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Programming to Teach Algebra: Lessons and Design Tools for Problem Solving

This workshop showcases how programming can be used to teach algebra, through lessons and design tools such as Cartesian plane graphing, four-corner design recipe, profit program process chart, and slope and graphic design. The research projects highlight the success of using programming to teach algebra, with improved test scores and automated thinking processes. Various lessons and examples are presented, including teaching plotting points on a Cartesian plane, solving rate-of-change problems, and using design recipes for data analysis and problem solving.

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Programming to Teach Algebra: Lessons and Design Tools for Problem Solving

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  1. 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. 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

  3. 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 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

  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.

  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.

  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. LESSON DEVELOPMENT 1. HISD Coordinate Plane and Transformation Lesson Tracey’s Algebra Practice Uses 4-quandrant Plane TeachPak Code

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

  15. 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. “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.

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