MATH-122: Mathematics for Elementary Teachers I

School
Science, Technology, Engineering and Math
Division
Mathematics
Department
Mathematics
Academic Level
Undergraduate
Course Subject
Mathematics
Course Number
122
Course Title
Mathematics for Elementary Teachers I
Credit Hours
4.00
Instructor Contact Hours Per Semester
77.00 (for 15-week classes)
Student Contact Hours Per Semester
77.00 (for 15-week classes)
Grading Method
A-E
Pre-requisites
MATH-110 with a C grade or better OR a satisfactory score on the placement test
Co-requisites
Enrollment in ENG-131 or ENG-131 with a C grade or better
Catalog Course Description

For students who are involved in a curriculum for elementary teachers. Includes problem solving, set theory, number theory, numeration systems, whole numbers, and fractions. Addresses two aspects of teaching children mathematics – content and pedagogy – focused on Michigan Department of Education Standards for the Preparation of Teachers of Lower Elementary (Pre-K – 3) and Upper Elementary (Grades 3 – 6). Also addresses concept development, algorithms, children’s mathematical work, and communication skills--both oral and written--important for teaching children.

Goals, Topics, and Objectives

Goal Statement
  1. To strengthen mathematical problem-solving skills pertaining to curricular topics related to the preparation of future elementary school teachers.
  2. To strengthen communication skills, both written and oral, of mathematical ideas.
  3. To strengthen mathematical competence in fundamental set theory and numeration systems that undergird
    1. Whole-number concepts and operations and
    2. Number theory fundamental to fraction operations.
  4. To develop pedagogical skills consistent with MDE Core Teaching Practices that are used for teaching mathematics to children.
Core Course Topics
  1. Michigan Department of Education Core Practices
    1. Demonstrate knowledge of leading a group discussion.
    2. Demonstrate knowledge of explaining and modeling content, practices and strategies.
    3. Demonstrate knowledge of eliciting and interpreting individual students’ thinking.
    4. Demonstrate knowledge of implementing norms and routines for classroom discourse and work.
  2. Problem Solving (MDE Standards: B-K M.9)
    1. Solve word problems using a variety of strategies.
    2. Solve word problems employing Polya’s four-step process.
  3. Numeration Systems (MDE B-K; M. 13, M.15. Pre-K – 3: M.9, M.10, M.11, M.12. Grades 3-6: M.5, M.6)
    1. Identify the characteristics of tally and place-value numeration systems.
    2. Give examples of tally and place-value numeration systems.
    3. Represent Base 5 numerals using a variety of manipulatives.
    4. Convert between Base 5 and Base 10 numeration systems.
    5. Add, subtract and multiply in Base 5 numeration system.
    6. Compose and decompose Base 10 numbers in a variety of ways.
    7. Use a variety of manipulatives to represent Base 10 numbers.
    8. State benefits and limitations of a variety of manipulatives.
  4. Set Theory
    1. Define: set, subset, proper subset, null/empty set, element, universal set, complement of a set.
    2. Demonstrate knowledge of element and subset relationships.
    3. Perform operations on sets (union, intersection, complement).
    4. Demonstrate knowledge of properties of set operations (commutativity, associativity, distributivity, identity).
    5. Use Venn Diagrams to solve problems.
  5. Whole Numbers and Their Operations (MDE B-K; M.13, M.14, M.15. MDE Pre-K-3. MDE Grades 3–6: M.5, M. 6., M.7, M.8)
    1. Use ordinal, cardinal, and nominal models to demonstrate whole numbers.
    2. Compare whole numbers and develop the meaning of <, > and = with whole numbers.
    3. Model and explain using manipulatives whole numbers operations.
    4. Demonstrate knowledge and understanding of the standard algorithms for whole number operations.
    5. Justify alternative algorithms for whole number operations.
    6. Make connections among whole number operation algorithms.
    7. Demonstrate proficiency in using estimation techniques for whole number operations.
    8. Demonstrate proficiency in mental mathematics for whole number operations.
    9. Demonstrate knowledge of the properties of whole number operations.
    10. Solve problems involving whole numbers.
    11. Respond to observations of children’s mathematical work.
    12. Develop sets of problems with varying degrees of difficulty
  6. Algebraic Reasoning (MDE B-K: M.10, M.11, M.12)
    1. Demonstrate an understanding of the concept of variable and apply this knowledge to problem solving.
    2. Demonstrate an understanding of equation solving and apply this knowledge to problem solving.
    3. Apply knowledge of functions represented in a variety of forms.
    4. Solve problems requiring equations in two variables.
  7. Number Theory
    1. Define: the unit, prime number, composite number, even number, odd number, factor and multiple.
    2. Demonstrate an understanding of greatest common factor (GCF) using a variety of techniques.
    3. Demonstrate an understanding of least common multiple (LCM) using a variety of techniques.
    4. Solve problems involving the concepts of GCF and LCM.
  8. Fractions (MDE: Pre-K-3: M.13, M.14, M.15, M.16. Grades 3 – 6: M.9, M.10, M.11, M.12)
    1. Model fractions using a variety of manipulatives and hand-drawn methods.
    2. Develop meaning of fraction using a variety of mathematical concepts.
    3. Define fraction.
    4. Compare fractions and develop the meaning of <, >, and = with fractions.
    5. Model and explain fraction operations using manipulatives.
    6. Demonstrate knowledge and understanding of standard algorithms for fraction operations.
    7. Demonstrate proficiency in using estimation techniques for fraction operations.
    8. Demonstrate proficiency in mental mathematics for fraction operations.
    9. Demonstrate knowledge of the properties of fraction operations.
    10. Solve problems involving fractions.
    11. Observe and respond to children’s mathematical work.
    12. Develop sets of problems with varying degrees of difficulty.

Assessment and Requirements

Assessment of Academic Achievement
  • Pre-Education students are required to create an e-portfolio as part of their academic work at HFC. Instructors must include a minimum of three e-portfolio assignments as part of course work. These assignments will be stored in each student's e-portfolio.
  • All students will be required to complete online homework. This online homework must be weighted in such a manner so that it is worth between six percent (6%) and twelve percent (12%) of the final course grade.
  • All students will be required to complete an arithmetic quiz (with no calculator) that is worth five percent (5%) of the final course grade.
  • All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives. This exam must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the final course grade. In selected semesters this exam may be a common exam administered to all sections of MATH 122.
  • All students will be required to complete journal assignments.
  • Additional assessment of student achievement may include assignments, quizzes, and exams.
  • Application problems must not only be included on chapter exams but also on the final exam.
General Course Requirements and Recommendations
  • Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.
  • No calculator may be used in this course.

Outcomes

General Education Categories
  • Mathematics
MTA Categories
  • Category 3: Mathematics (Quantitative Literacy Track)
Satisfies Wellness Requirement
No
Satisfies Honors Requirements
No
Effective Term
Fall 2024