Math for Elementary Teachers

Course Objectives

After this course students are expected to:

  1. have achieved competency in the fundamental mathematical concepts necessary for the teaching of mathematics up to the sixth grade.
  2. have become familiar with the main definitions, concepts, results and methods of proof relating to each part of the syllabus.
  3. be able to quote the definitions and results, and to reproduce the proofs of some key results.
  4. be able to solve problems relating to the material covered and present the solutions in a good mathematical style.


  1. Classroom Behaviour
  2. On the use of electronic aparati

Sample Exams

  1. MATH 3041 Exam I Semester 2, 2012
  2. MATH 3041 Exam II Semester 2, 2012
  3. MATH 3041 Exam III Semester 2, 2012
  4. Practice Problems

Course Notes and Readings

  1. Course Introduction
  2. Recomendaciones para Estudiantes Nuevos
  3. In Praise of Lectures
  4. Homeworks 1-13
  5. Relations
  6. Errata
  7. Section 1.1 Counting
  8. Section 1.2 Place Value
  9. Exercise on the Addition Table
  10. Section 1.4 Subtraction
  11. Section 1.5 Multiplication
  12. Exercise on the Multiplication Table
  13. Section 1.6 Division
  14. Section 3.3 Algorithms
  15. Section 3.4 A Division Algorithm
  16. Section 3.5 Estimation
  17. Section 4.1 Prealgebra
  18. Section 4.3 Divisibility
  19. Section 5.3 Factors and Prime Numbers
  20. Exercises on Factors and Primes
  21. Exercises on prime numbers and the greatest common factor
  22. Section 6.1 Fractions
  23. Section 6.1   Partitive and Measure Division
  24. Notes on the conversion of units
  25. Solving Algebra and Other Story Problems by Sybilla Beckmann
  26. Tree of Porphyry
  27. Some Educational References


  1. Course Introduction
    1. Cognition, Logic, and Instruction
  2. Numeration, Place Value and Arithmetic Operations
    1. Roman numerals
    2. Place value
    3. Expanded form of a number
    4. The four arithmetic operations for whole numbers
    5. Interpretations for subtraction: Part-whole, Take-away, Comparison
    6. Definition of division and the Quotient-Remainder Theorem
    7. Interpretations for division: Partitive, Measurement
    8. Basic properties of operations: commutative, associative, distributive properties, additive identity, multiplicative identity
  3. Mental Math and Word Problems
    1. Mental Math
    2. Word Problems
    3. The Art of Word Problems
  4. Algorithms
    1. An Addition Algorithm
    2. A Subtraction Algorithm
    3. A Multiplication Algorithm.
    4. Long Division by 1-digit Numbers
    5. Estimation
    6. Completing the Long Division Algorithm
  5. Prealgebra
    1. Letters and Expressions
    2. Identities, Properties, Rules
    3. Exponents
  6. Factors, Primes, and Proofs
    1. Definitions, Explanations and Proofs
    2. Divisibility Tests
    3. Primes and the Fundamental Theorem of Arithmetic
    4. More on Primes
    5. Greatest Common Factors and Least Common Multiples
  7. Fractions
    1. Equal division of a segment by ruler and compass
    2. A definition of the concept of fraction
    3. Representations of fractions
    4. Equivalence of fractions. The cancellation law
    5. Ordering fractions
    6. Addition and subtraction of fractions
    7. Bar diagrams illustrating addition and subtraction of fractions
    8. Multiplication and division of fractions
    9. Area models of fractions
  8. Ratios, Percentages, and Rates
    1. Ratios and Proportions
    2. Changing Ratios and Percentages
    3. Solving Percent Problems by the Unitary Method
    4. Rates, Speed, and Dimensional Analysis
  9. Negative Numbers and Integers
    1. Negative Numbers
    2. Arithmetic with Integers
    3. Integers as a Step Towards Algebra
  10. Decimals, Rational and Real Numbers
    1. Decimals
    2. Rational Numbers and Decimals.
    3. Real Numbers and Decimals


  1. Thomas Parker and Scott Baldridge, Elementary Mathematics for Teachers, Sefton-Ash Publishing, 2004.
  2. Singapore Primary Mathematics 3A, 4A, 5A, and 6A Textbooks. Primary Mathematics 5A Workbook. (
  3. Mario L. Rodríguez Barrios, Matemática para Maestros, Editora Centenario, 2001. (ISBN 1-8817736-21-0). Distribuidora: Los Hermanos López Inc, Río Piedras, Puerto Rico)
  4. Philip Pennance, Mathematics Standards of Puerto Rico: Analysis and Recommendations.


A list of texts and references for this course can be found in the Education Page.


Based on Homework and up to 4 exams.
A: 90-100;     B: 80-89;    C: 65-79;   D: 50-64;   F: < 50.