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.
Guest Blog Authors:
Malbert Smith III, Ph.D., MetaMetrics President and Co-founder
Jason Turner, MetaMetrics Director of Professional Development
U.S. students are consistently outperformed in mathematics by their international peers. While 2011 NAEP results show a modest increase in mathematics performance, only about one-third of our eighth-grade students achieved the proficiency level. The truth is that many U.S. students graduate unprepared for the challenges they will likely face in college and careers, and this trend will continue to negatively impact our students’ and our nation’s ability to compete globally.
The Common Core State Standards, which nearly all states have adopted, provides policy makers, educators and parents with a road map for preparing students for postsecondary mathematics demands. But, as districts and schools begin to implement the Standards, they must also have access to the curriculum resources to make this aggressive drive toward real-world readiness a reality for all students. The Quantile® Framework for Mathematics—and the many free tools that support its implementation—is a unique resource for providing the targeted instruction that both striving and struggling students need as they ready themselves for the demands of their academic and professional pursuits.
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A thank you to Jason Turner for contributing this guest post blog about maintaining math skills over the summer to the Math Hub. Jason is the Director of Professional Development at MetaMetrics Inc.
Summer is finally here. And for many students, an extended summer break means time spent with friends and family, summer jobs, camps, and well-deserved vacations. Unfortunately, for many students, a break in the school year also means a break from all academic activity, meaning that they could return to school with their math and reading abilities somewhat diminished from just three months earlier. This loss has been well researched, and many education reformers now consider fighting summer loss an important part of any serious education reform agenda.
The effects of summer learning loss in both math and reading have been well documented. Low-income students are especially susceptible to the corrosive effects of long interruptions in academic life. The reasons for this are complex, but it’s safe to say that in many cases low-income students do not enjoy the same academic opportunities (e.g. summer camps, academic retreats, tutors, etc.) as their high-income peers. Add in the fact that many low-income students may go home to text-free zones (lacking books, magazines, and newspapers) and it’s easy to see why the reading skills of so many students deteriorate over the summer months.
In mathematics the picture is even more dismal. Regardless of socio-economic levels, students experience a significant amount of learning loss in math. Though many states and districts offer multiple and intensive summer reading initiatives, too few have undertaken serious efforts to address the loss students experience in math. Admittedly, keeping students engaged in math activities during the summer is more difficult than engaging them in reading. There simply aren’t as many meaningful math resources available for students.
While it’s easy to dismiss summer slide as a fact of academic life, the consequences are profound. The learning loss that occurs each summer has an unfortunate cumulative effect. Add up the amount of learning loss over twelve consecutive summers, and the resulting gap is the difference between those that are prepared for the rigors of college and career and those that are not. It’s easy to see that any hiccup in the trajectory toward college and/or career represents a setback that can make a tremendous difference to where the student ends up.
One possible solution to summer slide would be to increase instructional time, which need not always mean more time in the classroom. Extending the school year can be done in a variety of ways, including providing students with resources that supplement and reinforce the skills and concepts acquired during the school year. In math especially, it is imperative that students continue to stay engaged in activities. Engagement does not necessarily mean learning new concepts and skills. During an academic hiatus, staying engaged in math may simply be brushing up and supplementing last year’s lessons.
For example, one specific solution is offered by MetaMetrics’ free online tool, Math@Home (full disclosure: I’m the Professional Development Director at MetaMetrics). Math@Home provides students (or educators or parents) with free, targeted math resources – like websites, worksheets, video tutorials, skill sheets, etc. – that support the textbook lessons studied throughout the year. Math@Home relies on a student’s Quantile measure as a way to target the student at just the right level of difficulty, though students can still use Math@Home even without a Quantile measure. Students and teachers have the ability to build specific lists of math resources to save for a later date. Best of all, Math@Home’s social networking features allow students and teachers to share multiple resource lists with others through e-mail and even post favorite math activities to Facebook and Twitter.
There are any number of ways to support year-round learning. Math@Home is just one way that educators and parents can keep students engaged in math activity throughout the summer months. As the focus shifts from proficiency to college and career readiness, it is critically important that educators and parents ensure that summer months are used to reinforce last year’s lessons and to prevent the pernicious effects of summer learning loss.
Our friends at MetaMetrics, who last month gave us an article on Quantile® Knowledge Clusters, here describe the value of the Quantile Teacher Assistant in planning out math instruction.
The Quantile® Teacher Assistant utilizes The Quantile Framework for Mathematics to provide teachers with a practical tool for differentiating mathematics instruction. The Quantile Teacher Assistant has information about the QTaxons associated with teachers’ own state standards. More than 23 state standards and the Common Core State Standards have been aligned with the Quantile Framework, and new states are added each month. Teachers can use their state standards to access the knowledge clusters and the free resources that are associated with each skill.
With the Quantile Teacher Assistant, teachers first identify the state, grade and standard they plan to teach. Based on this information, a three-tiered page of the QTaxons related to that standard is presented, with the focus QTaxon(s) listed in the middle column. Surrounding the focus QTaxon(s) are prerequisite QTaxons in the left column, supplemental QTaxons below the focus QTaxon(s), and impending QTaxons in the right column:
- The focus QTaxon(s) describes measurable skills connected with the chosen standard that are in the learning frontier of a student. The student is prepared for instruction in the skills associated with the focus QTaxon(s).
- Prerequisite QTaxons represent skills that must be learned before the student can fully understand the focus QTaxon skills. Prerequisite QTaxons can be used to identify extra support for students who are not at the level of the focus QTaxon(s).
- Supplemental QTaxons describe topics that will support or enrich the skills associated with the focus QTaxon(s).
- Impending QTaxons represent skills that extend beyond the focus QTaxon(s) and can be used to provide a challenge and breadth to students who have already received instruction and experienced success with the focus QTaxon(s).
By clicking on “(More)” after each QTaxon description, a teacher can access additional teaching resources for each QTaxon, such as activities and worksheets, web-based games and instructional videos, and key vocabulary words.
An additional feature of the Quantile Teacher Assistant is the ability to use the Quantile measures of students in a class to identify their likely success with an identified set of QTaxons. On the QTaxon display directly above the focus QTaxon is a bar with two sliders. The sliders can be moved to the left or right to capture the range of students’ Quantile measures. This range determines the color of the QTaxon boxes. Yellow/orange boxes identify the QTaxons that are within the range of the students’ Quantile measures. Green boxes identify the QTaxons that represent the skills that are below the students’ Quantile range and describe skills they can likely use in problem-solving situations. Red boxes identify the QTaxons that are above the Quantile measures of the students’ ability levels. These skills will be great enrichment to challenge the learners who can move forward through instruction quickly.
The Quantile Teacher Assistant takes the guesswork out of differentiating instruction in today’s diverse mathematics classrooms. By using the Quantile Teacher Assistant, teachers no longer need to search the internet for resources to ensure they reach all learners. The Quantile Teacher Assistant provides teachers with multi-leveled assistance for teaching the entire math curriculum with numerous resources that include lesson plans, worksheets, video tutorials, demonstration tools and worksheets.
Photo credit: http://qta.quantiles.com
Many thanks to our friends at MetaMetrics Inc. for contributing a useful guest blog entry about how teachers can match all students to the right instruction with the Quantile Framework for Mathematics.
The Quantile® Framework for Mathematics
is a tool teachers can use to make student test results useful at the classroom instruction level. A student’s Quantile measure (test score) provides information about which mathematical skills students are ready to learn in the classroom. These skills are called QTaxons. Once a teacher knows a student’s Quantile measure, the teacher knows which QTaxons the student is ready to be introduced to in the classroom. Underlying each QTaxon is a knowledge cluster that offers classroom teachers a wealth of information about the skills that come before the QTaxon skill and those that follow it. This information can be tremendously helpful in guiding decisions about instructional strategies.
A QTaxon is linked to prerequisite, supplemental and impending QTaxons that illustrate the developmental and inter-connective aspects that are so important in the study of mathematics. A prerequisite QTaxon includes the skills and concepts that should be addressed or mastered by the student before instruction on the focus QTaxon. A supplemental QTaxon includes skills that can enrich a topic or help teachers and students make connections across the spectrum of mathematical concepts. An impending QTaxon can provide insights into the levels of mathematics skills beyond the focus QTaxon.
Below is an example of a knowledge cluster in the Quantile Framework using a focus QTaxon about 'unit rates'.
QTaxon: “Calculate unit rates to make comparisons.”
This QTaxon has a Quantile measure of 830Q. (Each QTaxon has a Quantile measure that estimates its difficulty at the introductory level.)
- Use proportional reasoning to solve problems. (530Q)
- Identify equivalent decimals and fractions at the symbolic level, including simplifying fractions. Explain the equivalence. (710Q)
- Write a ratio to compare two quantities. (210Q)
- Convert measures of length, area, capacity, weight, and time expressed in a given unit to other units in the same measurement system. (820Q)
- Describe the probability of an event using a fraction or ratio. (440Q)
- Determine the ratio or rate of change of a relation given a table or graph. (810Q)
- Use dimensional analysis to rename quantities or rates. (950Q)
- Use scale factors to reduce and enlarge drawings on grids. (990Q)
With some Quantile information – the student’s Quantile measure, the Quantile measure of the focus QTaxon, and the Quantile measures of the prerequisite, supplemental and impending QTaxons – the classroom teacher can use assessment results to target instruction that addresses the needs of various populations of students in the classroom.
Consider the possibilities! By identifying the level of mathematics ability for students, educators can differentiate instruction, forecast performance on new material or assessments and benchmark progress throughout the year. The supplemental QTaxons in the knowledge cluster provide instructional tips on making connections across content strands and enriching instruction. The knowledge clusters found on the Quantile website at www.quantiles.com
are one aspect of the free materials available to teachers, students and families.
As students make their way back to school, teachers are gearing up to identify students’ diverse academic abilities and put them on an appropriate course of instruction. We’ve learned a lot about how to make that process easier and more effective by working with MetaMetrics on the release of our newest program, Scholastic Math Inventory. Today, our friends at MetaMetrics®* are sharing their expertise with you through this guest blog about differentiating math instruction. Enjoy!
Within a classroom, there will be a range of ability levels—from students who perform above grade-level to those who struggle to meet grade-level expectations. In order to meet the needs of individual learners, teachers will differentiate the math curriculum—by remediating or accelerating instruction, when necessary, and providing all students with opportunities to learn and grow. That’s where The Quantile Framework® for Mathematics can help.
The Quantile Framework measures student mathematical ability, the curriculum and teaching materials on the same developmental scale. Quantile measures help teachers determine which skills and concepts a student is ready to learn and those that will require more instruction. Educators can then use this information to better focus instruction to incorporate the necessary prerequisite skills that may be missing and accurately forecast understanding.
Quantile measures are available from a growing number of mathematics programs and assessments, including the new Scholastic Math Inventory. One of the benefits of these metrics is that they allow educators to link interim and benchmark assessments with year-end tests. Quantile measures provide valuable insights into students’ expected performance on these high-stakes tests so that educators can monitor whether each student is on track to meet the state standards throughout the school year. For more information on Quantile measures, visit www.Quantiles.com.
MetaMetrics, Inc. is focused on developing new methods of linking assessment with targeted instruction to improve learning. MetaMetrics built the Quantile Framework for Mathematics to provide a common, developmental scale for measuring student mathematics achievement, the difficulty of mathematical skills and concepts, and the materials for teaching mathematics.
As a Massachusetts resident, I have been watching the heated debate over the adoption of the Common Core State Standards in a state that prides itself on its consistently strong performance on national assessments. On Wednesday, Massachusetts education officials voted 9-0 to adopt the new national standards (see Wednesday’s Boston Globe article). With so many states suddenly sharing a core curriculum, a common assessment seems bound to follow.
It looks as though the United States is heading toward a much more unified education system. On the forefront of this movement is MetaMetrics with their Lexile and Quantile Frameworks for reading comprehension and mathematics, respectively. These measurement frameworks use a developmental scale, revealing both what students know and how their achievement compares to their peers’. They are ideal for use on a broad scale because schools, districts, and states can easily compare their results.
Already several states have begun using Quantiles to score their state assessments, and our newest program, Scholastic Math Inventory, uses the Quantile Framework to report student scores. The program, released today, is a fast and accurate computer adaptive math assessment system that tests student achievement by adjusting to student performance. It provides immediate, actionable reports to help inform instruction, so teachers can spend more time making sure their students are mastering the concepts and skills included in the Common Core Standards (or state standards).
What are your thoughts on the Common Core? For an interesting debate, check out http://www.nytimes.com/roomfordebate/2010/7/21/who-will-benefit-from-national-education-standards?ref=education.
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