Second Innovative Practices in Developmental Mathematics (IPDM)

1. Second Innovative Practices in Developmental Mathematics (IPDM) Why Graphing Calculators Should be Used in Algebra Classes March 31, 2017 Salvatore Sommella, Adjunct Lecturer ssommella@lagcc.cuny.edu

2. Why Graphing Calculators Should be Used in Algebra Classes • Objective/Aims • Give students opportunities to explore more comprehensive problems • Give students the chance to determine when to use “mental math” vs. electronic devices La Guardia Community College

3. Why Graphing Calculators Should be Used in Algebra Classes • Myths and Fears About Using Electronic Devices (Calculators) • If Individuals use calculators, they won’t learn the “Basics” • Calculators make students lazy • Students should learn the “Real Way” before using calculators • Students will become overly dependent on calculators La Guardia Community College

4. Why Graphing Calculators Should be Used in Algebra Classes • Benefits of Calculator Use • Can be used to develop concepts • Can be used for drill • Enhance problem solving • Help improve student attitudes • Save time • Commonly used in society La Guardia Community College

5. Why Graphing Calculators Should be Used in Algebra Classes • FYI • Graphing calculators used extensively for NYS high school regents exams • 9th grade integrated algebra • 10th grade geometry • 11th grade algebra 2/trigonometry • High school students are very familiar using the graphing calculator • One can use a graphing calculator to do some differentiation and integration • The Ti-84 is a handheld computer with extensive features La Guardia Community College

6. Why Graphing Calculators Should be Used in Algebra Classes • Some Arguments in Favor of Calculator Access • Availability of calculators does not detract from the development of basic skills. • Many excellent explorations in a problem-solving environment is enhanced by using calculators • Not using calculators promotes the belief that they are not common tools • Students must learn when to use calculators – tedious computations – and when to use mental math La Guardia Community College

7. Why Graphing Calculators Should be Used in Algebra Classes • What Graphing Calculators Offer • Permits compound expressions to be shown completely before being evaluated • Functions can be inserted into a list of table and stored directly • Variables can be used in expressions then assigned different values • Distinction between “negative” and “minus” is clear and useful • Points can be plotted either by entering them or moving the cursor to a particular coordinate on the screen La Guardia Community College

8. Why Graphing Calculators Should be Used in Algebra Classes • What Graphing Calculators Offer (# 2 cont’d) • Very large and very small numbers can be managed effectively • Built-in statistical functions allow for large sets of data without a computer • Graphs – box-and-whisker, histograms, pie charts, bar graphs are available • Random number generators allow for simulation of variety of probability experiments • Scatter plots for ordered pairs can be entered, plotted and examined for trends La Guardia Community College

9. Why Graphing Calculators Should be Used in Algebra Classes • What Graphing Calculators Offer (# 3 cont’d) • Functions can be explored in 3 modes – equation, table and graph. Easy to switch • Is programmable • Data, programs and functions can be shared between calculators. • Has the potential to significantly open up real mathematics for students La Guardia Community College

10. Why Graphing Calculators Should be Used in Algebra Classes • Mental math problem from Polya’s Stanford mathematics problem book • Among grandfather’s papers a bill was found • 72 turkeys $__67.9__ • The first and last digit of the number that presented the total price are replaced by blanks because they are illegible • What are the two faded digits and what was the price of one turkey? • Problem cannot be solved using a graphing calculator. A true mental math problem. La Guardia Community College

11. Why Graphing Calculators Should be Used in Algebra Classes • Hint from Polya Stanford mathematics problem book • Could you restate the problem? • What can the two faded digits be if the total price, expressed in cents, is divisible by 72? Note: divisibility rules taught as part of Math95. • Solution • If divisible by 72 then divisible by 8 and by 9. • 79__ must be divisible by 8 so 1000 is divisible then 79__ is 792. • If __792 is divisible by 9 then the sum of the digits must be divisible by 9. Therefore the 1st digit must be 3. $367.79 divided by 72 equals $5.11 La Guardia Community College

12. Why Graphing Calculators Should be Used in Algebra Classes La Guardia Community College

13. Why Graphing Calculators Should be Used in Algebra Classes • Extending systems of linear equations • Two equations, two unknowns • 5x = 4y +6; -3x +7y =1 • Using either addition or substitution method the solution set is [(2,1)] • The methods presented for 2 equations/2 unknowns becomes difficult when increasing number of equations and unknowns. Other techniques are necessary to solve this more tedious computation. Here learning how to recognize when and how to use the graphing calculator would help a student. • Real-world problems are generally more than 2 equations and 2 unknowns. La Guardia Community College

14. Why Graphing Calculators Should be Used in Algebra Classes • Simulation Probability Simulator (TI-84 Plus) • Toss Coins • Roll Dice • Pick Marbles • Spin spinner • Draw cards • Random number La Guardia Community College

15. Why Graphing Calculators Should be Used in Algebra Classes • Conclusion: using technology with mathematics (graphing calculators) • Enhances problem solving and depth of problems • Prepares students to tackle real-world problems • Strengthens quantitative modeling skills • Gives students opportunities to determine when to use mental math vs. use of technology for tedious computations La Guardia Community College

16. Why Graphing Calculators Should be Used in Algebra Classesat LaGuardia Community College? Thank You Salvatore Sommella