MTE 410, Elementary School Mathematics and the Computer, 4 credits—Summer (S01) 2009

• Detailed syllabus.
• Place and Time: Mon, Tue, Wed, Thu at 9:45–11:20 AM in SEB 185.
• Office hours: Wed: 1:00–2:00 PM, or by appointment (SEB 347).
  During office hours I let everyone who showed up into my office and discuss questions in a round-robin manner. If you need to see me outside regular office hours, ask or e-mail me to set up an appointment.
  
  
• Textbook: There will be two books recommended for this course:
  • Punished By Rewards: The Trouble with Gold Stars, Incentive Plans, A's, Praise, and Other Bribes, by Alfie Kohn, ISBN: 0618001816.
  • Knowing and Teaching Elementary Mathematics, by Liping Ma, ISBN: 0805829091.
• Software: Terrapin LOGO. This software is on all computers in the Kresge library computer labs (rooms 129A and 129B). I recommend that you purchase a copy for your own computer. If you wish to do so, Terrapin LOGO may be purchased at http://www.terrapinlogo.com/homediscount/index.php for $29.95. Reference manual and tutorial can also be bought for $19.95 per package each. You may also call 1-800-774-LOGO to order.
  
  
• Course Objectives: This course is an introduction to creative uses of computers in teaching mathematics in elementary school. The main tools are the LOGO computing language and Geometer's Sketchpad. We will also discuss related mathematical problems, teaching methods, and learning.
  
  
• Grading Policy: Your course grade will be based on your scores on the quizzes, midterm and final exams as discussed below. Your total percentage score will be converted to your final grade according to the usual OU scale: 95%->4.0, 50%->1.0 (linearly in between). I may adjust your grade if I deem it necessary.
  
  
• Homework assignments: Homework will be assigned regularly, but it will not be collected or graded, and it will not affect your final grade. Solutions for homework assignment problems will sometimes be discussed in class.
  
  
• Quizzes: There will be a short, 30-minute quiz to provide you with feedback on the following dates: May 11, May 18 (both Mondays); May 27 (Wednesday) (note the change in the date!); June 4, June 11 (both Thursdays). The quizzes will be worth 20% of your final grade. The lowest score will be dropped.
  • Quiz #5, June 11, 2009
  • Quiz #4, June 4, 2009
  • Quiz #3, May 27, 2009 (note the change in the date!)
  • Quiz #2, May 18, 2009
  • Quiz #1, May 11, 2009
  
  

• Midterm Exam: There will be a midterm exam worth 30% of your final grade on Tuesday, June 2 (note the change in the date!). This will be a closed-book exam. If you miss the midterm exam, its weight will be transferred to the final exam.
  

• Final Exam: The Final Examination is comprehensive. It will be given on Monday, June 22, 8:00–11:00 AM and it will be worth 50% of your final grade.
  Topics for Final Exam
  
  
• Logo Commands:
  Drawing commands:
  • forward n : (abbr: fd) go forward n pixels
  • back n : (abbr: bk) go backward n pixels
  • left n : (abbr: lt) turn left n degrees
  • right n : (abbr: rt) turn right n degrees
  • penup: picks up the pen
  • pendown: puts down the pen
  • clearscreen: (abbr: cs) clears the graphics window and moves the turtle back to the middle facing up
  • hideturtle: (abbr: ht) hides the turtle
  • showturtle: (abbr: st) shows the turtle
    
  Loop commands:
  • repeat n [commands]: repeats commands n times
  • while [condition][commands]: As long as condition is true, execute commands
  • if expression [then-commands][else-commands]: if expression is true, executes then-commands, otherwise executes else-commands
    
  • for "variable a b [commands]: for each value of variable from integers a to b (increased by 1 at each iteration) execute commands
    
  Colors:
  • colors: gives a list of available color names
  • setpc "color: sets the color of the pen to color
  • pencolor: gives the current color of the pen as a list of three integers
  • fill: fills a region with the current color (pen must be down and the turtle must be inside the region)
    
  Coordinate geometry:
  • setxy [x y]: moves the turtle to coordinates (x, y)
  • setx x: moves the turtle so that its x-coordinate becomes x
  • sety y: moves the turtle so that its y-coordinate becomes y
  • xcor: gives the x-coordinate of the turtle
  • ycor: gives the y-coordinate of the turtle
  • towards [x y]: gives the heading that would turn the turtle towards the point (x y)
    
  Lists and strings:
  • list x y: outputs a list with two elements, the values of x and y
  • (list x₁ x₂ … x_n): outputs a list with n elements, the values of x₁ x₂ … x_n
  • fput x y: outputs the list or word (depending on whether y is a list or word) obtained by putting x in the beginning of y
  • lput x y: outputs the list or word (depending on whether y is a list or word) obtained by putting x in the end of y
  • butfirst x: outputs the list or word (depending on whether x is a list or word) obtained by removing the first element of x
  • butlast x: outputs the list or word (depending on whether x is a list or word) obtained by removing the last element of x
  • first x: outputs the first element of x
  • last x: outputs the last element of x
  • empty? x: outputs TRUE if x is empty, otherwise outputs FALSE
  Algebra commands:
  • abs a: returns the absolute value of a
  • sqrt a: returns the square root of a
  • int a: returns the integer obtained by discarding the part after the decimal point in a
  • remainder a b: gives the remainder when a is divided by b
  Input-output commands:
  • print var: prints the value of variable var in the listener window and starts a new line
  • type var: prints the value of variable var in the listener window (does not start a new line)
  • stop: stops the current procedure and returns to the calling procedure
  • output expr: stops the current procedure and returns the value of expr to the calling procedure; if there was no such procedure, prints the result in the listener window
  • readprompt string: opens a window titled string for user input; the first word typed in is returned to the procedure
  • readchar: waits until a button is pressed on the keyboard, returns the first such symbol
  Other commands:
  • make "var v: sets the value of variable var to v
  • local "var: defines variable var to be local
  
  
• Material covered:

  Week	Date	Material covered
  7	June 18, Thursday	Notes in the class.
  	June 17, Wednesday	Notes in the class.
  	June 16, Tuesday	Procedure to draw a spiral, and picture of the resulting square spiral.  Procedure to draw a spiral using arcs, and picture of various other spirals: spiral with quarter circles, spiral with half circles, spiral with full cirles, and moving spiral.  Procedures to draw a binary tree, and pictures of the resulting binary tree and upward binary tree.  Procedure to draw a Koch curve, and picture of the resulting snowflake.  Content of the Listener window.  Notes in the class.
  	June 15, Monday	Notes in the class.
  6	June 11, Thursday	Homework #6  Topics for Final Exam  Procedure to print the balances on a debt.  Content of the Listener window.  Second content of the Listener window.  Notes in the class.
  	June 10, Wednesday	Procedure to print the computation of the gcd.  Content of the Listener window.  Notes in the class.
  	June 9, Tuesday	Procedure to print a dollar amount.  Content of the Listener window.  Notes in the class.
  	June 8, Monday	Procedure to add rational numbers given in a list.  Content of the Listener window.  Notes in the class.
  5	June 4, Thursday	Homework #5  Procedure to compute the gcd of two numbers in two ways, recursively and non-recursively.  Procedures to do rational arithmetic.  Content of the Listener window.  Notes in the class.
  	June 3, Wednesday	Notes in the class.
  	June 2, Tuesday	Midterm Exam  Notes in the class.
  	June 1, Monday	Procedure to convert a number to base ten, procedure to convert a number from base ten, and procedure to convert a number from any base to any base up to ten.  Procedure to convert a number to base ten if base can be up to 100, procedure to convert a number from base ten to a base up to 100, and procedure to convert a number from any base to any base up to 100.  Content of the Listener window (the end only, the beginning was cut off, unfortunately).  Notes in the class.
  4	May 28, Thursday	Homework #4  Procedure to find the kth element of a list and the number of elements in a list.  Content of the Listener window.  Notes in the class.
  	May 27, Wednesday	Quiz #3 Content of the Listener window.  Notes in the class.
  	May 26, Tuesday	Procedure to draw triangles and median triangles and doing the same with recursion, and a picture of the resulting triangles.  Content of the Listener window.  Notes in the class.
  	May 25, Monday	Memorial Day
  3	May 21, Thursday	Homework #3  Content of the Listener window.  Notes in the class.
  	May 20, Wednesday	Procedure to draw a lot of triangles with the same base and same angle opposite the base.  A picture of triangles with a 45 degree angle opposite the base, triangles with a 90 degree angle opposite the base, and triangles with a 150 degree angle opposite the base.  Procedure to draw a triangle if given SSS, and a picture of triangle drawn by it. Content of the Listener window.  Notes in the class.
  	May 19, Tuesday	Procedures to draw a triangle if given SAS or ASA; a picture of triangles drawn by SAS, a picture of triangles drawn by ASA, and the picture of triangles drawn by the end.  Content of the Listener window.  Notes in the class.
  	May 18, Monday	Quiz #2 Procedure to draw a parallelogram, a picture of parallelogram.  Content of the Listener window.  Notes in the class.
  2	May 14, Thursday	No class!
  	May 13, Wednesday	Homework #2  Procedures to draw a square, a picture of squares, and commands to draw these in the Listener window.  Procedures to draw a straight line connecting two points.  Procedure to draw a circle with given center and radius.  Second content of the Listener window.  Notes in the class.
  	May 12, Tuesday	Procedures to draw a flower and a colored flower with overlapping petals.  Picture of a flower with overlapping petals and another, picture of several flowers of different colors.  Commands to draw these in the Listener window.  Procedure to draw a colored flower with petals filled in and a resulting picture of a colored flower with overlapping petals.  Procedure to draw a crown and the resulting picture of a crown when I forgot to move back the turtle enough.  Second content of the Listener window.  Notes in the class.
  	May 11, Monday	Quiz #1  Procedure to draw an arc.  Procedures to draw petals and flowers.  First and second attempt to draw a flower using the petal command.  Flowers drawn using five flower commands.  Content of the Listener window.  Notes in the class.
  1	May 7, Thursday	Homework #1  Procedure to draw a square with more precise description.  Procedure to draw a chessboard one column at a time, and picture of one column of squares, and picture of a chessboard; content of the Listener window.  Procedure to draw a chessboard two columns at a time, one upward, one downward.  Procedure to draw a regular polygon, and a picture of 10-sided polygons.  Procedure to draw a circle, commands to draw a circle with a square around it, and the resulting picture.  Notes in the class.
  	May 6, Wednesday	Procedure to draw a triangle of any size, commands to draw a bunch of triangles, and the resulting picture of triangles.  A simplified procedure to draw a triangle, commands to draw a four triangles, and the resulting picture of four triangles.  Procedure to draw a pentagon of any size, commands to draw a four pentagons, and the resulting picture of four pentagons.  Notes in the class.
  	May 5, Tuesday	Basic operations in Logo.  Commands to draw a square of side 100 and to draw a square of side 200.  Procedure to draw a square of any size and the resulting picture of four squares.  Procedure to draw a square with its diagonal and the resulting picture of eight such squares (obtained by eight consecutive "squarediagonal 100" commands).  Second content of the Listener window.  Notes in the class.
  	May 4, Monday	Discussion of the syllabus.  Intro to Logo, basic drawing commands, and the resulting picture.  Commands to draw a square.  Notes in the class.

  
  
  
• Academic honesty:
  Cheating is a serious academic crime. Oakland University policy requires that all suspected instances of cheating be reported to the Academic Conduct Committee for adjudication. Anyone found guilty of cheating in this course will receive a course grade of 0.0 in addition to any penalty assigned by the Academic Conduct Committee. Working with others on a homework assignment does not constitute cheating; handing in a project that has essentially been copied from another team does. Solutions found on the Internet or similar resource may not be used. Receiving help from someone else (except possibly me) or from unauthorized written material during the final exam is cheating.
  
  
• Study Habits:
  I can only guide and help you by providing the framework for the course: you are responsible to learn the material. Most of this learning must take place outside the classroom. This will usually take two to three hours outside of class for each hour in class, but may take longer in some cases. Our aim is to be able to apply the material to new situations, hence the focus is on understanding rather than memorizing. You should come prepared for class, do the homework, regularly review earlier material, ask questions in class or during office hours. You may also find it helpful to work with others in study groups. In such cases make sure that you follow the policy guidelines of the course.
  
  

Last update on June 18, 2009.