Common Core, the Quantile Framework, and Math Excellence

Blog by:
Malbert Smith III, Ph.D.,
Co-Founder and President of MetaMetrics

 

Just last week, I was invited to speak at the CCSSO Rural Chiefs Conference in Kansas City on the topic of “Supporting Math Differentiation in a Common Core World”.  While there is much written and discussed on the idea of differentiated instruction, in practice there are limited tools and resources to support math differentiation, a deficiency well-documented in this recent Ed Week article, ‘’Educators in Search of Common Core Resources”. 

A theme permeating much of my presentation was the neglect of math in our country.  By almost any measure, e.g. instructional time, professional development, number of assessments, instructional programs, etc., math runs a distant second to reading in the amount of instructional attention given.  At least part of the challenge we face in addressing our math crisis in K-12 education will require that we remedy this neglect.

In my suggestions for addressing this imbalance I focused on four critical strategies. While the adoption of the CCSS is a significant first step in the right direction, its real success will rest upon how effectively we implement these standards.  It is critical that we recognize that math – like any other skill - can be learned.  Too often we subscribe, consciously and unconsciously, to the notion that math achievement is an inherent ability, as if math achievement was based on a “math gene”.  If we take more of a Carolyn Dweck growth perspective, as opposed to a fixed mind set, we will go a long way toward promoting the idea that math achievement is possible for all of our students.

Secondly, we need to build math tools and resources that support differentiated instruction.  Once, when leading a math workshop for a school district, the head of the math department informed me, tongue in cheek, that all math teachers know how to differentiate instruction:  “We say it louder and we repeat it.”  Yet I suspect we have all seen variations of this model, this when we continue to drill a student on a math problem or concept to no avail.  Meaningful differentiated instruction is really only possible when we are able to measure a student’s math level and the difficulty of the math concepts and skills on a common scale.  This possibility is now a reality with the Quantile Framework for Mathematics.  Once you know a student’s Quantile measure you know what math skills they are ready to learn.  And just as importantly, one can make sure that the learner has acquired the necessary pre-requisite skills.  Unfortunately, we often continue to employ the “repeat louder” model and fail to provide differentiated content and instruction to meet the unique needs of the learner. 

A third and critical step towards applying the math growth trajectory for all students is mitigating the devastating effects of summer loss.  While summer loss in reading mostly impacts our low income students, summer loss in math impacts students across socioeconomic levels.   During the summer months, we need to draw the same attention to math as we currently do to reading.  On our website (www.quantiles.com) we have built a free utility, Math at Home, which teachers, parents, and students can use to address this issue.

Fourth, students need access to personalized learning platforms that promote the basic elements of deliberate practice. Differentiated instruction through personalized learning platforms enable the learner to move through a learning progression of math skills at the right time, pace, and level.  The underlying engines for the delivery of content within these platforms will require the use of vertical scales, like the Quantile scale, so that the math level of the learner can be matched to the appropriate mathematics material.  Computer adaptive delivery of content and assessment require a common vertical scale that links student to skills.  And the Quantile Framework for Mathematics provides that link.

With the advent of the CCSS we are starting to have the right national conversations about mathematics instruction.  At MetaMetrics, we are dedicated to building the resources and tools to support differentiated instruction and help all students improve their math skills.

Engaging Middle School Students in Math

In a recent article published by MindShift, journalist Annie Murphy Paul questioned, “What is it about middle school and mathematics?” Indeed, research shows that it is during the middle school years that students begin to lose interest in math.  This disengagement often persists, which puts these students at a disadvantage in later schooling and even in their future careers.

Researchers from the University of Sydney in Australia investigated this middle-school phenomenon, looking specifically at factors that caused students to switch on or switch off in mathematics.  The Journal of Educational Psychology recently published the findings, based on data drawn from over 1,600 Australian middle school students.

One of the primary factors the researchers identified in turning students onto math is self-efficacy—students’ perceived capabilities to learn or accomplish mathematical tasks.  According to the published article, teachers can foster self-efficacy in students by maximizing opportunities for achievement.  For example, educators should build on skills students have already mastered and help students develop appropriate goal-setting (i.e. goals that are challenging but still realistic).  

Another critical factor they identified stems from students’ perception of the value of math.  Educators and parents can emphasize the importance of math and the development of math-related skills by demonstrating its usefulness in the real world.  In addition, it is important that educators and parents model positive attitudes toward math.

Improving Mathematical Problem Solving: A Research-Based Practice Guide

What Works Clearinghouse (WWC), a division of the Institute of Education Sciences (IES), publishes research-based education practice guides that address current educational challenges.  The most recent practice guide, Improving Mathematical Problem Solving in Grades 4 Through 8, provides five recommendations that educators and curriculum developers can use to help students in grades 4 through 8 develop better skills in mathematical problem solving. 

Unlike many of the mathematical educator guides floating around the Web, these IES publications are developed through rigorous research and the validity of this research is also evaluated.  After reviewing all available studies pertaining to the topic at hand, the authors of the practice guide assign a “level of evidence” (strong, moderate, or minimal) to each recommendation.  During this evaluation process authors examine individual studies and then consider the whole evidence base, evaluating factors such as the number, quality, and design of the relevant studies.  For more information on the role of evidence and the criteria for each level, see page 3 of the practice guide.  

Check out the practice guide and let us know what you think!  How helpful are the five recommendations?  Is the strength of evidence rating important to you? Does the evidence surprise you in any way?