Math 1011 Syllabus

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:

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:

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.

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	K/A	Activities	Assessment
8710.3200 Teachers of Elementary Education K-6		In this syllabus you will find the word TEACH. This will mean to: Launch: This is where the teacher sets the context of the problem or activity being worked on this day. This involves making sure the students clearly understand the mathematical context and the mathematical challenge of the day’s activities. Explore: This is the time where the students get to work in pairs, individually, or as a class to solve problems presented by the lesson. Share: This occurs when most of the students have made sufficient progress toward solving the problem presented with today’s lesson. It is during this phase that the students learn how others approached the problem and possible solution routes. Helps students deepen their understanding of the mathematical ideas presented in the day’s lesson. Summarize: During this phase the teacher concludes the lesson by clearly stating what the main idea was in the lesson, being sure to clear up any confusion that may arise during the “share” segment. Helps students focus their understanding of the mathematical ideas presented in the lesson.
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;
(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:
(a) identify and justify observed patterns;	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	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:
(a) possess number sense and be able to use numbers to quantify concepts in the students’ world;	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:
(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:
(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

Understand the problem
Devise a plan
Carry out the plan
Reflect

Lesson Sequencing

Intuitions Þ Concrete Û Semi-Concrete Û Abstract

Glen’s Teaching/Learning Principles

1. Teach the way students learn
2. Use group work, heterogeneous, 3-4, change monthly
3. Communication student Û student
4. Communication teacher Û student
5. Multiple solution paths
6. Use contextual settings / problem solving
7. Assessment

Grading
To inform instruction

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
	Homework, Sets list and rule specification, set operations
Week 2	Chapter 1 Problem Solving Homework, Sets list and rule specification, set operations
	16 Venn diagrams and notation for shaded regions
	Finite and infinite sets; equal vs equivalent sets; size of sets
Week 3	Chapter 1 Problem Solving attribute pieces, venn diagrams, set operations
	Cartesian Product of two sets;
	Venn diagrams to solve math word problems TEST 1
Week 4	Chapter 2 – Sets, Whole Numbers, and Numeration TV watching problem
	Class study problem; Win-A-Block
	Relations, Functions; Arithmetic, Geometric, other sequences; Lose-A-Block; equivalence relation, reflexive, symmetric, and transitive properties
Week 5	Chapter 3 Addition and Subtraction, Chapter 4 Mental Math, Estimation, and Calculators Voting and information problem; Number Systems Egyptian, Roman (no subtraction)
	Butchers, Bakers, Candlestick makers problem; Number Systems Babylonian, Mayan, Attic-Greek
	Number Systems; Number System Quiz Counting in other place value systems Craig’s Stories
Week 6	Chapter 3 Addition and Subtraction, Chapter 4 Mental Math, Estimation, and Calculators place value systems; conversion of value between bases addition models game board addition concrete
	Game board addition semi-concrete
	Subtraction models Game board subtraction concrete TEST 2
Week 7	Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators Game board subtraction semi-concrete; 4 fact tables addition and subtraction properties
	Abbot and Costello or Ma and Pa Kettle Multiplication Models
	Partial Product multiplication
Week 8	Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators Partial Product multiplication, Lattice method, Egyptian doubling algorithm
	Multiplication properties
	Division models grouping or sharing Scaffold long division
Week 9	Multiplication and Division, Chapter 4 Mental Math, Estimation, and Calculators Place value long division 5 steps
	Place value long division 5 steps
	Place value long division 5 steps TEST 3
Week 10	Chapter 5 Number Theory Fire drill locker problem; squares, perfect squares, factors, co-factors, primes, composite, special
	Factors – rectangles, prime factor trees, fundamental theorem of arithmetic, prime factorization, sieves of Erastothenes, table columns,
	Divisibility rules
Week 11	Chapter 5 Number Theory Divisibility rules
	Divisibility rules
	LCM GCF set definition
Week 12	Chapter 5 Number Theory LCM GCF prime factorization – connection to algebra
	LCM (formula) GCF (Euclidean Algorithm)
	TEST 4
Week 13	Chapter 6 Fractions Mixing Juice activity
	Land ownership activity
	Fraction models and manipulatives concrete and virtual
Week 14	Chapter 6 Fractions rectangular array, represent, compare, add, subtract, multiply
	rectangular array, represent, compare, add, subtract, multiply
	rectangular array, represent, compare, add, subtract, multiply
Week 15	Chapter 6 Fractions fraction division – road paving activity
	fraction division – road paving activity
	TEST 5
	Final Exam – 2 Hours Comprehensive

A	90 – 100 %
B	80 – 89 %
C	70 – 79 %
D	60 – 69 %
F	Below 60%

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. Win-a-block – emphasizes place value. Look at 2.4 homework.
Day 11	Look at addition on game board. Consider 145)₁₀ as 1 flat, 4 longs, 5 units & Counting in B4, B6, B8, B10, B12, … B23. Fix counting – teens are awkward!
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 algorithms (partial products, traditional, and lattice). 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
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	Final Exam, Wednesday, December 19th from 8:00 to 10:00 am

Department of Mathematics and Computer Science

K/A

Activities

Assessment