Counting - Rainbow Resource

Counting
to Calculus
Deanne Crawford
Consultant, Rainbow Resource Center
dcrawford@rainbowresource.com
Questions? Ask our Curriculum Consultants.
Email us at: consultants@rainbowresource.com
Janice Price
Donna Krahn
Deanne Crawford
Sara Carothers
Gina Burmeier
Ruth Tennis
www.rainbowresource.com • 888.841.3456
Counting to Calculus
Definitions:
• Algorithm: a set of steps used to solve mathematical computations.
• Common Core Standards: The Common Core State Standards define the rigorous skills
and knowledge in English Language Arts and Mathematics that need to be effectively
taught and learned for students to be ready to succeed academically in credit-bearing,
college-entry courses and workforce training programs. (www.corestandards.org)
• Constructivism: Educational theory and approach that emphasizes the ways that people
create meaning of the world through a series of individual constructs. In mathematics,
students construct their own understanding of mathematical concepts, so that the
primary role of teaching is not to lecture, explain, or otherwise attempt to ‘transfer’
mathematical knowledge, but to create situations for students that will foster their making
the necessary mental constructions.
“Knowledge is actively created or invented by the child, not passively received from the
environment. This idea can be illustrated by the Piagetian position that mathematical ideas
are made by children, not found like a pebble or accepted from others like a gift.”
— Constructivists Learning and Teaching, by Douglas Clements and Michael Battista
“The NCTM (National Council of Teachers of Mathematics) standards were a brew of
progressivism... and constructivism that adapted research from cognitive psychology to the
task of teaching and called it discovery learning. The standards were based on theories that
assumed children had an innate ability to understand math. The group’s math curricula were
thus structured to allow children to discover math concepts rather than to be given them,
through direct instruction.” — An A-MAZE-ing Approach to Math, by Barry Garelick
(www.educationnext.org/anamazeingapproachtomath/)
• Discovery Learning: a minimization of both teacher instruction and repetitive drills and
a disdain for standard procedures (algorithms) such as addition/subtraction or multiplication/division facts.
• Exercises: the teaching of mathematical skills by completing a large number of exercises
of a similar type.
• Mastery Learning: well-defined learning objectives organized into smaller, sequentially
organized units.
• Place value: is defined as the value of a digit as determined by its position in a number,
the name of the place or location of a digit in a number.
Continued…
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Counting to Calculus
• Reform (or Standards Based) Math: often called the “new, new” math based on constructivism (learning theory) and formalized by the National Council of Teachers of Mathematics (NCTM) which created the Principles and Standards for School Mathematics.
Published in 1989, these were an extensive set of mathematics standards for grades K-12,
which de-emphasized memorization of number facts, the learning of proofs, and algebraic
skills but encouraged the use of calculators and “discovery learning”. In 2000 and 2006, the
same NCTM released additional standards which many considered an admission that the
previous standards had mistakenly de-emphasized instruction of basic skills.
• Rote Learning: teaching of mathematical results, definitions, and concepts by repetition
and memorization. Typically used to teach multiplication tables. Sometimes referred to as
drill to instill or by the negative terms: Drill and Kill or Parrot Math.
“The NCTM view was that traditional teaching techniques , known as “drill and kill,” numbed
student minds, turned them off to math and taught them nothing.”
— Constructivists Learning and Teaching, by Douglas Clements and Michael Battista
“ ‘I have told you a million times!’ is a common expression. You ask your teenage son to clean
up his room. You ask your husband to take out the garbage. They forget, and you have to
repeat yourself…If a math book has to nag its students with fifty problems on every topic, it
means that the reader isn’t interested. It’s called ‘drill and kill’.”
— Dr. Stanley Schmidt (author of Life of Fred math curricula)
“Drill and Kill in its purest essence is a throwback to behaviorist theories of learning
psychology, from a time when meaning played a secondary role to form.”
— Michael Bush, Assoc. Professor of French and Instructional Psychology & Technology, BYU
• Scope and Sequence: a listing of the learning objectives and skills covered by a
curriculum product(s) by subject and grade level.
• Spiral Learning: a philosophy of math instruction where topics are covered several years
in a row, advancing slightly on each pass.
• Traditional Math: Method of instruction where the teacher presents a mathematical
concept, reviews the procedures required to find the solution, and then has students
practice these procedures with additional problems.
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Counting to Calculus
MATH BUILDING BLOCKS:
Basic math skills provide the floor of your math house, and the advanced math courses
(Algebra, Geometry, Calculus) provide the ceiling in your house. In between your floor joists and
the roof, lie five building blocks, which provide the cornerstones of your math house.
1. Numbers
2. Place Value System
3. Whole Number Operations
4. Fractions and Decimals
5. Problem Solving
Notes:
3
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Counting to Calculus
Activities you can do to prepare your child for Elementary math:
q Teach shapes/colors including larger than/smaller than; number of sides, distinctives.
q Teach how to recognize numbers and counting.
q Teach how to count forwards and backwards. Skip count.
q Count and Sort Activities with blocks and shapes.
q Cook Together.
q Telling Time.
q Calendar skills-day of week, number of days, months, weeks in months etc.
q Teach Place Value using M&Ms, Cuisenaire Rods/Unifix Rods.
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Math Programs— Grades K-8
GradeGR-LEVEL
level
Teacher
TEACHER
Teacher
TEACHER
Sequential
X
Minimal
Computer-based
K-12
Sequential
X
Interactive at
younger levels
Teacher edition included
in boxed sets
Lifepacs are a consumable
workbook format
3-12
Sequential
X
Minimal
All instruction is
computer-based
Computer-based; no workbooks
Horizons
K-8
Spiral
X
Interactive
Lesson plans, teacher
notes, and answer key
Tends to be faster paced and th
works ahead of grade level; 7 is
pre-algebra and 8th is algebra
Beast Academy
3-4
3-5
Conceptual
Topical
X
Minimal
Guide
Conventional
with
Bob Arithmetic
Jones
Spunky the Donkey
Conventional Arithmetic with
Study
Time
Spunky
theArithmetic
Donkey
1-12
1-2
Spiral
X
X
Teacher-centric
Interactive
1-2
3-8
Sequential
X
X
Interactive
Interactive
Lesson plans,
plans, teacher
teacher
Lesson
notes, and
and answer
answer key
key
notes,
Lesson plans, teacher
notes, and answer key
Study Time Arithmetic
Developmental Math
3-8
K-8
Sequential
X
Interactive
Minimal
Developmental
Kumon Math
K-8
1-6
Sequential
Sequential
X
Minimal
Minimal
LibertyKumon
Mathematics
1-6
K-2
Sequential
Sequential
X
X
Minimal
Minimal
Liberty Mathematics
Life of Fred
K-2
1-12
Sequential
Spiral
X
Minimal
Minimal
Lesson plans, teacher
None
notes, activities,
and
answer key
Lesson plans, teacher
notes,
activities,
No
teacher
guideand
for
answer key
elementary
level
·Cartoon style presentation
·Art of problem solving
A one-room schoolhouse
approach, so there is work to be
done independently
A one-room schoolhouse
Same
publisher
as Spunky
thebe
approach,
so there
is work to
done independently
Donkey
Samelevel
publisher
asaSpunky
Each
covers
specificthe
skill
Donkey
set;
placement is according to the
child’s ability
Each level covers a specific skill
Complete
curriculum=
all books
set; placement
is according
to the
at
gradeability
level
child’s
Complete curriculum= all books
Consumable
at grade levelworkbooks
Math Mammoth
(Light Blue
Life
of Fred
series)
1-12
1-7
Sequential
X
Minimal
Interactive
No teacher
for
Answer
keysguide
available
elementary level
Mathematical
Math
MammothReasoning
(Light Blue
series)
Making Math Meaningful
Mathematical Reasoning
PK-6
1-6
Spiral
Sequential
Virtual
X
X
Minimal
Interactive
K-6
PK-6
Spiral
Spiral
X
Virtual
X
X
Interactive
Minimal
MCP Math
Making Math Meaningful
K-6
K-6
Modified
sequential
Spiral
X
X
X
Interactive
Interactive
MCP Math
Miquon Math
K-6
1-3
Modified
sequential
Mastery
X
X
Interactive
Interactive
Mastering Mathematics
1-6
X
Practical
Arithmetics
Practical
Arithmetics
(Strayer-Upton)
(Strayer-Upton)
Sequential
Teaching suggestions
andkeys
answers
Answer
available
Lesson plans, teacher
Teaching
notes,
andsuggestions
answer key
and answers
Teacher notes & answer
Lesson plans,
key teacher
notes, and answer key
Annotations Book
(covers
6 books).
Teacherall
notes
& answer
Answers for
some of the
key
more “tricky” sheets;
Lesson
plans, teacher
most
worksheets
are
shown
answers.
notes,w/out
and answer
key
3-8
3-8
Spiral
Purposeful
Purposeful Design
Design
K-6
K-6
Mastery
Mastery
Sequential
Sequential
Ray’s Arithmetic
Ray’s Arithmetic
K-12
K-12
Sequential
Sequential
RightStart
K-4
RightStartMath
Right-Brained
K-4
2-7
Visual
Right-Brained
Rod & StaffMath
2-7
1-8
Visual
Mastery
Saxon K-3
1-3
Spiral
Saxon Math
Math Intermediate
Intermediate
Saxon
3-5
3-5
Spiral
Spiral
Saxon 5/4 through 8/7
4-8
Spiral
SINGAPORE
SAXON
SCHOOLAID
ALPHA OMEGA
Programs
5
Gr
Approach
PROGRAMS
GRADE
APPROACH
A+ Interactive Math
1-8
Alpha Omega
Lifepacs
Alpha Omega
Switched on Schoolhouse
Shiller Math
Math In Focus
Earlybird Math SE
Shiller Math
PK-7
K-8
PK-K
PK-7
Sequential
Sequential
Sequential
Sequential
Manipulatives
X
Used in early
grades
Interactive
Teacher notes and
answer key
Teacher notes and
answer
Nonekey
NOTES
Interactive self-paced;
multi-sensory
This
series offers
math within a
Consumable
workbooks
written context; for students who
like to read.
This series offers math within a
Consumable
workbooks
written context;
an optionorfor
pdf.files
children who like to read.
Hardcover books.
Consumable workbooks or
pdf.files
650 Lab Sheets in the six books
covering all mathematical topics.
Problem solving a focus, not just
Complete
one wayset
forincludes
studentscardstock
to reach
correct
solution.
manipulatives
and
consumable
workbooks
None
None
Themed based cross curriculum;
Themedemphasis
based cross
curriculum;
CCSS;
on mental
math
CCSS; emphasis
mental math
activities;
logical on
thinking
activities; logical thinking
X
X
Interactive
Requires
minimal
Requires
minimal prep
prep
from
Teacher
from Teacher
·Scope
and
sequence
·Scope by
andgrade
sequence
·Grade
·General sequences
information on
teaching
math
instructional
stages
·Planning Guide weekly
·Gradeplans
by grade
lesson
suggestions
teaching sequences
·Planning
Guide
weekly
Lesson plans
& ans.
key
lesson plans suggestions
X
X
Interactive
Lesson plans
None& ans. key
Reproducible
X
Interactive
None
Teacher
Guide
Reproducible
X
Scripted for
teacher
teacher
Lesson plans,
plans, teacher
teacher
Lesson
notes, and
and answer
answer key
key
notes,
X
X
Minimal
Minimal
Solutions Manual
Manual
Solutions
K-3
K-3
X
X
Interactive
Interactive
Interactive
Interactive
X
X
X
X
Classic Curriculum workbooks
are
written
to complement this
Classic
Curriculum
series
for
grades 1-4workbooks
are written to complement this
series for grades 1-4
·Hardcover
·Hardcover
·Manipulatives optional
optional
·Manipulatives
·Same methodology
methodology as
as Home
Home
·Same
School Edition
Edition
School
Strong support
support with:
with:
Strong
·DIVE &
& Saxon
Saxon Teacher
Teacher CDs
CDs
·DIVE
·Website
·Website
Minimal
Solution manual
manual
Solution
X
X
Interactive
Interactive
Interactive
Interactive
X
Interactive
Interactive
X
Interactive
Interactive
Parent Guide & Answer
Teacher Guides
guide or parent
guide offers lesson and
manipulative
Teacher
guidesuggestions
available,
butGuide
not required.
Parent
& Answer
Guides
Noneavailable,
Teacher guide
but not required.
Teacher guide or parent
guide which offers
lesson andNone
manipulative
suggestions
Teacher guide & Home
Instructor guides
available
Montessori
Employs Singapore methodology
Readers available but optional –
activity books are aligned to the
readers
Montessori
Same content as Earlybird but in
Readers
but optional –
b&w; useavailable
to supplement
activity
books
aligned
to the
Earlybird
or asare
a stand
alone.
readers
Same content as Earlybird but in
Employs
methodology
b&w;
useSingapore
to supplement
Earlybird or as a stand alone.
This series
is aligned to
California
Aligned
to California
State
Education
Standards;
has review
State Education
Standards;
has
review
afterchapter;
every chapter
after
every
pre CC
Essential Math
Earlybird Math SE
PK-K
PK-K
Sequential
Sequential
X
Math In Focus
Essential
Math
K-8
PK-K
Sequential
Sequential
X
X
Primary Math US
1-6
Sequential
X
Interactive
Primary Math SE
1-6
Sequential
X
Interactive
Teacher guide & Home
Instructor guides
available
Primary Mathematics
Common Core
1-5
Sequential
X
Interactive
Teacher Guide
Contact us: consultants@rainbowresource.com
Notes
Involvement
Edition
MANIPULATIVES
specific
SPECIFIC
INVOLVEMENT
EDITION
Placement tests available
CCSS
www.rainbowresource.com
Counting to Calculus
Resources for Math Games:
Auto Math
24 Games
Learning Wrap Ups
Snap It Up
Monkey Math
Equate
Muggins Math Games
S’Math Game
Monopoly/Jr. Monopoly
Life
Pay Day
Zingo! 1-2-3 Number Bingo Game
Math File Games (grade specific)
Math Dice (add/subtract, place value, etc.)
Math War (card games)
Number Please!
Games For Math (book by Peggy Kaye)
Right Start Math Games
Super Genius Math Games
Resources for Grade Level Standards:
World Book Typical Course of Study (Grades PK-12):
http://www.worldbook.com/free-educational-resources/typical-course-of-study
A-Beka Curriculum 2016 Scope and Sequence:
http://www.abeka.com/HomeSchool/ScopeAndSequence.aspx
Bob Jones Curriculum 2016 Scope and Sequence:
http://www.bjupress.com/product/502989
6
“On Core” Mathematics—Based on Common Core Standards
Common Core Standards: www.corestandards.org
Common Core Math (Grades K-12): http://www.corestandards.org/Math/
Grade Appropriate Test Prep Books: Spectrum, Scoring High, Higher Scores in Math
What Your _________ Grader Needs to Know—Books by E.D. Hirsch
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