kitchen table math, the sequel: MSMI 2011: Fractions and Rational Numbers

## Thursday, March 24, 2011

### MSMI 2011: Fractions and Rational Numbers

This year, Middle School Mathematics Institute (MSMI) is offering two professional development institutes this summer for elementary and middle school math teachers that are specifically geared to the math content they teach: MSMI 2011: Fractions and MSMI 2011: Rational Numbers.

MSMI 2011: Fractions is a 5 day (plus 5 day followup) institute, June 20-24, 2011 in downtown Saint Paul, MN. MSMI 2011: Rational Numbers is a 4 day (plus 5 day followup) institute, June 27-June 30, 2011. Both institutes will be held at the CoCo Coworking and Collaborative Space. Local arrangements are available at the Crowne Plaza in St. Paul, a short walk from CoCo.

These institutes are designed to develop fractions and rational numbers in a coherent, sequential, and precise manner that builds both conceptual understanding and procedural fluency. Teachers will learn how to help their students increase the depth of knowledge by providing the scaffolding needed for abstract mathematical reasoning. Teachers will develop a better understanding of how they math they teach relates to the math taught prior to and beyond their classroom. By teaching this material in a coherent, precise fashion, teacher will be able to lead students to understand and master this mathematics, enabling their students to achieve a solid foundation for Algebra 1.

Why fractions and rational numbers? MSMI concentrates on fractions and rational numbers following the National Mathematics Advisory Panel's recommendations on "Critical Foundations for Algebra". Fractions are the first abstractions in school mathematics. Fractions prepare students because they depend on precise definitions in order to be well defined. Fractions are handled best by thinking symbolically, not by analogies (no more pie pieces, pizza slices, etc.) Negative numbers have no grounding the way counting numbers do. They are best handled by thinking symbolically and working with definitions. Learning to work with fractions and negative numbers helps students because if they can handle these elements for fractions and negative numbers, they can handle them in algebra.

Institutes are not geared toward any specific textbook or pedagogy, but provide deeper content knowledge immediately applicable to any classroom. The textbook for these institutes is Hung-Hsi Wu's Understanding Numbers in Elementary School Mathematics . This material is aligned with both Minnesota state standards and Common Core standards.

Allison Coates will teach the Fractions institute. UC Berkeley Professor Emeritus Hung-Hsi Wu will teach the Rational Numbers institute.

Topics covered in Fractions Institute include:
Formal definitions of Fractions and Decimals

— Equivalent Fractions and the Fundamental Fact of Fraction-Pairs

— Addition and Subtraction of Fractions and Decimals

— Multiplication of Fractions and Decimals

— Division of Fractions

— Complex Fractions

— Percent

— Ratio and Rate

Topics for Rational Numbers institute include:

The Two Sided Number Line

— A Different View of Rational Numbers

— Addition and Subtraction of Rational Numbers

— Multiplication of Rational Numbers

— Division of Rational Numbers

While the summer session of 4 or 5 full days provides the bulk of the mathematics content, 5 follow-up Saturday sessions are provided throughout the school year. Saturday sessions review material from the institute and provide time for teachers to discuss implementation of institute material in their classes. In these sessions, teachers work together to determine what works best for their students in their classrooms, and provide feedback to each other.

Online registration is available here. Additional information is available on the www.msmi-mn.org web site.

Lsquared said...

An interesting approach. I think I prefer the Singapore bar diagram approach to multiplication and division of fractions, but Hu's (more abstract approach) has some advantages too. Certainly it's something teachers need to spend time working on. Too many teachers have only a very surface level of understanding fractions.

Allison said...

Well, the bar diagram is really just a number line with the pieces next to each other. So they complement each other very nicely.

Wu has two nice approaches to mulitiplication, one a "k/l of m/n" on the number line, and one which is k/l on the x axis, m/n on the y, where multiplication is then *defined* as "the area when the unit rectangle is broken into nl congruent rectangles and you take km of them.