MATH 113: Mathematics for Elementary Teachers II
It is important to ask yourself What do I want my students to learn,
and why? It may also be helpful to your students to know what
skills, strategies and information you expect them to master. Below
is my list of outcomes for MATH113. (Of course, the ultimate goal of
this course is to train you to teach mathematics. The list
below is the result of breaking that goal into parts, and should be
read in that context.)
To prepare for teaching mathematics, Mathematics for Elementary Teachers II students will:
- Understand and apply concepts of measurement:
- Estimate and calculate measurements using customary, metric and nonstandard units of measurement.
- Use unit conversions and dimensional analysis to solve problems.
- Derive and use formulas for calculating lengths, perimeters, areas, volumes and surface areas of geometric objects.
- Understand how the characteristics (area, volume, etc.) of an object is affected by changes in its dimensions.
- Solve a variety of measurement problems (e.g. time, temperature, rates) in real world situations.
- Understand and apply concepts of geometry:
- Classify and anlayze polygons using attributes of sides and angles.
- Classify and analyze three-dimensional objects using attributes of faces, edges and vertices.
- Recognize and use geometric transformations -- translations, rotations, reflections, and dilations.
- Use the language of geometric transformations to describe symmetry, similarity and congruence.
- Match three-dimensional figures and their two-dimensional representations -- e.g. nets, projections and perspective drawings.
- Recognize and apply connections between algebra and geometry (e.g. coordinate systems, area formulas, the Pythagorean theorem).
- Understand and use descriptive statistics:
- Use measures of central tendency (mean, median, mode) and range to describe and interpret real world data.
- Select appropriate ways to present data in communicating statistical information (e.g. tables, graphs, line plots, Venn diagrams).
- Analyze and interpret graphic and non-graphic data representations (e.g. frequency distributions, percentiles).
- Compare different data sets.
- Understand and apply basic concepts of probability:
- Calculate probabilities of simple and compound events and of independent and dependent events.
- Recognize and apply the concept of conditional probability.
- Recognize the difference between experimentally and theoretically determined probabilities in real-world situations.
- Apply knowledge of combinations and permutations to the computation of probabilities.