The National Council of Teachers of Mathematics recently issued a position statement on open education resources, urging educators to seek a “coherent, well-articulated curriculum” when curating openly resourced mathematics materials and tasks online.
This issue of curricular coherence is not particularly new, although the widespread availability and push to use openly licensed materials (many of which can be downloaded for free), makes the topic timely, said NCTM President Matt Larson.
“The authors of the Common Core State Standards for Mathematics also identified coherence as one of their guiding principles and organized the content standards into clusters and domains that weave content together from grade to grade or topic to topic to make conceptual connections and coherence more obvious to teachers and curriculum developers alike,” he wrote in a blog.
He explained that coherence, from NCTM’s perspective, means that connections are made ‘from one year to the next, from one idea to another, from one representation to another, and from one statement to many others that are implied by that statement.”
This also refers to coherence pedagogically, logically, and conceptually, “in terms of learning science, and with the real world,” the position statement said.
“Our Principles and Standards for School Mathematics, published in 2000, specifically said a curriculum is more than a collection of activities and that it must be coherent, focused on important mathematics, and well-articulated across the grades,” Larson said in an interview.
The publication further describes a well-articulated curriculum as making clear the most important math of the grade level, when concepts and skills are introduced and when they should be mastered, and how student conceptual understanding of “big ideas” develops across units and across multiple grade levels.
“The issue that perhaps led to the position statement … is that the recent widespread availability of online materials — some of which are free, some of which are of high quality, and some of which aren’t — makes the issue of coherence even more important today,” Larson said. “Simply stated, the potential downside of random selection of online curricular tasks is that it can undercut curriculum coherence because you potentially introduce disjointed tasks of questionable quality that do not fit within a mathematical learning progression.”
He said he believes the greatest potential danger in using open educational resources without proper scrutiny is that it can possibly lead to “vast inconsistencies in instruction and highly variable learning experiences that can lead to differences in learning outcomes [among students].”
Larson said the increasing availability of online instructional materials has added a “new dimension to the curricular landscape” for math teachers and local educational agencies.
Indeed, curating online tasks requires a complex set of skills, which is not something that is not yet widely understood nor appreciated, he said. That’s why he recommended that educators leverage professional learning communities and colleagues within a school when making web-based curricular selections.
NCTM said in its statement that a coherent curriculum at the school and district level is important because curriculum is often what establishes learning goals and helps teachers see and understand the multiple pathways that students might take through a mathematics learning progression.
However, they said to exercise caution when curating open education resources, as the risks can include:
- Teachers who are provided with little or no support for setting mathematical goals and organizing resources into a coherent learning progression.
- Resources students have access to will vary widely from teacher to teacher and school to school, reinforcing inequities in situations where students who struggle are more likely to have inexperienced teachers.
- School communities will abandon the process of vetting and adopting agreed-upon curriculum resources, creating a lack of transparency and accountability.
“I want to be clear that NCTM does not oppose open educational resources and, in fact, we provide online educational resources for our members and others,” Larson said.
“We’re simply stating that in this era, when so much is available now online, that we must be cautious in how we select and use those tasks to ensure they fit within an overall coherent learning progression and that teachers, when they engage in the selection of these sorts of tasks, really need to work together and not in isolation to ensure that each and every student still has access to a high-quality curriculum,” he said.
Emily Ann Brown covers education technology and STEM education issues for LRP Publications.
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