Math framework for Common Core ready for your critique - by John Fensterwald
A draft of the California math curriculum framework went online Wednesday for public comments and suggestions. While weighing in at 1,200 pages, the document is actually a readable grade-by-grade manual that puts meat on the bare-bones Common Core standards that the state adopted in 2010. It explains the rationale for key standards and puts them in context of what students will learn, while providing guidance on how they should be taught. Interspersed are numerous sample problems and illustrations that teachers can use in the classroom.
Framework sampler:
5th grade fractions
The Mathematics Curriculum Framework and Evaluation Criteria Committee made an effort to create a readable, comprehensible, as well as comprehensive, guide to the Common Core standards.
A look at a small but important piece, how to introduce fractions to third graders (pages 25-27 of the third grade chapter) provides a good example of how the committee strove to put each standard in a larger context and explain its relevance and its coherence.
“In grade three students develop an understanding of fractions as numbers, building on the idea of partitioning a whole into equal parts. An important goal is for students to see unit fractions as the basic building blocks of fractions, in the same sense that the number 1 is the basic building block of the whole numbers. …
Then it explains why this is important:
Student proficiency with fractions is essential for success in more advanced mathematics such as percentage, ratios, and proportions and in algebra at later grades. …
After explaining what was done in grades 1 and 2 to prepare for whole-unit fractions, it says,
This is the first time students represent fractions using a number line and other visual fraction models to develop an understanding of fractional parts, sizes, and how to compare fractions. This work will continue through grade six, preparing the way for work with the complete rational number system in grades six and seven.
It lists and explains the standards:
In grade three students understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (3.NF.1▲).
Students understand a fraction as a number on the number line and they represent fractions and compare fractions using visual fraction models (such as a circle, rectangle or a line segment) (3.NF.2-3▲).
The framework then gives a sample problem for students to place fractions on a number line, leading up to 1/2, 1/3/, 1/4 and 1/5. A commentary suggests ways to help students in anticipation that some will struggle.
Students learn to use the number line to represent whole numbers in second grade, but this is the first time they will use the number line to represent fractions.
Some students may have difficultly creating equal sized intervals, especially for thirds and fifths. Providing strategies, such as folding a separate piece of paper, might be helpful.
Although the Common Core Standards cover only transitional kindergarten through grade eight, the framework does provide suggestions for high school, where districts will have a choice between traditional subject courses (geometry, Algebra II and pre-Calculus) and integrated math courses, which blend traditional disciplines. Common Core is well suited for the latter. (Update:To quell rumors that it would not support integrated math courses, the University of California has issued a statement affirming its support for both the traditional and the integrated pathways.) And the document includes a chapter on options for accelerating math for those students ready to take Algebra I in eighth grade or, as an alternative for those taking Algebra I in ninth grade, combining three years of high school
Bill restricting ‘willful defiance’ for suspending students moves ahead - by Susan Frey
With new data showing that more than half of all suspensions and a quarter of expulsions in California schools are for “willful defiance” of school authorities, the Assembly Education Committee voted 6-0 on Wednesday to move forward a bill that would restrict the use of the vague category by school administrators. Assemblymember Roger Dickinson, D-Sacramento, who introduced Assembly...