Teacher Education Program Mission Statement:
BSU 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.
Math 1011
Math for Elementary Teachers I
Instructor: Todd Frauenholtz
Office: 372 HS
Phone: (218) 755-2817
Email: TFrauenholtz@BemidjiState.edu
Website: http://faculty.bemidjistate.edu/tfrauenholtz (you were just there!)
Class meets: M W F 9:00 to 9:50 am (sect 02) in HS 231
Office hours: M W F 8:00 - 8:50 am and by other arrangement
Math help center: HS 232
http://www.macmillanhighered.com/launchpad/reconceptmath3e/8847381
Text: Reconceptualizing Mathematics for Elementary School Teachers, third ed. by Sowder, Sowder, & Nickerson
Description: This course meets the Board of Teaching fundamental topics in arithmetic competencies. These topics include addition, subtraction, multiplication, and division of whole numbers; number theory related to fractions; fractions; decimals; and integers. This is the first of two mathematics courses providing the background for teaching in the elementary school. Emphasizes the use of mathematics manipulative for modeling the basic operations.
Prerequisite: Elementary education major or consent of instructor. It is recommended students fulfill their liberal education requirement before taking this course.
The topics addressed include mathematics found in elementary curricula. Including:
Student Learner Outcomes:
Competencies to be met by law:
Homework: Homework assignments will be made in class. You should read and understand all sections of the chapters and assigned problems to prepare for quizzes and exams. Points will be given for homework.
Class participation and quizzes: Class participation is expected and in order to participate you need to be present. Quizzes will be unannounced and given frequently to help you prepare for the exams. To take a quiz students need to be present at the beginning of the class session and missed quizzes cannot be made up but your lowest quiz score will be dropped from the calculation of your grade. Cell phones must be turned off during class.
Exams: There are three exams planned in addition to the comprehensive final exam. Make-up exams will be given only under special circumstances and need to be discussed with me before hand. The final exam is scheduled for Wednesday, December 19th from 8:00 to 10:00 am (section 2).
Grades: Grades for this course will be based upon homework, quizzes, tests, and a comprehensive final exam; some of the quizzes may be unannounced. Items for both will come from the assigned homework. The following grading scale will be used to determine grades:
A | 90 – 100 % |
B | 80 – 89 % |
C | 70 – 79 % |
D | 60 – 69 % |
F | Below 60% |
Make-ups are not allowed for missed quizzes, instead I will
allow you to drop your lowest quiz score from the term.
All tests will count toward your final grade.
The instructor reserves the right to adjust the grading scale if
necessary.
Working through the assigned problems is essential to
learning mathematics. Showing your
work is the only way to receive partial credit and hence is very important.
Academic integrity:
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 may include failure for part or
all of a course, as well as suspension from the University.
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.
Daily Course Outline
Day 1 |
Polya’s four steps. Strategies: guess & test, variable, picture, pattern, list, simpler problem |
Day 2 |
Review 4-steps, Give FOIL lesson – a good lesson?
Concrete to abstract. Hunter’s
anticipatory set, objectives, check 4 understanding.
Intro sets (N, W, ε, ø = {}, sets – listing or set builder
notation. Venn diagrams, U,
∩. |
Day 3 |
Polya, 4 steps/ Lesh model. Review sets: N, W, {} ≠ {ø}.
Equal sets, subset, proper subset, U, ∩, Venn diagrams,
difference sets. |
Day 4 |
Equivalent sets R3={Bill, Sue, …},
A={x│x ε R3 and a 1011 student}. R3=A, R3≤A,
R3≥A? U,
∩, Cartesian product, complement, ∞/finite, 1-1 (dance). |
Day 5 |
{}, { x│x…}, U and ∩ in Venn,
cross-product, complement, 1-1, difference |
Day 6 |
Review sets, look at 1-1 – important cause provides
framework for counting [2.1 #34] |
Day 7 |
Set notation: difference, cross-product, U, ∩.
Venn diagrams |
Day 8 |
Review subset, proper subset. How many 1-1 correspondences exist in a set with: 1, 2, 3,
4, 5, … n elements? How
many grains of sand (∞ or fin).
Which number is bigger: 5
or 7?
Larger numeral=5, number=7. Number
types: cardinal: # of elements. Ordinal:
pages in a book. Identification:
phone #, jersey. Place value
system vs. tally, Egyptian, Roman, Babylonian, Mayan (from text). |
Day 9 |
Number (concept) vs Numeral (symbol), cardinal,
ordinal, and identification number types.
Systems: additive (tally), additive w grouping (tally w bunches),
Additive w symbols (Egyptian), Additive/sub (Roman), Place value
(Babylonian and Mayan). Play
w B4 blocks -- SHOW ME YOUR PALMS! |
Day 10 |
Modeling place value concretely
B4 blocks – naming. Bruner’s flowchart of
learning: 1 preparation, 2 explore & discover, 3 abstraction &
organiztion, 4 fixing skills, 5 application. 3&4 in elem. |
Day 11 |
Look at addition on game board. Consider 145)10 as 1 flat, 4 longs, 5 units |
Day 12 |
TEST #1 – building towards addition in BFLU. |
Day 13 |
Look at addition on game board. Bridging and
modeling. |
Day 14 |
Adding in different bases, converting Base N to Base
10. |
Day 15 |
Review changing bases, TOE-ET in B12; 123)4+332)4= to B10. 137)8 to B10 |
Day 16 |
Bn to B10. When
will we use this? Review
converting to B10. Converting
to Bn. |
Day 17 |
Review addition.
Intro subtraction – Give one away game! |
Day 18 |
Converting base ten to another base & converting base n into another base (other than base 10) |
Day 19 |
Commutative, associative, distributive, and closure properties |
Day 20 |
Functions and Relations & Review for Test 2 |
Day 21 |
Test #2 |
Day 22 |
Intro multiplication’s 6 models: 1-cartesian product (outfits), array, repeated +, number line jumps, sets of sets, area model. |
Day 23 |
Multiplication – 6 models. Commutative (switchy), Assoc (groupy), Distributive (spready),
zero property (multiplication), identity prop (x / +).
Look @ x algorithm Check out a multiplication video at: http://www.wimp.com/visualway/ |
Day 24 |
Locker Problem Divisibility tests for multiplication |
Day 25 |
Multiplication with the array and partial products -- five different levels. Assign multiplication in alternate base (i.e. Base 6). |
Day 26 |
Check for understanding on multiplication in different bases. |
Day 27 |
Division -- what does 12/3 "look like" when thinking of blocks? |
Day 28 |
"The sharing game" and bridging to the division algorithm. Repeated subtraction, sets of sets - # of elements, sets of sets - # of sets. |
Day 29 |
Bridging to division - renaming 235 as 2 H 3 T 5 U or 23 T 5 U or 235 U |
Day 30 |
Test #3 |
Day 31 |
Prime and composite numbers on graph paper |
Day 32 |
Sieve of Erastothenes and primes |
Day 33 | Divisibility tests
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Day 34 | Common Factors & Common Multiples |
Day 35 | Fractions: Area model, Circle model, Set model, & Number Line model |
Day 36 | Comparing / renaming fractions |
Day 37 | Fraction addition and subtraction |
Day 38 | Fraction multiplication and division |
Day 39 | Test #4 |
Day 40 | Review for Final Exam |
Day 41 |
|
Course Description
MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS I (3 credits) This course meets the PELSB fundamental topics in arithmetic competencies. These topics include addition, subtraction, multiplication, and division of whole numbers; number theory related to fractions; fractions; decimals; and integers. This is the first of two mathematics courses providing the background for teaching in the elementary school. Emphasizes the use of mathematics manipulatives for modeling the basic operations.
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
Elementary education major or consent of instructor.
Required Text
Reconceptualizing Mathematics for Elementary School Teachers (2017) by Sowder, Sowder, & Nickerson; W. H. Freeman (pub), 3rd ed.
Resources: |
Minnesota K-12 Mathematics Framework (1998) by W. Linder-Scholer. SciMathMN (pub). Number Sense Activities section. Principles and Standards for School Mathematics (2000). NCTM; Reston, VA. |
Professional Education Licensing and Standards Board Standards
8710.3200 Teachers of Elementary Education K-6
Department of Mathematics and Computer Science
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K/A |
Activities |
Assessment |
8710.3200 Teachers of Elementary Education K-6
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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 |
H. A teacher of children in kindergarten through grade 6 must demonstrate knowledge of fundamental concepts of mathematics and the connections between them. The teacher must know and apply; |
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(1)concepts of mathematical patterns, relations, and functions, including the importance of number and the importance of the educational link between primary school activities with patterns and the later conceptual development of important ideas related to functions and be able to: |
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(a) identify and justify observed patterns;
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KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will identify, describe, and justify observed patterns on homework, in-class work, and on questions on Test 1. |
(b) generate patterns to demonstrate a variety of relationships; and
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KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will generate patterns to demonstrate a variety of relationships such as the number of handshakes that a person can share with people in a room, the number of hands in a room, or the number of heads in a room. Students will do this on homework, in-class work, or on questions on Test 1. |
(c) relate patterns in one strand of mathematics to patterns across the discipline;
|
KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will relate patterns in one strand of mathematics to patterns across the discipline such as paths across a square lattice (confined to grid lines) and pascal’s triangle on homework and in-class work. |
(3) concepts of numerical literacy:
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(a) possess number sense and be able to use numbers to quantify concepts in the students’ world;
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KA |
TEACH and discuss homework for sections 2.1-2.3, 5.1-5.2; complete “Craig’s Stories”
Weeks 4-6 |
Students will demonstrate that they possess number sense and can use numbers to quantify concepts in the world by completing stories with appropriate numbers on homework or in-class work. |
(b) understand a variety of computational procedures and how to use them in examining the reasonableness of the students’ answers;
|
KA |
TEACH and discuss homework for sections 3.1-4.3
Weeks 4-9 |
Students will use different estimation techniques, and different computational algorithms to determine the proper size and correctness of a computation on homework or in-class work. |
(c) understand the concepts of number theory including divisibility, |
KA |
TEACH and discuss homework for sections 5.1-5.2
Weeks 10-12 |
Students will demonstrate their understanding of divisibility by constructing factor trees and expressing numbers in prime factored form on homework, in-class work, or on questions on Test 4. |
factors, |
KA |
TEACH and discuss homework for sections 5.1-5.2
Weeks 10-12 |
Students will demonstrate their understanding of factors by constructing factor trees and expressing numbers in prime factored form on homework, in-class work, or on questions on Test 4. |
multiples, and |
KA |
TEACH and discuss homework for sections 5.1-5.2
Weeks 10-12 |
Students will demonstrate their understanding of multiples when they find the least common multiple of pairs of numbers on homework, in-class work, or on questions on Test 4. |
prime numbers, and |
KA |
TEACH and discuss homework for sections 5.1-5.2
Weeks 10-12 |
Students will be able to define a prime number and find prime numbers using a sieve of Eratosthenes on homework, in-class work, or on questions on Test 4. |
know how to provide a basis for exploring number relationships; |
KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will be able to apply different techniques to explore number relationships such as odd, even analysis or sequential differences on homework, in-class work, or on questions on Test 1. |
(7) mathematical processes:
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(a) know how to reason mathematically, |
KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will show that they know how to reason mathematically on homework, in-class work, or on questions on Test 1. |
solve problems, and |
KA |
TEACH and discuss homework for sections 1.1, 1.2 from the text.
Weeks 1-3 |
Students will show that they know how to solve problems on homework, in-class work, or on questions on Test 1. |
communicate mathematics effectively at different levels of formality; |
KA |
TEACH and discuss homework for sections 1.1-6.3.
Weeks 1-15 |
Students will demonstrate throughout the semester that they can communicate mathematics effectively and at different levels of formality on assignments, in group work, orally and on written work on tests and the final exam. |
(d) understand and apply problem solving, reasoning, communication, and connections; and |
KA |
TEACH and discuss homework for sections 1.1-6.3.
Weeks 1-15 |
Students will demonstrate throughout the semester that they understand and can apply problem solving, reasoning, communication and connections on assignments, in group work, orally and on written work on tests and the final exam. |
(8) mathematical perspectives: |
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(a) understand the history of mathematics and the interaction between different cultures and mathematics; and |
KA |
TEACH and discuss homework for sections 2.1-2.3.
Weeks 4-6 |
Students will demonstrate their understanding of the history of mathematics and the interaction between different cultures and mathematics and the development of number systems on homework, in-class work, or on questions on Test 2. |
(b) know how to integrate technological and non-technological tools with mathematics. |
KA |
TEACH and discuss homework for sections 1.1-6.3.
Weeks 1-15 |
Students will demonstrate that they know how to integrate technological and non-technological tools with mathematics on homework, in-class work, and on questions on Tests and the final exam. |
Technology Requirements and Expectations
Students will use internet browsers to access information and answer questions posed in class. Students 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 Þ Concrete Û Semi-Concrete Û 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
Upon request this document can be made available in alternate formats. Please contact Kathi Hagen at Disabilities Services at (218) 755-3883 for assistance or the AUC Office at 262-6753 or (800) 369-4970.
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 for those students who attend class regularly and complete assignments that they will earn an A or B.
- 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 at least every three weeks.
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 |
Chapter 1 Problem Solving course set up; Bruner, Glen’s 7 principles, Polya, R-model, Math Exercise vs Math Problem |
Solve triangle problem and homework |
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Homework, Sets list and rule specification, set operations |
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Week 2 |
Chapter 1 Problem Solving |
16 Venn diagrams and notation for shaded regions |
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Finite and infinite sets; equal vs equivalent sets; size of sets |
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Week 3 |
Chapter 1 Problem Solving |
Cartesian Product of two sets; |
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Venn diagrams to solve math word problems |
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Week 4 |
Chapter 2 – Sets, Whole Numbers, and Numeration |
Class study problem; Win-A-Block |
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Relations, Functions; Arithmetic, Geometric, other sequences; Lose-A-Block; equivalence relation, reflexive, symmetric, and transitive properties |
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Week 5 |
Chapter 3 Addition and Subtraction, Chapter 4 Mental Math, Estimation, and Calculators |
Butchers, Bakers, Candlestick makers problem; |
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Number Systems; Number System Quiz |
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Week 6 |
Chapter 3 Addition and Subtraction, Chapter 4 Mental Math, Estimation, and Calculators |
Game board addition semi-concrete |
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Subtraction models |
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Week 7 |
Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators |
Abbot and Costello or Ma and Pa Kettle |
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Partial Product multiplication |
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Week 8 |
Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators |
Multiplication properties |
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Division models |
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Week 9 |
Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators |
Place value long division 5 steps |
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Place value long division 5 steps |
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Week 10 |
Chapter 5 Number Theory |
Factors – rectangles, prime factor trees, fundamental theorem of arithmetic, prime factorization, sieves of Erastothenes, table columns, |
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Divisibility rules |
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Week 11 |
Chapter 5 Number Theory |
Divisibility rules |
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LCM GCF set definition |
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Week 12 |
Chapter 5 Number Theory |
LCM (formula) GCF (Euclidean Algorithm) |
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TEST 4 |
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Week 13 |
Chapter 6 Fractions |
Land ownership activity |
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Fraction models and manipulatives concrete and virtual |
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Week 14 |
Chapter 6 Fractions |
rectangular array, represent, compare, add, subtract, multiply |
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rectangular array, represent, compare, add, subtract, multiply |
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Week 15 |
Chapter 6 Fractions |
fraction division – road paving activity |
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TEST 5 |
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Final Exam – 2 Hours Comprehensive |
updated 8/16/2017
by Todd
Frauenholtz