KUTZTOWN UNIVERSITY
KUTZTOWN, PENNSYLVANIA
COLLEGE OF EDUCATION
DEPARTMENT OF ELEMENTARY EDUCATION
Pre-K – 4 Program
EEU 209 Math Foundations for Pre-K-1
I. Course Description: EEU 209 Math Foundations for Pre-K-1
A. This course is designed to prepare prospective teachers to teach mathematics to all children from preschool to grade one. Instructional strategies appropriate for various stages of intellectual development will be examined. The use of manipulatives and technology in the teaching of mathematics will be included. Pre-K through grade 4 candidates will be instructed to apply the principles that guide all mathematics instruction as well as the specific NCTM standards for early childhood that are based on the belief that “students learn important mathematical skills and processes with understanding”. Candidates must know and effectively deliver core academic content in the following learning areas and must have the skills to stay current with the research on best practices for content instruction for students, pre-K through grade 1. Prerequisites: MAT 103 and MAT 104. 3 ch, 3 sh.
II. Course Rationale:
This course is intended to prepare elementary education majors and special education majors to become high-quality teachers of mathematics. According to Early Childhood Mathematics: Promoting Good Beginnings, a joint position statement of the National Association for the Education of Young Children (NAEYC) and the National Council for Teachers of Mathematics (NCTM), high-quality mathematics education for 3- to 6-year-old children, teachers and other key professionals should:
• enhance children’s natural interest in mathematics and their disposition to use it in order to make sense of their physical and social worlds
• build on children’s experience and knowledge, their individual approaches to learning, and their informal knowledge
• base mathematics curriculum and teaching practices on knowledge of young children’s cognitive, linguistic, physical, and social-emotional development
• use curriculum and teaching practices that strengthen children’s problem solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas
• ensure that the curriculum is coherent and compatible with known relationships and sequences of important mathematical ideas
• provide for children’s deep and sustained interaction with key mathematical ideas
• integrate mathematics with other activities and other activities with mathematics
• provide ample time, materials, and teacher support for children to engage in play where they can explore and manipulate mathematical ideas with keen interest
• actively introduce mathematical concepts, methods, and language through a range of appropriate experiences and teaching strategies
• support children’s learning by thoughtfully and continually assessing all children's mathematical knowledge, skills, and strategies.
To support these guidelines, this course will enable candidates to learn best practices in guiding children’s learning of mathematical concepts and skills. They will learn to provide children with the opportunity to solve real-world problems and encourage demonstration and communication of what they have learned. Overall, this course will help the candidates meet the mathematical needs of the preschool students in their charge.
III. A. Course Objectives/Student Learning Outcomes
Content course objectives of this course are based on the appropriately leveled mathematics competencies required for certification in Pre-K-4 in the Commonwealth of Pennsylvania and are aligned with the standards and curricular focal points provided the National Council Teachers of Mathematics.
As a result of this course, the candidates will be able to develop, implement, assess and modify curriculum and lessons as evidenced by their ability to teach students how to:
- Count with understanding and recognize “how many”, then use this understanding to relate position, magnitude, and connections of whole numbers, cardinal numbers, and ordinal numbers; to connect number words with numerals using various physical models and representations; and to develop a sense of whole numbers by being able to represent them and use them in flexible ways, such as relating, composing, and decomposing numbers.
- Understand the various meanings of addition and subtraction of whole numbers by comprehending the relationship between the two operations and the effects of performing said algorithms; also by developing and using strategies, and a variety of methods and tools to compute.
- Use multiple models to develop initial understandings of place value and the base-ten number system; and to illustrate situations involving addition and subtraction of whole numbers by using objects, pictures, and symbols.
- Recognize, describe, and extend patterns by sorting objects and simple numeric patterns by their properties; then translate these patterns from one representation to another, including the analysis of repeating and growing patterns and the understanding of situations that entail multiplication and division such as equal groupings of objects or sharing equally.
- Illustrate general principles such as qualitative change and properties of operations such as commutative, using specific numbers.
- Recognize, name, build, draw, compare, and sort two-dimensional shapes by describing attributes of two and three dimensional shapes; and be able to create mental images of these shapes using spatial memory and spatial visualization; also be able to recognize geometric shapes and structures in their environment, specifying their location.
- Describe, name, and interpret relative positions in space and apply ideas about direction and distance using simple relationships such as “near to” on a map.
- Recognize attributes of length, weight, and area by understanding, and being able to measure using non-standard units and be able to compare and order objects based on these attributes.
- Pose questions and gather data about themselves and their surroundings then be able to describe parts of the data or the data as a whole to determine what the data show, represent the data using tables and graphs such as bar graphs and line graphs; also be able to sort and classify objects according to their attributes and organize data about the objects.
Student Process Learning Outcomes / PDE / SPA/ACEI / INTASC / NAEYC
A. Discuss the unifying strands of mathematics generally included in a preschool and an elementary school program, as well as the sequencing of subordinate concepts and skills. / I.D. / 2.3
3.3 / 1. / 4.
B Select, plan, and implement developmentally appropriate instructional strategies for both the concept/skill to be taught and the specific educational needs of the child. / I.D. / 2.3
3.3 / 2.
7. / 4.
C. Communicate the mathematical concepts that enable students at the primary level to understand and use mathematics. / I.D. / 2.3
3.3 / 1. / 1.
D. Make appropriate connections among topics in mathematics and to other disciplines in the curricular area and also to the children’s family and community environment. / I.D. / 2.3
3.3 / 1. / 2.
E. Identify, solve, and develop problems related to the child’s environment and involving the mathematical concepts and principles developmentally appropriate for students in these grades. / I.D. / 2.3
3.3 / 7. / 1.
F. Identify and use problem-solving strategies appropriate to these grades. / I.D. / 2.3
3.3 / 4.
7. / 4.
G. Identify resource materials (manipulatives, games, computer software, videotapes, periodicals, and children’s literature) that may be used to develop mathematical concepts. / I.D. / 2.3
3.3 / 4.
6. / 4.
H. Diagnose specific errors made by children in the application of mathematical concepts and skills and plan appropriate remedial instruction. / I.D. / 2.3
3.3 / 3.
8. / 5.
I. Make appropriate use of technology in problem solving and the exploration and development of mathematical concepts. / I.D. / 2.3
3.3 / 4. / 4.
B. Relationship to Conceptual Framework
EEU 209 demonstrates the following categories in the conceptual framework in the following ways:
Professional Methodology is modeled through the use of hands-on experiences using manipulatives and viewing videos of children in classroom settings. These are explained to the candidates as “methods of teaching using various strategies.” Communication is evident through written assignments and the study of language in a mathematics environment. Scholarly Inquiry is demonstrated through the use of professional materials, particularly those of the National Council of Teacher of Mathematics (NCTM). Reflection is a key component of the course through written exam questions that focus on questions that present possible mathematics situations and what would the teacher do in such a setting to assist the children in learning. One chapter in the text is devoted to cultural awareness and methods for creating a diverse classroom. The professor also presents experiences of her urban teaching background throughout the course. Children’s literature books are introduced that reflect diversity in content and storyline. Organization and classroom management is woven throughout the course especially as tips for using manipulatives in planning and teaching. Use of technology is present through viewing computer software.
IV. Assessment
A.Assessment will be based on a subset of the following:
- Participation in classroom projects and discussion
- Lesson plans: mathematics only or mathematics and another subject area
- Reflection on what is important about the teaching of mathematics to children and how does the teacher capture children’s learning
- Attendance at a mathematics conference
- Traditional multiple choice, short answer and essay written exams
- Oral and written presentation of a lesson to peer
- Construct portfolio problems using different problem solving strategies.
- Review of an Elementary Mathematics text. Pick a lesson from Geometry or Measurement and explain how the topic was taught.
- Explain how any additional manipulatives could be used to reinforce the lesson based on our classroom demonstrations and discussions.
- Develop a classroom activity for basic counting, numeration or place value, or operations/basic facts incorporating a form of the arts.
- Develop a classroom activity for basic counting, numeration or place value, or operations/basic facts incorporating a source from Children's Literature.
12.Keep a manipulative chart throughout the course identifying manipulatives and what topics these manipulatives would address.
B.Core Assignment
Faculty member will add when the course is taught.
V. Course Outline:
A.Young Children and Mathematics
1.Promote emergent mathematics
2.Differentiate approaches to teaching math based on levels
3.Discuss recent finding in teaching mathematics
4,Treat children as mathematicians
5.Help children related their environment and experiences to math
B.Helping Young Children build a Knowledge Base and Reflect
1.Understand own learning style and math learning
2.Understand child development
3.Understand student learning styles
4.Meeting individual student needs
C.Creating a constructivist Environment in the Math Classroom
1.Use of manipulatives
2.Prepare the environment
D.Infants and Toddlers in Math
1.Physical Development
2.Cognitive Development
3.Making relationships
a.Concept of one
b.Concept of more
c.Object permanence with numbers
4.NCTM Focal Points for Infants and Toddlers
a.Numbers
b.Operations
c.Measurement
d.Patterns, Reasoning, and Algebra
e.Geometry and Spatial Sense
5.Appropriate assessment methods for infants and toddlers in math
E.Preschool Children in Math
1.Physical Development
2.Cognitive Development
3.Making relationships
a.Conservation of number
b.Centration (Piaget experiment)
c.Reversibility of Thought
d.Play in math incorporating hands-on learning experiences
4.NCTM Focal Points for Preschool Children
a.Numbers
b.Operations
c.Measurement
d.Patterns, Reasoning, and Algebra
e.Geometry and Spatial Sense
5.Appropriate assessment methods for preschool children in math
F.Kindergarten and First Grade Children in Math
1.Physical Development
2.Cognitive Development
3.Linguistic and Socio-Emotional Development
4.Making relationships
5.NCTM Focal Points for Kindergarten and First Grade
a.Numbers
b.Operations
c.Measurement
d.Patterns, Reasoning, and Algebra
e.Geometry and Spatial Sense
6.Appropriate assessment methods in math
VI. Instructional Resources:
Books:
Billstein, R., Libeskind, S. & Lott, J. (2004). Mathematics for Elementary School Teachers (8th ed). Boston, MA: Pearson Addison-Wesley Publishing Co.
Burger & Musser. (2004). Mathematics for Elementary Teachers - A Contemporary Approach (6thed). New York: John Wiley & Son, Inc.
Burns, Marilyn. (2000). About Teaching Mathematics: A K-8 Resource. (2nd ed). Sausalito, CA: Math Solutions Publications.
Dolan, D., Williamson, J., & Muri, M. (2004). Mathematics Activities for Elementary School Teachers (5th ed). Boston, MA: Pearson Addison Wesley.
Geist, E. (2009). Children are Born Mathematicians: Supporting mathematical development, birth to age 8. (1st ed.). Upper Saddle River, NJ: Pearson Education, Inc.
Hyson, M. (2003). Preparing Early Childhood Professionals: NAEYC’s Standards for Programs. Washington DC: National Association for Education of the Young Child.
Kennedy, L & Tipps, S. (2004). Guiding Children’s Learning of Mathematics (10th ed). Belmont, CA: Wadsworth/ Thomson Learning.
National Council of Teachers of Mathematics. (1995). Assessment Standards for School Mathematics. Reston, VA.
National Council of Teachers of Mathematics. (1996). Communication in Mathematics K-12 and Beyond (1996 Yearbook). Reston, VA.
National Council of Teachers of Mathematics. (1991). First Grade Book. (Addenda Series, Grades K -6). Reston, VA.
National Council of Teachers of Mathematics. (1991). Kindergarten Book . (Addenda Series, Grades K -6). Reston, VA.
National Council of Teachers of Mathematics. (1987). Learning and Teaching Geometry K - 12. (1987 Yearbook). Reston, VA.
National Council of Teachers of Mathematics. (2000). Learning Mathematics (2000) for a New Century, (2000 Yearbook). Reston, VA.
National Council of Teachers of Mathematics. Navigation Series. Reston, VA.
National Council of Teachers of Mathematics. (1989). New Directions for Elementary School Mathematics. (1989 Yearbook). Reston, VA.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA.
National Council of Teachers of Mathematics. (1991). Professional Standards for Teaching Mathematics. Reston, VA.
National Council of Teachers of Mathematics. (1988). The Ideas of Algebra K - 12. (1988 Yearbook). Reston, VA.
Reys, R., Suydam, M., Lindquist, M. & Smith, N. (2004). Helping Children Learn Mathematics (7th ed). New York: John Wiley & Sons Inc.
Van DeWalle, J. (2004). Elementary School Mathematics (5th ed). Boston: MA: Pearson Education Inc.
Welchman-Tischler, Rosamond. (1992). How to Use Children’s Literature to Teach Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Videos:
Mathematics with Manipulatives - Cuisenaire Rods (Lytle 119)
Mathematics with Manipulatives - Six Models (Lytle 138)
Mathematics with Manipulatives - Pattern Blocks (Lytle 119)
Mathematics: Making the Connection - National Council of Teachers of Mathematics (Lytle 119)
Manipulatives:
Pattern blocks, attribute blocks, square inch tiles, 2 cm cubes, Cuisenaire rods, fractions bars, fraction circles, fractions strips, pentominoes, Unifix cubes, base ten blocks, counting sticks, color tiles, two color counters, abacus, chip trading games, tangrams, geoboards, Mira, balance scales, metric rulers, space figures, multi-link cubes, geofix shapes, polydrons, TI 108 calculators, TI-15 Explorer calculators
Electronic Resources:
NCTM Illuminations
Math Forum
Pennsylvania Department of Education Academic Standards for Mathematics
Professional Journals:
National Council of Teachers of Mathematics. Teaching Children Mathematics. Reston, VA.