KUTZTOWN UNIVERSIY
Department of Elementary Education
ELU 542 – Integration of Mathematics for Elementary Schools
COURSE DESCRIPTION
This course will explore the connections between traditional contents (science, social studies,
language arts, fine arts) in the elementary school with connections to mathematical concepts.
The course will enable the student to pursue elementary mathematics in a holistic thematic
approach within traditional elementary content subjects. 3 s.h. 3 c.h.
RATIONALE
Integrating school disciplines in elementary classrooms is not a new idea. E. H. Moore suggested
as easily as 1902 that mathematics and science be combined. Concepts such as quantity, data
collection, measurement, and graphing are content objectives that overlap in these subject areas.
Many countries have used an integrated curriculum successfully for years. Recently through
funding from the federal government various states have created curriculum frameworks in
mathematics that integrate subject matter and traditional modes of mathematics. These
frameworks support teachers in providing problem situations that involve a variety of
mathematical content areas that may take several weeks to complete. Through the technical
advances of computers and three dimensional CD-ROM programs, visual representations have
been added to the learning process that are unparalleled. Since traditional two dimensional plane
learning is no longer sufficient, effective teachers need to change the delivery of the traditional
mathematics program to one that incorporates active student learning within a contextual base.
This is best accomplished by providing stimulating mathematical problem situations that
promote mathematical learning where students become active participants in the pursuit of
knowledge.
OBJECTIVES
Through reading, discussion, experiments, research, and group project work the student will be
able to:
1.
2.
3.
4.
5.
Incorporate the tenets of sound mathematics instruction as detailed in the NCTM
Standards as a foundation for studying mathematics in other subject matter domains.
Create links between mathematical concepts and other subject matter domains concepts.
Work with other teachers to redesign the mathematics curriculum at their school to
incorporate content from other subject matter domains.
Develop a resource of materials that provides direction for incorporating mathematics in
other subject matter domains.
Develop an instructional delivery system for the classroom which incorporates the
integration of subject matter domains and mathematics.
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METHOD OF INSTRUCTION
A combination of brief lectures, explorations of mathematical concepts in subject matter
domains, construction of integrated lessons through classroom experiences, and connections to
technology and writing will be used to meet the objectives of this course.
ASSESSMENT
Assessment of each student’s level of accomplishment with reference to the course objectives
will be based upon the following:
1.
2.
3.
4.
5.
6.
Participation in classroom projects and discussion
Oral and written presentation of a cumulative unit of study integrating mathematics in
other content areas
Completion of a Who has mental math activity
Written reviews and reflections of 3 journal articles from Teaching Children Mathematics
published by National Council of Teachers of Mathematics
Written reviews and reflections of 5 text books or source book materials provided by the
instructor
Compiling of a set of resources to match a strand of mathematics, a grade level of
mathematics, or a special topic agreed upon by the instructor and the student
COURSE OUTLINE
Integration of Mathematics for Elementary School
(Note: The mathematics outline is listed to underscore the mathematics that connects with
other subject areas. Roman numerals I and III should be viewed together.)
I.
Theoretical Concepts to Incorporate Mathematics with Other Subject Matter Domains
A. Patterns, Relationships and Functions
1. Use patterns to create models and make predictions
2. Describe the nature of patterns and relationships
3. Construct representations of mathematical relationships
B. Geometry and Measurement
1. Identify characteristics and define shapes
2. Analyze situations to determine what measurement(s) should be made
to what level of precision.
C. Data Analysis and Statistics
1. Collect and explore data
2. Relate data to the situation from which they arose
3. Use data to answer questions
4. Draw inferences about unknown outcomes
5. Make predictions and identify the degree of confidence in prediction
D. Number Sense and Numeration
1. Develop understanding about early number sense
2. Develop understanding about number concepts (counting, relationships)
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E. Analytical Thinking
1. Analyze problems to determine an appropriate process for solution
2. Use appropriate notation to model or represent problems.
F. Discrete Mathematics
1. Make critical judgments about claims that are made in probabilistic
situations.
2. Investigate practical situations such as scheduling, routing, sequencing,
networking, organizing and classifying.
II.
Current Trends in Elementary Mathematics Instruction
A. The NCTM Standards
1. Reason mathematically
2. Communicate mathematically
3. Problem-solve mathematically
4. Make connections within and between mathematics and other fields
B. Desired School Based Outcomes
1. Curriculum that fosters depth and breadth of content
2. Content presented whole to part
3. Learner centered classroom
4. Questioning strategies exemplified
5. Authentic tasks calling for problem solving and critical thinking
6. Assessment and instruction woven together to foster self-evaluation
III.
The NCTM Standards and the Elementary Curriculum: Focus on Activities In Other
Subject Matter Domains
A. Science
1. Generate reasonable questions about the world based on observation to
generate hypothesis and collect data.
2. Develop solutions to unfamiliar problems through reasoning, observation
and/or experiment.
3. Use simple measurement devices to make metric measurement.
4. Develop strategies and skills for information gathering and problem
solving.
5. Construct charts and graphs and prepare summaries of observations.
6. Show how science concepts can be interpreted through creative expression
such as language arts and fine arts.
7. Describe ways in which technology is used in everyday life.
8. Classify common objects and substances according to observable attributes:
color, size, shape, smell, texture, flexibility, weight.
9. Measure weight, dimensions and temperature of appropriate objects and
materials.
B. Social Studies and Geography
1. Sequence events in time in order to examine relationships among them
and explain cause and effect.
2. Organize, graph, and explain past events to construct a narrative about their
family or significant historical event.
3. Describe, compare, and explain the locations and characteristics of places,
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cultures, and settlements.
4. Describe, compare, and explain the locations and characteristics of regions in
the immediate environment.
5. Use flowcharting to demonstrate how decisions are made the affect global
economics, political and legal processes, and interpersonal relationships.
C. Language
1. Employ multiple strategies to construct meaning for problem-solving situations.
2. Use graphic organizers to demonstrate relationships between mathematics and
real world experiences.
3. Reflect upon their construction of meaning or problem-solving schema to solve
problems.
D. Fine Arts
1. Cite examples of mathematics found in architecture, nature, and performance.
2. Articulate what mathematics is required for careers within these professions.
IV.
Redesign the Curriculum to Incorporate New Paradigms
A. Identification of mathematical concepts and link to other subject domains
B. Listing resources and activities by grade or concept level
C. Integration activities, methods and resources which reflect the integration
D. Creating teacher resource center of materials within the school
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Instructional Resources
Arithmetic Teacher
National Council of Teachers of Mathematics
renamed in fall of 1994 to
Teaching Children Mathematics (9 issues) for grades preK-6
Mathematics Teaching in the Middle School (new 1994)
National Council of Teachers of Mathematics
Science Teacher
National Council of Teachers of Science
The Reading Teacher
International Reading Association
Bagley, T. & Gallenberger, C. (1992). Assessing students’ dispositions: Writing journals to
improve students’ performance. The Mathematics Teacher, 85 (8), 660-662.
Becker, V. (1994). Chrysler and the environment. Highland Park, MI: Chrysler Corporation.
Beyer, A. (Ed.). (1993). Alternative assessments. Palo Alto, CA: Dale Seymour
Braselton, S. (1994). Using graphic organizers to improve the reading of mathematics. The
Reading Teacher, 48, 3, p276-281.
Burris, A. (2005). Understanding the math you teach: content and methods for prekindergarten
through grade four. Upper Saddle River, NJ: Person Merrill Prentice Hall.
Canning, C. & Bunting, K. (1987). Developing thinking skills across the curriculum and how
computing can help. Westland, MI: Michigan Association for Computer Users in
Learning.
Cook, J. (1995). Integrating math and writing. Teaching K-8, 22-23.
Economopoulos, K & Russell, S. (1998). Counting ourselves and others. White Plains, NY:
Dale Seymour Publications.
EQUALS. (1989). Get it together: Math problems for groups grades 4-12. Berkely, CA:
Lawrence Hall of Science.
EQUALS. (1995). Family science. Portland, OR: Portland State University.
Ford, M. (1990). The writing process: A strategy for problem solvers. Arithmetic Teacher,
35-38.
Garcia, A. (1994). Math & literature hands-on activities for 35 literature titles. Cypress, CA:
Creative Teaching Press, Inc.
Kapp, B. (1991). A magic carpet to learning geography. Journal of Geography, 90 (4), 173178.
Lacampagne, C. (1993). State of the art: Transforming ideas for teaching and learning
mathematics. Washington, DC: US Government Print Office.
Lappan, G. (1991). The NCTM Commission on Teaching Standards for School Mathematics.
Reston, VA: National Council of Teachers of Mathematics.
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Learning Magazine. (1986). Great ideas from Learning magazine: Science and social studies.
Springhouse, PA: Springhouse Corporation.
Litwiller, B. H. (1993). Curriculum and evaluation standards for school mathematics
addenda series. Reston, VA: National Council of Teachers of Mathematics.
Lorton, M. B. (1976). Mathematics their way. Mento Park, CA: Addison-Wesley
Publishing Company.
Maxim, G. (1991). Social studies and the elementary school child 5th ed. Englewood Cliffs,
New Jersey: Merrill.
McBride, J. & Silverman, F. (1991). Integrating elementary/middle school science and
mathematics. School Science and Mathematics, 9, (7) 285-292.
McIntosh, M. (1991). No time for writing in your class. The Mathematics Teachers, 84, (9)
423-433.
Maxim, G. (1991). Social studies and the elementary school child, 5th ed. Englewood Cliffs,
NJ: Merrill.
National Council of Teachers of Mathematics. (2001). Navigating through geometry in
prekindeergarten – grade 2. Reston, VA: NCTM.
____ (2001). Navigating through algebra in prekindergarten – grade 2. Reston, VA: NCTM.
_____ (2001). Navigating through algebra in grades 3-5. Reston, VA: NCTM.
_____(2001). Mathematics assessment a practical handbook for grades 3-5. Reston, VA:
NCTM.
_____ (2001) Mathematics assessment cases and discussion questions for grades k – 5. Reston,
VA: NCTM.
______ (2001). Mathematics assessment cases and discussion questions for grades 6 – 12.
Reston, VA: NCTM.
National Science Foundation. (1994). Discover: The world of science and technology.
Arlington, VA: National Science Foundation.
Parker, W. (1991). Renewing the social studies curriculum. Alexandra, VA: ASCD.
Payne, J. (1990). Mathematics for the young child. Reston, VA: National Council of
Teachers of Mathematics.
Richardson, K. (1984). Developing number concepts using Unifix cubes.
Menlo Park, CA: Addison-Wesley.
Russell, S. J. & Corwin, R. B. (1989). Used Numbers Series: Real data in the classroom.
Statistics: the Shape of the Data. (Grades 4-6). Part of the TERC Project. (Technical
Education Research Centers) Palo Alto, CA: Dale Seymour Publications.
Schoen, H., & Zweng, M. (1986). Estimation and mental computation. Reston, VA:
National Council of Teachers of Mathematics
Sivertsen, M. (1993). State of the art: Transforming ideas for teaching and learning science.
Washington, DC: US Department of Education.
Stenmark, J., Thompson, V., & Cassey, R. (1986). Family math. Lawrence Hall of
Science, University of California, Berkley, CA 94720
Stodolsky, S. (1988). The subject matters: Classroom activity in math and social studies.
Chicago: The University of Chicago Press.
Winograd, K. & Higgins, K. (1995). Writing, reading, and talking mathematics: One interdisciplinary
possibility. The Reading Teacher, 48(4), 310-317.
Revise 8/2005
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