Mathematics for Elementary Teachers II
hlascs (@) uwec.edu
Five out of four people don't understand fractions.
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.
- 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.
- Daily homework
- Daily quizzes
- Practicum experience (mostly outside of class)
- Two examinations during class time
- Comprehensive final exam
- 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.
- 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)