Today’s CDT has an article describing the conclusion of the math program change.

The SCASD report on the pilot testing that concluded this spring is available on the District website.

A key motivation for the change was Pennsylvania’s adoption of the Common Core standards.  SCASD’s review found that Investigations did not match up well at all with the new standards: About 50% agreement as compared to about 85% for Math Expressions.

In the public comment period, three people spoke against the recommendation.  They did not ask the Board to keep Investigations in place, but rather to restart the selection process and take another year to pilot different programs.  One of the speakers characterized Expressions (and Investigations) as “adequate” but not the “excellent” program the District needs.

The Board then voted on whether to endorse the report and recommendation, and this passed by an 8-0 vote.  Math Expressions materials will be available for public viewing before the Board approves purchase of the program at its next meeting on June 13.   Implementation and training plans are in the works and will be presented at the same meeting.

Overall, enVision was rated weakest in all areas and Math Expressions and Investigations II each demonstrated strengths and weaknesses in different aspects of the pilot.

One of the weaknesses of Investigations II, however, is that SCASD teachers found that Investigations II does not have “positive alignment to the Common Core and PA Standards.”  This is a major weakness – alignment with Common Core/PA standards has been a focus all along in this process and it is now clear that Investigations II will not meet those standards without extensive remediation.

The summary states that “Math Expressions and Investigations II were rated similarly by Pilot Teachers,” but the numbers in the reports appendices tell a different story, as the tables in Barb’s analysis show.

On the subject of teacher opinion: Readers of this blog will recall that last June, the District surveyed all of its teachers who use Investigations II in response to calls from some on the Math Review Committee who questioned whether the review process was even necessary – weren’t teachers generally satisfied with Investigations II?  The District conducted a non-anonymous survey in which teachers gave their answers to their principals in meetings.

The de-identified results of the survey were shared with the committee but never appeared in the CDT or on the SCASD website.  Here they are in PDF form, scanned from my paper original.  Readers can draw their own conclusions about the survey results, but in my view the results make it clear that SCASD teachers have serious concerns about this program.  After seeing the survey results, one elementary school principal told me that s/he didn’t see any way we would be using Investigations in 2011-2012.  From the recommendation in the math pilot report, it appears that this prediction will be proven accurate.

Candidates for SCASD Board of Directors were profiled in the CDT last week. There are seven candidates from whom five will be chosen.

UPDATE: All 7 candidates will be on the November 8 ballot because different groups of 5 won the Democratic and Republican primaries. If Democratic and Republican votes from yesterday were totaled, the five elected would have been (from most votes to least): Stahl, McGlaughlin, Concepcion, Zydney, Pawelczyk. CDT story here.

The Materials Review process identified Math Expressions as the strongest program in its rubric review and its alignment to the PA Standards and Common Core. Neither Investigations II nor enVision had a positive alignment to the Common Core and PA Standards. When the materials were piloted in classrooms, both Math Expressions and Investigations II were rated similarly by Pilot Teachers. enVision was rated poorly by our Pilot Teachers across grade levels. Students in Investigations II pilot classrooms scored statistically significantly higher than students in Math Expressions and enVision on the assessments. Overall, enVision was rated weakest in all areas and Math Expressions and Investigations II each demonstrated strengths and weaknesses in different aspects of the pilot.

…

A draft of this report was sent to the acting superintendent on May 11th. Although the Leadership Team recommended a continuation of the pilot with additional materials, the Acting Superintendent directed the Pilot Planning Team to select and recommend one of the three programs supported by the community committee that is highly aligned to the PA and Common Core Standards. Given this directive, Math Expressions is the only program meeting these criteria.

How the new program is to phased in is not addressed in the report and this will presumably be discussed at future Board meetings, starting with the one scheduled for Monday, May 23.

According to TERC, the developers of Investigations, their program their program aligns very well with the Common Core Standards:

There is also strong alignment between Investigations and the CCSS’s Content Standards. Each curriculum unit provides an in-depth study of a specific and related set of mathematical concepts and skills. The design of the materials offers students extended opportunities to make sense of, practice, and develop fluency with the key concepts and skills within a grade level and across grade levels.

The alignment is so strong, in fact,  that TERC is rushing to develop supplemental materials that will presumably create super-strong alignment between Investigations and Common Core:

The authors of Investigations are developing materials to support teachers and schools that use Investigations to implement the Core Standards. These companion materials, which will be available from Pearson, are designed for use in conjunction with the curriculum units at each grade level, K-5. New activities and sessions build on existing content and familiar contexts and representations within the grade level.

The truth behind this doublespeak is that Investigations doesn’t align well at all with the new Pennsylvania standards, and this should come as no surprise.  The Common Core Standards require proficiency with standard algorithms and operations with fractions, as well as facility with math facts, and – by design – none of these is emphasized in Investigations.

Similar strangeness is found on the website for Everyday Math, another strict constructivist program, one that was roundly rejected by the SCASD Math Review Committee following the presentation by its publisher last October.  The first thing one sees on the site is a large seal of approval proclaiming “COMMON CORE STATE STANDARDS – 100% ALIGNMENT”, but the text tells a different story:

Each grade-level author reviewed the content standards and developed a plan to adjust lessons so that Everyday Mathematics aligned 100% to the CCSS. Those plans are complete and we are now implementing those adjustments to the Everyday Mathematics program. Our author and editorial team are well on their way and we will have a program that aligns to the CCSS ready for implementation in the 2011-2012 school year.

Is there any reason to put much stock in these promises from TERC or Everyday Math?  A nominally compliant patchwork of supplemental materials will be offered (not to do so would effectively remove these programs from the market), but the developers of both programs are on record as objecting in principle to the goals behind the Common Core Standards.

“Pamela Francis, Marybeth Irvin and Deirdre Bauer review information and present the recommended Math Program and Implementation Plan for Board consideration.”

What will be announced on Monday is anyone’s guess.  The previous updates to the Board on the pilot process have not contained any indication of the reception received by any of the programs under consideration.  Just to recap, the three programs under consideration are:

1. Investigations (2nd Ed.): Yes, the current program, controversial though it may be, is being pilot tested alongside the two other programs identified last spring by the Math Review Committee.  It’s possible that the Math Leadership Team will simply recommend that no change in the math program be made.

2. enVision Math: This program has the same publisher (Pearson) as Investigations and it is possible to integrate Investigations units into the enVision program.  This is the manner in which enVision was pilot tested in SCASD.

3. Math Expressions: Released in 2005, this program (according to its publisher, Houghton Mifflin Harcourt) “combin[es] aspects of traditional approaches with the most powerful elements of reform teaching”.

Both enVision and Expressions were authored by math educators active in developing and implementing the NCTM standards, and both programs are touted as “standards-based”, as is Investigations.  The most substantial differences between  enVision or Expressions and what we have now in SCASD is that these two programs make use of a textbook and do not avoid the use of worked examples and other forms of direct instruction.

Of course all the programs claim to meet the Common Core Standards (also now the PA state standards), but the authors of strict constructivist programs like Investigations and Everyday Math have published objections to the new standards, perhaps because their programs do not align well with Common Core.

UPDATE: It now appears that this item has disappeared from the May 9 agenda and will be discussed on May 23.

… found that students who read a passage, then took a test asking them to recall what they had read, retained about 50 percent more of the information a week later than students who used two other methods.

One of those methods — repeatedly studying the material — is familiar to legions of students who cram before exams. The other — having students draw detailed diagrams documenting what they are learning — is prized by many teachers because it forces students to make connections among facts.

I’m mentioning this study not in support of the PSSAs or other testing, but because of this quote in the Times article:

Howard Gardner, an education professor at Harvard who advocates constructivism — the idea that children should discover their own approach to learning, emphasizing reasoning over memorization — said in an e-mail that the results “throw down the gauntlet to those progressive educators, myself included.”

“Educators who embrace seemingly more active approaches, like concept mapping,” he continued, “are challenged to devise outcome measures that can demonstrate the superiority of such constructivist approaches.”

This a priori assumption of which approach is best reminds me of true-believer syndrome among people who believe in psychic powers.  If a test shows that your favorite approach to learning is not working, this ought to lead researchers (and administrators and school boards) to question their initial assumption rather than send them looking for a new test.

To answer this question, one has to understand that NCLB requires states to label performance on their tests as “advanced”, “proficient”, “basic”, and “below basic”, but how those labels are applied is up to each state and can vary from year to year.  State standards can be compared, however, by examining student performance on a national test called the NAEP.  The U.S. Department of Education has done this analysis, and Pennsylvania proficiency standards are near the bottom of the pack.  In other words, the threshold for proficient in Pennsylvania is a lot closer to Alabama’s threshold than it is to Massachusetts’s.

But what about the actual test questions?  What kinds of questions are SCASD students answering correctly when they are rated proficient or advanced?  Example questions and scoring guides for past years’ PSSAs are available here, and it is worth taking a look.  Here is a question from the 2009-10 fifth-grade math test:

It is important to know how to measure using a ruler, but to me this question seems too easy to be on the 5th grade test and, in fact, measuring in fractions of an inch with a ruler is something expected to be mastered in 3rd grade under the Common Core Standards, which recently became Pennsylvania’s.  Only 46% of Pennsylvania fifth-graders were able to measure the paper clip correctly on last year’s test.

Another question from the 5th grade test:

17. A. Mr. Stevens bought 15 books for his store. He paid $11 for each book. He then sold all 15 books for $25 each.  What is the difference between the total amount of money Mr. Stevens sold the books for and the total amount of money he paid for the books? Show or explain all your work.

17.B. Mr. Stevens has $220 to purchase books at $8 each (tax included).  How many books can Mr. Stevens buy? Show or explain all your work.

Again, this is something 5th graders ought to be able to do, but it matches the 4th grade, not the 5th grade, standard under Common Core.

We all want our schools to be making “adequate yearly progress” (to use the NCLB term), but what’s much more important to parents is whether their own kids are progressing at the rate they ought to be.  Up until now, Pennsylvania and SCASD standards have not been very helpful in making that determination.  Maybe this will change once the new Common Core Standards are implemented across Pennsylvania, but even those standards are lacking in key respects.

One good way to assess your child’s math progress at home is with the free placement tests available at SingaporeMath.com.  For those not familiar with Singapore Math,

In the United States the Singapore Math Method of teaching mathematics is based on the primary textbooks and syllabus from the national curriculum of Singapore. These textbooks have a consistent and strong emphasis on problem solving and model drawing, with a focus on in-depth understanding of the essential math skills recommended in the NCTM Curriculum Focal Points (National Council of Teachers of Mathematics), the National Mathematics Advisory Panel,  and the proposed Common Core State Standards.