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Investigations Math Poll Results - Math Program Comparison
Below you will find a side-by-side comparison of Investigations Math and Saxon
Math's philosophy and curriculum. I am thoroughly satisfied that Investigations
Math is an inferior product when compared to other programs. The
school district touts studies used to show how great this program is, but
if you examine
the articles on the prior page you'll find those studies torn apart as works
of people that didn't follow the scientific method in their research. Read
what the Harvard professor had to say about the program and you'll wonder what
kind of research our school board did or if the allegation of kickbacks (Q10
page) might be true.
Traditional math is the type
of math
most of
us
grew up with and it's been sufficient in the past to produce good math students.
Traditional math focuses on a topic
or chapter
of
study,
has the students learn and practice it, then moves on. It is sometimes
up to the individual
to gleen what relationships that unit of study has with other units of study,
unless they have a good teacher that guides them in their comprehension of
such things. There is nothing wrong with the traditional method, but newer
methods have been developed to see if there is a better way to teach.
Saxon math operates more along
the lines of traditional math by focusing on math facts and "how to" do
it, rather than an exploration at early ages in understanding numbers. The
difference between Saxon and "traditional" is that Saxon takes
a study topic and never leaves it alone. In other words, when you move on
to
a new
topic,
the old topics are incorporated directly into the new topic so retention
is greatly improved and math facts are taken in incremental chunks. Please
read the brief
overview below for additional information on this.
The information I have put below comes from websites and information provided
to me by the head of the school district's Investigations Math program.
One topic in particular settled the whole debate for
me: Saxon math's 2nd grade curriculum says students will master multiplication
facts to 5 and the
3rd
grade curriculum says, "master all basic addition, subtraction,
multiplication, and division facts." Investigations NEVER has students
master these facts. In addition to this side by side comparison, check out
Singapore
Math's curriculum which has students starting the basics of multiplication
in 1st grade!
Investigations Math (from
site ) |
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Brief Overview |
| The Investigations curriculum embodies a different approach from the traditional
textbook-based curriculum. It is designed to invite all students into mathematics--girls
and boys, diverse cultural, ethnic, and language groups, and students with
different strengths and interests. Problem contexts often call on students
to share experiences from their families, culture, or community. The following
aspects of the curriculum ensure that all students are included in significant
mathematical learning.
Students:
- spend more time exploring problems in depth
- find more than one solution
to many problems they work on
- invent
their own strategies and approaches, rather than relying
on memorized procedures
- choose from a variety of concrete materials
and appropriate technology, including calculators as a natural
part of their
everyday mathematical
work
- express their mathematical thinking through drawing, writing,
and talking
- work in a variety of groupings such as a whole
class, individually, in pairs, and in small groups
- move around
in the classroom as they explore the mathematics in their environment
and talk with their peers
Investigations in Number, Data and Space looks and feels quite different
from a traditional mathematics program. The curriculum at each grade level
is organized into units. Each unit offers two to eight weeks of mathematics
work on topics in number, data analysis, and geometry and consists of a
series of investigations that involve students in the exploration of major
mathematical ideas. Because of the many interconnections among mathematical
ideas, units may revolve around two or three related areas—for example,
addition and subtraction or geometry and fractions.
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The Saxon Difference: Our Approach to Math Instruction
Saxon Math is the only major math program on the market today that systematically
distributes instruction and practice and assessment throughout the academic
year as opposed to concentrating, or massing, the instruction, practice
and assessment of related concepts into a short period of time -- usually
within a unit or chapter. Saxon Math 's unique approach to math instruction
ensures that students not only gain but also retain essential math skills.
The pedagogy used in Saxon Math is unique, effective and research-based.
The authors of Saxon Math began developing the series by first breaking
complex concepts into related increments, recognizing that smaller pieces
of information are easier to teach and easier to learn. Then they systematically
distributed the instruction, practice and assessment of those increments
across a grade level. Well-established research has shown that this spaced
(distributed) approach has produced significantly higher levels of student
learning than massed presentations such as those found in programs with
a chapter-based approach (Dempster & Farris, 1990).
Incremental Instruction Distributed Across the Level
In Saxon Math , each increment builds on the foundation of earlier increments,
leading students to a deeper understanding of mathematical concepts. The
instruction of related increments is carefully distributed throughout the
grade level, ensuring that students have the opportunity to master each
increment before being introduced to the next related one. Foundational
research has shown that instruction that presents material to be learned
over several intervals (distributed instruction) results in greater student
achievement than instruction that is not distributed (English, Wellburn & Killian,
1934). Further studies have confirmed that distributed instruction is more
effective in a variety of subjects including mathematics (Dempster, 1988;
Hintzman, 1974; Reynolds & Glasser, 1964).
Continual Practice Distributed Across the Level
Practice of an increment is distributed continually across each grade
level. Continual, distributed practice ensures that concepts are committed
to students' long-term memory and that students achieve automaticity of
basic math skills. Several research studies show that students who are
taught with a mathematics curriculum that uses continual practice and review
show greater skill acquisition and math achievement (Good & Grouws,
1979; MacDonald, 1984; Hardesty, 1986; Mayfield & Chase, 2002; Usnick,
1991; Ornstein, 1990). Additional studies have concluded that spaced (distributed)
practice results in higher performance than massed practice (Dhaliwal,
1987; Proctor, 1980).
Cumulative Assessment Distributed Across the Level
The frequent, cumulative assessments in Saxon Math assess both the acquisition
and maintenance of concepts. Assessments are built into each fifth lesson
to help teachers frequently gauge students' progress. And, since each of
the assessments is cumulative, teachers can also monitor students' retention
of skills. The Saxon Math assessment strategies are based on foundational
research showing that effective assessment is frequent and cumulative rather
than infrequent or related only to content covered since the last test
(Dempster, 1991). |
Kindergarten |
- Mathematical thinking
- Collecting, counting, measuring
- How many in all?
- Pattern Trains and hopscotch paths (exploring patterns)
- Building Blocks-exploring geometry
- Counting Ourselves and others (exploring data)
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- count forward and backward orally and on a
- number line
- count with one-to-one correspondence
- count by 1's, 2's, 5's and 10's
- compare and order numbers and objects
- identify, match, and divide sets
- identify ordinal position to fifth
- act out and draw pictures for addition
and
- subtraction stories
- identify a missing number in a sentence and a
- missing
shape in a matrix
- know a symbol can stand for a missing number
- in a sentence
- identify and count pennies, nickels, and dimes
- identify quarters and one-dollar
bills
- write money amounts using cent symbol (¢)
- select coins for given
amount
- write numerals to 30
- identify one half and one fourth
- identify right and left and use other
positional
- words and phrases
- identify, sort, and compare geometric
shapes
- and solids
- identify line of symmetry
and create symmetrical
- designs
- sort and identify sorting
rule
- identify and
extend patterns and geometric
- designs
- graph real objects
and pictures
- determine
questions
for a survey
- tell and
show
time to the hour
- use a calendar
and
identify its parts
- identify
which
of
two
events takes
more
or
less
- time
- compare,
order, and
measure using standard
- and nonstandard
units
- describe
likelihood
of an
event
|
1st Grade |
- Mathematical thinking (introduction of routines and comparing and combining)
- Building number sense (understanding numbers and number relationships)
- Number games and story problems (addition and subtraction)
- Building number sense (exploring patterns in numbers)
- Bigger, taller, heavier, smaller (measuring)
- Quilt Squares and block towns (2-D and 3-D geometry)
- Survey questions and secret rules (collecting and sorting data)
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- skip count by 1's, 2's, 5's, and 10's
- compare and order numbers
- identify place value to 100
- identify ordinal position to tenth
- identify a sorting rule
- identify and extend patterns
- solve routine and nonroutine problems
- master all basic addition facts
and most of the basic subtraction facts
- add and subtract two-digit numbers without regrouping
- use comparison symbols
- picture and name fractions
- identify a fractional part of a set
- measure using inches, feet, and centimeters
- compare volume, mass, and
area
- tell time to the half hour
- order events by time
- count pennies, nickels, dimes, and quarters
- identify and draw polygons
- identify geometric solids
- tally
- identify events as certain, likely, or impossible
- create, read, and write
observations from real graphs, pictographs, and bar graphs
|
2nd Grade |
- Mathematical thinking (introduction of routines with counting and categorizing)
- Coins, coupons, and combinations (addition combinations)
- Putting together and taking apart (addition and subtraction)
- Shapes, halves, and symmetry (geometry and fractions)
- Timelines and rhythm patterns (representing time and patterns in rhythms)
- How long? How far? (measuring)
- Survey questions and secret rules (collecting and sorting data)
- Does it walk, crawl, or swim (sorting, classifying data)
- How many pockets? How many teeth? (collecting and representing data)
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- skip count by 1's, 2's, 3's, 4's, 5's, 10's, 25's, and 100's
- compare and
order numbers
- identify ordinal position to tenth
- identify sorting and patterning rules
- solve routine and nonroutine problems
- master all basic addition and subtraction
facts
- identify commutative and associative properties of addition
- identify place
value in a three-digit number
- master multiplication facts to 5
- add and subtract two-digit numbers
- picture and name fractions
- measure to the nearest half inch, centimeter,
and foot
- compare volume
- compare and measure mass
- measure perimeter and area
- tell time to five-minute intervals
- count pennies, nickels, dimes, and
quarters
- show change from $1.00
- multiply by 0
- identify geometric solids
- identify lines of symmetry
- identify angles
- tally
- create, read, and write observations from real graphs, pictographs,
bar graphs, Venn
diagrams, and line graphs
|
3rd Grade |
- Mathematical Thinking (introduction of routines and materials)
- Landmarks in the hundreds (practice with base ten system to 100)
- Combining and comparing (addition and subtraction)
- Things that come in groups (multiplication and division)
- Fair Shares (exploring fractions)
- Up and down the number line (positive and negative changes on the number
line)
- Paces to feet (measuring)
- Flips, turns, and area (2-D geometry)
- Turtle paths (2-D geometry)
- Exploring solids and boxes (3-D geometry)
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- skip count by whole numbers
- compare and order numbers
- identify place value
- identify ordinal position to twentieth
- identify and complete patterns
- solve routine and nonroutine problems
- master all basic addition, subtraction,
multiplication, and division facts
- add/subtract multidigit numbers
- multiply a multidigit number by a single-digit
number
- divide by single-digit divisors
- add positive and negative numbers
- picture, name, and order fractions
- add and subtract fractions with common
denominators
- measure to the nearest quarter inch, millimeter, foot,
and yard
- identify the volume of standard
containers
- compare and measure mass
- measure perimeter and area
- tell time to the minute
- determine elapsed time
- count money
- make change for a dollar
- identify angles
- identify lines of symmetry
- identify function rules
- graph ordered pairs on a coordinate graph
tally
- write addition, subtraction, multiplication, and division
fact families
- write story problems for addition/subtraction
number sentences
- create, read, and write observations
from real graphs, pictographs, bar graphs, Venn diagrams,
and line graphs
|
4th Grade |
- Mathematical thinking (introduction to routines with thinking, reasoning,
and communication)
- Landmarks in the thousands (practice with number system to 1000)
- Money, miles, and large numbers (addition and subtraction)
- Arrays and shares (multiplication and division)
- Packages and groups (multiplication and division)
- Different shapes and equal pieces (fractions and measurement)
- 3 out of 4 like spaghetti (fractions and data)
- Changes and over time (exploring and representing changes)
- Sunken ships and grid patterns (coordinate grids and ordered pairs)
- Sunken ships and grid patterns (2-D geometry)
- Different shapes and equal pieces (geometry and fractions)
- Seeing solids and silhouettes
- The shape of the data (statistics)
|
- read, write, compare, and order large numbers
- write numbers in expanded
form and identify place value
- identify prime and composite numbers
- identify perfect squares and cubes,
square roots, and cube roots
- approximate square roots
- identify the approximate value of pi
- represent numbers using Roman numerals
- identify a function rule
- simplify expressions containing exponents
- label number lines using fractions,
decimals, and positive and negative numbers
- master basic addition,
subtraction, and division facts
- add, subtract, and multiply using
mental computation
- add, subtract, and multiply multidigit numbers
using algorithms
- divide a multidigit number
by a single-digit number
- represent division remainders as fractions
- represent mixed numbers as
improper
- fractions and improper fractions as mixed numbers
- add and subtract decimals
- write fractions as percents and percents
as fractions
- name and draw polygons
and geometric solids
- identify and draw parallel and
perpendicular lines
- draw lines
of symmetry and reflections
- identify congruent and similar polygons
- draw circles using a compass
- measure and draw angles using a protractor
- identify and draw right, acute,
and obtuse triangles
- measure to the nearest millimeter or sixteenth
of an inch
- estimate and measure distance using feet, yards, and
meters
- use a scale on a map
- estimate and compare the mass of objects
- find the volume of a rectangular
prism
- estimate and measure perimeter, circumference, and area
- read a thermometer
- use a perpetual calendar
- tell time to the second
- find elapsed time
- locate information on a table or chart
- create and read bar graphs, pictographs,
and line graphs
- create and read a Venn diagram
- conduct a survey and represent the results
- find the mean
- identify the probability of an event
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5th Grade |
- Mathematical thinking (introduction to routines and extending understanding
of base-ten number system)
- Building on numbers you know (addition, subtraction, multiplication and
division as well as estimation)
- Name that portion (fractions, percents and decimals)
- Patterns of change (exploring and working with tables/graph for changes
over time)
- Measurement benchmarks (estimating and measuring)
- Picturing polygons (2-D geometry)
- Containers and cubes (3-D geometry/volume)
- Data, cats, kids, and ads (statistics)
- Between never and always (probability)
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- whole-number concepts and computation
- estimation
- patterns and sequences
- fractions, decimals, and mixed numbers
- percent
- word-problems
- properties of operations
- integers
- divisibility concepts
- prime and composite numbers
- ratios
- square roots
- scale drawings
- measurement and unit conversion
- statistics
- probability
- data display and analysis
- perimeter and area
- volume
- symmetry
- tessellations
- transformations
- real-world connections
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6th Grade |
- Prime time (factors and multiples)
- Bits and pieces I, II, III (understanding and using rational numbers)
- Formalizing patterns into equations and rules (solving simple equations)
- Shapes and designs (2-D geometry)
- Covering and surrounding (2-D measurement)
- How likely is it? (probability)
- Data about us (statistics)
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- simplifying expressions containing
- parentheses
- operations with signed numbers
- graphing functions
- word-problems
- powers and roots
- ratios and proportions
- percents
- fractions, decimals, and mixed numbers
- divisibility concepts
- prime factorization
- estimation
- real-world connections
- integers
- functions
- unit multipliers
- statistics and probability
- frequency tables
- data collection, display, and analysis
- formulas
- geometric constructions
- scale factor
- capacity and volume
- complementary and supplementary angles
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Investigations Math Menu
** Most important pages to read (all have value but if you will only read
a few pages make it these)
* Very important
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