Sunday, March 1, 2009

A tangled mess

No, I am not referring to the several milk crates of external PC speakers we removed from the classrooms, with their accompanying tangle of wires, now in one -- I was tempted to say "Gordian knot", but that implies there is some prize for untangling the mess -- umm ... knotted mess. What a silly thing to provide with every classroom computer. Much better to have provided headsets...

No, I am referring to the mess of state math benchmarks, performance descriptors and assessment frameworks. (I understand that each of these is designed with a different goal in mind but...)

In Illinois, each content standard, including math, has five benchmarks "that describe what students should know and be able to do" (from the the Illinois State Board of Education's (ISBE) "Introduction - Design for Performance Standards" document). The benchmarks are organized into 5 broad grade level categories: early elementary, late elementary, middle/junior high, early high school, and late high school.

The standards and benchmarks explain "what" students should know at different periods of their education. "Performance descriptors" were added around 2002 to specify "how well students perform at various points on an educational development continuum." The performance descriptors use "stages", labelled A through J. Stages A-C map to the "early elementary" level, D-E to "late elementary", F-H to middle school, I to early high school, and J to late high school. These stages can span grades. For example, stages E, F and G correspond to sixth grade, to address students that are a bit behind schedule, on schedule and ahead of schedule. Three of the stages correspond to the state achievement test (ISAT) expectations: C for third graders, E for fifth grade, and H for eighth grade. "The other stages are not meant to explicitly correspond to the missing grades between." (Introduction referenced above, emphasis in the original.) The document above also provides a clear pyramid of the relationship of goals, standards, benchmarks and performance descriptors (see graphic).

Still with me? The first problem is that the performance descriptors use a different numbering scheme, indicating that they do not map clearly to the next level up, that is, to the benchmarks. For example, consider Benchmark 6.C.2a.

6.C.2a Deciphered:

  • "6" is a learning goal -- Illinois learning goal 6 is "number sense";
  • "6.C" is an Illinois learning standard -- "Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers";
  • "2" indicates the benchmark level (1 = early elementary, 2 = late elementary, 3 = middle school, etc.);
  • "a" identifies the specific benchmark: "Select and perform computational procedures to solve problems with whole numbers, fractions and decimals." Standards that have only one corresponding benchmark omit the lower-case a.
So Benchmark 6.C.2a states "Select and perform computational procedures to solve problems with whole numbers, fractions and decimals."

And Benchmark 6.C.2b (so same standard and level) states "Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable."

But the Performance Descriptors are not mapped to the benchmarks. Or at least I have not been able to find such a document from ISBE. The closest things I found were documents from the Chicago Public School (CPS) Standards-Based Curriculum Initiative (SBCI). Unfortunately, the initiative appears to be shut down, and I can no longer find the documents they produced anywhere on the Internet. I have copies of the English Language Arts for Grade 6 and for Grade 7, and the math documents for Grades 6, 7 and 8. [If anyone reads this, and has access to the other grade documents, I would very much like to see them!] The SBCI documents matched the Performance Descriptors with the Benchmarks (although they did not number them, where they are numbered in the ISBE documents). Some Performance Descriptors apply to multiple benchmarks, a problem which the SBCI authors tried to address. For example:

Performance Descriptor 6.C, stage F, number 1 in the ISBE descriptor document, says "Select and use appropriate operations, methods, and tools to compute or estimate using whole numbers with natural number exponents." SBCI lists this Performance Descriptor with Benchmark 6.C.2A and Benchmark 6.C.2B.

I suppose this is a relatively minor problem, and at least the SBCI documents exist to aid in translating between the benchmarks and the performance descriptors, if one has a copy of their document for the grade in question.

The problem is more difficult with the "Assessment Framework", which is one more Illinois system for organizing math learning tasks. According to the ISBE Assessment Framework website:

The Illinois Assessment Frameworks are designed to assist educators, test developers, policy makers, and the public by clearly defining those elements of the Illinois Learning Standards that are suitable for state testing. They are not designed to replace local curricula and should not be considered state curricula. They define the content that may be assessed on ISAT...
The Assessment Frameworks (AF from here on) are organized by standard, but that is the extent of the attempt (again, as far as I can tell) to correlate the framework with either benchmarks or performance descriptors. The AF has its own coding scheme. All items (referred to as "objectives") for a particular standard are numbered sequentially by grade (see the llinois Mathematics Assessment Framework Grades 3–8, 2006). For example, for item 6.6.12

  • The first "6" indicates the standard (in this case, "number sense")
  • The second 6 indicates the grade level (grade 6)
  • The "12" indicates the learning objective to be assessed, numbered sequentially from 1 for standard 6, grade 6.
AF objective 6.6.12 states, "Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers" which I think covers part of Performance Descriptor 6.C.F.1 and Benchmark 6.C.2A and 6.C.2B. But this is my guesswork. The Assessment Framework does group the items by standards (but not benchmarks!), although the document does sometimes lump together two standards (e.g., 6.B and 6.C are grouped together). The Assessment Framework also groups the objectives by general categories like "number operations", "properties", and "estimation" (again, for 6.B and 6.C), but there is no direct correlation between these categories and the performance descriptors.

There are at least two practical problems that arise from these parallel coding schemes. I have been putting together an online searchable database of online math activities (let me if you would like to see the work-in-progress). A user can assign benchmarks, performance descriptors and assessment framework items to resources he or she has located on the Internet. It would be very nice if setting one type (e.g. assessment framework) could automatically set a corresponding (or closely related) benchmark and performance descriptor (the latter especially, since it is more specific). But to do this, I need to create my own translation table. I started on this dreary task, but my brain quickly fogged over with the mind-numbing vocabulary of learning standards, benchmarks, etc. I would hope that the designers of the standards and tasks schemes would have done this already [please let me know, anyone!].

A second problem comes when trying to use CPS math assessments to do data-driven instruction. The CPS Math Benchmark Assessment (CMBA) only categorizes its questions to the standard level. This is too blunt -- the questions should be categorized by performance descriptor and assessment framework objectives (especially since the sample ISAT test questions are matched to assessment framework objectives), so that a teacher can know what general skill or concept to teach students that struggle with particular questions. Yes, the teacher should be able to determine that from the question, but teachers are notoriously short of time, so why not provide some direction for them already?

In addition, the numbering schemes provide a handy key for locating resources to address specific learning tasks, whether in the commonly used curricula or online. Without such a key, the teacher must do a lot of extra work. (I should note that the CPS Reading Benchmark Assessment does categorize questions by assessment framework; and the CMBA does provide distractors for each question, which are a big help in narrowing down what may have been the student's misunderstanding.)

As I noted, the standards, benchmarks, performance descriptors and assessment frameworks are designed for different things -- what a student should know vs. how well a student should know it at a given stage vs. what tasks they will be assessed on on a standardized test. But these categories are interrelated, and should correlate. According to "understanding by design" principles (and probably good educational principles in general), assessment should follow from
the Big Goals of learning, so it should be possible (or rather, it should be inherent in the design) to correlate the assessment framework items with specific benchmarks and performance descriptors.

And these correlation tables could exist for all I know. But I have been unable to locate them online. If anyone knows of such a thing, please let me know!

I could expand this further to the babel of different state standards and the various additional categories each state has come up with. (As an aside, see The State of State Math Standards 2005 by David Klein et. al. via the Thomas B. Fordham Institute, for an evaluation of different state math standards. Illinois received a C, up from a D in 2000.) Matching different state standards is sufficiently complex to allow the space for at least one commercial service to develop, Academic Benchmarks, to help curriculum publishers match their materials up to different state frameworks. I assume their general methodology is to develop a lingua franca of standard/benchmarks/etc. and then develop a database of state standards that they key to the common dialect. The National Council of Teachers of Mathematics standards, expectations and "focal points" may be sufficient, or at least a good starting point. I made a weak attempt to do this using BrainPOP videos as a common reference point, since they have been mapped to different state benchmarks, etc. ("powered by Academic Benchmarks"), but their videos don't hit every benchmark or descriptor, so the result was spotty (not to mention being an incredibly tedious task).

I think an open source, online tool is needed, that would look something like a currency converter. Need to translate Tennessee "Student Performance Indicator" 6.1.1 to a similar Illinois Performance Descriptor? Enter the Tennessee number on one side, select the source state and the destination state, and click the "Translate" button...


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