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

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. $ 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. Thank You Salvatore Sommella
Why Graphing Calculators Should be Used in Algebra Classes at LaGuardia Community College?
Thank You
Salvatore Sommella