TPCK+in+Math

=TPCK in Math=

Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment (NCTM, 2000, p.3).

**Preparing Teachers To Use Technology To Enhance The Learning Of Mathematics** **A Position of the Association of Mathematics Teacher Educators** The Association of Mathematics Teacher Educators (AMTE) supports the National Council of Teachers of Mathematics’ (NCTM) Technology Principle: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” Mathematics teacher preparation programs must ensure that all mathematics teachers and teacher candidates have opportunities to acquire the knowledge and experiences needed to incorporate technology in the context of teaching and learning mathematics.

**What is meant by the use of technology in the context of teaching and learning mathematics?** Technology in this context includes computers with appropriate mathematical software, Internet and other digital resources, handheld computing tools and their extensions, and future and emerging forms of similar devices and applications. Technology can be used in a variety of ways to improve and enhance the teaching and learning of mathematics. It can be used to facilitate mathematical discovery, understanding, and connections that may be difficult or impossible without its use. The computational and graphical capabilities of current technologies enable users to efficiently generate and manipulate a variety of representations of mathematical ideas and processes. Activities that engage students in connecting multiple representations (e.g., graphical, numerical, algebraic and verbal), and those that invite students to analyze or create images, visualizations, and simulations provide wide-ranging opportunities for mathematical exploration and sense- making. Instruction that takes full advantage of what technology has to offer can encourage, foster, and support students’ construction of mathematical knowledge in a variety of ways. Technology can also improve mathematical communication, facilitate more efficient use of mathematical resources, and raise the quality of mathematical products and presentations.

**What is AMTE’s position on the preparation of mathematics teachers to teach with technology?** AMTE recognizes that technology has become an essential tool for doing mathematics in today’s world, and thus that it is essential for the teaching and learning of mathematics. For mathematics teacher candidates to be able to implement appropriate uses of technology in the teaching of K-12 mathematics they should have: By the completion of their preparation, new mathematics teacher candidates should be able to: o demonstrate flexibility with high-quality and creative instructional techniques, both with and without technology, to help students explore and learn mathematics, develop mathematical thinking and communication abilities, and solve complex real-world problems, to understand, by reflecting on how technology affords and constrains student actions and thoughts, when and how use of technology can advance learning and critical thinking, and when it can hinder the mathematical development; to efficiently troubleshoot technology difficulties in both student and teacher use; and o incorporate a variety of assessment techniques, including the use of technology to evaluate students’ understanding of important mathematical concepts.
 * a deep, flexible, and connected conceptual understanding of K-12 mathematics that acknowledges the impact of technology on what content should be taught;
 * a research-based understanding of how students learn mathematics and the impact technology can have on learning;
 * a strong pedagogical knowledge base related to the effective use of technology to improve mathematics teaching and learning; and
 * appropriate experiences during their teacher preparation program in the use of a variety of technological tools to enhance their own learning of mathematics and the mathematical learning of others.

With the needs of future teachers of mathematics in mind, mathematics teacher educators should provide opportunities for teacher candidates to strengthen their knowledge of how to incorporate technology to facilitate student learning of mathematics through experiences that:
 * allow teacher candidates to explore and learn mathematics using technology in ways that build confidence and understanding of the technology and mathematics;
 * model appropriate uses of a variety of established and new applications of technology as tools to develop a deep understanding of mathematics in varied contexts;
 * help teacher candidates make informed decisions about appropriate and effective uses of technology in the teaching and learning of mathematics; and to provide opportunities for teacher candidates to develop and practice teaching lessons that take advantage of the ability of technology to enrich and enhance the learning of mathematics.

If technology is used to improve the learning of mathematics at all levels, students will be better prepared to use technology appropriately, fluently, and efficiently to do mathematics in the techno-rich environments in which they will study and work in the future. (January 2006) [|Association of Mathematics Teacher Educators] www.amte.net

**ATIP and Math** The data suggests TPCK give consideration to students by “engaging in good teaching” (p., 47) or attribute-treatment interaction pedagogy (ATIP). In doing so, teachers’ recognize the strengths and values of all of their students and devise strategies to assure all are successful. In the case of math, the following link is to an assessment tool that may aid in ATIP because it provides an analysis of students' learning styles specific to the subject:

http://www.metamath.com/lsweb/dvclearn.htm.

When paired with observation and engagement, the tool can enhance teachers’ attention to individual preferred learning styles of their students. media type="youtube" key="cX0teReijUk?fs=1" height="385" width="480" After viewing this brief learning styles video, you may choose to take the VARK questionnnaire to better gauge how your learning style affects your pedagogical beliefs about student learning styles

Linking Math to the Real World and applying TPCK

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The following quote is from William Duncan, a 21 year old who responded to the TED video on comments from teachers who believe the way to teach math is by continuing the practice of rote memory, especially when it comes to learning multiplication tables. ======

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" Math is not about calculation but rather problem modeling and solving. I'm widely considered by my peers to be mathematically gifted and I had a terrible time with multiplication tables. Not because I couldn't understand them but because I didn't see the point. After having the basic understanding of how multiplication and division work all calculations fall out of that knowledge given a little extra time or strategically placed transistors. Her students aren't incapable of division because they haven't memorized their tables, they're incapable of doing the calculations because no major emphasis was but on the concepts of division and multiplication, only on the insufferably boring practice of memorizing a group of calculations in base 10. " We need to focus on what is relevant instruction and its application to real life skills.media type="custom" key="7606509" ======

**Resource sites for connecting real life problems with math**:

1) Escape from Knab, a simulation sponsored by Firstar for grades 7-12, provides monthly online lessons for teaching students how deal with real-life financial decisions. The simulation takes participants through a series of financial decision- making experiences in the entertaining setting of the fictitious planet, Knab, where visitors discover the results of their TPCK in Mathactions and decisions. http://www.escapefromknab.com/educational.html

2) Exploring Data, from the Math Forum's Urban Systematic Initiative Workshops for K-12 teachers, provides a collection of lesson plans for collecting, analyzing, and displaying data. The lessons are organized by grade level as follows: [|K-4.], [|5-8], and [|9-12]. http://mathforum.org/workshops/usi/dataproject/

3) No Strings Attached-Wireless Laptops in Education This website features exemplary models of technology integration across Florida. Lessons are provided with videos. http://etc.usf.edu/plans/default.htm

4) The matrix illustrates how teachers can use technology to enhance learning. The five interdependent characteristics of meaningful learning environments are matched with the five levels of technology integration, making 25 cells. The lessons include detailed plans and videos of teachers implementing the lesson in a real classroom []

Preparing math teachers to use TPCK:
// Questions to ask yourself when using [|technology to teach mathematics]topics: //

What are your attitudes and beliefs about teaching mathematics with technology?

What technologies are adequate tools for learning and teaching mathematics?

Does this technology engage, excite, and enhance the learning of a diverse set of students?

How will these technologies be used to support teaching and learning?

What are the barriers and problems with using these types of technologies?

Will my students truly benefit from using this type of technology with this lesson?

** The video below demonstrates: Teaching Math with Innovative Technology **
media type="youtube" key="nlY-hafkOwM?fs=1" height="385" width="480"

**Math lessons that integrate technology:**
 * ==== **[|Wild Life Sampling -7th Grade]** ====
 * ** [|Order of Operations -7th Grade] **
 * ===**[|My Favorite Mathematician - 7th Grade]**===
 * ===**[|Solving Linear Equations - Review Game]**===
 * ===**[|Right Triangle Geometry]**===
 * ===**[|Understanding Probability - 6-8 Grade]**===

Websites that support technology integration in math:
[|//http://www.education.com/reference/article/integration-strategies-mathematics///] [|http://www.cited.org/index.aspx?page_id=116] [|http://www.powayusd.com/projects/EdTechcentral/TechForMath.htm] [|http://jc-schools.net/tutorials/ms/math.htm] [|http://www.freetech4teachers.com/]