With Common Core on the board’s agenda for its June 30-July 1 meeting, the board will hold a series of roundtables across the state – both to present preliminary results of a study comparing Common Core with Pennsylvania’s standards framework and to gather feedback from stakeholders.  The study is being conducted by professor Suzanne Lane of the University of Pittsburgh.  Dates and locations for the roundtables are below; each forum will begin at 10 a.m. and continue until all stakeholders are heard.

• Friday, May 21, University of Pittsburgh, Posvar Hall
• Thursday, May 27, Mt. Nittany Middle School, State College
• Wednesday, June 9, Philadelphia (location TBD)
  

Anyone who has questions or is interested in participating should contact the State Board office at (717) 787-3787.

Regarding the evaluation of curriculum and instruction needs, specifically with regard to materials, textbooks, and organization: Are materials and instruction structured sufficiently to meet the needs of Tier 1  students?  They note that “improving mathematics performance requires attention to both content coverage and content mastery” (p. 534).

Their recommendations for mathematics curriculum evaluation (p. 538):

General program design

1. Do the lessons include objectives with measurable student behaviors?
2. Are newly taught strategies integrated with those previously taught?
3. Is there a balance between computation instruction and problem-solving instruction?
4. Is the program organized using a spiral or strand design?

Instructional Strategies

1. Are strategies explicitly taught in the program?
2. Are the strategies appropriately generalizable – neither too narrow nor too broad?
3. Are critical component skills taught prior to the strategy?
4. Are there adequate examples provided for instruction?
5. Are discrimination examples included?

Assessment

1. Does the program include a placement test with options for various starting points?
2. Do in-program assessments include recommendations for accelerations or remediation?
3. Are the in-program assessments carefully aligned with instruction?

Notably, constructivist, “reform” curricula typically are spiral in design and are common in the U.S.  Alas, spirally designed programs often lack adequate initial instruction and review to promote student mastery of skills.

According to the National Math Advisory Panel (2008), “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.” (p. 22).

By way of introduction, a meta-analysis take groups of studies that have been done on a particular topic, innovation, or approach and combines their findings into a summary measure called “effect size”. An effect size of d = 1.0 indicates an increase of one standard deviation on the outcome (e.g., achievement), or advancing kids’ achievement by two to three years, or improving the rate of learning by 50%. An effect size of 1.0 means that, on average, the performance of students receiving that treatment would exceed 84% of students not receiving that treatment.

What does Hattie report for mathematics programs? Combining 13 meta-analyses covering 677 studies and 8565 people (2370 effects), the effect for mathematics programs is 0.45, a medium effect size that means they DO have an effect. Specifically, the highest effects were found when teachers provide feedback data or recommendations to students (d = .71) and peer-assisted learning (.62), explicit teacher-led instruction (.65), direct instruction (.65), and concrete feedback to parents (.43). Hattie states that “modern” mathematics that stress real-world problems and a high level of use of manipulatives (e.g., constructivist approaches) has an effect size of .24.  Effects are higher for teaching concepts (.36) and computation (.31) but not application (.06).

According to Hattie, “Overall, the presence of feedback, direct instruction, strategy-based methods, high levels of challenge and mastery has much effect on the learning of mathematics. That is, directive teaching makes the difference when teaching mathematics” (p. 147)

In a subsequent post, I’ll pull together Hattie’s findings regarding effect sizes for teachers as ‘activators’ and teachers as ‘facilitators’.

On a graded math homework assignment, students were expected to determine the perimeters and areas of various shapes, mostly rectangles. Given that this student had previously done this kind of work (at home with Singapore Math), this assignment was quite easy for the student. He did it efficiently and independently, and submitted it to the teacher. Upon receiving the graded assignment back, much to his parent’s surprise, the student received only 20 points out of 30 (66%, or a D).

Taking a closer look at the assignment, his parents were extremely upset with what they found.

For every single area problem, he had the correct answer but his answers were marked wrong. Why? He was using the standard notation for units of area: using the abbreviation for the units of measurement superscripted with 2 to indicate squared units (e.g., m^2, cm^2, km^2, ft^2, etc.).

I looked this up in Webster’s New Collegiate dictionary and, sure enough, it lists ” sq km” OR “cm^2″ as acceptable abbreviations. In my field, APA style expressly requires 1) use of the International System (SI), 2) the unit’s abbreviation be used when presented with a numeric value.  But — inexplicably — this standard, universally accepted mathematical notation for square units of measurement is NOT acceptable in this classroom. In Investigations? In our district!!!???!!!

No, indeed. Instead, all students were expected to write it out (e.g., “square meters”, “square centimeters”, etc.). So he lost 9 points for all 9 problems. How asinine is that?

Failure to accept, let alone teach, standard mathematical notation and language is yet another reason why Investigations doesn’t belong in our schools.

The fluency expectation for grade 2 is mastery of addition AND subtraction facts through 20. That means that all grade 3 students should easily have been able to complete all addition banks – certainly by April.  Only 28% have completed addition, and a mere 16% have finished subtraction.

The fluency expectation for grade 4 is mastery of multiplication facts through 12×12. That means that all grade 5 students should easily have been able to complete all multiplication banks at the start of the online evaluation in November. Even by April, only 46% has mastered each bank.  I don’t think there is a need to “investigate” the cause – Investigations IS the cause!

“I’m really glad you’re doing that,” he said, and sheepishly admitted that  – as a sophomore in college — he was struggling in his entry-level statistics class. Why? Well, he is not allowed to use a calculator on exams in the class, and he struggles with long division and multiplying decimals. He indicated that he watches some kids after school and was unable to even assist a 4th grader with his math homework on division. To further prove his point, he offered to do some problems for me, and — sure enough – he’s right. He had no idea where to start to answer 3156/27, and while he could do the multiplication involved for 43.6×21.4, he didn’t know to move the decimal in two places and moved it only one. Oh, dear! Lastly, he indicated that he still finger counts to do basic addition and subtraction. His hypothesis about the key to his difficulties:  he was handed a calculator in 6th grade and has been using it ever since, so he NEVER MASTERED THE BASIC MATH FACTS OR CALCULATIONS BY HAND!!!!????? Can you imagine? Do you think that testimonies like this would be enough to sway the board? One could only hope so.

I am absolutely sickened by this, and my heart goes out to him and others stuck in his position.   I feel horrid that he has a high school diploma from our district and yet doesn’t have the foundational math knowledge or procedural skills to be successful in a lower-level class required for his major. Truly, he is another heartbreaking example of a curriculum casualty. We absolutely cannot allow this to happen to any more of our kids!

(For the record: This student gave me the OK to share his story, so I am doing so with his permission. We talked at length about academic supports available on PSU’s campus, and other strategies he could use to address his educational needs. I really hope he can get the help he needs both in the short term and beyond!).

The National Math Advisory Panel Final Report (2008) defines proficiency as “students should understand key concepts, achieve automaticity as appropriate (e.g., with addition and related subtraction facts)…” (p. xvii). Clear benchmarks for critical foundations in mathematics are established, including:

“Fluency with Whole Numbers

1) By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.

2) By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.” (p. 20)

The expectations for this task? Answer each fact correctly within 4 seconds (4 times each fact), and practice at least once per week starting in early November.

To be fair, some contributing factors and other potential explanations posited by the math office for why these numbers are so low include that students could choose from all banks and actual frequency of use varied, as did computer availability, computer skills, and familiarity with the tool. Still, these numbers don’t look so good as only 28% of third graders have mastered addition facts, and only 46% of 5th graders have mastered multiplication facts 8 months into the school year. It appears as if we are missing these critical NMAP benchmarks.

If you find these SCASD outcomes to be concerning, please come to the next school board meeting 7:30 Monday night 4/12/10 to learn more, to urge the School Board to take immediate action to improve these outcomes by choosing an alternative core mathematics resource, and to help advocate for improvement in our kids’ math education!

This Practice Guide highlights the following recommendations and level of evidence in support of these recommendations as follows:

Recommendation [Level of evidence]
Tier 1
1. Screen all students to identify those at risk for potential mathematics
difficulties and provide interventions to students identified as at risk. [Moderate]
Tiers 2 and 3
2. Instructional materials for students receiving interventions should
focus intensely on in-depth treatment of whole numbers in kindergar-
ten through grade 5 and on rational numbers in grades 4 through 8.
These materials should be selected by committee. [Low]
3. Instruction during the intervention should be explicit and systematic.
This includes providing models of proficient problem solving, verbal-
ization of thought processes, guided practice, corrective feedback, and
frequent cumulative review.  [Strong]
4. Interventions should include instruction on solving word problems
that is based on common underlying structures. [Strong]
5. Intervention materials should include opportunities for students to
work with visual representations of mathematical ideas and interven-
tionists should be proficient in the use of visual representations of
mathematical ideas. [Moderate]
6. Interventions at all grade levels should devote about 10 minutes in each
session to building fluent retrieval of basic arithmetic facts. [Moderate]
7. Monitor the progress of students receiving supplemental instruction
and other students who are at risk. [Low]
8. Include motivational strategies in tier 2 and tier 3 interventions. [Low]

In Pennsylvania, the RTI term has expanded to include Response to Instruction and Intervention (RTII). As defined by Pennsylvania’s Training and Technical Assistance Network (www.pattan.net), RTII is “a comprehensive, multi-tiered, standards aligned strategy to enable early identification and intervention for students at academic or behavioral risk.”  A key component of RTII is appropriate Tier 1 interventions, also known as the core curriculum. One might posit that these principles and recommendations for Tiers 2 & 3 should also be generously applied to core instruction ,and the targeted curriculum and textbook selection should clearly embrace these recommendations as well.

Dr. Russell Gersten, professor emeritus at University of Oregon and an expert on effective math instructional practices, was one of the presenters at the workshop. When asked what he would recommend if a district was utilizing a constructivist approach that avoided explicit and systematic instruction and instead relied upon students’ self-discovery of their own methods for answering questions, he laughed, seemed to do a double take, and nearly answered “Pshwft!”…. before awkwardly handing it over to a woman from PDE who indicated that yes, some districts in Pennsylvania might be using that approach in Tier I core instruction. Clearly, he didn’t think it had ANY place in Tier II or III interventions for kids having difficulty in math (or much of one in Tier I core instruction either, I assume), as he made a point of highlighting the IES randomized study of grade 1 students that showed that using a totally discovery-focused approach is NOT effective. Yes, indeed – this must be our very own Investigations curriculum that scored poorly in that IES study (NCEE 2009-4053: Achievement effects of four early elementary school math curricula).

Overall, this was a good workshop. Additional highlights and other aspects of the IES Practice Guide will follow in subsequent posts.