Infinitely Better Than Nothing

You can review NCTM’s arguments in the letter, which amount to three major points of contention. First, the EdReports alignment ratings were focused on “only a subset” of the Common Core State Standards for Math (CCSSM). Second, the ratings methodology used a gateway system that essentially disqualified programs upon their failure to simply meet the first gateway. Finally, there are errors in interpretation of CCSSM concepts.

Before addressing each argument, I think it’s fair to question NCTM’s role in this entire process. Their letter states that:

“Determining the extent to which materials support student learning of a set of college- and career-ready standards is time-consuming and demanding work.  Research and experience have taught us that identifying instructional materials with the potential to support learning for a broad range of students requires an analysis of the content (skills, concepts and practices), the nature of tasks, lessons, and assessments, and finally the sequencing of content within and across grades/courses. Individually and together, these features contribute to or undermine the opportunity for students to learn.

Any effective review methodology will incorporate each of these elements.”

Evaluating the main marketed Math curriculum materials on a broad scale is demanding work. It is also work that NCTM has never undertaken. There are many solid reasons for their neutrality on the subject of which Math curriculum programs are preferable, but their credibility in criticizing the first major effort to answer this question is limited as a result. EdReports didn’t come to their original research question out of nowhere. The claim that the major Math curriculums on the market are inadequate is well-researched and well-documented. NCTM has yet to independently provide the service that EdReports now offers.

Dr. Morgan Polikoff, of the University of Southern California, published a comprehensive study of fourth grade Math curriculum materials available for purchase by school districts and found that publishers’ claims of alignment with the CCSSM were false. Articles hinting at this conclusion were being published in early 2014, also citing Dr. William Schmidt of Michigan State University. Schmidt’s research, comprised of 34 textbook series, is startling in its criticism of major Math curriculums in publication at the time. Perhaps the most alarming finding was that “only half of the total standards covered in a typical textbook focus on Math considered appropriate for grade level.” The need for an EdReports-like ratings system has been met with silence by NCTM, an organization that would seem uniquely suited to provide this type of information.

There is a larger irony here though in NCTM’s claim that the EdReports findings are “leading educators … to make decisions that will do a disservice to our students and will squander the potential of the standards to improve mathematics education.” Dr. Polikoff and Dr. Schmidt undertook their research stated above to prevent this exact impact. Their motivation is the inability of teachers and schools to effectively implement the CCSSM due to the dearth of well-aligned published curriculum materials. The worry over the quality of Math education existed long before EdReports entered the discussion. There is something disingenuous about NCTM ending its silence now after an absence from this discussion for decades (both pre and post CCSSM). Which influence is more risky to the quality of Math education: the significant lack of quality published curriculum materials or the EdReports findings that may have nuanced errors in their methodology? Clearly, the former is more damaging, and yet NCTM never wrote a letter to the education community about this well-publicized problem. We first hear very specific criticism from them only now that others are attempting to address the issue.

As to the specific arguments in the NCTM letter, there is plenty of opportunity for criticism here as well.

#1 - The EdReports alignment ratings were focused on “only a subset” of the Common Core State Standards for Math (CCSSM).

This problem stems from disagreement between EdReports and NCTM on what the “Major Work” is for each grade level in the CCSSM. NCTM’s letter states that all areas of the CCSSM should have been analyzed. But the precedent has been clearly set with the CCSSM that certain domains (topic areas) are more “major” than others. The Model Content Frameworks for the PARCC assessment state that “not all of the [CCSSM] content in a given grade level is emphasized equally in the standards…the assessments will strongly focus where the standards focus.” Another problem with NCTM’s argument here is the lack of magnitude. Their letter states that “critical areas” are “excluded” by EdReports and gives the example of geometry in K-5. But Geometry is the ONLY area that EdReports and NCTM disagree on in K-5. The NCTM letter is ambiguous as to whether geometry is just one of many examples or not. Even the attachment that NCTM provided with the letter showing the misalignment between areas of “Major Work” clearly indicates that geometry is the exclusive concern in terms of analysis in the K-5 standards. This is a crucial point and an enormously mitigating factor in the concerns about EdReports.

#2 - The ratings methodology used a gateway system that essentially disqualified programs upon their failure to simply meet the first gateway.

This is true, yet the NCTM letter conveniently leaves out the focus of each gateway. The criteria to pass the first gateway is alignment with the focus and coherence of the CCSSM. This circularly connects NCTM argument #2 with argument #1 in that EdReports may be looking at the wrong areas of the CCSSM. The EdReports methodology of skipping gateway two, the rigor of the CCSSM, for all materials initially disqualified seems sound. While an analysis of these published programs’ mathematical rigor would be helpful information, it would not change the fact that the same programs don’t meet the criteria for focus and coherence. To be clear, NCTM isn’t claiming that the programs criticized by EdReports are aligned with the CCSSM. NCTM is only stating that EdReports should have kept going in its analysis of a given program even after it was clear upon initial analysis that a program was misaligned. EdReports has stated that it will adjust the gateway process going forward and review even further evidence of gateway one for previously analyzed programs. However, the research by Polikoff and Schmidt mentioned above would seem to foreshadow similar conclusions about published curriculum programs regardless of this change in methodology.

#3 - There are errors in interpretation of CCSSM concepts.

While EdReports’ analysis was conducted by Math experts, this is one area where it seems reasonable to defer to NCTM in its interpretation of the CCSSM. However, the letter is very brief in its evidence of misinterpretations by EdReports. Further, the errors are minor and it is difficult to imagine a scenario where an entire published curriculum program was found to be non-aligned based on a misinterpretation of a single standard here and there in the analysis.

A consultant offers information, resources, and expertise. What struck me was my prior assumptions about a coach essentially performing this same role. After learning from Dr. Kuchar, I still see an effective coach as a person who uses expertise to support others. However, there’s a finer distinction that makes one a coach and not a consultant. Coaching requires a different mindset and skills. A coach “enhances staff capacity,” but a consultant arguably does the same thing. The mindset distinct to coaching is collaboration, as opposed to expertise. An analogy can be made to effective instructional practices in the classroom. The teacher should focus on facilitating student learning instead of simply transferring knowledge to students. Similarly, a coach cannot effectively develop capacity in a hierarchical environment. The most effective professional learning for staff will occur when coaching is offered as a parallel layer in the process.

Specifically, Mark Phillips references in his blog the book “50 Myths & Lies That Threaten America’s Public Schools: The Real Crisis in Education, a new book by David Berliner and Gene Glass, two of the country’s most highly respected educational researchers.” The argument he cites is that because socioeconomic factors have a direct correlation with high and low student learning, as a result it is a myth that “Teachers Are the Most Important Influence on a Child’s Education.” He concludes by stating, “the bottom line is that teachers have far less power to improve student achievement than do varied outside factors.”

While economic and broader societal issues negatively impact student learning, it’s a false conclusion to infer that as a result teachers and schools have little impact.

The significant work of drawing the distinction between the two concepts was done by Seymour Papert nearly twenty five years ago. To oversimplify for the sake of this post, constructivism is an educational theory/philosophy/belief that knowledge and learning are created by the learner. Its non-example is instructionism, or the concept of a teacher providing knowledge to students that can be absorbed and expelled when necessary. To severely oversimplify, think student-centered vs. teacher centered.

Constructionism, however, is much more closely related to a constructivist viewpoint. If constructivism refers to the overall process of learning, then constructionism is arguably an evolution or at least a more detailed concept. It posits that learning is best accomplished when the learner creates (“constructs”) something in the process. Teachers often call this a project or artifact or portfolio item or etc. It can be any resulting item that involved the student in its construction. Constructionism partially explains why a constructivist approach is successful.

While an interesting (and valuable) analysis, the unique difference between the -nism and the -vism seems less profound on examination. Would it be possible to have a constructivist approach that does not involve constructionism? Likely not, as any activity not involving a constructed, tangible item would originally center around transfer of information from an external source to the student. The external source may be a teacher, a peer, a text, etc. Regardless, this transfer process is inherently instructionist, as the student is a recipient and not an author. They may extend their understanding, but that does not change the origins of the activity. On initial consideration, any amount of constructivism guarantees that constructionism is also present, at least with very rare exception.

But let’s complicate the connection of the -nism to the -vism further. Nearly thirty years ago Jerome Bruner examined the most ideal models for learning. Aside from discovery and invention, he added the concept of community and the sharing of knowledge. The theory goes that students must construct (-nism and -vism) their own understanding in a communal context. As a person who appreciates both communal and solitary learning, I don’t particularly agree that community is as prevalent. But clearly students need to develop collaborative strategies and the ability to communicate with others in order to have “21st century skills” or to be “college and career ready” or choose your generalization.

First, consider the excellent marriage of Literacy and Social Studies in the English-Language Arts Common Core standards. While a similar relationship exists between science and math, the two core subjects are already being rethought (with new standards) in silos. The disconnect between the standards for science and math could serve to only continue this separation.

Second, this makes consistency in STEM curriculum and instruction work more difficult. The CCSSM and NGSS offered a potential opportunity to lay a STEM blueprint at a time when it is drastically needed. 

On the brighter side, the technology and engineering concepts needed for quality STEM instruction do appear to be reasonably embedded in the NGSS. 

Traditionalists are sure to be quite wary of Spritz's claim that comprehension can even be increased with their method. Clearly, further analysis of the tool with students of varied ages would be needed to validate its usage in schools.

But what are the theoretical benefits?

The obvious positive to this reading approach would be efficiency; i.e. less time to read content leaving more time to think about & discuss information.

The tool can be differentiated at several different speeds allowing for usage by students at all skill levels. 

At first glance, reading fluency seems like an area that can be addressed using the unique approach of what the company refers to as "optimal recognition points."