Math 3065 (4 credits)
Mathematical Foundations of Algebra for Teachers
Fall 2019
Instructor: Todd Frauenholtz |
Email: -- TFrauenholtz@BemidjiState.edu |
Office hours: M - F by arrangement | Class meets: T Th 2:00 – 2:50 pm in DH 113 |
Office: S 207G | Phone: (218) 755-2817 |
Professional Education Department Mission Statement:
“The Bemidji State University Professional Education program is preparing today's teachers for tomorrow, through effective, inquisitive, and reflective practice. Our students are proficient, self-reliant, and thoughtful practitioners, developed in a viable and growing program, who can teach effectively in various settings with diverse learners."
Course Description
MATHEMATICAL FOUNDATIONS OF ALGEBRA FOR TEACHERS (4 credits)
This course meets or helps meet the new BOT rule with respect to concepts of patterns, relations, and functions; discrete mathematics; probability; and statistics that are pertinent to middle school mathematics.
Prerequisites
MATH 1011 or consent of instructor.
Required Text
No required text.
Resources: |
Algebra in the Early Grades (2008) by J. J. Kaput, D. W. Carraher, & M. L. Blanton. Lawrence Erlbaum Associates; New York (pub).
Hands On Equations (1996) by H. Borenson. Borenson and Associates; Allentown, PA (pub). Mathematics for Elementary Teachers: A Contemporary Approach (2014) by G. L. Musser, W. F. Burger, & B. E. Peterson; John Wiley & Sons (pub), 10th ed. Mathematics In Context: Comparing Quantities (2006) by T. A. Romberg. Encyclopedia Britannica (pub). Mathematics In Context: Building Formulas (2003) by T. A. Romberg. Holt, Rinehart, and Winston (pub). Minnesota K-12 Mathematics Framework (1998) by W. Linder-Scholer. SciMathMN (pub). Number Sense Activities section. Navigating through Algebra in Grades 3-5 (2005) by G. J. Cuevas & K. Yeatts. National Council of Teachers of Mathematics; Reston, Virginia (pub). Navigating through Algebra in Grades 6-8 (2007) by S. Friel, S. Rachlin, & D. Doyle with C. Nygard, D. Pugalee, & M. Ellis. National Council of Teachers of Mathematics; Reston, Virginia (pub). Patterns and Functions Activities for Teachers by T. Frauenholtz, C. Rypkema; Bemidji State University. |
Board of Teaching Standards
8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.
Department of Mathematics and Computer Science
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8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS |
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In this syllabus you will find the word TEACH. This will mean to:
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Standard |
K/A |
Activity |
Assessment |
C.A teacher with a middle level endorsement for teaching mathematics in grades 5 through 8 must demonstrate knowledge of fundamental concepts of mathematics and the connections among them. The teacher must know and apply: |
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(1) concepts of patterns, relations, and functions: |
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(a) recognize, describe, and generalize patterns and build mathematical models to describe situations, solve problems, and make predictions; |
K A |
TEACH: Assignment: The School Store – from Math In Context Comparing Quantities. Relatives – from Musser, Burger, & Peterson; Section 9.3, #’s: 2,3,6,7,8.
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Assessment:
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(b) analyze the interaction within and among quantities and variables to model patterns of change and use appropriate representations, including tables, graphs, matrices, words, algebraic expressions, and equations; |
K A |
TEACH: Assignment: Building Houses problem – from Navigations through Algebra in Grades 3-5; Growing letters – Patterns and Function Activities for Teachers Exploring Houses; Bouncing Tennis Balls; & Tiling Tubs – from Navigations through Algebra in Grades 6-8.
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Assessment:
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(c) represent and solve problem situations that involve variable quantities and be able to use appropriate technology; |
K A |
TEACH: Assignment: Hands On Equations (1996) by H. Borenson. Borenson and Associates, Allentown, PA (pub).
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Assessment:
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(d) understand patterns present in number systems and apply these patterns to further investigations; |
K A |
TEACH:
Examine different contextual problem situations that contain patterns present in number systems, build models (tables, matrices, words, graphs, algebraic expressions, equations) for the patterns, generalize the patterns, solve the problem for the solution or extend the pattern to predict the solution. Encourage multiple approaches or solution paths. Assignment: n-gon numbers – from Algebra in the Concrete (1973) by M. Laycock & R. A. Schadler; Activities Resource Company (pub). Pp. 7.
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Assessment:
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Technology Requirements and Expectations
Students will use internet browsers to access information and answer questions posed in class. Students will may use graphing calculators, Geometer’s Sketchpad, or data programs such as Excel, Tinkerplots, Fathom 2, or Minitab as needed. Written assignments for class will be composed using a word processor such as Microsoft Word.
Teaching Methodology
Polya’s problem solving steps
Lesson Sequencing
Intuitions - Concrete - Semi-Concrete - Abstract
Glen’s Teaching/Learning Principles
University Policies and Procedures
http://www.bemidjistate.edu/students/handbook/policies/
Academic Integrity
BSU students are expected to practice the highest standards of ethics, honesty and integrity in all of their academic work. Any form of academic dishonesty (e.g., plagiarism, cheating and misrepresentation) may result in disciplinary action. Possible disciplinary actions may include failure for part of all of a course as well as suspension from the University.
Students with Special Needs
I would like to make sure that all the materials, discussions and activities that are part of the course are accessible to you. If you would like to request accommodations or other services, please contact me as soon as possible. It is also possible to contact Disability Services, Sanford Hall, 201. Phone: 218/755-3883 or E-mail address Disabilityservices@bemidjistate.edu. Also available through the Minnesota Relay Service at 1-800-627-3529.
Student Rights and Responsibilities
Student Code of Ethics
http://www.bemidjistate.edu/academics/catalog/10catalog/GradCatalog/Frontpages/sectionIV/rights.html
Student Academic Rights and Responsibilities
http://www.bemidjistate.edu/students/handbook/policies/academic_integrity/rights_responsibilities.cfm
Instructor Rights and Responsibilities
- I work with all students and expect success from all students. It is my expectation that students who attend class regularly and complete assignments will pass.
- I am available for help whenever I am in my office. I encourage students to do homework at a table outside of my office so that I can help them whenever they have difficulties. Help is also available through email and at my home, if prior arrangements have been made.
- I will try to give grade status reports weekly.
Course Grades
A: 100 – 90% B: 89 – 80% C: 79 – 70% D: 69 – 60%
Course Policies
Attendance: Daily attendance is expected
Participation: Class participation and group work is expected
Tentative Course Calendar
Week 1 |
Introductions, values, and 88 problem |
Continue introductions and wrap-up 88 problem. Examine Juicy Juice problem and student work. |
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Look at Juicy Juice solutions and view IMAP video #3 |
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Week 2 |
Wrap-up solutions to problem solving -- look at Cryptarithms / Ninebl.sol The Border Problem (& video) |
LYNNE + LOOKS = SLEEPY ; USA + USSR = PEACE ; percentages |
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Introduce variables (candy boxes) and patterns |
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Week 3 |
Growing letters – construct and share |
Growing letters – presentations |
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Growing letters – presentations |
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Week 4 |
Growing letters – presentations |
Growing letters – analysis |
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Growing letters – analysis |
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Week 5 |
More patterns -- number of arms in classroom, growing letters, ... What is algebra? (NCTM: concrete / pictoral representation, graph, formula, table, and words) |
Multiple representations on single page (from NW Service coop website) Rectangles with a perimeter of 20 |
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Examine recursive (Next = Now...) and explicit (y=ax+...) formulae |
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Week 6 |
Paul’s Points - School store -- pencils 15 cents and erasers 25 cents; relatives, Skeeters (having four babies, poison, and simultaneous) |
Using manipulatives - a balance scale approach. Solve: x+2=6, x-2=7, x+3=-8, x-4=-9, 2x+4=x+5, 3x+2x=x+8, 3x+-2x=-x+8, 2x+6=-x, 2x+3=2x-5, ... |
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Balance scales continued |
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Week 7 Midterm Exam |
Virtual balance scales |
Virtual balance scales |
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Issues with balance scales: can you move from one side to the other? |
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Issues with balance scales: negatives? |
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Week 8 |
Alge-blocks |
Algeblocks - multiplying terms |
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Algeblocks - factoring |
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Week 9 |
Algeblocks - what is a cubic |
Algeblocks - maybe a surprise quiz? |
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Three island problem Building Houses and I Spy Patterns (from NCTM Navigations through Algebra in grades 3-5) |
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Week 10 |
Three island problem Building With Toothpicks and Exploring Houses (from NCTM Navigations through Algebra in grades 6-8) |
Beams |
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Beams & Frogs (https://nrich.maths.org/1246) |
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Week 11 |
Review algeblocks, islands, balance scales, patterns, ... |
Squares Cubed (from NCTM Navigations through Algebra in grades 3-5) |
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Bouncing Tennis Balls and Triangle Rule Machine (from NCTM Navigations through Algebra in grades 3-5 & 6-8) |
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Week 12 |
Review Houses on Islands problems |
Relating intuition and algebra |
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Wrap-up Triangle rule machine |
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Week 13 |
Wrap-up bouncing tennis balls -- regression on calculators |
Line of best fit -- slope and intercept |
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Wrap-up slope and intercept |
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Grad Students | Instructional Lesson and Task (Graduate Students only) – Improve at least 15 days of instruction by including technology and concepts from class. Include assessment to evaluate students and the effectiveness of the changes in the instructional unit. |
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Final Exam – 2 Hours Comprehensive on Thursday, December 12th 10:30 am - 12:30 |
updated 9/6/2019
by Todd
Frauenholtz