MTE 410, Elementary School Mathematics and the Computer, 4 credits—Spring 2007

• Detailed syllabus.
• Place and Time: Mon, Tue, Wed, Thu at 8:00–9:35 AM in SEB 185.
• Office hours: Mon, Wed: 9:45–10:45 AM, 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 would like a one-to-one meeting, e-mail me to set up an appointment. According to university policy I will use your official OU e-mail to reply. If you are using non-OU e-mail, always provide me with your OU e-mail address.

• Textbook: There will be two books required 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. Documentation and tutorial can also be bought for $19.95 per package, respectively. 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 grades on the midterm and final exams as discussed below. 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.
  

Week	Date	Assignment
7	June 21, Thursday	—
	June 20, Wednesday	—
	June 19, Tuesday	—
	June 18, Monday	—
6	June 14, Thursday	Homework #9
	June 13, Wednesday	—
	June 12, Tuesday	—
	June 11, Monday	—
5	June 7, Thursday	Homework #8
	June 6, Wednesday	—
	June 5, Tuesday	Homework #7
	June 4, Monday	—
4	May 31, Thursday	—
	May 30, Wednesday	—
	May 29, Tuesday	Homework #6
	May 28, Monday	—
3	May 24, Thursday	—
	May 23, Wednesday	—
	May 22, Tuesday	Homework #5
	May 21, Monday	—
2	May 17, Thursday	Homework #4
	May 16, Wednesday	—
	May 15, Tuesday	Homework #3
	May 14, Monday	—
1	May 10, Thursday	Homework #2
	May 9, Wednesday	—
	May 8, Tuesday	Homework #1
	May 7, Monday	—

• Quizzes: There will be a short, 30-minute quiz to provide you with feedback every Monday. During the first week and the week of Memorial day this quiz will be on Tuesday instead. If you miss a quiz, you will need to download it from my webpage, do it on your own at home under the same conditions (notes, textbooks, and calculators are not allowed), and bring it in the next time you come to class. Your quizzes will not affect your final grade as long as you follow these instructions.
  • Quiz #6, June 18, 2007
  • Quiz #5, June 11, 2007
  • No quiz on June 4, 2007
  • Quiz #4, May 29, 2007
  • Quiz #3, May 21, 2007
  • Quiz #2, May 14, 2007
  • Quiz #1, May 8, 2007
  
  

• Midterm Exam: This is a take-home midterm exam worth 40% of your final grade. You may consult only me about the exam (several students may be present when this takes place). Outside material may not be used (this includes material found on the Internet or some similar resource). After submitting you will need to make an appointment with me to explain your solutions for some of the problems of my choice. Your grade on the exam will be based on your written solutions and your oral explanations.

  Additional data for the midterm: Find your initials, and the corresponding row contains the data you need for the midterm.

  Initials	Info for problem				Initials	Info for problem
  	2	3	4			2	3	4
  D.A.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 9		S.A.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 9
  G.B.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 12		P.B.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 12
  C.Ci.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 15		C.Co.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 15
  M.C.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 9		J.D.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 9
  S.D.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 12		H.F.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 12
  L.F.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 15		A.G.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 15
  R.G.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 9		S.K.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 9
  A.M.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 12		K.M.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 12
  S.M.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 15		T.M.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 15
  A.P.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 9		K.P.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 200 side2 = 150 angle = 45°	side = 9
  C.R.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 12		E.S.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 250 angle = 90°	side = 12
  K.S.	(i) b < 0; c = 0 (ii) b < 0; c < 0	hor. side = 100 side2 = 250 angle = 135°	side = 15		J.T.	(i) b = 0; c < 0 (ii) b < 0; c < 0	hor. side = 150 side2 = 260 angle = 60°	side = 15

  
  
• Projects: There will be several projects to provide you opportunity to learn from each other. You will need to form project teams of up to four students, and then it will be your responsibility to organize meetings so you can work together on the projects. In case of conflicts or disagreements you may change the formation of teams (splits, mergers, team of one student will be acceptable). No team is allowed to discuss the projects with another team. Outside material may not be used (including material found on the Internet or some similar resource). Your projects will not affect your final grade as long as you follow these instructions.
  • Project 2
    First draft due Wednesday, June 13, 2007.
    Final version due Wednesday, June 20, 2007.
    Additional examples you should try with your procedure:
    1. Debt: $20,000, APR: 6%, Monthly payment: $50, n=5
    2. Debt: $2,000, APR: 18%, Monthly payment: $200, n=15
  • Project 1
    First draft due Thursday, May 24, 2007.
    Final version due Thursday, May 31, 2007.
  
  
• Final Exam: The Final Examination is comprehensive and it will be worth 60% of your final grade. You will need to make an appointment to take it during June 25–27 (Mon–Wed) in 542 SEB. The Final Exam will have a written and an oral portion, and your grade will be based on both. If I am incapacitated during the final exam period, the final exam will be held instead on June 26th, 8–11 AM, in 185 SEB as originally scheduled.
  Topics for the 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
  
  
• Math Topics:
  1. Sum of angles in triangles, polygons
  2. Quadratic formula, factoring
  3. Integer exponents, properties of exponents
  4. Fractions, operations on fractions
  5. Pythagorean theorem, distance formula (law of cosines)
  6. Radicals, n^th roots and their properties
  7. Rational exponents
  8. Circumscribed circle, law of sines
  9. Base 10, change of base
  10. Division Property
  11. Greatest common divisor (gcd), Euclidean algorithm
  12. Compound interest
  13. Arithmetic and geometric series
  14. Divisibility rules
  
  
• Material covered:

  Week	Date	Material covered
  7	June 21, Thursday	Discussion on teaching and assessment
  	June 20, Wednesday	Discussion on the book, Punished by Rewards
  	June 19, Tuesday	Logarithms
  	June 18, Monday	Quiz #6.  Procedure to find the kth element of a string or list.  Procedure to reverse a string or list.  Mystery procedure and the image of a snowflake it drew.  Content of the listener window.
  6	June 14, Thursday	Homework #9, Topics for the Final Exam.  Divisibility rules.
  	June 13, Wednesday	Compound interest continued.  Arithmetic and geometric series.  Content of the listener window.
  	June 12, Tuesday	Compound interest.  Procedure to print exactly two digits after the decimal point.  Content of the listener window.
  	June 11, Monday	Quiz #5.  Procedure to get the digits separated by parentheses.  Content of the listener window.
  5	June 7, Thursday	Project 2, Homework #8.  Procedures performing rational arithmetic, and adding fractions interactively.  First and second content of the listener window.
  	June 6, Wednesday	Greatest common divisor, Euclidean algorithm, computing the gcd using the Euclidean algorithm and recursively.  Content of the listener window.
  	June 5, Tuesday	Homework #7.  Division property.  Another procedure to find the base b representation of a number given in base 10.  Procedure to find the base 10 representation of a number given in base b.  Procedure to change base from any base to any other.  Content of the listener window.
  	June 4, Monday	No quiz this week. Procedure to find the base b representation of a number given in base 10. First and second content of the listener window.
  4	May 31, Thursday	Midterm Exam and additional data.  Existence of circumscribed circle, diameter of circumscribed circle, law of sines.  Base 10, change of base.  Content of the listener window.
  	May 30, Wednesday	nth roots and their properties, rational exponents.
  	May 29, Tuesday	Homework #6, Quiz #4.  The Pythagorean theorem, distance formula.  A procedure to draw a triangle if given the three sides.  Image of triangles and the content of the listener window.
  	May 28, Monday	Memorial Day
  3	May 24, Thursday	A procedure to draw a triangle if given two angles and the side between.  Image of triangles. Content of the listener window.
  	May 23, Wednesday	Division, fractions, operations on fractions
  	May 22, Tuesday	Homework #5.  A procedure to draw a square from the current position of the turtle if given the side of the square, and the image of squares.  Drawing a cirle with given center, and the corresponding image of a circle.  Procedures to draw triangles if given (1) the coordinates of the three vertices; or (2) two sides and the angle between.  Image of some triangles drawn with the first triangle command, and with the second triangle command.  Content of the listener window.
  	May 21, Monday	Quiz #3.  A procedure to draw a square if given its lower-left corner and its side.  Content of the listener window, and the image it created.
  2	May 17, Thursday	Project 1, Homework #4.  Integer exponents.  Content of the listener window, and the image it created.
  	May 16, Wednesday	Quadratic formula, factoring.  Image of a colored square, content of the listener window.
  	May 15, Tuesday	Homework #3.  Procedures to draw a flower of given size; flower of size 100 with circle; procedures to draw a spiral.  Picture of a spiral, and an infinite spiral.  Content of the listener window.
  	May 14, Monday	Quiz #2, problem 9 in Quiz #2, problem 10 in Quiz #2.  Procedures to draw petals and flowers; some petals, flower with eight petals, and flower with 13 petals.  Content of the listener window.
  1	May 10, Thursday	Homework #2.  Using a regular polygon to approximate a circle having the same perimeter.  A circle approximated with 100-side polygon, 200-side polygon, 400-side polygon.  Using a regular polygon to approximate a circle having the same radius of its circumscribed circle.  Drawing an arc, image of a couple of arcs.  Content of the listener window.
  	May 9, Wednesday	Draw a square of side 200 using repeat.  Draw a square of side 100.  Draw a square of any size.  Picture of squares.  Procedure to draw an equilateral triangle, and a picture of triangles.  Angles of a regular polygon.  Procedure to draw a regular pentagon, and a five-point star.  Procedure to draw a regular polygon, and a picture of polygons.  Content of the listener window.
  	May 8, Tuesday	Quiz #1, Homework #1.  Intro to Logo, basic operations and drawing commands, and the resulting picture.  Commands to draw a square.  Procedure to draw a square, and a picture of four squares.  Last content of the listener window.
  	May 7, Monday	Discussion of syllabus

  
  
  
• 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 21, 2007.