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Mathematics 312

MATH 312
Elementary and Middle Grades Mathematics for Social Analysis

Catalog Entry

MATH 312. Elementary and Middle Grades Mathematics for Social Analysis
Credit hours (3).

Prerequisites: Math 111 and 112, or permission by instructor.

The primary purpose of this course is to prepare future and current elementary and middle school teachers to critically analyze and explore the world using mathematics. Students will conduct meaningful and carefully reasoned real-world investigations and critiques using elementary and middle school mathematics and also communicate the results of these problem-posing and problem-solving investigations both orally and in writing. This course examines the interplay among mathematical topics and integrates mathematics across the curriculum. Students are introduced to the National Council of Teachers of Mathematics [NCTM] Standards and to the Virginia Standards of Learning. Mathematical content emphases are also based on the NCTM Standards and include topics in number and operations, algebraic thinking, geometry, measurement, and data analysis and probability. Students cannot earn credit for both Math 312 and Math 315.


Detailed Description of Course

This course has several emphases:

  • First, this course provides students with opportunities to deepen and increase the flexibility of their understanding of elementary and middle grades mathematics content.
  • Second, this course helps students begin thinking about how to teach mathematics for understanding. We will use mathematics manipulatives and technology and also discuss and use the Virginia SOLs and the NCTM Standards documents (1989, 2000).
  • Third, and perhaps most importantly, this course prepares students both to identify and carry out applications of mathematics to other disciplines and to identify and examine the relevance and significance of having and using mathematical knowledge for civic purposes.

Given the general reputation mathematics has as an isolated discipline, separate from the issues students confront in their daily lives, and given also how many students who enroll in this course will eventually teach multiple academic content areas (e.g., those students planning to teach in elementary schools), this course addresses important and yet widely overlooked topics and issues in elementary and middle grades mathematics education.

Mathematical content varies depending in part on the nature of the projects that students create, select, and pursue. Mathematical content always includes components from each of the following five content strands, and includes the majority of the following topics:

  • Number and Operations:
    • Number systems and place value
    • Number lines
    • Mental math and estimation
    • Ratios and proportions
    • Fractions, decimals, and percents
    • Factors and multiples
  • Algebraic Thinking:
    • Variables
    • Patterns and functions
    • Graphing
    • Mathematical models
    • Analysis of change
  • Geometry:
    • Shapes
    • Angles
    • Spatial relationships and transformations
    • Coordinate systems
    • Geometry outside the classroom
    • Geometric vocabulary
  • Measurement:
    • Length, weight, area, surface area, circumference, and volume
    • Standard and non-standard units of measurement
    • Ratio and proportion
    • Velocity and density
  • Data Analysis and Probability:
    • Measurement and categorical data
    • Formulating questions, designing studies, and collecting data
    • Graphical representations of data
    • Mean, median, mode, and range
    • Probability concepts and simple experiments

Interdisciplinary content varies semester to semester depending on current issues, student interest, and text selection. Students are encouraged and supported to participate in mathematical investigations of the world that span all content areas and that make use of available technologies. Interdisciplinary content always includes many diverse relationships to science, social studies, and language arts. Course content includes discussions of political, social, and economic challenges and implications associated with reading and writing the world using mathematics.


Detailed Description of Conduct of Course

Course instructors model the type of instruction they support students to also use as future teachers. Instruction includes cooperative/group learning and projects, student research and presentations both in and outside the classroom, small group and whole class discussions and questioning, and student explorations of mathematical concepts using manipulatives and technology. Diverse assessments are used, including formative assessments where students monitor their own learning, and this information helps guide instructional decisions.


Student Goals and Objectives of the Course

Course content and design addresses an historic problem in mathematics education of instruction based on rote calculations, drill and practice, worksheets, and “the” right answer. It also addresses the problem in schools of the relative isolation of mathematics from other disciplines and its segregation from the issues that students confront outside of school classrooms. This course aims to help future and current elementary and mathematics teachers identify and engage seriously with mathematics and its relevance in the world and in their own and children’s lives. Students use mathematics as a tool for participating in and investigating local and global issues, and they give serious consideration to the social and ethical consequences of how mathematics and statistics are sometimes used in society. By performing individual and group research combined with studies of elementary and middle school mathematics as it relates to social phenomena and issues, students link math and history, math and politics, math and literature, and math and people. This course helps students deepen their understandings of elementary and middle school mathematics and its applications and allows students to discuss as current and future teachers the need and implications for children’s learning, understanding, and investigating of mathematical concepts and their relevance in their own communities as well as globally. The emphasis in this course on elementary and middle grades mathematics for social analysis currently represents a distinctive approach to mathematics teacher education coursework. The course uniquely addresses and extends the emphases of the NCTM Standards by combining these mathematics-based recommendations with critical literacy emphases and with popular recommendations for urban and multicultural education for socially and culturally relevant instruction.


Assessment Measures

Graded tasks are diverse and may include individual or group projects and/or presentations, writing assignments, self or peer assessments, and class participation. They may also include assessments such as homework, quizzes, and written exams.


Other Course Information



Review and Approval

Revised 08/17/05