Educating All Parents To Ensure The Future Of Our Republic

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 )

Saxon Math (from site)

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.

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)
  • 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)
  • 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)
  • 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)
  • 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

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)
  • 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

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)
  • 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

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

Research and Information Press Coverage

THE PETITION TO REMOVE INVESTIGATIONS MATH** (OVER 5% of ASD represented--still ignored by ASD)

MASTER SUMMARY AND INTRODUCTION**

Math With Madeline Video

All Weekly Email Updates **

Edspresso Article on WMD Comics

Weapons of Math Destruction Comics**

What Can You Do About Fuzzy Math in Your Area - 13 Ideas**

Brain Programming

ASD's Saxon Math Deception
Part 2 of the Deception

4/21/07 ASD Superintendent Calls Parents Extremists (for wanting the times tables in schools)

Alpine School District Residents Should Choose Saxon Math

9/13/06 Dual Enrollment Guidelines - Opting Out of Math or Other Classes

9/2/06 Jaime Escalante and NCTM Standards**

9/2/06 Amber Lee's Independent Research

The Math Story (ie. How I Got Started)

7/31/06 Educators Ignore Project Follow-Through**

7/26/06 Comparison of Alpine to Nebo and Provo Districts and comments on Orem City Breaking Off **

3/30/06 Utah Public Radio Broadcast with David Wright and Damon Bahr* (Right-Click and use Save As to download)

Insane Supplementary Materials Compound Investigations Math Nightmare**

Map of ASD Precincts and Election information- You must register to run by 3/17

3/2/06 David Wright's Mathematician Petition to the State of Utah*

2/14/06 Why are Charter School Scores Better than Alpine School District's?*

2/14/06 Alpine School District IOWA Test Math Scores

10 Myths About Math Education and Why You Shouldn't Believe Them

2/1/06 The Case for Utah adopting California's Math Standards-Testimony to Utah Congress**

1/10/06 School Board Meeting challenge to find just one valid study by 1/31/06 ** (I'm still waiting)

Math Tutors in Utah (find one/list one)

11/9/05 Update - How ASD is failing more children each year**

ASD's statement to teachers authorizing them to teach traditional math without fear of repercussion

California Study showing tripling of scores for schools that left constructivist math and implemented Saxon Math**

10/31/05 Petition Maps (see where people are signing the petition-blue dots are schools, red are petitions)

How About Grades 6-12 Connected and Interactive Math?**

Raising Critical Thinking Skills*

Pro-Investigations websites (for anyone interested)

8/15/05 Update (compares Alpine to other districts and charter schools) *

7/29/05 Update (resources given to ASD, sample problems, ASD vs. Nebo School District) *

Investigations Math Origins and Articles*

Math Programs Compared ("Traditional", Investigations, Saxon)

Supplementing your Public School Student's Education**

The California Investigations Math Failure**

Community comments - both Pro/Anti Investigations **

Investigations Math Poll Introduction and Question Summary*

 

Additional articles are covered in weekly updates since April 2007

Victory in Utah - State to Revamp Standards (11/16/06)

Major Breaking News...NCTM does a 180 after 17 years of destroying math in America

It must really irritate the folks at Alpine School District (ASD) who have taken to calling all my work "biased and flawed" to have such no-name disreputable organizations pandering to my lies. The legacy of ASD will be the disenfranchisement of tens of thousands of students unable to obtain a technical higher education degree.

4/25/07 Provo Daily Herald - Math petitioners called 'extremists' in Alpine District

4/24/07 Deseret News Article - So how many different programs are appropriate to use at one time Mr. Henshaw?

3/1/07 - Deseret News - Schools' grades mixed - Utah system rated by U.S. Chamber in a new report

2/14/07 Provo Daily Herald - Committee makes math program suggestions for Alpine: Many in district pine for 'Investigations'

2/14/07 Deseret News - Alpine seeking balance in math

2/12/07 Deseret News - Math Program Deleted - Alpine District dumps controversial approach

11/16/06 Deseret News - State leaders support math overhaul for schools

11/16/06 Salt Lake Tribune - Utah's 'fuzzy math' curriculum scrapped; legislators endorse plan to revamp state standards

11/15/06 New York Times - As Math Scores Lag, a New Push for the Basics

10/29/06 Provo Daily Herald - Survey: Math Program Doesn't Add Up

10/25/06 Deseret News - Students decline at 5 Utah colleges

10/19/06 Deseret News - Math learning is shallow in U.S., professor says

10/19/06 Deseret News - Math in Utah — 'fuzzy' or A-OK?

10/06 Salt Lake Tribune - Bad marks for Utah's schools

10/9/06 BYU NewsNet - Alpine School District Under Attack

9/30/06 Provo Daily Herald - Districts evaluate 'failures' in testing

9/29/06 Provo Daily Herald - Utah schools receive progress rankings

9/26/06 Townhall.com - Parents Know the Right Equation for Teaching Math - by Phyllis Schafly

9/12/06 Wall Street Journal - New Report Urges Return to Basics In Teaching Math

9/6/06 Provo Daily Herald - Parent suggests Alpine district be responsive

8/28/06 Provo Daily Herald - Alpine readies to let schools choose curriculum for math (be sure to check out the comments section)

8/26/06 Provo Daily Herald - Charter schools attract parents concerned about public education

7/29/06 Deseret News - Burned-out teachers problematic

7/26/06 Deseret News - Most favor creation of small school districts

5/28/06 Salt Lake Tribune - Alpine School District relents and will change its math offerings***

5/26/06 Deseret News - Alpine opts for choice in its math programs***

5/25/06 Provo Daily Herald - District Reviews Math Options***

5/23/06 - Provo Daily Herald -Orem OKs feasibility study of splitting from Alpine district

5/23/06-Deseret News - Orem not hastening into a schools split

5/23/06-Salt Lake Tribune Article-Orem to study Alpine District split

5/12/06 Provo Daily Herald - Math decision delayed

5/10/06 Provo Daily Herald - Petition Requests District Division

5/6/06 Deseret News - Utah to study states' math programs

4/16/06 Provo Daily Herald- Alpine District continues to lose students to charters

4/6/06 Provo Daily Herald- Charter school debate heats up in Alpine school district

3/20/06 Salt Lake Tribune - Alpine in grip of 'Math Wars'

3/3/06 Provo Daily Herald-Professor: Clearer math standards needed

3/2/06 Deseret News- Math Petition Circulating

2/19/06 San Jose Mercury News - Math back in forefront, but debate lingers on how to teach it.

2/18/06 Salt Lake Tribune-Battle over math teaching spreads

2/15/06 Salt Lake Tribune-Indifference to math skills part of the problem

2/15/06 Deseret News-Parents voice their views on Alpine math

2/15/06 Provo Daily Herald-Provo district seeks math balance

2/9/06 Deseret News - Alpine trio defend approach to math
Rebuttal Letter to Editor: Math approach is harmful

2/7/06 Deseret News - Alpine defends math classes

2/2/06 Deseret News - Lawmaker Gives Alpine Math an F

1/29/06 Salt Lake Tribune - Charter School Funding Tight

1/20/06 Deseret News Letter to Editor: Rote exercises pay vital role in mathematical education

1/7/06 Provo Daily Herald - Investigations: Not your parent's math

12/18/05 Provo Daily Herald -Math doesn't add up for all

12/13/05  15 Charter Schools Scheduled to Open Next Year

11/24/05 Provo Daily Herald - Parents mad over new math curriculum (be sure to read the comments)

 

 

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