Not just mathematics, but mathematics problem solving!

Not just mathematics, but mathematics problem solving!

Dr. Cristal JonesForum 2011 New YorkOctober 27, 2011cristaljones34@comcast.net

Not just mathematics….

• I am not a mathematics teacher…

• But a mathematics problem-solving teacher...

• Through teaching computer science content….

Do Now (Sponge Activity)

Solve:

13 + 8 / 2 + (7 + 16) =

* = Multiplication

/ = Division

Jot down how long it took to solve the problem. One minute? Longer?

Background

• New York Native

• Single parent home

• Attended P.S. 5, P.S. 233 in Brooklyn; Brian Piccolo I.S. 53; Far Rockaway High School and Baruch College

Background

• Moved to Atlanta, Georgia

• Taught computer science to African-American and Hispanic middle and high school students in face-to-face and online environments for 15 years

• Received Doctorate in Education at Georgia Southern University

Background

• I taught programming languages such as DOS , Q-BASIC (Quick Basic), Visual Basic, C++, HTML, XHTML, JavaScript and Java.

• Students can learn programming languages as early as third grade (Wiebe, 1991)

The Present of Education

Do Now:

Solve: A circle has a radius of 7 inches. Find the circumference of the circle.

Ask yourself: Describe your initial reaction to solving the problem. Write down your answer. How long did it take you to solve the problem?

The Future of Education

• We can identify the non-verbal and verbal behaviors of solving mathematics problems through metacognitive processes.

• Metacognitive framework handout (excerpt)

• A mixed-method research study was conducted to code metacognitive processes when solving precalculus and computer science problems.

The Future of Education

Polya’s 4 steps of problem solving

Understanding the problem

Devising a plan

Carrying out the plan

Looking Back

Broad categories of problem-solving

Orientation

Organization

Implementation

Verification

The Present of Education

• How do we build not just mathematics, but mathematical problem-solving activity for students to: – Understanding advanced content

– maintain interest in STEM careers?

• By building conceptual thinking

• By developing metacognitive ability.

• By engaging in problem-solving ability.

The Future of Education

• Teaching object-oriented programming concepts builds conceptual thinking and metacognitive thinking needed to gain mathematical problem-solving ability (Jones, 2010)

The Future of Education

The National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (CESSM) termed how the mathematical problem solving should be the focus of a mathematics activity for the student:

The Future of Education

To develop such [problem-solving] abilities, students need to work on problems that may take hours, days, and even weeks to solve. Although some may be relatively simple exercises to be accomplished independently, others should involve small groups or an entire class working cooperatively. Some problems also should be open-ended with no right answer, and others need to be formulated (National Council of Teachers of Mathematics, 1989, p.1).

Object-Oriented Programming

Classes – classified information

Objects – a category of the class

Methods – characteristics of class

Animals

Cats, Dogs, Birds

Say Meow, Bark, Fly

public class Animals{

public static void main (String[] args){

System.out.println (“Meow”);}}

Object-Oriented Programming

Let’s solve both math problems using the Java programming language.

OOP and Mathematics

To tell the computer system to display string values to the computer

System.out.println ((13+8/2 + (7+16));

To define the method:

public static void main (String[] args){

To define the class:

public class OrderOfOperations{{

Research

• A classroom-based, mixed-method research study was conducted with African-American high school students who have taken or were jointly enrolled in Advanced Placement Computer Science and precalculus courses.

• Two male and three female high school students participated in the study

• One male high school graduate participated in the study.

PrecalculusProblems

1. State the number of complex roots of the equation 18x2

+ 3x – 1 = 0. Then find the roots (Holliday et. Al., 2001, p. 207, 221)

2. The sine of an acute <R of a right triangle is 3/7. Find the values of the reciprocal trigonometric ratios for this angle. (p. 289)

Precalculus Problems

Computer Science Problems

1. Create a Quadratic

Equation application

that gives the solution

to any quadratic

equation. The

application should

prompt the user for

values for a, b, and c

(ax2 + bx + c = 0) and

then display the roots,

if any. Use the

quadratic equation.

(Brown, 2005, p.127)

2. Create a TrigFunctions application that displays trigonometric and

reciprocal ratios given the following conditions: The sine of an acute <R

of a right triangle is 3/7. Find the values of the reciprocal trigonometric

ratios for this angle. The application should display output similar to:

The angle in degrees are: Sine: Cosine: Tangent:

The values in radians are:

The Math library (Java) provides methods for performing trigonometric

functions. Class Math (java.lang.Math)

Methods

sin (double angle) - returns the sine of angle, where angle is in radians.

cos (double angle) - returns the cos of angle, where angle is in radians.

tan (double angle) - returns the tan of angle, where angle is in radians.to Radians (double deg) converts degrees to radians p.130

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Problem-Solving Strategies

Comparison of Jay's Precalculus and Computer Science Problems

PreCalc 1

PreCalc 2

CompSci 1

CompSci 2

Jay's Pre-Calculus Problem 1 & 2

Analytic Scoring Scale Results

Pre-Calculus Problems 1 & 2

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Jay's Computer Science Problem 1 & 2

Analytic Scoring Scale Results

Computer Science Problems 1 & 2

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Jay exhibited a high frequency of problem-solving strategies in the understanding the plan phase when solving precalculus problem and implementation phase when solving computer science problems. Jay averaged scores indicated average levels of problem-solving ability when solving precalculus problems; low level of problem-solving ability when solving computer science problems.

Jay's Precalculus Problem 1

Time Series of Problem-Solving Strategies

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Jay's Precalculus Problem 2

Time Series of Problem-Solving Strategies

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Time Series of Problem-Solving Strategies

Jay's Computer Science Problem 1

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Jay's Computer Science Problem 2

Time Series of Problem-Solving Strategies

What is metacognition?

• Metacognitive is thinking about thinking.

• There are two facets to metacognition:– 1) Knowledge of cognition – knowledge of facts and

beliefs

– 2) Regulation of cognition – effective decision-making strategy choices

The Future of Education

Research study revealed that computer science content (i.e. object-oriented programming languages) builds knowledge of cognition such as conceptual thinking and analytic thinking needed to develop mathematical problem-solving activitybased on the high frequency of the implementation phase needed to solve a computer science problem.

The Future of Education

• We need longitudinal research with large student populations to determine metacognitive processes and mathematics problem-solving activity.

• We need to focus on building the levels of problem-solving ability in students, not solely on obtaining the solution to the problem.

The Future of Education

• The National Council of Teachers of Mathematics (1989) Curriculum and Evaluation Standards for School Mathematics (CESSM) in 1989 regarded mathematical problem solving among high school students (grades 9-12) as learning that should be mature and extend through real-world applications in areas such as business, engineering, physical sciences to further connect mathematical theory (National Council of Teachers of Mathematics, 1989).

The Future of Education

Strategies to increase mathematics problem-solving ability1. Offer PD in computer science2. Develop departments with mathematics and

computer science teachers3. Conduct research, collect and analyze data for

computer science as an alternative curriculum4. Keep mathematics content in ‘tact’; strategies

are needed to enhance mathematics learning, while keeping mathematics knowledge ‘pure’.

The Future of Education

Computer science is the laboratory of mathematics problem-solving activity.

Questions?

Contact Information:

Dr. Cristal Jones

5095 Roswell Road Suite 308

Atlanta, GA 30342

404-402-6677

cristaljones34@comcast.net

ReferencesReferences:

Far Rockaway High School Image http://schools.nyc.gov/SchoolPortals/27/Q465/default.htmBaruch College image http://aux.zicklin.baruch.cuny.edu/yue/Yu_Ryan_Yues_Acaemdic_Website/Welcome_files/shapeimage_2.pngAtlanta, Georgia image http://www.tripadvisor.com/Tourism-g60898-Atlanta_Georgia-Vacations.htmlProgramming languages. White Fang. http://www.whitefang.com/programming-languages.htmlTop 10 Lego Creations http://www.techeblog.com/index.php/tech-gadget/feature-top-10-lego-mindstorms-creationsWiebe, J. (1991). At-computer programming success of third-grade students. 24 (2) p.214+. Journal of Research on Computing in Education. Retrieved February 27, 2004, from Professional Development Collection Database.National Council of Teachers of Mathematics. (1989). Introduction. In 1989 Curriculum and Evaluation. Retrieved July 2, 2007, from http://my.nctm.org/index.htmJones, C. (2010). Understanding African-American students’ problem-solving ability in the precalculusmathematics and advanced placement computer science classroom.