Active Outline

General Information

Course ID (CB01A and CB01B)
MATHD046.
Course Title (CB02)
Mathematics for Elementary Education
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2023
Course Description
This course is designed for prospective elementary and middle school teachers. It gives an introduction to the discipline of mathematics as the use of logical, quantitative, and spatial reasoning in the abstraction, modeling, and problem solving of real-world situations. The main topics in the course include the origins of mathematics, mathematical reasoning and problem solving strategies, theory of sets, integers and integral number theory, rational numbers and proportion, real numbers and decimal notation, and measurement. Throughout the course students will experience the learning of mathematics in a way that models how they can create an active learning environment for their future students.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This course is transferable to CSU and UC. This course meets a general education requirement for °®¶¹´«Ã½ and CSUGE and belongs on the Liberal Arts AA degree. The course is a required mathematics content course for elementary education credential students, and many students take the class here at °®¶¹´«Ã½ before transferring to an education program. This course provides students with an insight into the depth of mathematics needed to adequately teach elementary and middle school mathematics.

Foothill Equivalency

Does the course have a Foothill equivalent?
No
Foothill Course ID

Course Philosophy

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
°®¶¹´«Ã½ GEArea(s)StatusDetails
2GA3°®¶¹´«Ã½ GE Area A3 - Critical ThinkingApproved
CSU GEArea(s)StatusDetails
CGB4CSU GE Area B4 - Mathematics/Quantitative ReasoningApproved

Units and Hours

Summary

Minimum Credit Units
5.0
Maximum Credit Units
5.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours5.010.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
60.0
Laboratory
0.0
Total
60.0
Course Out-of-Class Hours
Lecture
120.0
Laboratory
0.0
NA
0.0
Total
120.0

Prerequisite(s)

Intermediate algebra or equivalent (or higher), or appropriate placement beyond intermediate algebra

Corequisite(s)

Advisory(ies)

ESL D272. and ESL D273., or ESL D472. and ESL D473., or eligibility for EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

(Not open to students with credit in the cross-listed course(s).)

(Also listed as EDUC D046.)

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids;

Discussion of assigned reading;

Discussion and problem-solving performed in class;

In-class exploration of internet sites;

Quiz and examination review performed in class;

Homework and extended projects;

Fieldwork and field trips;

Guest speakers;

Collaborative learning and small group exercises;

Collaborative projects;

Problem solving and exploration activities using applications software; Problem solving and exploration activities using courseware.

Assignments

  1. Project(s) such as a Mathematical Autobiography, Book Review, etc.
  2. Essay on a contemporary or historical mathematical source, for example the Crest of the Peacock by Gheverghese, the writings of Martin Gardner, or Multicultural Mathematics by Nelson et al.
  3. Collaborative class assignments and investigations.
  4. Problem solving exercises from the text and other sources
  5. Reading assignments and class discussions, based on the text, websites and/or recent news articles
  6. Student presentations to the class

Methods of Evaluation

  1. A minimum of one in-class one hour exam composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format.
  2. A minimum of two of the following: an additional one hour in-class exam or take home exam composed in the same format as part A; a project such as a Mathematical Autobiography which describes the student's mathematical background, identifies important cultural influences on the student's mathematical experiences, and relates any crucial events in the student's mathematical history, or a Book Review which describes an issue in mathematics, mathematical history, or mathematics education, and critiques the book or resource in question; or an extensive oral presentation on a topic related to the course, such as mathematical history, math education issues, or a topic in mathematics, and demonstrating understanding of, engagement in, and critical analysis of the topic.
  3. Participation in and contribution toward classroom activities which require the use of mathematical manipulatives and calculators.
  4. Participation in and contribution toward classroom discussions and collaborative group written analytical work involving comparative source materials such as the text or recent news articles.
  5. Submitting an essay on a contemporary or historical mathematical source which may require the student to read and present the essay in oral form to the class. Such presentation may also require visual aids, demonstrations, etc. The essay should demonstrate understanding of the issue and show the relationship of the source material to the subject matter of the course.
  6. Periodic quizzes given regularly during the class in which the student demonstrates understanding of the mathematical material of the course, and/or homework problems assigned from the text and turned in regularly during the course, in which the student demonstrates ability to solve these assigned homework problems.
  7. Two-hour comprehensive final exam composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Scientific calculator
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Long, Calvin T., DeTemple, Duane W., Millman, Richard "Mathematical Reasoning for Elementary Teachers", 7th Ed., Pearson, 2014.
Musser, Gary L., Burger, William F., and Peterson, Blake E., "Mathematics for Elementary Teachers: A Contemporary Approach", 10th edition, John Wiley and Sons, Inc., 2013.

Examples of Supporting Texts and References

AuthorTitlePublisher
Ascher, Marcia, "Ethnomathematics: A Multicultural View of Mathematical Ideas", 1991.
Baroody, Arthur J. and Coslick, Ronald T., "Fostering Children's Mathematical Power: An Investigative Approach to K-8 Mathematics Instruction", Lawrence Erlbaum Associates, Publishers, Mahwah, NJ, 1998.
Burns, Marilyn. "About Teaching Mathematics", A K-8 Resource, Sausalito, CA: Math Solutions Publications, 1992.
Burns, Marilyn. "Math, Facing an American Phobia". Sausalito, CA: Math Solutions Publicatons, 1998.
Carpenter, Thomas P., John A. Dossey, and Julie L. Koehler, editors. "Classics in Mathematics Education Research". National Council of Teachers of Mathematics, 2004.
Cohen, Don, Editor, Crossroads in Mathematics: "Standards for Introductory College Mathematics Before Calculus", Prepared by the Writing Team and Task Force of the Standards for Introductory College Mathematics Project. American Mathematical Association of Two-Year Colleges September 1995. Available at http://www.imacc.org/standards/
Gardner, Martin. "Martin Gardner's Mathematical Games: The Entire Collection of His Scientific American Columns". Searchable CD, The Mathematical Assoc. of America, 2005.
Girard, Kimberly Wilke, and Margaret Plouvier Aukshun, editors. Using Activities from the "Mathematics Teacher" to Suport "Principles and Standards". National Council of Teachers of Mathematics, 2004.
Joseph, George Gheverghese, "The Crest of the Peacock: Non-European Roots of Mathematics", 1991.
Kilpatrick, Jeremy, W. Gary Martin, and Deborah Schifter, editors. "A Research Companion to Principles and Standards for School Mathematics". National Council of Teachers of Mathematics, 2003.
Masingila, Joanna O., Lester, Frank K., Raymond, Anne M., "Mathematics for Elementary Teachers via Problem Solving: Student Activity Manual, Prentice Hall, Upper Saddle River", NJ, 2002.
Masingila, Joanna O., Lester, Frank K., Raymond, Anne M., "Mathematics for Elementary Teachers via Problem Solving: Student Resource Handbook", Prentice Hall, Upper Saddle River, NJ, 2002.
National Council of Teachers of Mathematics (NCTM), "Multicultural and Gender Equity in the Math Classroom: the Gift of Diversity", 1997 yearbook of the National Council of Teachers of Mathematics., Reston, VA: NCTM, 1997.
National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", Reston, VA: NCTM, 2000.
Nelson, David, Joseph, George Gheverghese, and Williams, Julian, "Multicultural Mathematics", Teaching Mathematics from a Global Perspective, 1993.
Sousa, David. "How the Brain Learns Mathematics", and "Facilitator's Guide to How the Brain Learns Mathematics". Corwin. 2008.

Learning Outcomes and Objectives

Course Objectives

  • Use a variety of problem-solving strategies and their applications to the world. Model and solve mathematical problems using concrete, pictorial, graphical, numerical, algebraic, and technological methods and representation, and learn how to communicate about them orally and in writing.
  • Use inductive and deductive reasoning to discover and analyze patterns.
  • Use set theory to represent and solve problems.
  • Analyze the structure and properties of whole numbers, integers, rational numbers, and real numbers, use a variety of algorithms to do computations with numbers, and identify common errors in computation.
  • Examine patterns and modular arithmetic: use the properties of numbers to explain numerical and visual patterns.
  • Measure and compute the lengths, areas, and volumes of mathematical shapes as well as real objects.
  • Use algebraic thinking and modeling to represent and solve problems.
  • Utilize a variety of mathematical resources including reference books, histories, essays, the internet, news articles, and interviews to analyze contemporary trends in mathematics and math education; relate and apply the Common Core Mathematics Standards and other frameworks and standards to the teaching of elementary mathematics.

CSLOs

  • Analyze mathematical problems from elementary mathematics, apply problem solving techniques using a variety of methods, solve these problems individually and in groups, and communicate results mathematically through a variety of forms.

  • Utilize ideas from number theory, distinguish types and properties of numbers, and employ mathematical rules for operating on rational and irrational numbers using verbal, symbolic, geometric, and numerical methods.

  • Examine and evaluate myths and realities about the contemporary discipline of mathematics and its practitioners.

  • Identify and discuss developments in the history of elementary mathematics from a variety of cultures.

Outline

  1. Use a variety of problem-solving strategies and their applications to the world. Model and solve mathematical problems using concrete, pictorial, graphical, numerical, algebraic, and technological methods and representation, and learn how to communicate about them orally and in writing.
    1. Develop problem solving strategies utilizing diverse approaches as related to differing learning styles and to cultural diversity
    2. Formulate varied mathematical representations: oral, written, visual, symbolic, numerical, technological
    3. Communicate results of mathematical representations both orally and in written format
  2. Use inductive and deductive reasoning to discover and analyze patterns.
    1. Use inductive reasoning
    2. Use deductive reasoning
    3. Generating new patterns
  3. Use set theory to represent and solve problems.
    1. Examine sets, subsets, attributes, and categorization principles
    2. Formulate set notation and Venn diagram representations of sets
    3. Compute the result of set operations and calculate the cardinality of sets
  4. Analyze the structure and properties of whole numbers, integers, rational numbers, and real numbers, use a variety of algorithms to do computations with numbers, and identify common errors in computation.
    1. Understand the structure of the whole number system. Use whole numbers for computation and counting problems, and place whole numbers accurately on a number line.
    2. Understand the structure of the integers number system and understand number theory concepts, including
      1. Order the integers and place the integers accurately on a number line
      2. Understand, identify, and apply properties of the integer number system and understand their relationship to the algorithms
      3. Find the prime factorization of a number, and represent the number using exponential notation
      4. Least common multiple, greatest common divisor, and the Euclidean algorithm
      5. Contemporary applications of modular arithmetic in coding systems
    3. Compute with rational numbers and explain their properties
      1. Understand the structure of the rational number system
      2. Understand properties of the rational number system and their relationship to the algorithms
      3. Percents
      4. Ratio, and proportion
      5. Explore Egyptian fractions
    4. Understand and explain the properties of real numbers
      1. Understand and explain irrational numbers
      2. Understand and explain decimal representation of real numbers
      3. Order integers, mixed numbers, and rational numbers and real numbers (including fractions, decimals, and percents), and place accurately on a number line
      4. Understand properties of the real number system and their relationship to the algorithms
    5. Analyze arithmetic operations and algorithms, and their history and origins, including multiplication techniques developed in Egypt, India, China, the Islamic world, Europe, and elsewhere
      1. Demonstrate fluency in standard algorithms for computation
      2. Evaluate the correctness of nonstandard algorithms, using symbols, pictures, and physical models
      3. Describe relationships between the operations of and algorithms for addition, subtraction, multiplication, and division. Understand properties of the whole number system and their relationship to the algorithms, both standard and alternative.
      4. Demonstrate understanding of the order of operations
      5. Perform operations with positive, negative, and fractional exponents, as they apply to whole numbers and fractions
      6. Represent numbers in scientific notation
      7. Identify the informal thinking strategies children use to find basic facts and show how properties of whole numbers justify this thinking
    6. Develop mental and paper and pencil estimation skills and use in appropriate situations; estimate the results of calculations, using techniques such as
      1. Rounding
      2. Front-end or "working from left to right"
      3. Substitution of compatible numbers
      4. Clustering
    7. Use calculators competently and appropriately. Use and explain various calculation techniques for complex calculations, using technology
    8. Use manipulatives to develop, explain and inform computation rules
    9. Demonstrate understanding of base-ten place value, bases other than ten, their history and usage. Should include at least four topics such as
      1. Egyptian and Russian base two multiplication and division procedures
      2. Babylonian base sixty and its remnants in systems of timekeeping
      3. Incan quippu
      4. Chinese/Hindu/Islamic/Mayan inventions of place value
      5. African base five and base two systems
      6. Roman numerals and their remnants in contemporary society
      7. European development of base ten metric system, including attempts to apply it to the calendar in France and Russia.
    10. Examine common errors in computation and utilize them to inform understandings of mathematical learning
  5. Examine patterns and modular arithmetic: use the properties of numbers to explain numerical and visual patterns.
    1. Use modular arithmetic to investigate visual and geometric patterns
    2. Investigate connections to mathematics used in various cultures and settings, such as
      1. Chinese and other calendar calculations
      2. Islamic art
      3. Contemporary and historical works of art
      4. Various scientific applications
    3. Examine remnants of Babylonian base 60 and modular arithmetic in a variety of number and time measurement systems
  6. Measure and compute the lengths, areas, and volumes of mathematical shapes as well as real objects.
    1. Compute length and perimeter
    2. Compute area and surface area
    3. Compute volume
    4. Examine and utilize systems of measurement: foot-pound, metric, ant their origins in various cultures
    5. Use the Pythagorean Theorem and examine earlier versions in China and Babylonia
    6. Investigate the area and volumes of similar shapes
  7. Use algebraic thinking and modeling to represent and solve problems.
    1. Examine the origins in Egyptian, Babylonian, Islamic, Chinese, Greek, and Indian mathematics
    2. Construct and investigate relations and functions
    3. Utilize verbal, algebraic, tabular, and graphical representations of functions and relations
  8. Utilize a variety of mathematical resources including reference books, histories, essays, the internet, news articles, and interviews to analyze contemporary trends in mathematics and math education; relate and apply the Common Core Mathematics Standards and other frameworks and standards to the teaching of elementary mathematics.
    1. Examine the Common Core Mathematics Standards and related standards and organizations
    2. Utilize and analyze resources for mathematics and mathematics teaching, including essays, interviews, web sites, and the news media
    3. Examine challenges in mathematics education such as access, equity, math anxiety, or testing
Back to Top