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Graphing Calculators & Student Learning. Amy DeYoung planet/adeyoung. Arguments Against Calculators. “Takes away from teaching time” – Laughbaum “Undermine mathematics learning” – Choi-Koh Generally in algebra, etc. Specifically, computational skills
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Graphing Calculators&Student Learning Amy DeYoung planet/adeyoung
Arguments Against Calculators • “Takes away from teaching time” – Laughbaum • “Undermine mathematics learning” – Choi-Koh • Generally in algebra, etc. • Specifically, computational skills • Cause confusion because of scaling and dimensions – Choi-Koh
Common Abilities Displays graphs of functions Table of Values Regression Models Parametric and Polar graphing Unique Abilities Color screen Source: http://www.casioeducation.com Calculators: CasioCFX-9850GC Plus
Common Abilities Displays graphs of functions Table of Values Regression Models Parametric and Polar graphing Unique Abilities Pen-Touch Operation Source: http://www.sharp-world.com/ Calculators: SharpEL-9650
Common Abilities Displays graphs of functions Table of Values Regression Models Parametric and Polar graphing Unique Abilities Built in infrared two way port for communicating with other HP 39g+ Calculators: Hewlett PackardHP 39g+ Source: http://www.hp.com/calculators/ graphing/index.html
Common Abilities Displays graphs of functions Table of Values Regression Models Parametric and Polar graphing Unique Abilities Data collection devices Calculators: Texas InstrumentsTI-83/84 Series Source: http://education.ti.com/
The ACT and Calculators Prohibited calculators include all calculators in all of the following series: • Casio CFX-9970G (including, for example, CFX-9970GE) • Casio Algebra fx 2.0 • Hewlett-Packard HP-40G • Hewlett-Packard HP-49G • Texas Instruments TI-89 • Texas Instruments TI-92 (including, for example, TI-92 Plus) • Calculators in the Hewlett-Packard HP-38G series and HP-48G series may be used only if the infrared communications port is covered with heavy opaque material such as duct tape or electrician's tape. • The Sharp EL-9600 is permitted for use, because it is not considered a pen-input device. You may bring the stylus that comes with the calculator • Source: http://www.act.org/caap/sample/calc.html
General Benefits of Calculators • Students can check results –Vasquez • By substituting results into equation and evaluating with calculator • By using graphical tools (observe solutions to a quadratic in its graph: x-intercepts) • Opportunity for students to practice math communication skills – Vasquez
Specific Benefits of Calculators • The use of calculators allows exploration-based learning– Choi-Koh • Scientific/organized approach to learning • Invetigate, conjecture, and verify findings • Calculators motivate student curiosity – Choi-Koh
Example of Exploration-Based Learning y=x2 y=5x2 y=2x2
Example of Exploration-Based Learning y=x2 y=(1/5)x2 y=(1/2)x2
Specific Benefits of Calculators • Calculators allow students to make observations at ease – Choi-Koh • Calculators have an element of accuracy and speed – Choi-Koh • Students do not need to focus on difficult computations and can focus on the “whole picture” – Bethell • Particularly helpful to students with disabilities – Bethell
Specific Benefits of Calculators • Using calculators to teach helps students to understand the meanings of math concepts – Choi-Koh • Understand the why • Also, helps students to make logical connections from one topic to another topic – Davis • In math (the effects of a coefficient on a linear graph to the effects on a parabola) and in real life (physics and speed)
Specific Benefits of Calculators • Using calculators encourages students to: • Take control of their learning • Work independently (without the teacher) • Students use the calculator to explore and learn for themselves • Choi-Koh & Bethell
Specific Benefits of Calculators • Proper use of calculators in the classroom should effect the level of thinking • Students should move from “Knowledge” (recollection of facts) on Bloom’s Taxonomy to at least “Synthesis” (by creating formulas, etc) and possibly even “Evaluation” • Choi-Koh • Example: Synthesis – Creating equations that correspond to graphs
Text References • Choi-Koh, Sang Sook. (2003). Effect of a graphing calculator on a 10th-grade student’s study of trigonometry. The Journal of Educational Research, v.96 no6, Retrieved July, 24, 2006, from http://newfirstsearch.oclc.org/. • Bethell, Sandra Callis. (1998). From an E to an A in first-year algebra with the help of a graphing calculator. Mathematics Teacher, v. 91, Retrieved July 24, 2006, from http://newfirstsearch.oclc.org/. • Vasquez, Selina. (2003). Developmental mathematics students: Investigating calculator keystroke choices to learn mathematics rules and concepts. Mathematics and Computer Education, v. 37 no3, Retrieved July 20, 2006, from http://newfirstsearch.oclc.org/. • Davis, Sarah Jeanne Hollister. (1997). How mastering technology can transform math class. Educational Leader, v. 55, Retrieved July 20, 2006, from http://newfirstsearch.oclc.org/. • Laughbaum, Edward D. (2003). Hand-held graphing technology in the developmental algebra curriculum. Mathematics and Computer Education, v. 37 no3, Retrieved July 20, 2006 from http://newfirstsearch.oclc.org/.
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