Teaching With Technology Modified From FL PROMiSE Module

 BOK (Bodies of Knowledge): Trigonometric Functions – Standard 1 ◦ Students extend the definitions of the trigonometric functions beyond right triangles using the unit circle and they measure angles in radians as well as degrees. They draw and analyze graphs of trigonometric functions (including finding period, amplitude, and phase shift) and use them to solve word problems. They define and graph inverse trigonometric functions and determine values of both trigonometric and inverse trigonometric functions  Benchmark MA912.R.1.6: ◦ Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology.

Exploration using the Graphing Calculator

y = a sin b(x + c) + d

Without using a graphing utility, describe the following graphs as they relate to y = sin(x).

Suppose graphing calculators are not available, what are other ways we could teach this lesson utilizing technology?

Exploration using an Online Applet Teacher directed/whole class

abhk y = a sin b(x + c) + d

 What is the role of the teacher and students?  Did the lesson keep you “actively” engaged? Why?  What are advantages/disadvantages for each? ◦ Graphing Calculator ◦ PPP  What considerations must teachers make if they would like to use graphing calculators?  How could PowerPoint help teachers and students manage make-up work?

Visual Representation of Mathematical Ideas  Example: National Library of Virtual Manipulatives

Modeling multiplication of algebraic expressions

NCTM Illuminations   Activities & Lessons  Available Free of Charge

 Multiple Examples  Students Make & Test Conjectures

Using the Graphing Calculator  Texas Instruments Texas Instruments ◦ Activity Center Activity Center

 GeoGebra GeoGebra ◦ A freeware version  The Geometer’s Sketchpad & Cabri Geometry The Geometer’s SketchpadCabri Geometry ◦ Dynamic construction & demonstration tools  Fathom Fathom ◦ Software to help students learn about data  Maple & Mathematica MapleMathematica ◦ Both are very powerful Computer Algebra Systems ◦ Both have activities/demonstrations appropriate for high school courses  Florida Center for Instructional Technology Florida Center for Instructional Technology ◦ Wealth of Resources for teachers (Lit2Go, Clipart, FCAT lessons)

Equation Editor (as part of Word or PPP)  Allows you to Express Mathematics accurately as part of Presentation or Worksheets  Without EE With EE _____ \| x – 3 = x + 5

WinPlot and TI-Screen Capture (as part of Word or PPP) Allows you to Express Mathematical representation as part of Presentations or Worksheets Screen Capture of TI CalculatorGraph created using WinPlot

Test Generating Software  Every textbook publisher offers one  Others commercially available as well  Generate multiple versions of same test easily

Online access to mathematics resources  Tutoring (e.g., Dr. Math) Mathematics Dictionaries with examples FCAT Explorer

Textbook Websites  Usually have practice tests and/or quizzes  Also have other resources tied directly to the text.  Florida’s adopted Algebra 1 texts  Glencoe Glencoe  Holt, Rhinehart, & Winston Holt, Rhinehart, & Winston  Key Curriculum Press Key Curriculum Press  McDougal Littell McDougal Littell  Prentice Hall Prentice Hall

 Is it important to use technology to teach mathematics? Why or why not?  What are appropriate uses of technology? Inappropriate uses?  What should you consider when deciding to use technology or not?

Technology is an essential tool for learning mathematics in the 21st century, and all schools must ensure that all their students have access to technology. Effective teachers maximize the potential of technology to develop students’ understanding, stimulate their interest, and increase their proficiency in mathematics. When technology is used strategically, it can provide access to mathematics for all students. Full position statement

Teacher productivity  Producing Mathematically accurate representations  Keeping and recording class information Student Supports  Example: Ask Dr. Math  Textbook Websites

 Allows the visualization of concepts difficult to show otherwise.  Allows the examination of multiple examples with ease.  Allows a focus on concepts rather than calculations  Allows access to real-time data to make mathematics relevant to students. ◦ (e.g., use of real world examples such as orange production in Florida for analysis).  Allows student to make and test conjectures. ◦ What happens when …  Promotes student independence in mathematical problem-solving.  Reinforces mathematics learning.

An online Curriculum Planning Tool  Access will be through the Florida Standards DatabaseFlorida Standards Database

The CPT will:  Increase access for all teachers to high quality information and resources aligned with the standards.  Support the delivery of teacher professional development.  Support teacher application of new content and pedagogical knowledge in the classroom.

The CPT will include the following:  Searchable database of standards and benchmarks  Levels of cognitive complexity for each benchmark  Mathematics and Science Course Descriptions  Course builder tool for districts  Electronic course approval system  Online PD on the use of course descriptions

It will be launched during school year.

We’ve only touched the surface of what’s available. Don’t be afraid to learn from your student.  It is better than struggling and failing or avoiding it altogether. Just like any tool, technology only helps when used correctly/appropriately.