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Oglala Lakota College
Course Syllabus
(SA, 1/05)
Name of Course: Mathematics for Elementary Teachers I
Course Number: Math 223
Semester Hours: 3
Semester: Fall 2010
Class Time: Thursday, 5:00 8:00 pm
Meeting Date:
Day / Location: He Sapa College Center, Rapid City
Instructor:
Instructor Office Hours: Th 4:00 5:00 pm (One hour before each class)
Phone:
Text(s) & Supplemental Material: Bassarear, Mathematics for Elementary School
Teachers, 4th Edition
Bassarear, Mathematics for Elementary School
Teachers Explorations, 4th Edition
Course Prerequisite(s): Math 103 Elementary Algebra
*Must have received a C or better
Oglala Lakota College's Education Department Vision and Mission:
Vision Statement: To graduate highly qualified, professional, motivated, and reflective teachers who possess and teach Wolakolkiciyapi in a multicultural, changing world. (Wolakolkiciyapi refers to the whole person in balance and in harmony, spiritually, physically, mentally and socially.) The professional teacher education program views Wolakolkiciyapi as reflection and conduct of the Lakota virtues as a means of improving self and others.Mission Statement: Graduates from our programs will be proficient as competent reflective teachers of content, theory and application with an emphasis on character education while emphasizing community empowerment through reflection of traditional Lakota Perspectives.
Course Description: This course utilizes an inquiry-based approach to gain understanding of mathematical concepts at the concrete, representational and abstract levels. Topics include problem solving, sets, algebraic thinking, the study of numeration systems, fundamental operations of arithmetic (properties and algorithms), and elementary number theory. The processes of problem solving (representation, reasoning, making connections, and communication of ideas) are emphasized throughout the course. Direct connections are made between course content and the SD K-8 Content Standards for Mathematics
Rational: This course will stress understanding the mathematical structures and the connectedness within and between concepts, as well as to other curricula and real-life. The foci of this course are: using deductive, inductive and intuitive reasoning to make sense of mathematics; reawakening a curiosity about math and numbers; and understanding the importance of disequilibrium as integral to the learning process.
Intended Course OutcomesStandardsAssessmentTeacher candidates will be able to:
examine and explain their own mathematical processes in a clear and understandable way
respond with openness and acceptance to processes differing from their own in order to broaden their own store of processes and to prepare themselves to be open and knowledgeable when evaluating the validity of the various processes of their own students
explain and use a variety of strategies for problem solving
demonstrate using verbal, pictorial, concrete and abstract explanations the connectedness within and between mathematical concepts
relate mathematics to other ideas as well as to everyday life
recognize and accept deductive, inductive and intuitive reasoning in themselves and their peers, thus preparing them to recognize and accept the various forms of reasoning used by their students
explain in a variety of ways mathematical structures and the underlying mathematical foundations of the concepts contained in the content areas developed in the part of the course
show their mathematical understanding by the quality of their explanations, representations, and hypotheses in the content areas of this course
speak mathematically using the appropriate professional vocabulary while in dialogue with their peers, discussing solution paths, strategies, representations, hypotheses, and conclusions, and while presenting and discussing articles from professional journals.
Participate in cooperative learning groups, sharing their thoughts and actively listening to their peers with care and compassion
Show proficiency in each of the specific content areas described in the course outline contained within this syllabus
Make sense of elementary mathematics confidently and thereby have the content knowledge to be efficient teachers of mathematicsINTASC
1.1, 1.2, 1.4, 1.6
4.1, 4.2, 4.3
5.1, 5.2, 5.3
6.1, 6.2, 6.3, 6.4
7.1
8.2, 8.3
9.1, 9.2
10.2
NAEYC
1, 2, 3, 4abcd, 5Teacher candidates will demonstrate understanding through:
active participation in class discussions and activities; journal reflections and reflective dialogue with peers; article reviews and discussions; demonstrations, modeling and presentation of mini-lessons; completion of class assignments; and course assessments.
Methods of Instruction: This class will use an exploratory method in order to lead students to discover the meaning behind arithmetic in elementary education. While doing these explorations the students will use math materials, pictures, graphs, or other forms of representation to clarify ideas. They will work in cooperative groups during which they will share their strategies and explanations while exploring the concepts developed in the class. In addition, students will present mini-lessons and facilitate small learning groups.
General Course Requirements: Students are expected to
Be present for all classes, on time, and for the entire class.
Actively engage in discussions and activities with peers and the instructor.
Respond to assignments thoughtfully and with creative insight.
Prepare for and facilitate mini-lessons.
Lakota Perspective:
Lakota cultural practices will frame the work for our class. The Lakota values of wacantognaka (generosity), woohitika (courage), woksape (wisdom), and wowacintanka (respect) will guide course interactions and activities. Students are encouraged to consider and incorporate cultural perspectives in their development and application of concepts related to exceptional learners.
Course Assignments:
Active participation in class discussions and activities.
Prepare 3 mini-lessons and facilitate cooperative group engagement in the activities.
Reflect upon learning through journal entries.
Complete 2 written article reviews and present/discuss these articles in class.
Complete section exercises as assigned for course topics.
Complete chapter review exercises as assigned for course topics.
Complete a comprehensive final exam.
Grading and Evaluation:
Grading:
Letter GradeScaleUndergraduate
PointsA90 - 100675 - 750B80 - 89600 - 674C70 - 79525 - 599D60 - 69450 - 524F 0 - 59 0 - 449
*"C" or above is required for all professional courses.
Course Requirements/AssignmentsValuePoints PossibleMini-Lessons / Group Facilitation (3)2575Journal Reflections (15)575Article Reviews and Discussions (2)2550Section Exercises (12) 25300Chapter Review Exercises (4)50200Comprehensive Final5050Total Possible750
Attendance Policy: Students are required to attend class regularly and are reminded of the values such as responsibility, integrity, courage and fortitude. A student may be dropped after three consecutive absences (at the discretion of the instructor and the district director) and will be dropped after five total absences. Please see Policy stated in catalog.
Assignments: All assignments are due at the assigned time. It is important to have assignments done on time because these assignments are an integral part of class discussions and activities. Thus students who do not have their assignments done on time come to class unprepared and in so doing are not able to participate in the class discussions nor share their strategies. This lack of preparation results in a lack of respect for their classmates. The values of responsibility, respect, fortitude, and generosity are as important as academic content, thus all assignments need to be completed and submitted on time.
Make-up Work: On occasion unexpected situations will arise, however, students are responsible for knowledge of the content of the course. Assignments submitted one session late will be subject to a 15% point deduction. No more than half-credit will be given for any assignment submitted later than two sessions following the due date. In the case of an absence from class, students will be expected to complete as much of the missed sessions work as possible. Students should plan ahead for any known absences. In addition, students should meet with the instructor during office hours the class immediately following any unplanned absences.
Academic Integrity: Academic dishonesty is the taking of an examination or the preparation of papers for credit wherein the student knowingly represents the work of another as his/her own; and/or knowingly breaks stated examination rules. A student may be expelled and barred from further classes upon proof in a hearing of academic dishonesty.
Student Disability Services: If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and the OLC Coordinator of Support Services (455-6040) as early as possible in the semester.
Course Outline:
Foundations for Learning Mathematics
Getting Comfortable with Mathematics
Problem-solving
Patterns
Representation
Reasoning and Proof
Communication
Connections
Fundamental Concepts
Sets
Algebraic Thinking
Numeration
Fundamental Operations of Arithmetic
Addition
Subtraction
Multiplication
Division
Number Theory
Divisibility and Related Concepts
Prime and Composite Numbers
Greatest Common Factor and Least Common Multiple
NOTE: Information contained in this syllabus was, to the best knowledge of the instructor, considered correct and complete when distributed for use at the beginning of the semester. The instructor reserves the right to make changes in the syllabus in collaboration with the class with reasonable notice to all concerned.
INTASC Standards
STANDARD 1: CONTENT PEDAGOGY The teacher understands the central concepts, tools of inquiry, and structures of the discipline he or she teaches and can create learning experiences that make these aspects of subject matter meaningful for students.
STANDARD 2: STUDENT DEVELOPMENT The teacher understands how children learn and develop, and can provide learning opportunities that support a childs intellectual, social, and personal development.
STANDARD 3: DIVERSE LEARNERS The teacher understands how students differ in their approaches to learning and creates instructional opportunities that are adapted to diverse learners.
STANDARD 4: MULTIPLE INSTRUCTIONAL STRATEGIES The teacher understands and uses a variety of instructional strategies to encourage student development of critical thinking and problem solving.
STANDARD 5: MOTIVATION & MANAGEMENT The teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation
STANDARD 6: COMMUNICATION & TECHNOLOGY The teacher uses knowledge of effective verbal, nonverbal, and media communication techniques to foster active inquiry, collaboration, and supportive interaction in the classroom.
STANDARD 7: PLANNING The teacher plans instruction based upon knowledge of subject matter, students, the community, and curriculum goals.
STANDARD 8: ASSESSMENT The teacher understands and uses formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the learner.
STANDARD 9: REFLECTIVE PRACTICE: PROFESSIONAL DEVELOPMENT The teacher is a reflective practitioner who continually evaluates the effects of his or her choices and actions on others and who actively seeks out opportunities to grow professionally.
STANDARD 10: SCHOOL AND COMMUNITY INVOLVEMENT The teacher fosters relationships with school colleagues, parents, and agencies in the larger community to support students learning and well-being.
Math 223: Tentative Course Schedule
This calendar is subject to change depending upon the needs of the students, amount of content, and the availability of resources.
SessionTopic(s) of DiscussionOko Wanji
Course Introduction
Text: Foundations for Learning Mathematics
Section 1.1 Getting Comfortable with Mathematics (p. 1 6)
Explorations
Preface p. xi xiv
Exploration 1.1 Patterns and Connections (p. 2-6)
Exploration 1.3 Real-Life Problems (p.8)
Oko Nunpa
Text: Foundations for Learning Mathematics
Section 1.2 Problem Solving (p. 6-16)
Section 1.3 Patterns (p. 16-22)
Explorations
Exploration 1.4 Patterns and Proof (p. 9-11)
Oko Yamni
Text: Foundations for Learning Mathematics
Section 1.4 Representation (p. 23-29)
Section 1.5 Reasoning and Proof (p. 30-44)
Explorations
Exploration 1.5 Master Mind (p. 12)
Exploration 1.6 Magic Squares (p. 13-14)
Exercises (p.26)
Oko Topa
Text: Foundations for Learning Mathematics
Section 1.6 Communication (p. 44-48)
Section 1.7 Connections (p. 48-54)
Explorations
Exploration 1.7 Magic Triangle Puzzles (p. 15-16)
Exercises (p.55)
Chapter 1 Review Exercises (p. 59)
Oko Zaptan
Text: Fundamental Concepts
Section 2.1 Sets (p. 61-76)
Explorations
Section 2.1 Exploring Sets (p. 21-23)
Exercises 2.1 (p. 76)
Oko Sakpe
Text: Fundamental Concepts
Section 2.2 Algebraic Thinking (p. 80-96)
Explorations
Section 2.2 Exploring Algebraic Thinking (p. 24-37)
Exercises 2.2 (p. 96)
Oko Sakowin
Text: Fundamental Concepts
Section 2.3 Numeration (p. 101-118)
Explorations
Section 2.3 Exploring Numeration (p. 38-47)
Exercises 2.3 (p. 119)
Chapter 2 Review Exercises (p. 123)
Oko Saglogan
Text: The Four Fundamental Operations of Arithmetic
Section 3.1 Understanding Addition (p. 127-150)
Explorations
Section 3.1 Exploring Addition (p. 49-54)
Exercises 3.1 (p. 150)
1st Article Review Due
Oko Napciunka
Text: The Four Fundamental Operations of Arithmetic
Section 3.2 Understanding Subtraction (p. 152-166)
Explorations
Section 3.2 Exploring Subtraction (p. 55-58)
Exercises 3.2 (p. 166)
Oko Wikcemna
Text: The Four Fundamental Operations of Arithmetic
Section 3.3 Understanding Multiplication (p. 168-185)
Explorations
Section 3.3 Exploring Multiplication (p. 59-69)
Exercises 3.3 (p. 185)
Oko Ake Wanji
Text: The Four Fundamental Operations of Arithmetic
Section 3.4 Understanding Division (p. 189-207)
Explorations
Section 3.4 Exploring Division (p. 70-78)
Exercises 3.4 (p. 207)
Chapter 3 Review Exercises (p. 212)
Oko Ake Nunpa
Text: Number Theory
Section 4.1 Divisibility and Related Concepts (p. 215-229)
Explorations
Section 4.1 Exploring Divisibility and Related Concepts (p. 79-81)
Exercises 4.1 (p. 229)
Oko Ake Yamni
Text: Number Theory
Section 4.2 Prime and Composite Numbers (p. 232-239)
Explorations
Section 4.2 Exploring Prime and Composite Numbers (p. 83-89)
Exercises 4.2 (p. 239)
2nd Article Review Due
Oko Ake Topa
Text: Number Theory
Section 4.3 Greatest Common Factor and Lease Common Multiple
(p. 241-251)
Explorations
Section 4.3 Exploring GCF and LCM (p. 90-93)
Exercises 4.3 (p. 252)
Chapter 4 Review Exercises (p. 254)
Oko Ake Zaptan
Course Wrap-up
Comprehensive Final
Note: Mini-lessons will be scheduled throughout the semester on a rotation cycle.
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