Skillful and Flexible Teaching with the Quantile Framework for Mathematics

In the January 2011 edition of Educational Leadership (subscription required), Deborah Loewenberg Ball and Francesca M. Forzani argue that, although the general layperson believes teaching is a simple and non-specialized skill, there are, in fact, many aspects to teaching that require specialized training, cultural awareness, empathy, and insights into student thinking and processing, and in-depth insight into the content they are teaching.

Teaching is a complex, multi-faceted skill because, to be effective, teachers must first identify   how each student’s experience base influences his reasoning powers. Educators must diagnose various student misunderstandings of content using more than intuition. The “high-leverage practices” that Ball and Forzani suggest include becoming familiar with the family or cultural background, utilizing sophisticated questioning skills in order to identify any misunderstandings, developing an awareness of student needs based upon their differing learning styles, as well as accessing intricate content level knowledge.

Additionally, teachers must help students make and articulate those connections. One free resource available for mathematics teachers that will help them organize those connections and order topics in mathematics is The Quantile® Framework for Mathematics.

In the Advanced Search of the Math Skills Database or in the Quantile Teacher Assistant, teachers can find Knowledge Clusters for various math skills and concepts as they align to the curriculum of their state and grade level. Each skill or concept within the Quantile Framework has a Knowledge Cluster that consists of the prerequisite and supplementary skills. The prerequisite skills and concepts are those skills or concepts that are necessary in order to be successful with the identified or primary skill in question. Additionally, the Quantile Framework also provides impending skills – the skills that come next, the skills that a primary skills is building toward.  The Quantile Framework makes it possible for an educator to transform separate skills in mathematics into a structured study of the content.   The Quantile Framework also makes it possible to easily access task analysis for any particular math skill or concept.  Additionally, each skill or concept is organized by Quantile measure – essentially a difficulty measure – which offers insights into the difficulty of the material they will be teaching in a unit.

With time and thoughtful consideration, mathematics teachers will find the Knowledge Clusters helpful in developing their approaches for new material, informing their expectations of student reasoning, and identifying which lessons students will manage easily based upon the Quantile measure of the identified math skills and concepts that match that lesson.

Students in North Carolina, Wyoming, Kentucky, Oklahoma, and West Virginia already receive Quantile student measures on their NCLB assessment.  And partner products, like Scholastic’s SMI report student Quantile measures every time a student completes an assessment.  If you haven’t already, be sure to take a look at the free resources on the Quantile website, including the Math Skill Database and Quantile Teacher Assistant.

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