For students who are involved in a curriculum for elementary teachers. Topics include rational numbers, proportional reasoning, algebraic reasoning. Also, topics from geometry including Van Hiele levels of understanding, definitions of geometric concepts, measurement, conversions between units, concepts of perimeter, area and volume, derivations of formulas, flat patterns and symmetry. Addresses two aspects of teaching children mathematics – content and pedagogy – focused on Michigan Department of Education Standard for the Preparation of Teachers of Lower Elementary (Pre-K – 3), Upper Elementary (Grades 3 – 6), and Middle Grades (Grades 5 - 9). Also, addresses concept development, algorithms, children’s mathematical work, communication skills--both oral and written--important for teaching children, and problem-solving skills.

### Goals, Topics, and Objectives

- To strengthen mathematical problem-solving skills pertaining to curricular topics related to the preparation of future elementary school teachers.
- To strengthen communication skills, both written and oral, of mathematical ideas.
- To strengthen mathematical competence in rational numbers, algebraic and proportional reasoning, and geometry.
- To develop pedagogical skills consistent with MDE Core Teaching Practices that are used for teaching mathematics to children.

- Michigan Department of Education Core Practices
- Demonstrate knowledge of leading a group discussion.
- Demonstrate knowledge of explaining and modeling content, practices and strategies.
- Demonstrate knowledge of eliciting and interpreting individual students’ thinking.
- Demonstrate knowledge of implementing norms and routines for classroom discourse and work.

- Proportional Reasoning
- Identify additive and multiplicative comparisons.
- Apply the understanding of ratio to a variety of contexts.
- Represent proportional situations using a variety of models.
- Apply proportional reasoning using the unit-rate method.

- Integers
- Model integers using a variety of models such as colored chips, number line, and charged particle.
- Use the relations of <, >, and = with integers.
- Model and explain integer operations using manipulatives.
- Develop and use the rules for integer operations.
- Demonstrate knowledge of the properties of integer operations.
- Solve problems involving integers.

- Decimals (MDE Grades 3 – 6: M.9, M.10, M.11, M.12)
- Model decimals using a variety of manipulatives and hand-drawn methods.
- Model decimals using a variety of mathematical concepts.
- Compare decimals and develop the meaning of <, >, and = with decimals.
- Model and explain decimal operations using manipulatives.
- Demonstrate knowledge and understanding of the standard algorithms for decimal operations.
- Demonstrate proficiency in mental mathematics for decimal operations.
- Convert between fraction and decimal equivalents for both terminating and repeating decimals.
- Solve problems involving decimals.
- Respond to observations of children’s mathematical work.
- Develop sets of problems with varying degrees of difficulty.

- Algebraic Reasoning (MDE: B-K: M.9, M.10, M.11, M.12.)
- Apply the concept of variable to problem solving.
- Demonstrate an understanding of children’s approaches to problem solving.
- Apply equation solving to problem solving.
- Apply knowledge of functions represented in a variety of forms.

- Introductory Geometry (MDE: B-K: M.5, M.6, M.7, M.8.)
- Demonstrate an understanding of the Van Hiele levels of geometric understanding and implications for instruction.
- Use coordinate grids to locate objects in a variety of contexts.
- Decompose and recompose shapes.
- Give descriptions, properties and real-world models of points, rays, lines, planes, line segments and angles.
- Define terms related to angles and angle relationships.
- Define various types of polygons and their parts.
- Identify and model properties of and relationships among various types of polygons.
- Describe, classify and understand relationships among types of 2- and 3-dimensional objects.
- Define various types of polyhedra and curved shapes in 3 dimensions.
- Identify and model properties of and relationships among various types of polyhedra and curved shapes in 3 dimensions.
- Perform translations, rotations, reflections and combinations of these transformations on geometric figures.
- Describe and analyze tessellations with polygons, particularly but not exclusively, with regular polygons.

- Concepts of Measurement (MDE: B-K: M.17, M.18, M.19, M.20)
- Develop the concepts of perimeter, area and volume using non-standard units and appropriate tools and units.
- Measure with standard units (English and metric) and nonstandard units for length, area and volume.
- Convert between various units, including those of length, area and volume, by using proportions and dimensional analysis.
- Do “rough” conversions between the metric system and the English system.
- Find the perimeter of a geometric figure, including polygons and circles.
- Derive and apply area formulas to find areas of rectangles, squares, triangles, parallelograms, trapezoids and circles.

- Data Analysis (MDE: B-K: M. 21, M.22, M. 23, M.24)
- Unpack mathematical content and identify mathematical competence for collecting, representing, using and organizing information
- Use concrete materials in purposeful, relevant activities for collecting, representing, using and organizing information.
- Use graphs to interpret data.

### Assessment and Requirements

- 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 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 221.
- All students will be required to complete journal assignments.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- These application problems must not only be included on chapter exams but also on the final exam.

- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.
- A scientific calculator is required of each student.

### Outcomes

- Mathematics

- Quantitative Literacy

- Category 3: Mathematics (Quantitative Literacy Track)