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// TPACK In Math Education // = 1. Math Matters = It does matter to understand Math. This particular domain is associated to science, art, music, and language. It is a subject that relates to the real world. To define mathematics, one must think of all the elements and components of mathematics from an early age until today. Mathematics emerged as human kind began to search for understanding the world. They sought to describe the natural world around them, looking for answers while reasoning for truths.

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Wikipedia, define the mathematics education as a practice of teaching and [|learning] [|mathematics], as well as the field of scholarly [|research] on this practice. Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice. Mathematics is the study of numbers, sets of points, and various abstract elements, together with relations between them and operations performed on them. Mathematics deals with size, order, shape, and other relationships among quantities. Today, most view mathematics as the study of patterns and relationships of numbers or the study of logic and intuition as it relates to the world.

//There are four defined concepts of mathematical thinking://
 * //Problem Solving:// Explore problems, attempt solutions and explain reasons. Here is where math is linked to science. It is the science of logical reasoning, in which valid conclusions are sought from a set of data.
 * //Communication:// Express ideas in words, symbols and diagrams. Language is essential for communicating ideas and mathematics. It helps build stronger language and vocabulary.
 * //Reasoning:// Thinking through, finding useful answers to problems. Reasoning requires problem-solving skills. It is an art of mathematical thinking.
 * //Connections:// Making mathematics easier to understand by relating it to real world experiences. Making connections allows application for common rules in our daily life.

Throughout the elementary math education filed there are seven concepts of mathematical contents defined and studied. These are estimation, number sense, geometry and spatial sense, measurement, statistics and probability, fractions and decimals, and patterns and relationships.


 * //Estimation:// Is making reasonable predictions. It involves thoughtful connections to some prior knowledge.
 * //Number sense and Numeration:// Allows us to think and work with numbers easily. As we make sense of numbers we begin to understand the various ways they are used. It provides us with the ability of counting and understanding of the simple computation systems.
 * //Geometry and spatial sense// : This is where mathematics involves size, shape, position, space, direction along with movement. Geometry allows us to make sense of the physical world around us.
 * //Measurement// : Is finding relationships in the real world. What is tall, how much does an object weigh, and how long or far a distance is.
 * //Statistics and probability:// Making sense of graphs and charts along with analyzing data to interpret information and observe relationships.
 * //Fractions and Decimals// : Understanding parts of a whole and the relationships in between.
 * //Patterns and relationships:// Help us understand the structure of things around us. They help us build confidence and ability to know what will come next, even when we can't see it yet. Patterns and relationships are found everywhere and all around us. We find patterns in music rhythm, art displays, and design on clothing, along with other aspects of math such as counting and geometry. Understanding patterns and relationships means understanding rhythm and repetition as well as ordering, sorting, and categorizing.

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When students reach secondary schools, the math requirements and standards become much more complicated. Currently in Michigan, students are exposed to a much more rigorous curriculum than ever before, with the idea students need to be better prepared for college in math. Colleges are dictating to high schools that math matters. Students now need four credits in math with three of them being in Algebra 1, Geometry, and Algebra 2. Regardless of grade level, mathematics study remains correlated with the concepts of mathematical thinking.

<span style="color: #c00000; font-family: 'Arial','sans-serif'; font-size: 16pt; line-height: 115%;">**2. Mathematics teaching and TPACK**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">__**Mathematics Teaching and TPACK**__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">

Math is the science of patterns, and it involves observing, representing, and investigating patterns and relationships. Math is also a discipline that helped mankind build pyramids, navigate oceans, and send rockets into space. As math is evolving and technology is rapidly growing, there are a variety of pedagogical strategies available.

__**Content of Mathematics**__

In //Principles and standards for school mathematics// published by the National Council of Teachers of Mathematics (NCTM) in 2000, one strand of standards discussed is content standards. Content standards address the important aspects of mathematical content that should be learned and include numbers and operations, algebra, geometry, measurement, and data analysis/probability.

Technology has had a considerable impact on the content of math which involves observing, representing, and investigating patterns and relationships. Take for example, a fractal, which is a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry. Striving for accuracy in defining or measuring various things such as geographic features, plant growth, blood vessels, lightning, and, predicting flooding of rivers, fractal mathematics and computer technology can be very useful today. Using fractal algorithms that make allowances for such different scales, computers can provide a much more accurate and consistent measure of the above mentioned examples. Fractals are just one example of the many topics in math that have evolved due to technology.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Content Knowledge (CK)

 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Michigan Mathematics Grade Level Content Expectations K-8
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Michigan Curriculum Framework- High School Mathematics
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">[|Algebra 1]
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">[|Geometry]
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">[|Algebra 2]

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">__**Pedagogy of Mathematics**__

There are a variety of ways in in which teachers can teach math with technology. A math teacher needs to imagine technology connections, determine the related benefits, and put it all together. Students with different learning styles may become steadily linked to effective technology use, whether it is through online calculators, electronic geoboards, fractal or tessellation images, various websites, instructional videos, etc.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">
=<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Pedagogical Content Knowledge (PCK) = <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Teachers are no longer the only ones leading the class in which students are sitting and receiving the information. Students need to be more involved by interacting with the teacher in order to complete the lessons. The best way to do this by completing several activities related to the topic many of which can be enhanced by using technology. There are many technology resources a teacher can use to involve the students including; developing a wiki; completing a WebQuest; creating a podcast; searching various websites; etc.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Transforming Teacher Learning to Student Learning
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Outlook on teaching math


 * __ Technology of Mathematics __**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: left;">Handbook of Technological Pedagogical Content Knowledge (TPCK) for Educators points out the position statement made by NCTM saying, “Using the tools of technology to work within interesting problem contexts can facilitate a student’s achievement of a variety of higher-order learning outcomes, such as reflections, reasoning, problem posing, problem solving and decision making” (p.153).

Handbook of TPCK for Educators (2008) points out, in recent work of Heid (2005), several areas in mathematics education were identified that seemed to be the most promising in technology use for the mathematics classroom (p.154). These areas include: dynamic computation tools, or software that facilitates interactive computation; microworlds, which allowed focused experimentation of various mathematical relationships; intelligent tutors, which facilitate symbolic manipulation of algebraic symbols; handheld devices, which permit convenient technology access; web-based instruction, which allows systematic, cost-effective instruction; and interactive learning communities, that can facilitate educational collaboration in classrooms across many different states and even nations.

Other areas in math that have been affected by technology include: statistics; graphing; coordinate geometry; matrices; probability; and combinatorics. Just as technology is in a state of flux, these areas of mathematics are also in a state of change and evolution due to technology. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">__Michigan Department of Education: Educational Technology Standards and & Expectations__
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: left;">Technology Knowledge (TK) **
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Kindergarten - 2nd Grade
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Grades 3 - 5
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Grades 6 - 8
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Grades 9 - 12

<span style="color: #c00000; font-family: 'Arial','sans-serif'; font-size: 16pt; line-height: 115%;">**3. Qualities of a mathematics teacher with TPACK** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">1.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would have a relative openness to experimentation with the ever-evolving technological tools available to them in the classroom. Such teachers will try new technology-based lessons with their students, confident that students can learn something value each time they try something new. 2.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would strive to be consistently “on-task” for the mathematical topic. That means teachers with strong TPCK backgrounds are effective at focusing on the mathematics concepts while taking advantage of the instructional opportunities offered by technology. 3.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would strive to know where their students are conceptually, what they need to do to achieve the next step in an instructional process, and how they generally want their students to proceed through careful sequences of classroom interactions and tasks. 4.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would consistently offer explanations to their students on what they are doing with the technology, why a specific tool is appropriate for a particular mathematical situation, and how a selected technology fundamentally works. 5.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would use student assessment data, such as criterion-referenced tests. Such assessment data can help a teacher identify gaps in student understanding which might form the rationale for switching instructional strategies or taking a different pedagogical approach with some or all of the students. 6.<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> Would also do their best to be caring teachers who are comfortable and optimistic for change. Teachers with strong TPCK backgrounds should be caring instructional leaders that are welcoming to all students as they enter this changing and evolving world of mathematics. <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%;"> media type="youtube" key="mxja7cldKV0" height="364" width="445" align="center" = = <span style="color: #c00000; font-family: 'Arial','sans-serif'; font-size: 16pt; line-height: 115%;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 11pt; line-height: 115%;">As teachers, we need to remember our own experiences and frustrations as learners, as well as link prior knowledge with newly constructed knowledge. Teachers should be aware that students learn at different paste and try to use various ways in the class with the students when explaining a new lesson. <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 14pt; line-height: 115%;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 11pt; line-height: 115%;"> Teachers should consider these points we practice teaching. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">1. Not every student will be interested every minute. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">No matter how much experience you have<span style="font-family: 'Arial','sans-serif';"> or how great you are at teaching, you will encounter<span style="font-family: 'Arial','sans-serif';"> times in the classroom when no student is interested!<span style="font-family: 'Arial','sans-serif';"> The solution is to change your tone of voice, move<span style="font-family: 'Arial','sans-serif';"> around the room, or switch from lecturing to some<span style="font-family: 'Arial','sans-serif';"> other activity. Maybe you can even use a manipulative<span style="font-family: 'Arial','sans-serif';"> to increase the students’ understanding and,<span style="font-family: 'Arial','sans-serif';"> possibly, their level of interest.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">2.If a lesson is going badly, stop. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Even if you have planned a lesson and have a clear goal in mind, if your approach is not working—for whatever reason—stop! Regroup and start over with a different approach, or abandon your planned lesson entirely and go on to something else. At the end of the day, be honest with yourself as you examine what went wrong and make plans for the next day.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3. Teaching will get easier. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Maybe not tomorrow or even next week, but at some point in the year, your job will get easier! Try to remember your first day in the classroom. Were you nervous? Of course; all of us were. See how much better you are as a teacher already? By next year, you will be able to look back on today and be amazed at how much you have learned and how much easier so many aspects of teaching are!


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4. You do not have to volunteer for everything. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Do not feel that you always have to say yes each<span style="font-family: 'Arial','sans-serif';"> time you are asked to participate. Know your limits.<span style="font-family: 'Arial','sans-serif';"> Practice saying, “Thank you for thinking of me, but<span style="font-family: 'Arial','sans-serif';"> I do not have the time to do a good job with another<span style="font-family: 'Arial','sans-serif';"> task right now.” Of course, you must accept your<span style="font-family: 'Arial','sans-serif';"> responsibility as a professional and do your fair share,<span style="font-family: 'Arial','sans-serif';"> but remember to be realistic about your limits.<span style="font-family: 'Arial','sans-serif'; font-weight: normal;">


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5.Not every student or parent will love you. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">And you will not love every one of them, either! Those feelings are perfectly acceptable. We teachers are not hired to love students and their parents; our job is to teach students and, at times, their parents as well. Students do not need a friend who is your age; they need a facilitator, a guide, a role model for learning.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6.You cannot be creative in every lesson. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">In your career, you will be creative, but for those subjects that do not inspire you, you can turn to other resources for help. Textbooks, teaching guides, and professional organizations, such as NCTM, are designed to support you in generating well-developed lessons for use in the classroom. When you do feel creative and come up with an effective and enjoyable lesson, be sure to share your ideas with other teachers, both veterans and newcomers to the profession.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. No one can manage portfolios, projects, journals, creative writing, and student self-assessment all at the same time and stay sane! **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">The task of assessing all these assignments is totally<span style="font-family: 'Arial','sans-serif';"> unreasonable to expect of yourself as a beginning<span style="font-family: 'Arial','sans-serif';"> teacher. If you want to incorporate these types of<span style="font-family: 'Arial','sans-serif';"> exercises into your teaching, pick one for this year<span style="font-family: 'Arial','sans-serif';"> and make it a priority in your classroom. Then,<span style="font-family: 'Arial','sans-serif';"> next year or even the year after that, when you are<span style="font-family: 'Arial','sans-serif';"> comfortable with the one extra assignment you<span style="font-family: 'Arial','sans-serif';"> picked, you can incorporate another innovation into<span style="font-family: 'Arial','sans-serif';"> your teaching.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Some days you will cry, but the good news is, some days you will laugh! **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Learn to laugh with your<span style="font-family: 'Arial','sans-serif';"> students and at yourself!


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">9. You will make mistakes. **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">You cannot undo your mistakes, but berating yourself for them is counterproductive. If the mistake requires an apology, make it and move on. No one is keeping score.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">10.This is the best job on earth! **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Stand up straight! Hold your head high! Look people in the eye and proudly announce, “I am a teacher!”

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Reading the article, Professional Development of Mathematics Teachers in the Process of Informationalization by Yangong Yin was very effective. He mentioned that teaching of mathematics is interactive between teachers and students. The roll of a teacher changed, from a knowledge deliver to a teaching designer, from an individual who separated from other teachers to a member of teachers group, from a repeatedly laborer to a creator. This trend is a requirement for teachers to keep up with times, to improve the professional quality. To build the new idea of students first, a teacher must learn the new curriculum reform theory, improve the quality of teaching, possess valuable information and internet technology which can help him/her judge and choose the information on internet. As a qualified teacher, he/she should know how to learn form the others teachers’ successful plans and research independently, fulfill teaching preparation on net.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">NCTM’s Tips for Teachers
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Have an activities folder** that is categorized by subject and topic. On a fractured day, grab an activity from the folder. These are often game-like and reinforce the current topic. A math bee is a favorite activity.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Manipulatives and calculators should be visible** in the classroom and easy for students to access. Allow students to explore these materials when they have free time. When the time comes to use the items to learn about mathematics, the novelty will have worn off—students will be familiar with them and ready to use them to solve problems.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Let students choose the tools** they think will help them solve problems. By watching students select and use materials, you’ll get glimpses into their mathematical thinking, including their problem-solving abilities. Sometimes you’ll even learn new ways to consider a problem.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Survey materials you have on hand.** Look through mathematics catalogs. Make a wish list, and share it with school administration. Do not let your classroom go without pattern blocks, base-ten materials, and geoboards.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Learn to write [|grants]** to obtain materials for the classroom. Grants help you expand your professional development and can benefit you and your students.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Make it multisensory.** Mathematics instruction should stimulate all senses—touch, sight, hearing, smell, and taste. For example, when students use orange peels to demonstrate that the surface area of a sphere is four times the area of one great circle of the sphere, they will not forget the concept or the experience.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">**Use a “hands-off” approach.** Do not touch the hardware when demonstrating to your students how to use, for example, a spreadsheet or a graphing calculator. Instead, select a student who has limited experience using the technology that is to be demonstrated; have the student follow your directions while using a workstation that is projected to the entire class. You are then free to move about the room while giving directions and monitoring your students’ progress. This approach regulates the pace of the presentation, allowing students to keep up with the demonstration and focus on the topic.

=** 4. Math Teacher Education: Learn More, Do More, The TPACK Way **= The mathematics teacher with TPACK (Technology Pedagogy Content Knowledge) is a chess player. The constantly evolving trends during a chess game change the roles of the interdependent pieces; involving a persistent need to rework proficiency with the different pieces just as the mathematics teacher has to continually reason logically and progressively with current tools. If “TPACK is a way of thinking strategically while involving in planning, organizing, critiquing, and abstracting” (Niess. 2008:224) to fulfill teaching and learning needs with today’s technologies, the teacher makes preparations to face challenges, systematizes approaches, consistently does analysis or appraisals of situations, and condenses information by updates. Hence, for the mathematics teacher, to learn more is to do more. With TPACK, it is learning more and doing more with technology in a meaningful context.

Taking the cue from this standpoint, pre-service and in-service mathematics teachers have to be educated with the TPACK model regularly. Considering the importance of experiencing the progression of mathematical inquiry in assimilating technology with pedagogy and content, these programs are designed generally to include discussions of the latest issues in mathematics and technology, Internet browsing for navigational and research purposes, simple programming, exploring mathematical softwares, problem solving with technology, and even showcasing video vignettes. These set up are intended to accomplish investigative learning to foster ease and insight on the use of technology in mathematics; to exemplify the proper uses of reputable and new applications of technology within the mathematics context; to guide teachers in making practical but sensible determination as to the suitability of the technology in the teaching and learning of mathematics; and to give teachers the chance to acquire and expand their technological skills to improve the understanding of mathematics. Adhering to Grandgenett’s “successful mathematics teacher education program” (2008: 161-162), examples are drawn for each attribute in the following chart: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 15px;"> As mathematics dynamically transforms with the developments in technology, the mathematics teacher with TPACK incessantly strives to keep up with these changes. Strengthening these core values of TPACK, the National Technology Leadership Coalition ([|NTLC]), which umbrellas educational technology associations and teacher educator organizations in specific content areas; endeavors to concentrate technology knowledge (TK) with the pedagogy content knowledge (PCK) of the teacher educator organizations in a subject area by setting standards, endorsing TPACK practice, and advancing research on the judicious use of TPACK. Its mathematics wing is known as the Association of Mathematics Teacher Educators ([|AMTE]). <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"><span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">With teacher education programs emphasizing on the TPACK approach, the mathematics teacher becomes well-rounded, fully informed, adaptable, and effective. It just proves to say that to learn more is to do more with the TPACK way. __References:__ **B**lubaugh, W. L. (2009). A course for pre-service mathematics teachers that focuses on mathematics and the integration of technology. //Mathematics and Computer Education//, 43(1), 41-46. G**randgenett, N. (2008). Perhaps a matter of imagination: TPCK in mathematics education. //Handbook of Technological Content Pedagogical Knowledge (TPCK) for Educators//, New York: Routledge, 145-165.
 * B**ull, G., Bell, L., & Hammond, T. (2008). Advancing TPCK through collaborations across educational associations. //Handbook of Technological Content Pedagogical Knowledge (// // TPCK) for Educators //, New York: Routledge, 273-287.
 * E**lliott, R., Kazemi, E., Lesseig, K., Mumme, J., Carroll, C., & Kelley-Petersen, M. (2009). Conceptualizing the work of leading mathematical task in professional development. //Journal of Teacher Education//, 60(4), 364-379.
 * F**romboluti, C.S., & Rink, N. (1999). Early childhood where learning begins mathematics. US Department of Education, ** http://www.ed.gov/pubs/EarlyMath/title.html

<span style="color: #ff0000; font-family: arial,helvetica,sans-serif; font-size: 21px; line-height: 32px;">**5. Resources **
__** Types of Technology **__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"> The calculator is the most basic form of technology used within a math classroom. The two major calculators used are the scientific and graphing calculators. The scientific calculator is mostly used for basic operations, whereas the graphing calculator can be used for many things. There are many advantages and disadvantages to using these forms of technology in a class. Most of this depends on what stage of a students' development in math they are used. One advantage of calculator use is being able to focus more on the present concepts because a calculator will help speed along calculations that are not crucial to the learning of the new concept. With graphing calculators, a major advantage is a different way to visualize graphs. Students are able to change things about a graph or even graph more than one equation at once to help them visualize how graphs change. With a few of these advantages come many disadvantages as well. If students are using calculators at an early age in elementary school, they are at risk of not learning the content and relying on a calculator to do all the work for them. A calculator will never help a student understand the basic operations of addition, subtraction, multiplication and division. The other disadvantage of all calculators is students have a bad habit of thinking the calculator is always right when human error is always involved. [] [] []
 * Calculator**
 * Websites:**

The SMART Board <span style="font-family: 'Times New Roman',serif;"><span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">is a large whiteboard that uses touch technology for detecting user input (e.g. scrolling interaction) that are equivalent to normal PC input devices, such as mice or keyboards. A projector is used to display a computer's video output onto the whiteboard, which then acts as a huge touchscreen. The SMART Board usually comes with 4 digital writing utensils that use digital ink replacing the traditional whiteboard markers. The digital ink works by using an active digitizer that controls the PC input information for writing capabilities such as drawing or handwriting. You are able to use the SMART Board tools that are included when installing the software. Such tools include simulators, graph paper, tables, geometric shapes, videos, podcasts, PowerPoint presentations, and/or interactive function tools. Using a SMART Board you could record your self and the lesson you are presenting (works like a screen capturing device), and save your notes for students that were absent. This interactive board has many applications with literally no downfall. It could be used with all students, at any level; it helps students with special needs but also helps deepen the knowledge for the other students. With the help of the SMART Board the students would be more engaged and interactive in participating in the class discussion and practice. Reference: [|Wikipedia] media type="youtube" key="rCILbQGRDtQ" height="344" width="425" align="center"
 * SMART Board**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: center;">Jason Stone - Instructional Designer - VIDEO 1 media type="youtube" key="cb-iYBEuyzU" height="344" width="425" align="center"

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: center;">Jason Stone - Instructional Designer - VIDEO 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Internet ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">The Internet is a global system of interconnected [|computer networks] that use the standardized [|Internet Protocol Suite] (TCP/IP) to serve billions of users worldwide. It is a <span style="font-family: Times New Roman,serif;">//network of networks// that consists of millions of private and public, academic, business, and government networks of local to global scope that are linked by [|copper] wires, [|fiber-optic] cables, [|wireless] connections, and other technologies. The Internet carries a vast array of [|information] resources and services, most notably the inter-linked [|hypertext] documents of the [|World Wide Web] (WWW) and the infrastructure to support [|electronic mail]. In addition it supports popular services such as [|online chat], [|file transfer] and [|file sharing], [|gaming], [|commerce], [|social networking], [|publishing], [|video on demand], and [|teleconferencing] and [|telecommunications]. [|Voice over Internet Protocol]<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"> (VoIP) applications allow person-to-person communication via voice and video. The Internet offers teachers and students a wide variety of tools that could be used in a classroom to enhance students' learning and engagement in the class. A teacher would create their own webpage or blog page that could help the students keep up with the homework, ask questions when in difficulty and/or get help using the websites available on the teacher's website. I have posted a few interactive webpages below to give you an idea of where you could use TPACK in your classroom. http://fun-math.wikispaces.com [|http://mcioban.blogspot.com] [|Ms. Cioban's Blog] [|Khan Academy] References: [|Wikipedia] **
 * Websites:**
 * Blogs:**
 * Videos:**
 * Podcasts:

<span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 22px; text-align: left;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">A video camera <span style="font-family: Helvetica,sans-serif;">is a <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;">[|camera] used for electronic [|motion picture]<span style="font-family: Helvetica,sans-serif; font-size: 11pt; font-weight: normal;"> acquisition, initially developed by the television <span style="font-family: Helvetica,sans-serif; font-size: 11pt; font-weight: normal;">industry <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">but now common in other applications as well. There are different types of cameras that teachers could use in their classrooms: digital cameras and/or webcams. The digital camera could be used in a classroom when the teacher has a project for the students to present their findings/conclusions/work. The webcam is mostly used to communicate with others around the world about mathematics and that presents a great opportunity for students to learn other methods of solving problems or other experiences (successes and difficulties) regarding the concept taught. <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 10px; font-weight: normal; text-align: left;"> References: [|Wikipedia] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Microsoft Office** Microsoft Office is a collections of programs of interrelated desktop applications. It included Word, Excel, Powerpoint, Outlook and Access. These programs have a great benefit for both teachers and students when it comes to teaching and learning mathematics. They could be used at any level with students but it depends a lot on the teacher the level of knowledge the students needs to reach at that particular moment. In mathematics we mostly use Excel and Powerpoint to enhance our lessons. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Excel:** [|Microsoft Excel] is a [|spreadsheet]<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">program. This program could be used in a classroom setting when talking about tables of value, box and whisker plots and/or stem and leaf problems. Easy calculations could be done is such a program especially mean, median and mode plus many formulas that the students have concluded in a lesson. [|Microsoft PowerPoint] is a popular [|presentation program] for Windows and Mac. It is used to create [|slideshows], composed of text, graphics, movies and other objects, which can be displayed on-screen and navigated through by the presenter or printed out on [|transparencies] or [|slides]. This is convenient for [|school] or work presentations. PowerPoint is widely used by business people, educators, students, and trainers and among the most prevalent forms of [|persuasive technology]. New concepts could be taught using a Powerpoint presentation to captivate the students' attention and enhance the lesson using tools this program offers. [|Wikipedia] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Google Earth** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: left;">Google Earth is a [|virtual globe], [|map] and [|geographic] information program. It displays satellite images of varying resolution of the Earth's surface, allowing users to visually see things like cities and houses looking perpendicularly down or at an [|oblique] angle, with [|perspective] (see also [|bird's eye view]). This tool could be use more into elementary and middle school level even though if well planned it would help students in geometry classes understand perpendicular and oblique angles but also their meaning and how they are used in a real life situation. TI-Navigator ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">The TI-Navigator system creates a powerful connection between students and educator wirelessly networking each student’s graphing calculator to the classroom computer. A growing body of research* shows that effective use of the TI-Navigator system and graphing calculators improves student engagement, understanding and performance. Educators can: <span style="display: block; font-family: 'Times New Roman',serif; text-align: left;">**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">TI-Navigator system's integrated approach is based on: ** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 14px; text-align: left;">[|**Instruction**] that becomes more dynamic, intimate and intuitive in a more connected and collaborative classroom [|**Assessment**] of student comprehension that can be performed at any point to monitor progress and instantly adjust instruction [|**Content**] that is standards-based, fast and easy to deliver, and designed to promote an engaging, interactive classroom <span style="font-family: 'Times New Roman',serif;">[|Texas Instruments] ELMO ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">The ELMO is a device that projects items onto a screen in front of the class very similar to an overhead projector. The difference is it acts like a camera to give clear picture on the screen so you can use a variety of writing tools instead of only using a smearable dry erase pen. This technology can be used effectively in a collaborative learning environment because you can use it to display student work and even have students contribute to the teaching of a class. Another use of this tool is the ability to take pictures of specific work to save for showing at a later time. This helps if you are trying to cut down on the amount of paperwork you want to save for future use or even can come in handy if you are interested in saving a students' work for future display. **View Demo: [|ELMO Demo]** = = = = = = =<span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit design lesson plans (TPACK) =
 * Video cameras**<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;">
 * Powerpoint:**
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 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"><span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Track the progress** of individual students or the class in real time
 * <span style="display: block; font-family: 'Times New Roman',serif; text-align: left;">**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">View student ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"> coursework, check problem solving techniques and guide performance<span style="font-family: 'Times New Roman',Times,serif;">
 * <span style="display: block; font-family: 'Times New Roman',serif; text-align: left;">**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Use instant feedback ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;"> to create a dynamic learning environment proven by research* to increase student success
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Understanding Multiplication

Solving equations





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