Ohio's Learning Standards Progressions
The Ohio Learning Standards progressions
are intended for curriculum leaders and teachers to better understand the standards
and to analyze where their curriculum fits related to the learning progressions.
Learning progressions within mathematics domains are important to the
understanding and coherence of math topics within and across the grade levels.
Coherence Map
Mathematics standards are not isolated concepts. Standards relate to one another, both within and across grades. The Coherence Map illustrates the coherent structure of the standards for mathematics.
- Build student understanding by linking together concepts within and across grades.
- Identify gaps in a student's knowledge by tracing a standard back through its logical pre-requisites.
- Visualize and understand how supporting standards relate to the major work of the grade.
Arizona Progressions: Overview
The standards in
mathematics were built on progressions: narrative documents describing the
progression of a topic across a number of grade levels, informed both by
research on children's cognitive development and by the logical structure of
mathematics.
The Arizona Progressions are
intended to inform teacher preparation and professional development, curriculum
organization, and textbook content. Thus, their audience includes teachers and
anyone involved with schools, teacher education, test development, or
curriculum development. As with any written mathematics, understanding the
Arizona Progressions may take time and discussion with others.
Arizona Progressions: K, Counting & Cardinality; K-5, Operations and Algebraic Thinking
Counting and Cardinality and Operations
and Algebraic Thinking are about understanding and using numbers.
Counting and Cardinality underlies Operations and Algebraic
Thinking as well as Number and Operations
in Base Ten. It begins with early counting
and telling how many in one group of objects.
Addition, subtraction, multiplication, and division grow from these early roots.
From its very beginnings, this Arizona Progression involves
important ideas that are neither trivial
nor obvious; these ideas need to be taught, in ways that are interesting and engaging to young students.
Arizona Progressions:
6-8, The Number System; High School, Number
In Grades 6–8, students build on two important conceptions which have developed throughout K–5, in order to understand the rational numbers as a number system. The first is the representation of whole numbers and fractions as points on the number line, and the second is a firm understanding of the properties of operations on whole numbers and fractions.
In Grades 6-8, students began to widen the possible types
of number they can conceptualize on the number line. In Grade 8, they glimpse the
existence of irrational numbers such as the square root of 2. In high school, they start
a systematic study of functions that can take on irrational values, such as exponential,
logarithmic, and power functions. The first step in this direction is the understanding of numerical expressions in which the exponent is not a whole number.
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