Foundations of Elementary Mathematics I

Course Number: MTH 211
Transcript Title: Foundations of Elem Math I
Created: April 20, 2020
Updated: April 20, 2020
Total Credits: 4
Lecture Hours: 40
Lecture / Lab Hours: 0
Lab Hours: 0
Satisfies Cultural Literacy requirement: No
Satisfies General Education requirement: Yes
Grading options: A-F (default), P-NP, audit
Repeats available for credit: 0

Prerequisites

MTH 95 or MTH 98 or higher or equivalent placement test scores

Prerequisite / Concurrent

Course Description

Prepares prospective elementary teachers to teach math by strengthening their mathematical background.  Explores the following topics: problem solving, sets, whole numbers, number theory, and fractions. First term of a three-term math sequence.Prerequisites: MTH 95 or MTH 98 or higher or equivalent placement test scores; Prerequisite/concurrent: WR 121. Audit available.

Intended Outcomes

Upon successful completion of this course, students will be able to:

  1. Extend mathematical content knowledge, including: problem solving, sets, whole numbers, number theory, and fractions.
  2. Apply various problem-solving strategies to create mathematical models that will help analyze real world scenarios. 
  3. Use appropriate mathematical vocabulary to strengthen skills needed for communicating while teaching elementary math. 
  4. Provide examples of mathematical problems that will strengthen students’ ability to reason, reflect, observe and engage more deeply in mathematical thinking.

Alignment with Institutional Core Learning Outcomes

Major 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not addressed

4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Not addressed

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Core Learning Outcomes (CLOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

  1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
  2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

  1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
  2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Outcome Assessment Strategies

  • Reflective Writing
  • Quizzes
  • Class Discussions
  • Homework
  • Problem Solving Assignments
  • Projects
  • Presentations
  • Exams

Texts and Materials

Mathematics for Elementary Teachers -
A Conceptual Approach by Bennett, Burton, Nelson, and Ediger

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

Course Content (Themes, Concepts, Issues and Skills)

Outcome #1: Improve and deepen mathematical content knowledge, including: problem solving, sets, whole numbers, number theory, and fractions.
  1. Sets and Reasoning
    • 1.1 Venn Diagrams
    • 1.2 Deductive Reasoning
  2. Whole numbers
    • 2.1 Numeration
    • 2.2 Addition and Subtraction
    • 2.3 Multiplication
    • 2.4 Division and Exponents
  3. Number Theory
    • 3.1 Factors and Multiples
    • 3.2 Greatest Common Factor and Least Common Multiple
  4. Integers and Fractions
    • 4.1 Integers
    • 4.2 Fractions
    • 4.3 Operations with Fractions         
Outcome #2: Apply various problem-solving strategies to create mathematical models that will help analyze real world scenarios.
  • Introduction to problem solving
    • Use and present an example of Polya’s Four-Step Process
    • Demonstrate the problem-solving strategies which include: drawing, guessing and checking, making a table, working backward, finding a pattern.
    • Explain the concept of conjecture
  • Patterns
    • Show how patterns and sequences can be used to solve problems
Outcome #3: Use appropriate mathematical vocabulary to strengthen skills needed for communicating while teaching elementary math.
  • Show how mathematical vocabulary is necessary to explain problems
  • Compare and contrast non-mathematical vocabulary with proper mathematical vocabulary.
Outcome #4: Provide examples of mathematical communication that will strengthen student’s ability to reason, reflect, observe and engage more deeply in mathematical thinking.
  • Demonstrate the steps (algorithms) needed for addition, subtraction, multiplication and division of whole numbers, integers and fractions and explain how they work. 
  • Explain the thought processes used for whole number operations: estimation, rounding, divisibility tests.
  • Apply the definition of fraction and identify the relationship of fractions to whole numbers.
  • Recognize the models for a variety of conceptual approaches for addition, subtraction, multiplication and division of whole numbers, integers and fractions.
  • Identify how application problems can be modeled mathematically.