Vision Statement
We develop educational leaders who create tomorrow's opportunities in a globally engaged society.
Mission Statement
The Yuma Branch Campus of Northern Arizona University provides opportunities in higher
education for the diverse and growing communities of the Lower Colorado River Region and
other populations we serve. It is the mission of the Education Department to prepare competent
and committed professionals who will make positive differences for children. We support the
mission of NAU-Yuma by preparing citizens who understand and value diversity, environmental
sustainability, and global engagement
EDU 314 Integrated Mathematics in Early Childhood
Fall 2015
(3 credit hours)
Instructor: Susan Stutler, Ph.D.
Office: AC 229
Office Hours: T, W, Th 1:00 – 3:45 p.m.
.
I. Course prerequisites: Acceptance into BSED Elementary Education - Yuma, BAS Early
Childhood, or
B Interdisciplinary Studies – Early Childhood
II. Course description: The course will investigate a variety of developmentally appropriate
strategies and materials to facilitate young children’s, Pre-K – Grade 3, construction of
mathematical understandings through exploration of number concepts; geometric concepts;
measurement; patterns & algebraic concepts; persistence in problem-solving, flexible and logical
thinking; and authentically integrated experiences in language, science, social studies, movement
and the arts. The course will challenge teachers’ beliefs and knowledge about how children
develop understandings of mathematics as we explore both the theory and practice of teaching
major concepts of the discipline. Aligned to AZ Early & ACCR Standards, to NAEYC standards,
and to InTASC.
III. Student Learning Expectations/Outcomes:
A. Demonstrate knowledge and understanding of child development and learning in the
cognitive, emotional, physical, communicative, and adaptive domains of human awareness;
and the ways that children make meaning in each of these domains to construct
mathematical understandings and build logical thinking and reasoning.
B. Demonstrate knowledge and understanding of the big ideas and major mathematical
concepts that young children are working on in every day situations as they construct
understandings of their world in order to design and implement learning experiences in each
C.
D.
E.
F.
G.
of the mathematical strands: numbers and operations, measurement, geometry, data and
analysis, and patterns, function and algebra.
Demonstrate knowledge and understanding of core principles of child development and the
essential concepts and tools of inquiry of mathematics to design and implement appropriate,
child-centered explorations that integrate math with language experiences, social studies,
science, art, movement, and music.
Demonstrate knowledge and understanding of the core principles of child development to
effectively use multiple, appropriate differentiated approaches and instructional strategies to
teach mathematics in ways that match learning characteristics, needs and strengths of all
children and to create child-centered learning materials, curricula and environments that
scaffold emerging mathematical knowledge, understandings and thinking processes.
Demonstrate knowledge and understanding of developmentally appropriate approaches,
uses and benefits of assessment of young children’s mathematical learning and
progressions, particularly observation and documentation, to implement effective, databased instruction.
Demonstrate knowledge and understanding of effective ways to communicate mathematical
understandings with diverse families, cultures & communities in order to engage and
empower families through learning partnerships that are responsive, respectful and
inclusive.
Demonstrate the knowledge, dispositions and actions of professional collaboration, ethical
practice, advocacy, and the teacher as a researcher/learner
IV. Course structure/approach:
A variety of strategies will involve students in meaningful investigations of the core
principles of child development and effective methods for teaching math in early education
environments. To examine both the theory and practice of math education in early
childhood, we will use inquiry, lecture, discussion, review of literature and peer-reviewed
journals, research, collaborations to design and implement instruction, modeling and field
experiences.
V. Textbook and required materials:
Cross, C.T. (2009). Mathematics learning in early childhood: Paths toward excellence and equity.
Washington, DC: The National Academies Press.
Arizona Department of Education. (2010). Arizona’s Common Core Standards – Mathematics.
Free download primary math standards.
http://www.azed.gov/standards-practices/mathematics-standards/
Students are to download and print a copy of the AZ Early Learning Standards:
http://www.ade.state.az.us/earlychildhood/downloads/EarlyLearningStandards.pdf
VI. Course Outline:
Week 1: Meet in Teacher Resource Room. Introduction. Young children and math. How young
is too young to start learning math? Math in the everyday lives of young children. What do
we mean when we say that children “construct mathematical understandings” as they
explore their world? “The Math Curse”by John Skieska. Explore math manipulatives.
Week 2: Meet in the NAU Academic Library to explore on-line research data-bases and peerreviewed journals in early child mathematics. Research and practice in the field of early
child mathematics: How do we share our practice? Our lessons? Our stories? NAEYC
Position Statement: Early Childhood Mathematics: Promoting Good Beginnings – Jigsaw.
Week 3: Numbers - Counting and one-to-one correspondence. “Benny’s Pennies”. Cardinal,
ordinal, nominal. Piaget and the concept of Conservation. Conservation of quantity, length,
liquid. Continuous quantities, discrete quantities. Playing with Metric Blocks. Article
Review 1 due.
Week 4: Math in the everyday lives of young children – a natural interest in math. Mathematical
thinking – logical-mathematical thinking and problem solving. The playful nature of
mathematics. Assessment of mathematical learning in early childhood. Estimating with
gumdrops, beans, & rice: How to Make a Million. Night Noises by Mem Fox.
Week 5: Geometry -The power of blocks. Proximity and spatial relationships. Vertical and
horizontal. Shapes and form. Reasoning, communication and argumentation with blocks:
Transitivity, equalities and inequalities. Playing with pattern blocks, tangrams and
geoboards. Marshmallows & Straws. The Wing on a Flea by Ed Emberly. Article Review 2
due.
Week 6: Measurement – Non-standard and standard units of measurement. “Ladybug Lengths”.
Measuring with lima beans, licorice, lollipops & paperclips. Creating our own non-standard
units. By the way, what is a unit? The language of measurement in early childhood. Playing
with measurement. Scales, clocks, and measuring sticks. Begin individual lesson planning.
Week 7: Data and statistics – Collecting, counting, & displaying data in early childhood.
Pictographs. Skittles: Estimating, counting, comparing, displaying data with Skittles.
Graphing and classification, seriation, number relationships, spatial relationships: Logical
thinking. Playing with Cuisenaire Rods. Article Review 3 due.
Week 8: Patterns, Function & Algebra – “Algebra in the early years? Yes!” NAEYC research
article: Jigsaw sharing. Natural and man-made patterns. Repeating & growing patterns,E
qual and not equal, transitivity, solving for the unknown. Playing with Hundreds Boards.
The Rabbit Problem by Emily Gravitt. Counting Book due.
Week 9: Mathematical Operations – Addition, Subtraction (with and without regrouping),
Multiplication, Division & Fractions in early childhood. Playing with Base 10 Blocks. The
Doorbell Rang by Pat Hutchins. Unpacking the Early Childhood Common Core Standards
to align with instruction.Article Review 4 due.
Week 10: No class this week. Instead, we will meet during the week at Sunrise Elementary
School with teachers from Pre-K, Kindergarten, 1st & 2nd grade to plan Family Math Night.
Each group of students will work with the teachers and with groups of children to design
centers that 1) align to standards, 2) are age and grade appropriate, 3) represent each of the
math strands. 1st Draft of paper/article due.
Week 11: Games and math in early childhood. Planning for Family Math Night.
Week 12: Collaborative Planning for Family Math Night. 2nd Draft of paper/article due.
Week 13: Family Math Night Sunrise Elementary School
Week 14: Family Math Night Debriefing. Peer critiques of research paper/articles.
Week 15: Student Lesson Presentations/Teaching. Remember to bring a copy of your lesson
plan for every member of the class.
Week 16: Research Paper/Article due. Lesson evals and debriefing.
VII. Assessment of Learning Outcomes
Students will:
A. Participate in all class discussions, activities, collaborations, field experiences.
B. Develop and maintain a professional reflective journal. Journal will be turned in
four times over the semester.
C. Read and review 4 articles from peer-reviewed journals in early child
education such as Teaching Children Math or Mathematics in Early
Childhood Education. Your review will include a summary, analysis &
discussion.
D. Collaborate to create 5 mathematics centers – one for each strand of
mathematics; numbers and operations, measurement, geometry, data,
chance & statistics, patterns functions & algebra. Centers will be
implemented at “Family Fun with Math Night”at Sunrise Elementary School.
E. Create a “Counting” book that is aligned to AZ Early Math Standards
that builds knowledge and understanding of concepts of the Numbers and
Operations Strand such as one-to-one correspondence, zero, one more, etc. Your
book may also scaffold the learning of other big ideas and mathematical
concepts such as conservation, transitivity
F. Design a lesson plan aligned to AZ Early Math Standards and to Common
Core Mathematics for young learners, Pre-K to Grade 3. The lesson must
include all essential elements of instruction and be developmentally appropriate
to support children’s emerging understandings of mathematical concepts.
This is the signature assignment for this course.
G. Present /teach the developmentally appropriate lesson that you designed.
H. Write a 3 to 5 page paper to describe and explain your lesson so that teachers
will be able to implement. Begin with a rationale for practicing teachers
supported by a brief review of literature The paper/article should include
alignment to Common Core, NAEYC, and/or NCMT Standards. Use APA
format. and be publication ready.
40 pts.
40 pts.
80 pts.
50 pts.
50 pts.
100 pts.
40 pts.
100 pts.
Total Points
500 pts.
VIII. Grading System:
Points
450 – 500
400-449
350-399
300-349
Percentage
90-100%
80-89%
70-79%
60-69%
Grade
A
B
C
D
National Association for the Education of Young Children
Professional Standards
STANDARD 1. PROMOTING CHILD DEVELOPMENT AND LEARNING
1a: Knowing and understanding young children’s characteristics and needs, from birth - age 8.
1b: Knowing and understanding the multiple influences on early development and learning
1c: Using developmental knowledge to create healthy, respectful, supportive, and challenging
learning environments for young children
STANDARD 2. BUILDING FAMILY AND COMMUNITY RELATIONSHIPS
2a: Knowing about and understanding diverse family and community characteristics
2b: Supporting & engaging families and communities through respectful, reciprocal relationships
2c: Involving families and communities in young children’s development and learning.
STANDARD 3. OBSERVING, DOCUMENTING, AND ASSESSING TO SUPPORT
YOUNG CHILDREN AND FAMILIES
3a: Understanding the goals, benefits, and uses of assessment – including its use in development of
appropriate goals, curriculum, and teaching strategies for young children
3b: Knowing about and using observation, documentation, and other appropriate assessment tools
and approaches, including the use of technology in documentation, assessment & data collection.
3c: Understanding and practicing responsible assessment to promote positive outcomes for each
child, including the use of assistive technology for children with disabilities.
3d: Knowing about assessment partnerships with families and with professional colleagues to
build effective learning environments.
STANDARD 4. USING DEVELOPMENTALLY EFFECTIVE APPROACHES
4a: Understanding positive relationships and supportive interactions as the foundation of their
work with young children
4b: Knowing and understanding effective strategies and tools for early education, including
appropriate uses of technology
4c: Using a broad repertoire of developmentally appropriate teaching /learning approaches
4d: Reflecting on own practice to promote positive outcomes for each child
STANDARD 5. USING CONTENT KNOWLEDGE TO BUILD MEANINGFUL
CURRICULUM
5a: Understanding content knowledge and resources in academic disciplines: language and
literacy; the arts – music, creative movement, dance, drama, visual arts; mathematics; science,
physical activity, physical education, health and safety; and social studies.
5b: Knowing and using the central concepts, inquiry tools, and structures of content areas or
academic disciplines
5c: Using own knowledge, appropriate early learning standards, and other resources to design,
implement, and evaluate developmentally meaningful and challenging curriculum for each child.
STANDARD 6. BECOMING A PROFESSIONAL
6a: Identifying and involving oneself with the early childhood field
6b: Knowing about and upholding ethical standards and early childhood professional guidelines
6c: Engaging in continuous, collaborative learning to inform practice; using technology effectively
with young children, with peers, and as a professional resource.
6d: Integrating knowledgeable, reflective, and critical perspectives on early education
6e: Engaging in informed advocacy for young children and the early childhood profession
STANDARD 7. EARLY CHILDHOOD FIELD EXPERIENCES
7a. Opportunities to observe and practice in at least two of the three early childhood age groups
(birth – age 3, 3-5, 5-8)
7b. Opportunities to observe and practice in at least two of the three main types of early education
settings (early school grades, child care centers and homes, Head Start prog
Northern Arizona University Policy Statements
http://nau.edu/OCLDAA/_Forms/UCC/SyllabusPolicyStmts2-2014/