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Integrating CAS

Integrating CAS. casmusings.wordpress.com Chris Harrow Atlanta, GA casmusings@gmail.com. 1. Why CAS?. Levels the playing field/scaffolding; you focus on how to ask good questions and interpret the answers. Keeps the focus on student THINKING

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Integrating CAS

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  1. Integrating CAS • casmusings.wordpress.com • Chris Harrow • Atlanta, GA • casmusings@gmail.com 1

  2. Why CAS? • Levels the playing field/scaffolding; you focus on how to ask good questions and interpret the answers. • Keeps the focus on student THINKING • Has forced me to rethink assessment – what is my goal for each question? • Output form is sometimes unpredictable. Lesson = just because an answer LOOKS different doesn’t mean it IS different. • Teacher isn’t the sole expert – instant/pressure-free confirmation & sometimes new math is motivated. 2

  3. In my classes • All students own a TI-Nspire CAS & many bring a laptop • Implication = Full-time CAS access & free computer software. • Encourage use of Nspire CAS, Wolfram Alpha, & Geogebra • CAS is assumed, but isn’t the focus • It’s about asking good questions in 3 languages: English, Math, & CAS • Split assessments 3

  4. Sources • PreCalculus Transformed • http://bit.ly/ypCgft • Precalculus with Trigonometry, 3rd ed, Foerster, (TE & Instructor’s Resources) • http://bit.ly/yjplJP • http://casmusings.wordpress.com 4

  5. Quadratics • In Foerster Instructor’s Resource Book (CAS Activity 1-3a) plus extensions • TI Nspire CAS file: Quadratics • Form is no longer a boundary. • Vertex, intercept, standard form are all equally accessible (plus others) • CAS Lesson: Different forms tell different stories about the underlying function/data. • CAS makes most forms equally accessible. 5

  6. Quadratics II • In PreCalculus Transformed • TI Nspire CAS file: QuadSurprises • Unexpected formatting sometimes leads to additional math • What do each of the coefficients of a standard form quadratic equation do to the corresponding graph? 6

  7. Quadratics III • Evolved from a student’s exploration that was published in the Mathematics Teacher • TI Nspire CAS file: QuadSurprises • What pattern emerges when you compute the areas of quadratic sectors of equal width? 7

  8. Probability • From http://casmusings.wordpress.com/ • TI Nspire CAS file: Probability • Find the probability of exactly 3 heads in 10 tosses of a coin. • Proportions of colors when P(same color) = P(different colors) 8

  9. Linear Regressions • In Foerster Instructor’s Resource Book (CAS Activities 3-2a & 3-2b) • TI Nspire CAS file: LinReg • What does a linear regression do? • This is 100% understandable by any algebra student. 9

  10. Straightening Data • In Foerster Instructor’s Resource Book (CAS Activities 3-4a) • TI Nspire CAS file: Straightening • What do Power & other Regressions really do? 10

  11. Graphing in Cartesian & Polar • New Idea we’re planning to incorporate into the next edition of PreCalculus Transformed. • TI Nspire CAS file: CeilingsFloors • Trig function centers, ceilings, & floors • Polar function centers, ceilings, & floors 11

  12. Transformations II • Trig identities via the SQ transformation 12

  13. Misc • Number of zeros in 200! ? • One term of (Ax+By)^n is 27869184x^5y^3 . Define A, B, & n. 13

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