Some parents have e-mailed to ask why Singapore Math is not among the four programs to survive the initial math program review in SCASD.  Singapore received some very high ratings but also some very low ratings, and in the end its totals were not enough for it to rank among the top four.  To answer the question of why this program, used by many parents in SCASD for home supplementation, did not receive a more favorable reception from the committee as a whole it is important to first clarify that there are really two Singapore programs:

Currently, there are two comprehensive Singapore Math series, enhanced for the United States, that are available through US-based companies. Primary Mathematics by SingaporeMath.com and Math in Focus: The Singapore Approach published by Great Source, an imprint of Boston-based Houghton Mifflin Harcourt. The former has been used in the United States since 2003, while the latter – the American edition of Singapore-based publisher Marshall Cavendish’s My Pals Are Here! Maths, a textbook series that is currently used by over 80% of schools in Singapore  – is a relatively new entry, only available since 2009.

The SCASD math curriculum staff chose to provide Primary Mathematics for the Committee to review instead of the more accessible Math in Focus.  It is difficult to say whether Math in Focus would have been received more warmly by the Committee or whether either Singapore program would be a good fit for SCASD.  Singapore is a challenging program, not only for students but sometimes also for teachers, and it does seem that a successful implementation of Singapore requires excellent teacher training. Still, districts across the country are finding Singapore to be an effective antidote to strictly constructivist math programs like Investigations and Everyday Math:

And with Singapore math, the pace can accelerate by fourth and fifth grades, putting children as much as a year ahead of students in other math programs as they grasp complex problems more quickly.

“Our old program, Everyday Math, did not do that,” said Danielle Santoro, assistant principal of Public School 132 in Williamsburg, Brooklyn, which introduced Singapore math last year for all 700 students in kindergarten through fifth grade. “One day it could be money, the next day it could be time, and you would not get back to those concepts until a week later.”

Singapore math’s added appeal is that it has largely skirted the math wars of recent decades over whether to teach traditional math or reform math. Indeed, Singapore math has often been described by educators and parents as a more balanced approach between the two, melding old-fashioned algorithms with visual representations and critical thinking.

This week on Wednesday evening and Thursday evening, representatives from textbook publishers will make presentations of their programs in the MNMS cafeteria.  There will be presentations of five programs, the four programs receiving the top ratings from the SCASD Elementary Math Program Review Committee and the 2nd edition of TERC’s Investigations, which is the program currently in use in grades K, 3, and 4 (and some classrooms in grade 5).  Superintendent Mextorf has indicated that he wants the field of four narrowed to two programs that would be pilot-tested in SCASD classrooms during this school year.  The District would then make a determination regarding whether one of those programs would replace Investigations as its core elementary math curriculum.

As a member of the Committee I have had the opportunity to examine materials from the four candidate programs.  Below are my thoughts on the four, as well as on Investigations 2 (in the order they will be presented).  I invite other member of the Committee to add their own comments on these programs.

Everyday Math (McGraw Hill; update: changed to 7:30 pm Wed): Probably no program has generated more controversy in school districts nationwide than Everyday Math, and for the same reasons that TERC’s Investigations has become controversial here in SCASD.  This program takes a strict constructivist approach in which students are expect to construct their own knowledge and in which direct instruction, worked examples, practice, and standard algorithms are de-emphasized or absent.  That said, I found many things I liked in EDM’s presentation of adding fractions of unlike denominator.  As with Investigations, however, the main problems are not with what is included, but what is left out.

Math Expressions (Houghton Mifflin; update: changed to 8:45 pm Wed): Every elementary math program bills itself as “balanced”, which these days is code for being based on constructivist philosophy while still containing worked examples, practice, and attention to standard algorithms (such as carrying in addition).  Of course, not all programs actually are “balanced”, but Math Expressions seems to me to be one of them.  My impression of this program was that it was good but not great, a serviceable program without particularly inspired materials.

Think Math! (School Specialty; 6:00 pm Thu): Some SCASD administrators on the Committee seemed excited about this program, but I could not see why.  This summary chart created by a consultant hired by the Texas BOE highlights its deficiencies: minimal practice and minimal presentation of the standard algorithms for multiplication and division.

Investigations (Pearson; 7:15 pm Thu): It’s never been clear to me why this presentation on Investigations was scheduled.  It is not for the benefit of the Committee; it’s been made very clear that the Committee will be dissolved as soon as pilot programs have been identified.  Investigations is in the mix with the yet-to-be-named pilot programs by default.  One by-product of the math review has been that we have learned that there are many SCASD elementary teachers who have serious concerns about this program.  The District conducted a survey of its teachers who use Investigations 2 that revealed that teachers find that it has “not enough practice”, “redundant activities”, “limited evidence of differentiation”, and “nothing to support algorithm instruction or use”.  The teachers identified “Strengths” as well, but these were easily outnumbered by “Areas of Need”.

enVision (Pearson; 8:30 pm Thu): This was my favorite program of the four, and that opinion was shared by a majority of the Committee.  enVision received more overall ratings of 4 (out of 4) than any other program considered, and fewer ratings of 1 or 2 than any other.  I liked its clear presentations, worked examples, attention to the standard algorithm, and its consideration for conceptual understanding.  The numbers in the Texas BOE analysis bear these observations out.  This program was the clear consensus choice of the Committee after it spent weeks evaluating the eight programs put forth for initial consideration; the other three programs were essentially tied for a distant second once the ratings were tallied.

The following message went out to elementary school parents via e-mail yesterday:

Dear Elementary Parents and Guardians,

As you may know, the district has been going through a curriculum review process for the elementary math program. As a result of the process guided by the math review committee, the choices have been narrowed to four, along with Investigations II.

The math review committee invites you to presentations by the publishers of the top four math curriculums and Investigations II. They will be held in the Mount Nittany Middle School cafeteria, 656 Brandywine Drive, State College, PA 16801, on the following dates:

Wednesday, 6 October 2010, at 6:00 p.m. and 7:15 p.m.
update: these Wed times have been changed to 7:30 and 8:45 pm
Thursday, 7 October 2010, at 6:00 p.m., 7:15 p.m., and 8:30 p.m.

For more information about the math review committee and the process, please go to http://www.scasd.org/2497105317322843/site/default.asp

Thank you,

Dr. Marybeth Irvin
Director of Curriculum K-8

The latest PSSA scores have been released by the Pennsylvania Department of Education, and below is a graph of overall performance of area school districts’ students by grade level. Previously in 2009 [see 9/8/2009 post], grades 3 and 4 in SCASD were both below 90% advanced and proficient; now both are above 90%. Notably, for grade 6, Penns Valley’s direct instruction approach continues to serve its students well and they outperform SCASD’s kids receiving instruction using the constructivist approach endorsed by Connected Math.

In a pattern similar to PSSA results in 2008 and 2009, socioeconomically disadvantaged kids are consistently doing better in surrounding districts at every single grade level in comparison to SCASD. While improvement in grade 4 in SCASD is visible and 85.7% are advanced or proficient (perhaps parts of the Action Plan were beneficial, e.g., giving kids more practice and fluency with math facts?), we still have only 58.1% and 63.3% of the disadvantaged 5th and 6th graders performing at that level, whereas 72.7-87.5% of similar Penns Valley and Bald Eagle students in those grades are proficient or better. One might posit that this ‘cumulative deficit’ directly reflects the impact of Investigations in K-5 on kids’ math skills.

Notably, the average instructional expenditure per pupil per year for the other four local districts is $6,255 (range: $6,096-$6,395), whereas SCASD spends $7,782 per pupil (per IES Common Core Data, 2010). Put another way, for each classroom of 20 students in SCASD, we spend $30,540 more than the surrounding districts. I certainly believe this is a worthwhile investment; however, it is also clear to me that a change in core curriculum/program and a smarter expenditure of instructional funds in mathematics cannot come quickly enough for our kids, especially for those who are economically disadvantaged.

The SCASD Math Program Review Committee met on August 12th to review committee members’ ratings of each of the eight math programs under consideration. After much discussion it was generally agreed that, based on the overall ratings of the full committee, four programs (Saxon Math, Math Connects, HSP Math and, sadly, Singapore Math) would be dropped from further consideration. The remaining four (enVisionMATH, Math Expressions, Think Math!, and Everyday Mathematics) will be reviewed in more detail with the goal of narrowing these down to 2-3 to “try out” during a unit piloting phase across the 2010-11 school year.

Following the states’ widespread adoption of the Common Core Standards this summer, major publishers such as Pearson, McGraw-Hill Education, Houghton Mifflin Harcourt and others have been evaluating the extent to which their existing programs meet the new standards.

Gewertz’s recent article in Education Week (8/20/2010) indicated, “As teacher guides, course outlines, lesson plans, and other supports for the common standards begin to flow into the marketplace, many in education policy circles are raising questions about how to interpret the makers’ claims that their products are “aligned” to the common standards.” Notably, this article highlighted that “Some skills in math, for instance, are introduced at different grade levels in the common standards than in some publishers’ programs.”

The SCASD has invited the publishers of the math programs still being considered to present their materials to the district and Math Program Review Committee in early October. Parents, teachers, and community members are encouraged to attend and learn more about the available program options.

Wednesday, October 6th – Mount Nittany Middle School Cafeteria
6:00pm  -  Everyday Mathematics, McGraw-Hill, https://www.everydaymathonline.com/
7:15pm  -  Math Expressions, Houghton Mifflin Harcourt, http://hmheducation.com/mathexpressions/
update: these Wed times have been changed to 7:30 and 8:45 pm
Thursday, October 7th – Mount Nittany Middle School Cafeteria
6:00pm  -  Think Math!, School Specialty, http://www.harcourtschool.com/thinkmath/
7:15pm  -  Investigations in Number, Data & Space, Pearson, http://investigations.terc.edu/
8:30pm  -  enVisionMATH, Pearson, http://www.envisionmath.com/

Reviews of some of these programs are available through links on the right (e.g., NYCHOLD, etc).

As I’ve been reading more about the Common Core Standards adopted by PA (see 7/3/10 post), it appears that they do not match the best in the country (CA, MA, IN, MN) but may be an improvement for some states. James Milgram’s critique caught my eye and is food for thought. An excerpt:

“Compare the first grade California Green dot standard

2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory.

with the much weaker standard in Core Standards:
1-OA(6) Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

This standard misuses “Fluent,” I believe. One does not want students to develop fluent command of special tricks for doing arithmetic, as this could very well result in severe difficulties un-learning these methods in later grades where Core Standards asks for at least some degree of proficiency with standard algorithms.

Compare 5-NBT(5) Fluently add, subtract, and multiply multi-digit whole numbers using the standard algorithm for each operation.” (Milgram, 2010, p. 14)

As Wu points out in the Fall 2009 American Educator, the elegant simplicity of the standard algorithms is that “all whole-number computations are nothing but a sequence of single-digit computations artfully put together” (p. 6)

Happily, with the adoption of the Common Core Standards, teaching the standard algorithms now will be required in Pennsylvania and students will need to be able to fluently apply them. Three cheers for that!

Pennsylvania’s State Board of Education didn’t waste any time adopting the new national standards developed by the Common Core Standards Initiative sponsored by the National Governors Association.  By adopting these standards, the state is maximizing its chances for receiving additional federal funding as part of the “Race to the Top” program.

SCASD Superintendent Richard Mextorf has already indicated that it is critical that SCASD’s elementary math program meet the new standards, whether it is the Investigations program currently in use or any new program considered for adoption in the District.

UPDATE: Virginia has said no to the national standards.  GA and DE are expected to adopt them, joining PA, NJ, WY, HI, MD, and OK.

Everyone in SCASD seems to agree that we need a “balanced” math program.  The problem is that there are different ideas of what “balance” means.  In my view, the most important balance that needs to be struck is between strict constructivism (the idea that children should construct their own math knowledge with a teacher serving as a facilitator) and direct instruction (which has teachers and texts showing students how to solve problems followed by student practice).

This guy seems to me to be an excellent teacher who has found a great way to balance these approaches:

Dan Meyer is a young high school math teacher in Santa Cruz, CA, who has found creative ways to interest students in math through the use of “real life” examples and who strongly believes that highly structured problems in math textbooks are unhelpful.

In the above video, he sounds like a teacher who would prefer a strict constructivist approach like that employed in Investigations, but that turns out not to be the case.  On his blog, Mr. Meyer makes it clear that the benefits of strict constructivism are outweighed by the inefficiency that comes with it.  He prefers to follow up his examples with direct instruction:

I have to take great pains to point out to skeptical teachers that, even though you’re investing extra time on these kind of investigations, that investment into rigorous mathematical thought processes pays off huge dividends in direct instruction where you find students less impatient, more tenacious, and quicker to learn new skills by evaluating them against their existing intuition.

In a perfect world with unlimited time, he might like to stick with constructivism, but in this world Mr. Meyer believes that his use of direct instruction along with examples that appeal to students’ intuition results in a time savings of 75%:

I have determined my constructivism multiplier to be four, which is to say it takes me four times longer to bring a student to conceptual understanding through conversation and questioning in a social situation the student helped create than it does to get up in front of the class and simply give it to them straight, no chaser, through direct instruction and a handout of questions I wrote.

What I find maddening about conversations with committed constructivists (cf. the conversation here) is the reflexive assumption that educators choose direct instruction because they’re either power-drunk or self-obsessed or because they lack faith, courage, or high expectations. I can’t, personally, wave so dismissively at the massive institutional impediments to student-constructed learning.

A SCASD parent traveling in the People’s Republic of China says that this site is blocked there, presumably by the Chinese government.  This explains why we get only about 50 visits a day, and not 1,300,000,050.

Yesterday was our highest traffic day since we started this website, so it might be a good time to reiterate why some of us object to Investigations, the elementary math program currently in use in SCASD.  From this site’s “About PQME” page:

What’s the Problem with TERC’s “Investigations”?

Parents who have complaints about “Investigations” are not arguing for rote memorization of math facts or “mindless” drilling.  No one has suggested that considering the concepts behind math operations is a bad idea.  Students and parents have been frustrated by “Investigations” overemphasis on written explanations of thinking, lack of the practice that that is necessary for computational efficiency, excessive use of calculators, failure to introduce the standard U.S. algorithm, simplistic homework, and poor preparation for pre-algebra, algebra, and higher math classes.  For further background on how programs like “Investigations” came to be, read this historical account by Cal State-Northridge mathematician David Klein.  For detailed explanations and critiques of TERC’s “Investigations” follow the links in the sidebar at right, particularly Bill Quirk’s site and the video “Math Education: An Inconvenient Truth”.