MT 119 - Mathematics for Elementary Education Teachers II

1. demonstrate visualization skills:
   1. demonstrate the use of projections, cross-sections, and decompositions of common two- and three-dimensional figures; and
   2. represent three-dimensional shapes in two dimensions and construct three-dimensional objects from two-dimensional representations.
2. demonstrate familiarity with basic shapes and their properties:
   1. identify fundamental objects of geometry;
   2. demonstrate an understanding of angles and how they are measured;
   3. demonstrate an understanding of plane isometries: reflections (flips), rotations (turns), and translations (slides)-and symmetries;
   4. demonstrate an understanding of congruence and similarity; and
   5. demonstrate an understanding of technical vocabulary and an understanding of the importance of definition.
3. demonstrate an understanding of the process of measurement:
   1. demonstrate different aspects of size;
   2. demonstrate an understanding of the idea of the unit and the need to select a unit appropriate to the attribute being measured;
   3. demonstrate a knowledge of the standard (English and metric) systems of units;
   4. demonstrate an understanding of comparing units; and
   5. demonstrate an understanding that measurements are approximate and that different units affect precision.
4. demonstrate an understanding of length, area, and volume:
   1. demonstrate an understanding of one, two, and three dimensions;
   2. illustrate rectangles as arrays of squares, rectangular solids as arrays of cubes;
   3. demonstrate an understanding of the behavior of measure (length, area, and volume) under uniform dilations;
   4. devise area formulas for triangles, parallelograms, and trapezoids; know the formula for the area of a circle; become familiar with formulas for prisms, cylinders, and other three-dimensional objects; and
   5. demonstrate an understanding of the interdependence of perimeter and area; surface area and volume.
5. demonstrate the ability to design data investigations:
   1. demonstrate an understanding of the kinds of questions that can be addressed by data;
   2. demonstrate an understanding of creating data sets; and
   3. demonstrate the ability to move back and forth between the question (the purpose of the study) and the design of the study.
6. demonstrate the ability to design data investigations:
   1. Demonstrate an understanding of describing the shape of a distribution: symmetry versus skewed data distribution and what this indicates about the question being addressed;
   2. Demonstrate an understanding of describing the spread of a distribution: range, outliers, clusters, gaps, and what these indicate about the question to be addressed by the data;
   3. Demonstrate an understanding of describing the center of a distribution: mean, median, and mode and what these indicate about the question to be addressed by the data;
   4. Demonstrate an understanding of different forms of data representation, e.g., line plots, and stem-and-leaf plots, among others; recognizing that different forms of representation communicate different features of the data; and
   5. Demonstrate the ability to compare two sets of data (not always of the same size).
7. demonstrate the ability to draw conclusions:
   1. demonstrate the ability to choose among representations and summary statistics to communicate conclusions;
   2. demonstrate an understanding of variability; and
   3. demonstrate an understanding of some of the difficulties that arise in sampling and inference.
8. demonstrate an understanding of probability:
   1. demonstrate an ability to make judgments under uncertainty;
   2. demonstrate an ability to assign numbers as a measure of likelihood; and
   3. demonstrate an understanding of the idea of randomness.
9. demonstrate an understanding of functions:
   1. demonstrate a conceptual understanding of what is a function; and
   2. demonstrate the ability to read and create graphs of functions, work with formulas, and use tables of values.
10. demonstrate the ability to use manipulatives to develop an understanding of mathematical concepts throughout the course.

Technology Objectives:

11. demonstrate the ability to use the arithmetic operations on the scientific calculator to solve algebraic and real-world algebraic problems;
12. demonstrate an understanding of the keys
    
    √n ,x²,y^x,π,±,%, (  ) 2^nd inv key; and
     
13. demonstrate an understanding of the order of operations on the scientific calculator.