# Mathematics for Elementary Teachers II

Professor Hlas

hlascs (@) uwec.edu

Hibbard 530

*Five out of four people don't understand fractions.*

—unknown

## Course Information

This is the second of three mathematics courses designed to develop *conceptual understanding* of fundamental mathematics. "A significant indicator of conceptual understanding is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes" (*Adding It Up*, 2001). Specifically we will focus on the following:

- Creating problems
- Solving problems with multiple representations (concrete, visual, abstract)
- Explaining why

Topics addressed: percentages, decimals, fractions, proportions, ratios, similarity, and probability.

More course information is posted on D2L.

### Goals

- Explore a curriculum that focuses on the following learning sequence: percents, decimals, then fractions.
- Investigate how the Common Core State Standards builds proficiency of fraction concepts, ratio, and proportions.
- Effectively switch between representations of rational numbers (percents, decimals, fractions).
- Apply fractions, decimals, and percents to solve problems of scale and probability.

### Structure

- Daily homework
- Daily quizzes
- Practicum experience (mostly outside of class)
- Two examinations during class time
- Comprehensive final exam

### Required

- Productive disposition!
*Reconceptualizing mathematics for elementary school teachers*(Sowder, Sowder & Nickerson, 2009)- Fraction strips
- Pattern blocks (4:hex, 8:trapezoids, 10:parallelograms, 12:triangles)

Note: Calculators will **not** be allowed to remind preservice teachers of the learning difficulties involved for these topics.

### Research background

- Common Core State Standards
- CCSS Learning Progressions - Fractions
- Pipes, tubes, and beakers: New approaches to teaching the rational-number system (Moss, 2005)
- Developing essential understanding of rational numbers: Grades 3-5 (NCTM, 2010)
- Teaching fractions and ratios for understanding (Lamon, 2012)