Moving Up! Educators - Early Math
What should my students be learning?
Mathematics Resources for California Students
The California Department of Education has developed grade-level specific foundations, standards, guidelines, assessments and/or best practices to guide your teaching and curriculum development. Listed below are a few resources applicable to the early grades – spotlighting early mathematics. Visit CDE's CCSS Mathematics Resources for Administrators page for a comprehensive list of materials and resources.
Grade: Pre-K
California Preschool Learning Foundations, Volume I
Our youngest learners are working on math acquisition every day, in every setting. The California Preschool Learning Foundations, Volume I (the Mathematics section begins on page 143) outlines a set of behaviors in mathematical learning that older three year olds and older four year olds will develop during the preschool years. Includes number sense, algebra and functions (classification and patterning), measurement, geometry and mathematical reasoning.
Desired Results Developmental Profile – Preschool (DRDP–PS)
Assessment – a Teacher’s Best Friend! The DRDP-PS separates out the different developmental domains and provides a range of developmental level mastery: exploring, developing, building and integrating. This tool covers the ages of 3 years old to Kindergarten entry. Includes number sense of quantity and counting, number senses of mathematical operations, classification, measurement, shapes, and patterning.
Grade: TK
Desired Results Developmental Profile – School-age (DRDP – SA) and School-Readiness (DRDP-SR)
California’s newest grade – Transitional Kindergarten (TK) – serves as the bridge grade between Preschool and Traditional Kindergarten. As such, TK can make use of both Preschool and Kindergarten resources and materials. For assessment purposes, TK teachers can consider the DRDP-PS together with the DRDP-SA. The DRDP-SA(Kindergarten – 12 years) overlaps with the DRDP-PS. Taken together these tools provide a continuous measure of learning and development. Like the DRDP-PS, the DRDP-SA also separates out the different developmental domains and provides a range of developmental level mastery: exploring, developing, building and integrating. Includes number sense of mathematical operations, measurement, shapes, and time.
Alternatively, the TK teacher can use the DRDP - SR (School Readiness) which is aligned to the California Preschool Learning Foundations and the California Kindergarten Content Standards
Grades: K-12
K-12 California’s Common Core Content Standards for Mathematics
As MUSD moves toward implementation of the Common Core Content Standards in the fall of 2013, inquiring minds want to know what these standards are and how to teach them! The first step is familiarization with the new standards. The newest version of the K-12 California’s Common Core Content Standards for Mathematics, updated April 2013, includes counting and cardinality, operations and algebraic thinking, number and operations in base ten, measurement and data, and geometry.
TK-12 Mathematics Framework Chapters
Take a look at the Mathematics Framework Chapters! "The purpose of this framework is to guide the curriculum development and instruction that teachers provide in their efforts to ensure that all students meet or exceed the CCSSM. The framework provides a context for implementing the standards in the form of guidelines for educators and developers of instructional materials. Building on the standards, the framework addresses how all students in California public schools can best meet the standards." Includes guiding principles, grade-level and course-level chapters!
A Look at Kindergarten through Grade Six in California Public Schools – Transitioning to the Common Core State Standards in English Language Arts and Mathematics, 2011
Navigating the transition to the Common Core State Standards will take work! Transitioning to the Common Core State Standards is a handy guide that shows you how the 1997 California Mathematics Standards map out onto the Common Core State Standards (by grade level). Once you see how the old relates to the new, you will be able to begin to integrate the new standards into your classroom teaching practice… thinking ahead for those new Smarter Balanced Assessments coming up in 2014-15!
The California Department of Education has developed grade-level specific foundations, standards, guidelines, assessments and/or best practices to guide your teaching and curriculum development. Listed below are a few resources applicable to the early grades – spotlighting early mathematics. Visit CDE's CCSS Mathematics Resources for Administrators page for a comprehensive list of materials and resources.
Grade: Pre-K
California Preschool Learning Foundations, Volume I
Our youngest learners are working on math acquisition every day, in every setting. The California Preschool Learning Foundations, Volume I (the Mathematics section begins on page 143) outlines a set of behaviors in mathematical learning that older three year olds and older four year olds will develop during the preschool years. Includes number sense, algebra and functions (classification and patterning), measurement, geometry and mathematical reasoning.
Desired Results Developmental Profile – Preschool (DRDP–PS)
Assessment – a Teacher’s Best Friend! The DRDP-PS separates out the different developmental domains and provides a range of developmental level mastery: exploring, developing, building and integrating. This tool covers the ages of 3 years old to Kindergarten entry. Includes number sense of quantity and counting, number senses of mathematical operations, classification, measurement, shapes, and patterning.
Grade: TK
Desired Results Developmental Profile – School-age (DRDP – SA) and School-Readiness (DRDP-SR)
California’s newest grade – Transitional Kindergarten (TK) – serves as the bridge grade between Preschool and Traditional Kindergarten. As such, TK can make use of both Preschool and Kindergarten resources and materials. For assessment purposes, TK teachers can consider the DRDP-PS together with the DRDP-SA. The DRDP-SA(Kindergarten – 12 years) overlaps with the DRDP-PS. Taken together these tools provide a continuous measure of learning and development. Like the DRDP-PS, the DRDP-SA also separates out the different developmental domains and provides a range of developmental level mastery: exploring, developing, building and integrating. Includes number sense of mathematical operations, measurement, shapes, and time.
Alternatively, the TK teacher can use the DRDP - SR (School Readiness) which is aligned to the California Preschool Learning Foundations and the California Kindergarten Content Standards
Grades: K-12
K-12 California’s Common Core Content Standards for Mathematics
As MUSD moves toward implementation of the Common Core Content Standards in the fall of 2013, inquiring minds want to know what these standards are and how to teach them! The first step is familiarization with the new standards. The newest version of the K-12 California’s Common Core Content Standards for Mathematics, updated April 2013, includes counting and cardinality, operations and algebraic thinking, number and operations in base ten, measurement and data, and geometry.
TK-12 Mathematics Framework Chapters
Take a look at the Mathematics Framework Chapters! "The purpose of this framework is to guide the curriculum development and instruction that teachers provide in their efforts to ensure that all students meet or exceed the CCSSM. The framework provides a context for implementing the standards in the form of guidelines for educators and developers of instructional materials. Building on the standards, the framework addresses how all students in California public schools can best meet the standards." Includes guiding principles, grade-level and course-level chapters!
A Look at Kindergarten through Grade Six in California Public Schools – Transitioning to the Common Core State Standards in English Language Arts and Mathematics, 2011
Navigating the transition to the Common Core State Standards will take work! Transitioning to the Common Core State Standards is a handy guide that shows you how the 1997 California Mathematics Standards map out onto the Common Core State Standards (by grade level). Once you see how the old relates to the new, you will be able to begin to integrate the new standards into your classroom teaching practice… thinking ahead for those new Smarter Balanced Assessments coming up in 2014-15!
Ready, Set, Count!
Counting Principles
listed below are general explanations of the common mathematics principles that young children demonstrate, learn and/or develop over time (as outlined by LInda and Yasmin).
Counting words in order
remembering the sequence of words for counting, such as “one, two, three, four…”, “nineteen, twenty, twenty-one…” etc.
One-to-one correspondence
the exact matching of two sets when each element of the first set maps onto a specific element of the second set, for example each bear gets assigned a number – the first bear is “one”, the second bear is “two”, the third bear is “three”, and so on.
Cardinality
the understanding that that last counting word used not only indicates the last item but also the total number of items in the set. When counting five frogs, (one, two, three, four, five) the word five represents the last frog in the line and also the total number of frogs in the pond.
Any order
objects may be counted in any order with one-to-one correspondence and the total number in the set does not change (objects do not need to be in a line to be counted).
Anything
can be counted! The items in the set do not need to match to get a total: one chair, one frog, one bear, one person and one shoe equals five.
Subitizing
the ability to instantly recognize the number of objects in a small group without counting them.
listed below are general explanations of the common mathematics principles that young children demonstrate, learn and/or develop over time (as outlined by LInda and Yasmin).
Counting words in order
remembering the sequence of words for counting, such as “one, two, three, four…”, “nineteen, twenty, twenty-one…” etc.
One-to-one correspondence
the exact matching of two sets when each element of the first set maps onto a specific element of the second set, for example each bear gets assigned a number – the first bear is “one”, the second bear is “two”, the third bear is “three”, and so on.
Cardinality
the understanding that that last counting word used not only indicates the last item but also the total number of items in the set. When counting five frogs, (one, two, three, four, five) the word five represents the last frog in the line and also the total number of frogs in the pond.
Any order
objects may be counted in any order with one-to-one correspondence and the total number in the set does not change (objects do not need to be in a line to be counted).
Anything
can be counted! The items in the set do not need to match to get a total: one chair, one frog, one bear, one person and one shoe equals five.
Subitizing
the ability to instantly recognize the number of objects in a small group without counting them.
