Bemidji State University
 M3065/ MATHEMATICAL FOUNDATIONS FOR MIDDLE SCHOOL TEACHERS (4 credits)
Spring 2017
MWF, 1-2pm

Instructor:  Glen Richgels

Email: -- grichgels@bemidjistate.edu

Office Phone: 755-2824

Office hours: Office Hours Spring

 

 

 

Professional Education  Department Mission Statement:

 

 ÒThe 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

MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS I (3 credits) This course meets the BOT 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

Mathematics for Elementary Teachers: A Contemporary Approach (2011) by G. L. Musser, W. F. Burger, & B. E. Peterson; John Wiley & Sons (pub), 9th 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.



Board of Teaching 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:

  1. 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 dayÕs activities.
  2. 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.
  3. Share: This occurs when most of the students have made sufficient progress toward solving the problem presented with todayÕs 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 dayÕs lesson.
  4. 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 ÒshareÓ 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 pascalÕs 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 studentsÕ world;

 

KA

TEACH and discuss homework for sections 2.1-2.3, 5.1-5.2; complete ÒCraigÕs StoriesÓ

 

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 studentsÕ 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,

 

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

 

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

 

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;

 

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, GeometerÕs 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
PolyaÕs problem solving steps

1.     Understand the problem

    1. Devise a plan
    2. Carry out the plan
    3. Reflect

 

Lesson Sequencing

                  Intuitions Þ Concrete ó Semi-Concrete ó Abstract

 

GlenÕs Teaching/Learning Principles

1.     Teach the way students learn

2.     Use group work, heterogeneous, 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

    1. Grading
    2. 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, GlenÕs 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
CraigÕs 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