ELU 542 Integration of Mathematics for Elementary Schools

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. Incorporate the tenets of sound mathematics instruction as detailed in the NCTM Standards as a foundation for studying mathematics in other subject matter domains.

2. Create links between mathematical concepts and other subject matter domains concepts.

3.Work with other teachers to redesign the mathematics curriculum at their school to incorporate content from other subject matter domains.

4. Develop a resource of materials that provides direction for incorporating mathematics in other subject matter domains.

5.Develop an instructional delivery system for the classroom which incorporates the integration of subject matter domains and mathematics.

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:

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)

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,

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

Creating teacher resource center of materials within the school

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

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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.

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Lacampagne, C. (1993). State of the art: Transforming ideas for teaching and learning mathematics. Washington, DC: US Government Print Office.

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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