2008 Texas 3rd Grade Math Textbook ranking
by Educational Research Analysts

Summary -- Empahsis on mastery of computational skills in 3rd Grade Math programs approved for 2008 local Texas adoption
by Educational Research Analysts

Scott Foresman Addison Wesley "enVisionMATH"
Ilionois Loop

Review of how enVisionMath presents fractions.

Characteristics of the enVisionMath program

  • · Tries to reconcile reform and non-reform approaches
  • · Conceptually oriented
  • · Lacks depth in multi-digit add and subt
  • · Practice inadequate for procedural fluency
  • · Skill mastery not achieved
  • · Understanding by Design
  • · Problem based learning
  • · Spiral review

The Case for Math In Focus: The Singapore Approach
This document makes a strong case for the adoption of Math in Focus in a district that considered Math in Focus, enVisionMath, and Math Expressions. Any district considering adopting any of these three programs is well advised to read this document. You can download the document by clicking here.

From this document:

3. Two districts who adopted EnVisionMATH in 2009 (Richland and Snoqualmie Valley) averaged a 4.9% drop in MSP pass rates.

3. Performance Results from 2 Districts Using EnVision
EnVisionMATH is a relatively new program, so MSP results for 2010 adopters such as Shoreline and Lake Washington are not available. The only data from Washington state comes from the Snoqualmie Valley (4th-5th Grades) and Richland districts who adopted EnVisions in 2009.
MSP/WASL Pass Rates:
School: Snoq Vl Richland
Curriculum: Growing EnVsn Invstgns EnVsn
School Year: '08-09 09-10 Diff '08-09 09-10 Diff
3rd Grade: N/A N/A N/A 71.6% 69.4% -2.2%
4th Grade: 70.0% 68.1% -1.9% 53.8% 56.6% 2.8%
5th Grade: 78.1% 68.3% -9.8% 68.2% 55.9% -12.3%
Average: 74.1% 68.2% -5.8% 64.5% 60.6% -3.9%

Note that both districts struggled with the first year of EnVisions, and showed an average 4.9% drop in MSP scores.
For the record, the demographic data below shows that neither Richland nor Snoqualmie Valley are significantly disadvantaged by socio-economic factors.
Demographic Data: Snoq Vly Richland
Race/Ethnicity (October 2009)
American Indian/Alaskan Native 1.00% 1.20%
Asian 4.10% 4.60%
Pacific Islander 0.20% 0.20%
Asian/Pacific Islander 4.30% 4.80%
Black 0.90% 2.60%
Hispanic 3.90% 8.80%
White 86.60% 80.70%
Special Programs
Free or Reduced-Price Meals (May 2010) 13.10% 30.00%
Special Education (May 2010) 10.20% 10.80%
Transitional Bilingual (May 2010) 1.70% 2.30%

6. A Parent’s Firsthand Experience with EnVisions
Below are the relevant portions of an email from a parent of a 5th grader in Richland who has had direct experience with the recent adoption of EnVisions.
“Hi . . . ,
“ . . . My son was in the 4th grade when we started using Envision. At home, we were struck with the poor quality of the homework problems. It's as if a completely different staff wrote the homework. This group of homework authors sometimes wrote unsolvable problems, made errors, were generally careless and not mathematical in their thought. We often sent our son's homework back to school with a sticky note to the teacher, saying things like "this problem involves a negative number, which 4th graders can't handle". The extension homework problems were often totally unrelated to the lesson, and not at all useful in building a mathematical foundation. They were often brain teasers, which I found very irritating. I know that many if not most of the kids didn't know their math facts and couldn't do basic computations fluently and accurately, so there was no time for time-eating, sometimes unsolvable and usually frustrating brain teasers. When our adoption committee reviewed Envision, we did not see the homework materials, so this issue was a surprise to me.
“About halfway into the year (or maybe it was around March), parents of the second graders started coming to me complaining about the way EnVision teaches subtraction. Kids and parents alike were struggling with it. They use a strange system of a visual tool they created (gotta come up with something original, after all) that I think was called "10 cards" or "10 spot cards" or something of the sort. It's positively awful. The parents were clueless. I struggled for quite some time to figure out what they were doing in the illustrations. I then compared it side-by-side with Singapore and the flaws in the Envision method were numerous and obvious.
“ Third grade teachers complained about the need for rampant photocopying (and we all know how budget cuts have affected copying!) because there are no consumables for 3rd grade. 3rd graders are still slow writers, so recopying is arduous and slows the math learning.
“The DVD materials got rave reviews from the teachers. They liked how it was organized and friendly to them. I know the kids loved the Smartboard lessons. There is an online component which our son's teacher started to use but he later fizzled out on it. Not sure why.
“ . . . That's my personal experience with Envision. Hope this helps.”

The letter above explains clearly why EnVisions would be a poor choice for Highline. As a footnote, this parent has now removed her son from public school and is homeschooling with Singapore Math.

Parent letter to Principal about the enVision Math curriculum
Wed, January 20, 2010

One parent's experience with enVisionMath...

I’ve experienced enVision for 3rd grade and 4th grade with my son. I’m not a fan. It’s better than Investigations but needs a lot of supplementing, especially in calculations. I have found it to go into more depth in some areas, exceeding standards in some cases but since there is not enough background to form a decent foundation, parents end up doing the homework. The workbook does not give examples and no support notes or text comes home - so if your kids needs help with prime and composite numbers and you don’t remember what that is, you will have to reference something else – maybe the online text (if you remember the logon and password) to figure it out and explain it (my friends just call me).

Even knowing the math and having a kid who is a year ahead in calculations (Kumon) it’s a frustrating curriculum. Here’s my favorite homework question this week: WRITE TO EXPLAIN. If a fraction has a prime number in the numerator, can it be reduced? Just what every 4th grader has the vocabulary and thought process to explain.

In the past 2 weeks, they have thrown the following math at my son - prime and composite numbers, factors, reducing fractions, converting fractions to equivalent fractions, comparing fractions with like and unlike denominators, adding fractions with like denominators, area and perimeter, as well as geometry concepts such as point, line, plane, parallel lines, intersecting lines, perpendicular lines and identifying various geometric figures. There is only one page of limited practice per area and my son only retains anything because I have pre-taught it to him.

Some areas on the NYS assessment regarding fractions –comparing UNIT fractions, decimal equivalents of a few fractions – have not been part of the materials. Again – I do it myself at home – only because I know about it.

I give enVision a thumbs down as a stand-alone math curriculum. I find the workbook homework to be an irritation and in our home we put the more logical Kumon math work and my own supplementing as the priority.

by Stefanie N.

A Comparison of Math Connects, Math Expressions, and enVisionMath


I set out on this effort to compare what I could find in the online sample materials available that develop the skills required to divide fractions, and compare these findings between the three curricula. The main obstacle I encountered is the fact that the three publishers don’t make the same material available. The manner in which the materials available differs substantially as well, further confounding direct comparison. Given the differences, it was not practical to view the three at once, as I might have done if I had three actual textbooks. So I reviewed each text on its own first, created the three documents that present my findings in each text series, and in this document will present what I can as a comparison.

Review of how Math Connects presents fractions.

Review of how Math Expressions presents fractions.

Review of how enVisionMath presents fractions.


Math Expressions is the weakest of the three curricula here. It discounts fundamental principles to teachers as being “complicated and error prone” and relies instead on semantic arguments to convince students that certain procedures are valid. The concept of the “reciprocal”, essential to fraction division, is absent, and a contrived and confusing argument takes its place. Differences between the format and availability of online material for the other two texts make it difficult to find stand-out distinctions between the other two. Both appear to handle basic principles behind all four fraction operations with comparable clarity and completeness, with each of the two having highs and lows that leave them pretty much even. The grade six Math Connects text, where multiplicaiton and division of fractions was not available for me to review.

Online Materials

Math Expressions made the teacher’s manual and student “Activity Books” available for viewing online, but not the student “hardbound” book. Apparently “Activity Books” and “Homework and Remembering” books are available as softbound books to students, and the teacher’s manuals make reference to these. It isn’t clear if the “hardbound” version is just a combined and bound version of the other two, or if it contains more material. If the former is the case then the students don’t get an adequate reference of definitions and examples to take home. The teacher’s manual appears to direct classroom activities, and from what I could see was the sole source of reference material, as it is structured in large part as a script for teachers to follow.

EnVision Math Online materials were easy to use and contained both teacher and student texts. The teacher’s text is essentially an expanded and annotated version of the student text, so it is easy to see and follow what the student has in front of them and what the teacher has in the way of hints and emphasis. The student book is complete in that it contains the definitions, examples, problems, a glossary, index, etc.

Math Connects Online materials were comprised of the student book only, so I wasn’t able to see anything that the teacher had to back it up. That said, the student books appear to be a complete and conventional text with reference material, examples, etc.,


The three texts cover the four operations either in fifth grade or straddled over fifth and sixth. All three address addition and subtraction of fractions in grade 5. Math Expressions covers multiplication and division in grade 5 as well, where Math Connects appears to hold both until grade 6. I didn’t have the G6 MC material available for this review. Math Envisions covers addition, subtraction, and multiplication in Grade 5, leaving division for Grade 6.

Fraction division is based on an understanding of what fractions are, and how operations work on them. So I couldn’t start with any of these books at the point where division occurs. I had to go back to where fractions were introduced and developed. What are they? What does the numerator represent? The denominator? All three of these texts address these basic questions in essentially the same manner. Pictures of wholes are presented, divided up into equal parts, etc. All four operations on simple fractions can be represented pictorially with pictures, and all three texts do this with comparable results. Where the three differ is in how long is spent with pictures and when more abstract yet efficient methods are justified and employed. Math Expressions seems to have students use pictures the longest, where EnVision Math weans students away sooner. Math Connects lands somewhere in the middle. Although coverage of multiplication and division is held off until sixth grade, somewhat more emphasis is placed on laying a foundation for it in fifth.

Facility with factors is fundamental to skill with fractions. Math Expressions’ standout weakness, compared to the other two, is its lackluster treatment of factors. Although all necessary content is present in the teacher’s manual, it is presented in an “oh, by the way” sort of fashion, as if a teacher should use their own judgment on whether or not they bother to present the material. The greater emphasis is on tying the meaning of verbal phrases that imply multiplication or division to operations that can be proven to work, rather than teaching the foundational mathematical principles that guarantee that they will. As a result, operations are taught as “Do this. See? It gives you the answer you’d expect, so you can believe it” as opposed to “Here are some named properties, and examples of why they are always true with the integers we’re familiar with. Now, let’s apply them to fractions and see what we get.”

The concepts of “Common Denominator” and “Least Common Denominator” are not developed with any coherence in the student material. They appear in the teacher’s manual, but transmission to the students is apparently left to happen in during the scripted classroom discussion. From page 504 of the teacher's book:

Teaching Note

Math Background The GCF of unlike denominators can be used as a greatest common divisor (GCD) to simplify fractions, and the LCM of unlike denominators can be used as a least common denominator (LCD) to add or subtract the fractions. However, it may be easier for students to simplify fractions and find common denominators using other methods.

Also, the teacher’s manual discourages systematic prime factorization as being too “complicated and error prone”. This discounts not only the value of the exercise but the intelligence of the students.

Equally damning is the omission of any coverage of the concepts of multiplicative inverse or identity; missing the fork in the road that shows how since division is the inverse of multiplication, division by a fraction is equivalent to multiplication by the reciprocal of that fraction. The text uses an odd and confusing (to me, at least) method in place of this, which will not serve a student well when they get to algebra. The “parent’s letter” presents a summary informing them that their children will learn to “invert and multiply” yet does not go into detail as to the odd manner in which this happens. The word “reciprocal” appears in the teacher’s manual, but not in the student book’s glossary.

EnVision Math develops the number properties behind fraction operations reasonably well. Since the teacher’s manual follows the student book directly, it is clearer to see how this is likely to happen in a typical classroom. Factor-based reasoning behind simplifying fractions (such as finding the GCF, why “canceling works” etc.) are all developed. Grade 6, section 5.1 has an excellent run-down on factoring and divisibility. Prime factorization is covered in 5.2. The idea behind the Greatest Common Factor is presented in 5.3. Sections 5.2 and 5.3, however, are under an “Enrichment” heading. Finally, however, students are reminded that multiplication and division are inverse operations, and that division is the same as multiplication by its reciprocal. This is the key concept behind dividing fractions that will prepare students for similar operations in algebra.

Math Connects also seems to do a decent job with the presentation of factors. The material is presented in dribs and drabs, though, which may be a good thing, or bad. The pace, as it appears in grade five, may explain why both multiplication and division of fractions are pushed out to grade six. At any rate, prime factorization and full development of the concepts of LCM and GCF are present in the student’s book.

As is difficult to avoid, multiplications of fractions appears in the development of how to simplify fractions, without introducing it as such. In my experience teaching remedial algebra in a community college, it is best to present multiplication of fractions before addition, and this is how it is done in many texts. But that’s neither here nor there.

I can only imagine how Math Connects presents multiplication and division, since I don't have the sixth grade text to look at, but the groundwork is well established in fifth grade.

To share relevant information or if you have a question, you may send an email to MSFSoundMath at gmail dot com. If you are looking for information or resources we can sometimes point you in the right direction. There is no guarantee that your email will receive a response, but you never know.

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