1. Using DrScheme and The Design Recipe in Algebra
Pre-AP Strategies in Computer Science and Math
Programming Through the Arts
Problem Solving and Design Tools
Using DrScheme and
The Design Recipe in Algebra
The Anniversary TeachScheme! Workshop
Brown University, Providence, RI
June 11, 2005
Karen North
Westside High School,
Houston ISD, Houston, Texas
Technology Systems, Computer Science, Algebra Teacher

2. Michael’s Programmed Koenig Car
OVERVIEW - CONTRIBUTION
Lessons using Programming to Teach Algebra:
Cartesian Plane Graphing Points Program
Four-corner Design Recipe
Profit Program Process Chart Example
Slope and Graphic Design Lesson
Lesson Development – Trapezoid
My Box Program
School Context
9th Grade Public High School Combo Algebra-CS Class
Michael’s Programmed Koenig Car
So we have developed lessons based on art for one of our tools.
We are going to show you one of the programming tools we are using in our outreach effort. We have a short video that shows the application of lessons presented via a series of modules using DrScheme.
Graphics start with simple programs so students are empowered to tackle other problems, such as creating a variable 5-pointed star using trig functions. That star background here and all the backgrounds in this PowerPoint were created with the DrScheme drawing tools which will be demonstrated after the video.

3. Laura’s Ying Yang Graphic
RESEARCH PROJECT
Houston A+ Challenge Teacher as a Research Grant:
Problem – Designing Solutions to Word Problems
Solution – Developed Lessons to use Programming to Teach algebra
Beta–tested ideas in a combo 9th grade algebra-CS class
Result:
100% passed the HISD Snapshot tests and
100% passed the state accountability 9th grade math TAKS Test Texas Assessment of Knowledge and Skills
Key to Success:
Algebra Lessons being presented at this workshop
Online practice quizzes and lessons
Integrated computer science and algebra assessment
This is just the very beginning of a design recipe used to help students solve problems. The graphics you will see in this video are examples that help students look for patterns to create variable function. This process is also used in the teaching of algebra, which starts in the primary grades with arithmetic. Students discover creative thinking through programming graphics.
Laura’s Ying Yang Graphic

4. RESEARCH PROJECT Houston A+ Challenge Teacher as a Research Grant:
Problem – Designing Solutions to Word Problems
Solution – Developed Lessons to use Programming to Teach algebra
Beta–tested ideas in a combo 9th grade algebra-CS class
Result:
100% passed the HISD Snapshot tests and
100% passed the state accountability 9th grade math TAKS Test - Texas Assessment of Knowledge and Skills
Key to Success:
Continuous practice writing computer programs that use the design recipe to solve problems helped students automate the thinking process
Practice looking for functional relationships and patterns by designing graphics
This is just the very beginning of a design recipe used to help students solve problems. The graphics you will see in this video are examples that help students look for patterns to create variable function. This process is also used in the teaching of algebra, which starts in the primary grades with arithmetic. Students discover creative thinking through programming graphics.

5. RESEARCH PROJECT LESSONS
KEY TO SUCCESS  Continuous practice writing computer programs that used the HTDP DESIGN RECIPE to solve word problems helped students automate the thinking process. Practice looking for functional relationships and patterns by DESIGNING GRAPHICS.
This is just the very beginning of a design recipe used to help students solve problems. The graphics you will see in this video are examples that help students look for patterns to create variable function. This process is also used in the teaching of algebra, which starts in the primary grades with arithmetic. Students discover creative thinking through programming graphics.

6. 1. CARTESIAN PLANE
Developed a Teach-Pak: to practice plotting points in 4 quadrants - to practice negative integer computation to practice planning on graph paper
David’s Clown
Cara’s Singer

7. 1. CARTESIAN PLANE Developed a Teach-Pak:
;; > Canvas Size Constants <
(define L 400) ;; Length of Canvas
(define M (/ L 2)) ;; Middle
;; > Drawing Commands <
;;line: posn posn color -> true
;;Draws a line given the start and end points and a color on a Cartesian plane
(define (line start end color)
(draw-solid-line (make-posn (+ (posn-x start)M)(- M (posn-y start)))
(make-posn (+ (posn-x end) M) (- M (posn-y end))) color))
;;circle: posn number color -> true
;;Draws a circle on a Cartesian plane given the center point, radius and a color.
;;disk: posn number color -> true
;;Draws a solid-disk given the center point, radius and a color on a Cartesian
;;rect: posn number number color -> true
;;Draws a solid-rectangle given the top-left corner point, the length, width and color

8. 2. FOUR-CORNER DESIGN RECIPE
Rate-of-change problems – Programming the functions were easy after developing the algebra equation. Scheme was the test.
;;Find the nth y-coordinate in the
series (6, -1)(9, -2)(12, -3)
given the x-coordinate.
;;series: n -> n
(define (series x)
(+ (* -1/3 x) 1))
(= (series 6) -1)
(= (series 9) -2)
(= (series 12) -3)

9. 3. PROCESS CHART – PROFIT PROGRAM
Data Analysis and EXAMPLES from the design recipe was applied continually throughout Algebra I to solve world problems. Wrote equations in slope-intercept form –TAKS ?s.
Attendees
Profit 10
5 * 10 – ( * 10) = 25 20
5 * 20 – ( * 20) = 70 30
5 * 30 – ( * 30) = 115 A
5 * A – ( * A) = P
Slope-Intercept Form
P = 9/2A - 20

10. 3. PROCESS CHART – DESIGN RECIPE
Data Analysis and EXAMPLES from the design recipe was applied continually throughout Algebra I to solve world problems.

11. 4. SLOPE AND GRAPHIC DESIGN

12. 4. SLOPE AND GRAPHIC DESIGN
;;triisoc: N N N -> True
;;draws an isosceles triangle with proportional sides that consumes the point position coordinates and the scale factor
(define (triisoc x y f)
(and
(draw-solid-line (make-posn (+ x f) y) (make-posn x (+ y f)) 'red)
(draw-solid-line (make-posn x y) (make-posn (+ x f) y)'red)
(draw-solid-line (make-posn x (+ y f)) (make-posn x y)'red)))

13. 1. HISD Coordinate Plane and Transformation Lesson
LESSON DEVELOPMENT
1. HISD Coordinate Plane and Transformation Lesson
Tracey’s Algebra Practice
Uses 4-quandrant Plane TeachPak Code
Function name is the ACTION
Parameters are the data matching the expected data type in the contract.

14. 2. Algebra Transformation Application
LESSON DEVELOPMENT
2. Algebra Transformation Application
Adam’s Trapezoid Art
Plan Examples on Graph Paper.
Plot to check.
Enhance Design.

15. The Structure of the Data Determines the Structure of the Program.
LESSON DEVELOPMENT 3. Variable Trapezoid
The Structure of the Data Determines the Structure of the Program.
Determine Parameters
From Examples discover patterns.
Translate to variables.
Use Trapezoid Function for a creative art design.
David’s Trapezoid Art

16. LESSON DEVELOPMENT
4. Recursive Trapezoid

17. Using Dr Scheme and The Design Recipe in Algebra
My students said the design recipe helped to determine, organize, and process data by providing a step-by step skeleton to solve word problems and check answers.

18. “Fallen Angel” by Laura

19. Black Outline Programmed in DrScheme
Black Outline Programmed in DrScheme. “Just Breathe” then colored in Paint.

20. Laura’s Story
“I used the design recipe to take a step by step approach on difficult problems.”
Laura was an artist. She struggled all year in both algebra and CS. The “light bulb” finally went off at the end of the year. As I watched her sitting cross-legged with her graph paper in hand planning her last graphic in May, I knew this experiment was a success.
I am finally getting students to think and plan before coding! And that same thinking and planning is carried over to solving word problems. After failing the first semester of algebra, Laura passed a test-by-exam to receive credit. And not only did Laura pass the Texas math accountability test, she received commended on TAKS.

21. Thanks TeachScheme! PLT for the last 10 years of support!
As the first public school teacher to implement TeachScheme! using V501, working with the PLT team has changed the way I teach.