Tentative
Syllabus Math 3065
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Course: |
Math 3065 4 credits |
MATHEMATICAL FOUNDATIONS FOR
MIDDLE SCHOOL TEACHERS |
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Department: |
Mathematics
and Computer Science |
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Program(s): |
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Meeting: |
9:00-9:50 AM
MWF |
HS 231 |
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Extras: |
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Dr. Glen
Richgels |
HS 360 Office:
218-755-2824 Email:
grichgels@bemidjistate.edu www: http://faculty.bemidjistate.edu/grichgels/ |
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7- 8 M-F 11-12 M-F |
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3065 MATHEMATICAL FOUNDATIONS FOR MIDDLE
SCHOOL 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. |
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Prerequisite: |
MATH
1011
or consent of instructor. |
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Professional
Education Mission Statement |
Bemidji State
University prepares teachers through inquisitive, involved, reflective
practice. The framework outlining our program sets a standard that is
rigorous, exemplary and innovative. The curricular structure is research
based and organized around the Standards of Effective Practice. Graduates are
proficient, collaborative, technologically literate and environmentally aware
teachers, who work effectively in various settings with diverse learners. |
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Text: |
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Recommended: |
Mathematics
for Elementary Teachers a Contempory Approach, |
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Technology: |
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A calculator |
Attendance by all students is expected
for all classes.
Homework: Homework assignments will be made in
class. You should come prepared to
discuss the various reading assignments and compare and contrast them with what
you have observed in schools.
Class participation and
quizzes: Class participation is expected and in
order to participate you need to be present.
Exams: Exams will be
approximately tri-weekly. There will be a final exam.
Evaluation:There will
be 3-5 tests given throughout the quarter. Quizzes may be given frequently and may be unannounced. The content for the quizzes and tests
will be based on assignments, classroom discussion and lecture, and textbook
material.
Grades: Grades will be based on the homework, quizzes, tests, and final
exam.
Homework,
Quizzes - one-sixth
Tests -
one-half
Final -
one-third
The
following grading scale will be used to determine grades:
A 90%
- 100%
B 80%
- 89%
C 70%
- 79%
D 60%
- 69%
A grade of C or better indicates that the student has successfully
met the competencies measured in this class through discussion, homework, and
projects.
Incomplete: An incomplete (I) grade will only be
given in documented emergency situations. BSU policies will be followed.
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, misrepresentation) may result
in disciplinary action. Possible
disciplinary actions include failure for part or all of the course, as well as
suspension from the University.
NOTE: Upon request, this
document and others distributed in this course can be made available in
alternate formats. If you have a documented disability and need
accommodations for this course please contact the instructor, the Disability
Services Office in 202 Sanford Hall, Bemidji State University or Kathi Hagen in
the Office for Students with Disabilities at 755-3883 for assistance.. Any
other questions about this course should be directed to the instructor.
Change in
Course Syllabus:
The Instructor reserves the right to change this syllabus as this course proceeds
if the need arises. Should a change be required the class will be notified.
Course Outline:
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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; |
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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; |
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(c) represent and solve problem
situations that involve variable quantities and be able to use appropriate
technology; |
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(d) understand patterns present in
number systems and apply these patterns to further investigations; |
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discrete mathematics: |
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(a) application
of discrete models to problem situations using appropriate representations,
including sequences, finite graphs and trees, matrices, and arrays; |
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(b) application
of systematic counting techniques in problem situations to include
determining the existence of a solution, the number of possible solutions,
and the optimal solution; |
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(c) application
of discrete mathematics strategies including pattern searching; organization
of information; sorting; case-by-case analysis; iteration and recursion; and
mathematical induction to investigate, solve, and extend problems; and |
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(d) exploration, development,
analysis, and comparison of algorithms designed to accomplish a task or solve
a problem; |
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number sense: |
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(a) understand
number systems; their properties; and relations, including whole numbers,
integers, rational numbers, real numbers, and complex numbers; |
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(b) possess an
intuitive sense of numbers including a sense of magnitude, mental
mathematics, estimation, place value, and a sense of reasonableness of
results; |
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(c) possess a
sense for operations, application of properties of operations, and the
estimation of results; |
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(d) be able to
translate among equivalent forms of numbers to facilitate problem solving;
and |
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(e) be able to estimate quantities and evaluate the reasonableness of estimates; |
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Instructional Strategies used by instructor
in course:
PolyaŐs problem solving steps
1.
Understand
the problem
- Devise a plan
- Carry out the plan
- Reflect
Lesson
Sequencing
Intuitions
Þ
Concrete ó
Semi-Concrete ó Abstract
GlenŐs
Teaching/Learning Principles
1.
Teach
the way students learn
2.
Use
group work, heterogenous, 3-4, change monthly
3.
Communication
student ó student
4.
Communication
teacher ó student
5.
Multiple
solution paths
6.
Use
contextual settings / problem solving
7.
Assessment
a. Grading
b. To inform instruction
Updated
by Glen Richgels
March 2, 2010
TENTATIVE
Daily Course Outline
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Day 1 |
Introductions and 88 problem |
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Day 2 |
Continue introductions and wrap-up 88 problem. Examine Juicy
Juice problem and student work. |
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Day 3 |
Look at Juicy Juice solutions and
view IMAP vidoe #3 |
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Day 4 |
Wrap-up solutions to problem solving -- look at Cryptarithms /
Ninebl.sol |
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Day 5 |
LYNNE + LOOKS = SLEEPY |
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Day
6 |
Irrational numbers on the geoboard |
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Day 7 |
Making squares on the geoboard using irrational numbers |
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Day 8 |
Now that you can make a square of area five, find a decimal to
represent the square root of five. Bisection method |
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Day 9 |
Continue with the bisection method and look at "divide and
average" method to approximate irrational numbers |
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Day
10 |
Wrap-up irrational numbers. Begin to look at patterns |
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Day 11 |
No class - Todd's at a meeting in the Cities |
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Day 12 |
More patterns -- number of arms in classroom, growing letters,
... What is algebra? (NCTM: concrete / pictoral representation, graph,
formula, table, and words) |
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Day 13 |
Examine recursive (Next = Now...) and explicit (y=ax+...)
formulae |
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Day
14 |
School store -- pencils 15 cents and erasers 25 cents |
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Day 15 |
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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Day 16 |
Balance scales continued |
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Day 17 |
Greta arrives - quiz on balance scales |
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Day 18 |
No class - Greta |
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Day
19 |
Issues with balance scales: can you move from one side to the
other? |
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Day
20 |
Alge-blocks |
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Day
21 |
No class - University planning day |
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Day 22 |
Algeblocks - multiplying terms |
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Day
23 |
Algeblocks - factoring |
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Day
24 |
Algeblocks - what is a cubic |
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Day
25 |
Algeblocks - maybe a surprise quiz? |
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Day 26 |
Building Houses and I Spy Patterns (from NCTM Navigations
through Algebra in grades 3-5) |
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Day
27 |
Building With Toothpicks and Exploring Houses (from NCTM
Navigations through Algebra in grades 6-8) |
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Day
28 |
More toothpicks |
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Day
29 |
More houses |
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Day 30 |
Review algeblocks, islands, balance scales, patterns, ... |
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Day
31 |
Squares Cubed (from NCTM Navigations
through Algebra in grades 3-5) |
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Day
32 |
Bouncing Tennis Balls and Triangle Rule Machine (from NCTM Navigations
through Algebra in grades 3-5 & 6-8) |
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Day
33 |
TEST 1 -- Friday, October 24th |
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Day 34 |
Review Houses on Islands problems |
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Day
35 |
Relating intuition and algebra |
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Day
36 |
36th Annual Northern MN Mathematics Contest -- no class |
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Day
37 |
Wrap-up Triangle rule machine |
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Day 38 |
Wrap-up bouncing tennis balls -- regression on calculators |
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Day
39 |
Todd home sick |
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Day
40 |
Todd home sick |
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Day
41 |
Line of best fit -- slope and intercept |
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Day 42 |
Wrap-up slope and intercept |
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Day
43 |
SHOES -- random sampling |
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Day
44 |
SHOES -- displaying data |
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Day
45 |
Wrap-up slope, intercept, sampling, and displaying data. |
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Day 46 |
Flip, Bam, and Spin -- experimental and theoretical probability |
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Day
47 |
Expected value -- pick a card, any card. Face card pays $10,
anything else loses $5. Wanna play? |
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Day
48 |
Fair games |
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Day
49 |
Fair game is when expected value = 0 |
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Day 50 |
Monte Carlo casino day |
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Day
51 |
no class -- Thanksgiving |
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Day 52 |
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Day
53 |
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Day
54 |
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Day
55 |
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Final Exam – 2 Hours Comprehensive |
Board of Teaching Standards
8710.3320 MIDDLE LEVEL
ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.
Department of Mathematics and Computer Science
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EVIDENCE OF LEARNING & ASSESSMENT
OPPORTUNITIES |
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8710.3320
MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS |
Course ID Number |
Activity or unit |
Assessment |
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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; |
3065 |
PaulŐs points, school store; relatives |
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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; |
3065 |
Growing letters; 3 island problem |
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(c) represent and solve problem
situations that involve variable quantities and be able to use appropriate
technology; |
3065 |
Beams |
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(d) understand patterns present in
number systems and apply these patterns to further investigations; |
3065 |
n-gon numbers |
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(2) concepts of discrete
mathematics: |
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(a) application
of discrete models to problem situations using appropriate representations,
including sequences, finite graphs and trees, matrices, and arrays; |
3065 |
Tournament matrix; Euler circuits/Hamilton circuits; |
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(b) application
of systematic counting techniques in problem situations to include
determining the existence of a solution, the number of possible solutions,
and the optimal solution; |
3065 |
Sales routes; fib seq, lucas seq, golden ratio; sprouts; discrete yearbook |
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(c) application
of discrete mathematics strategies including pattern searching; organization
of information; sorting; case-by-case analysis; iteration and recursion; and
mathematical induction to investigate, solve, and extend problems; and |
3065 |
Sorting algorithms; tower of H anoi; |
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(d) exploration, development,
analysis, and comparison of algorithms designed to accomplish a task or solve
a problem; |
3065 |
Greedy algorithm; NN |
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(3) concepts of number sense: |
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(a) understand
number systems; their properties; and relations, including whole numbers,
integers, rational numbers, real numbers, and complex numbers; |
3065 |
Reals, modular, dihedral group; complex numbers (# and operations 9-12) |
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(b) possess an
intuitive sense of numbers including a sense of magnitude, mental
mathematics, estimation, place value, and a sense of reasonableness of
results; |
3065 |
Craigs stories (number magnitude); scientific notation |
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(c) possess a
sense for operations, application of properties of operations, and the
estimation of results; |
3065 |
Other base arithmetic from m1011 |
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(d) be able to
translate among equivalent forms of numbers to facilitate problem solving;
and |
3065 |
Fractions, decimals, percents |
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(e) be able to estimate quantities and evaluate the reasonableness of estimates; |
3065 |
Items and estimate magnitudes |
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Professional
Education Mission Statement |
Bemidji State
University prepares teachers through inquisitive, involved, reflective practice.
The framework outlining our program sets a standard that is rigorous,
exemplary and innovative. The curricular structure is research based and
organized around the Standards of Effective Practice. Graduates are
proficient, collaborative, technologically literate and environmentally aware
teachers, who work effectively in various settings with diverse learners. |
The middle level teachers from BSU that take the
campus M3065 class will increase their content knowledge and understanding of
how students learn as they experience studying fundamental operations, number
sense, discrete mathematics and patterns and functions. M3065 is a mixture of
challenging students in the understanding of number sense, discrete mathematics, foundations of algebra and
experiencing activity based pedagogy. This translates into a more positive
attitude toward mathematics for themselves that hopefully they will take with
them into their teaching.
The best practices of activity oriented learning
is demonstrated in class from day one. In addition group work and collaborative
learning are encouraged and used almost daily. These best practices are
discussed at the beginning of the course and pointed out and discussed
throughout the semester.