCA 99
• The goal of this puzzle is to put three numbers inside of
each circle so that they add up to 99.
• Solve the puzzle by dragging the black numbers to the blank
spaces. You cannot move the blue numbers.
• When the three numbers inside any circle add up to 99, the
circle changes color.
(Mayend Dagunan)

SAMPLE WEBSITES
LADYBUG MAZES
• program a lady bug to move through a maze
• Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–
5), Measurement (3–5), Geometry (6–8), Measurement (6–8)
FRACTALS- ITERATIVE
• to generate 6 different fractals
• Geometry (3–5), Geometry (6–8), Geometry (9–12)
(Mayend Dagunan)

SAMPLE WEBSITES
COB WEB PLOT
• change variables and observe patterns from the graphing simulation
• Geometry (6–8), Geometry (9–12)
Pattern Blocks
• use 6 common geometric shapes to build patterns and solve problems
• Algebra (Pre-K–2), Geometry (Pre-K–2), Measurement (Pre-K–2),
Algebra (3–5), Geometry (3–5), Measurement (3–5), Algebra (6–8),
Geometry (6–8), Measurement (6–8), Algebra (9–12), Geometry (9–
12), Measurement (9–12)
(Mayend Dagunan)

SAMPLE WEBSITES
Fill and Pour
• solve puzzles requiring you to fill and pour containers
• Measurement (3–5), Measurement (6–8), Measurement (9–12)
DIFFY
• solve an interesting puzzle involving the difference of the given numbers
• Number & Operations (Pre-K–2), Number & Operations (3–5), Number
& Operations (6–8), Number & Operations (9–12)
• nlvm.usu.edu
(Mayend Dagunan)

Dynamic Geometry Software
(Divine Grace Cabahug)
A computer program for interactive creation
and manipulation of geometric constructions
Help build a geometric model of objects such
as points, lines, circle, etc and their
relationship to one another
is a visualization of an abstract model (of
geometric nature) and, in particular, provides a
visual interface for its manipulation

Typical Uses
graphical presentation of geometry on the screen
exploring geometric properties, testing hypotheses
 visualizing complex data
geometric reasoning
 illustrations in document preparation
 illustrations for the Web
 libraries for geometric programming.

Features
 2D or 3D
constructive richness
 easy to use interface and other convenience-related issues
kinds and degrees of dynamism (incl. animation)
adaptability to specific domains and needs
accepting text commands
 extensibility (through programming)

Popular DGS
The Geometer’s Sketchpad (1990s).
•This lets one publish Sketchpad sketches on the Internet and
interact with them independently. The program can be
obtained for free, separately from Sketchpad.
http://www.dynamicgeometry.com/

Popular DGS
Cabri (1990s)
•The current releases offer 3D construction
capabilities.
http://cabri.com/en/

Popular DGS
Cinderella
•A Java-based program. Has a scripting language
equipped with data and control structures for general
programming.
https://cinderella.de/files/HTMLDemos/

Popular DGS
Archimedes Geo3D
•An advanced 3D DG program.
http://archimedesgeo3d.weebly.com/index.html

Popular DGS
GeoGebra
•is a typical modern DG system for planar geometry.
•Features:
1. rich, well thought-out set of constructive and other commands
2. easy to learn and use
3. all parts of the drawing are draggable and always accessible for
adding, changing or deletion of attributes
4. output formats for different uses
https://www.geogebra.org/

Popular DGS
Polyhedron
•A collection of 250 problems built into a computer
program and dealing with polyhedra. Simulates ruler,
protractor, compass, bisector, and other construction
and measuring tools
https://www.journals.elsevier.com/polyhedron/

Popular DGS
GEONExT
•A modest Java program whose distinguishing property is
that it is executed as an applet in a Web browser, and can
be run directly from a website, without downloading and
installation.
http://geonext.uni-bayreuth.de/

Popular DGS
CLUCalc/CLUViz
•A program for 3D visualisation and scientific
calculation, originally for geometric algebra. CLUCalc
interprets a script language, CLUScript, and CLUViz
is a visualisation engine
http://www.clucalc.info/

Computer Algebra System
(Marie Christine Regis)
• relates to the use of machines, such as computers, to
manipulate mathematical equations and expressions
in symbolic form, as opposed to manipulating the
approximations of specific numerical quantities
represented by those symbols.
• Such a system might be used for symbolic integration
or differentiation, substitution of one expression into
another, simplification of an expression, etc.

• is a software program that allows computation over
mathematical expressions in a way which is similar
to the traditional manual computations of
mathematicians and scientists
• is a software package having capabilities for
• Numerical computations
• Symbolic computations
• Graphical computations

• is a software program that facilitates symbolic
mathematics.
• Computer algebra systems may be divided into two classes:
specialized and general-purpose.
• The specialized ones are devoted to a specific part of
mathematics, such as number theory, group theory, or
teaching of elementary mathematics.
• General-purpose computer algebra systems aim to be
useful to a user working in any scientific field that requires
manipulation of mathematical expressions.

Use in education
• There have been many advocates for increasing the use of
computer algebra systems in primary and secondary school
classrooms. The primary reason for such advocacy is that
computer algebra systems represent real-world math more
than do paper-and-pencil or hand calculator based
mathematics. This push for increasing computer usage in
mathematics classrooms has been supported by some
boards of education. It has even been mandated in the
curriculum of some regions.

• Computer algebra systems have been extensively used in
higher education. Many universities offer either specific
courses on developing their use, or they implicitly expect
students to use them for their course work. The companies that
develop computer algebra systems have pushed to increase
their prevalence among university and college programs.
• CAS-equipped calculators are not permitted on the ACT, the
PLAN, and in some classroom though it may be permitted on
all of College Board's calculator-permitted tests, including the
SAT, some SAT Subject Tests and the AP Calculus, Chemistry,
Physics, and Statistics exams.

Sample Computer Algebra Systems
• Axiom
• Cadabra
• CoCoA-4
• CoCoA-5
• Derive
• DataMelt (DMelt)
• Erable (aka ALGB)
• Fermat
• FORM
• FriCAS
• GAP
• GiNaC
• KANT/KASH
• Macaulay2
• Macsyma
• Magma
• Magnus
• Maple
• Mathcad
• Mathematica
• Mathics

Sample Computer Algebra Systems
• Mathics
• Mathomatic
• Maxima
• MuMATH
• MuPAD
• OpenAxiom
• PARI/GP
• Reduce
• Scilab
• SageMath
• SINGULAR
• SMath Studio
• Symbolic Math
Toolbox
(MATLAB)
• SymPy
• TI-Nspire CAS
(Computer
Software)
• Wolfram Alpha
• Xcas/Giac
• Yacas

Presentation Software
(Mary Alyssa Cacha)
What are presentation softwares?
These are software packages used to display or show
information in the form of a slideshow.
What are its major functions?
•An editor that allows text to be inserted and formatted.
•A method for inserting and manipulating graphic images.
•A slideshow system to display the content.

(Mary Alyssa Cacha)
Why use presentation software in teaching Math?
To address the abstract nature of mathematics.
To make math class discussions more engaging to the
learners.
To make math class discussions more interactive.
To increase the learners’ participation and confidence.
To link mathematics in real-life context.
To present math lessons clearer.

Features:
• Embed and edit video within a slide
• Embed audio or voice over your PowerPoint presentation
• Add bookmarks to media files to pause or enhance media at
designated points
• Microsoft-designed themes and animations to bring your
slides to life
Examples of Presentation Softwares:
Microsoft PowerPoint
(Mary Alyssa Cacha)

(Mary Alyssa Cacha)
Features
• Built in narration tool
• Powerful tools for adding and editing graphics and other
media files
• Apple-designed themes and animations to bring your
slides to life
• Keynote app for iPad and iPhone has surprisingly similar
functionality and ease-of-use as the software itself
KeyNote

(Mary Alyssa Cacha)
Features
•Better depicts the complexity and interrelatedness of
material; contrasted with the linearity of PowerPoint
or Keynote
Prezi

(Mary Alyssa Cacha)
Other Presentation Softwares

Spreadsheet
(Mayend Dagunan)
Computerized worksheet
standard feature of an electronic spreadsheet
which uses cells that are represented in rows
and columns designed to perform arithmetic
operations.
calculate numeric information such as
budgets, income, expenses, scientific, and
statistical data.

Spreadsheet
(Mayend Dagunan)
3 Types of Data that can be Entered into
a Spreadsheet
• Label - The term given to the data entered as text in a
spreadsheet.
• Values - The term give to the data entered as numbers in a
spreadsheet.
• Formulas - Mathematical equation consisting of numbers,
other cell designators, and symbols for mathematical operations.
The result of the formula is displayed in the cell, the formula is
displayed in the data entry bar. Formulas are calculated using the
normal algebraic rules concerning order of operations.

Spreadsheet
(Mayend Dagunan)
Spreadsheet Skills to Know
 Resizing columns and rows - To quickly re-size a
column/row so that you can see all the contents within the
cells, place your mouse on the border between cell headers
until your cursor has arrows, then click and drag the divider
to make it wider. Data in a cell that is too small may display
##### in the cell. To remove the error, resize the cell.
 Deleting row/columns - Click on row or column heading
which will highlight the entire row/column and then delete.
 Adding data using fill series

Spreadsheet
(Mayend Dagunan)
 Calculating using formulas
 Creating a graph from spreadsheet
 Inserting a new worksheet
 Renaming a worksheet
 Merging cells
 Formating cells - Identifying the type of data found in the cells
- Examples: show how time or dates will be displayed or how
many decimal places will be displayed.
Spreadsheet Skills to Know

Spreadsheet
(Mayend Dagunan)
Importance of Spreadsheet
Spreadsheets are an important, powerful and versatile
business tool, and can provide and store valuable
information. Spreadsheets can hold as little or as much
information as necessary. Some spreadsheet programs can
also work together with other programs, such as word
processing and presentation software.

Internet and Java Applets
(Angerica Gellecania)
Internet
 “information superhighway”
 the original name was ARPANET
• ARPA – Advanced Research Projects Agency
• to create network that would allow scientists to share
information on military and scientific research
 the thousands of interconnected networks were called
an Inter-Net-Network (internet / network of networks)

Applet
 is a special kind of program that is transmitted over
the internet and automatically executed by the java-
compatible web browser
 helped in moving some user interactive programs
from server to client
 improves the usability of the web application

Java
 a programming language for the Web which
can be downloaded by any computer
 influenced internet by simplifying the web
programming and inventing applets which
expanded the scope of internet

 addressed two other important issues of
internet:
•security
 there are restrictions on what can be done
in applets
they can use only a subset of all the
functions supported by Java

• portability
since internet is comprised of many different
types of computers and operating systems, it is
important for the programs to run all these
systems
is achieved by using Bytecode in Java

Basic Java Applet Examples
 Interactive/ complex Java applet
animations
• watchful eyes
• sliding puzzle
• randomly blinking text
 Providing services over the WWW
• temperature conversion
• calculator

 Controllable information display
• Weather statistics
 Toy demo applets
• the classic “Hello World!”
• Editable text- jumps with mouse clicks
• Simple graphics: Display a diagonal line
• a simple game , etc.

 Some “real” applets:
• The ripple effect applet
• A proper game
 More advance examples:
• A bouncing ball animation, using threads
• An event monitor

Netiquettes
1) Netiquette: Expectations of good behavior online
1. Always think before you write. In other words without the
use of non-verbals with your message, your message can be
misinterpreted. So please think twice before you hit submit.
2. Keep it relevant. There are places to chat and post for fun
everyday stuff. Do not stray from the discussion in the assigned
questions.
3. Never use all caps. This is the equivalent of yelling in the
online world. It is not fun to read. Only use capital letters when
appropriate.

Netiquettes
4.Make sure that you are using appropriate grammar and
structure. In other words I don’t want to see anyone writing “R U”
instead of “are you”. There are people in the class that may not
understand this type of abbreviation, not to mention it does nothing to
help expand your writing and vocabulary skills. Emoticons are fine as
long as they are appropriate. A smile ☺ is welcome, anything offensive is
not.
5.Treat people the same as you would face-to-face. In some cases it
empowers people to treat others in ways they would not in person.
Remember there is a person behind the name on your screen. Treat all
with dignity and respect and you can expect that in return.

Netiquettes
6. Respect the time of others. This class is going to require you to
work in groups. Learn to respect the time of others in your group
and your experience will be much better. Always remember that
you are not the only person with a busy schedule, be flexible. Do
not procrastinate! You may be one that works best with the
pressures of the deadline looming on you, but others may not be
that way. The same is true for the reverse. The key to a successful
group is organization, communication and a willingness to do what
it takes to get it done.

Movies and Videos in Mathematics Teaching
(Miriam Grace Ceprado)
How movies/videos help in the teaching -
learning process?
• Facilitating thinking and problem solving
• Assisting with mastery learning
• Inspiring and engaging students
• increased student motivation
• enhanced learning experience
• development potential for deeper learning of the subject

• enhanced team working and communication skills learning
resources for future cohorts to use
• Authentic learning opportunities
• Meets additional learning styles
• Provide teachable moments
• Can be a good thing to do on days where students would be
unfocused
How movies/videos help in the teaching -
learning process?

Drawbacks of using films & videos
• Movies can be distracting.
• May take too much time
• May not be completely historically accurate

Agora
• Hypatia and her Apollonian Cones.
• Hypatia makes an experiment with
relative motion
• A student presents the Ptolemaic
system with epicycles (solar
system)
• History of Math
SAMPLE MOVIES

SAMPLE MOVIES
Calculus of love
• An obsession with the
Goldbach conjecture
• Advance Mathematics

Jane Eyre
• Some arithmetic problems on
the blackboard, mostly with
wrong solutions.
• Numbers and number sense
SAMPLE MOVIES

SAMPLE MOVIES
Fermat’s room
• This brilliant movie is essentially
about math only. A few famous
math puzzles appear in this
movie, where 4 mathematicians
are trapped in a room where the
walls slowly crush them.

SAMPLE MOVIES
Phantom Tollbooth
• The dodecahedron asks some
riddles to get to Digitopolis.
Fibonnacci series, vectors and
scalars, equivalence relations
and 4827659 hairs.

SAMPLE MOVIES
Stand and Deliver Tic-Tac-toe
• Drop out student learns calculus.
Tic-Tac-Toe method for integration
by parts.

Book Sources:
De Jesus, Joy T.(2008).Java Programming by Example. Quezon
City: Tech Factors Inc.
Wells, Dr. Dolores.(2009). Basic Computer Concepts. Singapore:
Cengage Learning Asia Pte Ltd.
Jema Development Group (2014) Office Productivity. Philippines:
Jemma,Inc.
Electronic Sources:
K to 12 Math Curriculum Guide (2010)
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https://education.ti.com/sites/UK/downloads/pdf/Research%20Not
es%20-%20Why%20CAS.pdf
http://www.math.tamu.edu/~dallen/papers/strategies.pdf
http://ucsmp.uchicago.edu/resources/conferences/2012-03-01
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Art/instructions-for-polyhedra-project.html
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tangrams-important-and.html
https://sciencing.com/what-math-compass-5006442.html
http://mathedu.hbcse.tifr.res.in/geoboard

http://www.edugains.ca/resourcesMath/CE/LessonsSupports/Mani
pulatives/Manipulatives_FractionStrips&FractionTowers.pdf
http://www.thefullwiki.org/Symbolic_mathematics
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algebrasystemmaple
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www.java.meritcampus.com
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definition.html
http://www.uq.edu.au/teach/video-teach-learn/ped-benefits.html
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https://www.youtube.com/results?search_query=mathematics+chan
nels
https://www.ldlewis.com/Teaching-Mathematics-with-Art-
instructions-for-polyhedra-project.html

https://computerskills4teachers.wikispaces.com/SPREADSHEET+T
ERMS+AND+SKILLS
https://www.avidian.com/resources/how-to-use-excel
https://www.youtube.com/watch?v=xOU_hL2_zBo
https://www.atm.org.uk/write/MediaUploads/Shop%20Images/Loo
k%20Inside/DNL037.pdf

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