Scholastic Math Inventory Receives High Marks

The National Center for Response to Instruction (NCRTI) rated the Scholastic Math Inventory (SMI) with highest marks for validity and reliability as a progress monitoring tool.  Progress monitoring allows educators to better understand student achievement over time, which is often difficult.  Many assessment tools may diagnose specific topics in which students struggle but often do not provide sufficient feedback to help educators monitor student growth over time or inform their instruction.

Response to Intervention is a methodology for identifying and providing timely intervention for struggling students.  With funding from the US Department of Education, the American Institutes for Research and researchers from Vanderbilt University and the University of Kansas formed NCRTI to assist states and districts in implementing proven Response to Intervention strategies.  NCRTI rated SMI as offering “convincing evidence” for the following areas:

•             Reliable performance level score

•             Valid performance level score

•             Availability of alternate forms

•             Sensitivity to student improvement

•             End-of-year benchmarks identification

•             Rates of improvement specification

SMI provides computer-adaptive benchmark assessments for students beginning in grade two through a first course in Algebra. Each time a student completes an assessment, SMI provides a student with a metric called a Quantile® measure.  Because all of the assessments, from grade two through Algebra I, use the same Quantile metric, this student measure can be used by teachers to monitor student growth, not only within a school year but also from year to year.

The student measure also helps teachers analyze students’ readiness for instruction on mathematics skills and concepts.  The Quantile® Framework for Mathematics also provides Quantile measures for individual skills and concepts taught in grades two through Algebra I (and actually more than that – kindergarten through high school).  A teacher can use the measure of the concept being taught in comparison with the student measure to gain insight as to whether the student is ready for instruction on that particular topic.  If the student measure does not match with the measure of the skill or concept, the teacher can identify other related topics with measures that do match.  The measure provided by the SMI assessment can be used to target instruction and provide students with related material for which the student is prepared.

The Quantile Framework can work with most mathematics assessments to provide a student Quantile measure.  Please visit the Quantile website to see the instruments  that currently report Quantile measures.

Pushing Through to the Top

Interesting take over at Scholastic Math Hub on what the common core portends for the publishing world.  Hung-Hsi Wu, a math professor at UC-Berkeley, has argued that the common core offers a unique opportunity to publishers – the opportunity to recreate far more effective mathematics textbooks, textbooks which capture which capture the depth and richness of the new standards.  Specifically, Wu is hoping for textbooks that capture the inter-relatedness of all math content:

Preparing to teach proper school mathematics is not about learning a craft, but, rather, a discipline that is cognitively complex and hierarchical.  Each topic, no matter how basic, is essential to some future topic.

Wu’s right.  And the interconnectedness of each strand is well illustrated by the Quantile Framework, which not only places student and task difficulty on the same scale, but also provides the prerequisite skills for each and every math skill and concept.  We share Wu’s hope that the common core will provide the impetus for richer and more comprehensive math textbooks.

Math Prize for Girls

Congratulations to Victoria Xia for winning the Math Prize for Girls at M.I.T.  Xia, a 15 years old high school sophomore, won first place and a $25,000 prize for taking first place.  The contest was sponsored by Advantage Testing Foundation and consisted of 20 challenging math problems to be solved in 150 minutes. Xia has won previous math distinctions such as helping the US team win a gold medal at the 2011  Girls Mathematical Olympiad and also a honorable mention at last years Math Prize for Girls contest.  Kudos to Victoria!

It’s refreshing to see students take a deliberate and focused interest in mathematics.  With the recent focus on STEM education, along with increased demand for math and engineering majors in the workplace, it’s good to see U.S. students committed to high level math.  Our own contribution to improving student math achievement is the Quantile Framework for Mathematics, which allows teachers to differentiate math instruction for struggling students.  Plus, tools like Math at Home allow students to engage with targeted math resources all year long.

Implementing the Common Core: the Quantile Framework

The adoption of the Common Core State Standards is promoting the development of curriculum pathways that most states will collectively implement.  Many states have developed crosswalks or configuration maps to aid in this transition. Currently, most states are still waiting to see how the new common accountability assessments will be designed for the implementation of the new standards. 

According to the Great Lakes Comprehensive Center, Ohio, Illinois, Minnesota, Michigan, and Indiana formed the Midwest Common Core consortia to work together to plan the best implementation.  “The Midwest Common Core Consortia creates an avenue for the five states to work together to share resources, knowledge, and promising practices to improve implementation of the Common Core State Standards across the region. The work of the consortia is focused on the areas of leadership, communication, alignment, teaching, and learning.”  Additionally, many states’ department of instruction have joined forces with CCSSO by employing the Common Core Standards Collaborative that focus on six principles of teaching and learning.  The implementation of the standards is still being discussed at the state level and only small populations of teachers have gained the tools that will enable them to transfer methods of instruction to the new standards.

Yet, during this transition, teachers in the classroom are beginning the school year still searching for more specific directions regarding instruction that will incorporate the new Common Core State Standards as well as the old state standards.  The Quantile Framework® of Mathematics can help teachers do this through the use of its website.  Quantile.com offers teachers the ability to find free, internet based resources aligned to both the former year’s state standards and the new Common Core standards. 

Through the website, teachers can access the Math Skills Database, by activating the Advanced Search tool. With this search engine teachers can create a list of their state’s curriculum standards and Common Core State Standards for the grade level they are teaching.  This tool gives teachers the ability to compare the two standards and find free resources that will complement both sets of standards. 

Users also have access to the “knowledge cluster” of each skill or concept demanded by the standard which provides a means of task analysis.  Having access to these knowledge clusters allows a teacher to reach struggling students who may be unfamiliar with some of the required prerequisite skills.

The implementation of the new Common Core State Standards will require patience and planning to best allow educators to thoroughly address the new standards.  In the meantime, the Quantile Framework for Mathematics can provide support for educators as they move through this transition. 

Todays Discoveries Aid Tomorrow’s Understandings!

According to eSchools News, a study released by the University of Missouri suggests that students beginning first grade with a good understanding of number lines and basic math facts were more successful in math skills over the next five years. This should be no surprise – just as building a house on a strong foundation makes for a stronger home, building new math skills on a strong foundation of math knowledge makes for a more robust understanding.  These recent findings also suggest that teaching ‘a mile wide and an inch deep’ may not fully develop a conceptual understanding of key math concepts. Young students need a lot of modeling, time, and a variety of experiences to practice math skills for true understanding.

One way to help develop these skills at an early age is to incorporate the Quantile Framework for Mathematics in specific math lessons. Utilizing the Framework allows teachers to determine which prerequisite skills are necessary for success with a particular math skill or concept, allowing educators to target struggling math students with the appropriate prerequisite skill.  For example, if a third grade student is working on estimation for sums and differences with whole numbers he/she must first be able to:

  • Make reasonable estimates of the number of objects.
  • Subtract 2- and 3-digit numbers with regrouping.
  • Round whole numbers to a given place value.

These prerequisite skills are necessary for students to understand before they are able to extend to estimation skills when they add and subtract whole numbers.

And the Quantile Framework allows teachers to go even lower: if a student is having trouble making reasonable estimates of the number of objects the knowledge cluster for this skill may indicate that he or she is having trouble with:

  • Use counting strategies for totals to 100 that include counting forward, counting backwards, grouping, ten frames, and hundred charts.

The Quantile Framework allows for the possibility of identifying areas where students are deficient.  Furthermore, for educators looking to differentiate math instruction, the Quantile Framework can serve as a valuable classroom resource by helping teachers target lessons to the needs of the students. Additionally, the Quantile Framework is linked to a variety of free tools and resources that – in addition to providing tools for task analysis – provide access to a host of free targeted resources, including worksheets, online tutorials, videos, websites, literature guides, and classroom activities. 

As we enter the new school year (and as many students are suffering the effects of summer slide), be sure to check out the Quantile Framework as a way to help struggling math students.

Welcome Back: Starting with Success

A brand new school year is here, offering teachers, students, and parents the opportunity for a fresh and positive outlook for the coming months in the classroom. In the article Starting the School Year Right in the August edition of The School Administrator, Thomas R. Guskey emphasizes that the first two weeks of school are critical for students and parents to feel good about what the students know and what is possible to achieve in the coming months.

Many teachers try to formally or informally assess the ability level of students at the beginning of the school year.  But Guskey cautions that the first assessments need to “help students experience successful learning” during the first two weeks of the year.   It may be important for the educator to firmly establish what students know rather than what they don’t know.

Guskey’s right.  Educators can help put students at ease early in the year by ensuring that the material they receive is at or near their ability level.  With regards to reading, many students across the United States are assessed in the spring and many states report Lexile measures as an indication of a student’s reading level.  The student Lexile measure allows educators to match students to targeted material, a useful way to develop student confidence and promote motivation. 

Because reading levels in a single classroom vary considerably, teachers would be well-advised to differentiate material so that students are able understand the text and experience success.  The Lexile Framework for Reading offers tools to measure text as well as ‘Find a Book’ tool, which provides the Lexile measures of trade books and textbooks in all kinds of categories and genres. Matching the text measure to a student Lexile measure can be a strong asset for helping struggling readers be successful.

Similar to the Lexile scale, the Quantile Framework for Mathematics utilizes a scale that places the math level of students and the difficulty of the math skills and concepts on the same scale.   The Quantile measure for specific mathematics skills and concepts can be found at the Quantile website where the topics are aligned to state standards as well as to the Common Core State Standards.

When student Quantile measures are available from state assessments or other products aligned to the Quantile Framework, then targeting student needs in the mathematics classroom becomes much more manageable, allowing content to be tailored to the student ability level as well.

Dr. Guskey offers numerous suggestions for facilitating positive experiences for students. Critical stakeholders include not only students and teachers, but also parents and administrators. This community of supporters has a strong influence over the long-term success of our children. We often speak of differentiating instruction to meet the needs of our students. But differentiating can mean much more to the students if they recognize their abilities and use that information to grow into motivated and self-assured students throughout their academic career.

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.

A Museum for Math…Finally!

In Curriculum Matters, Education Week’s blog, Erik Robelen writes about a new math museum that will “strive to ‘reveal the wonders’ of math.” 

The Museum of Mathematicsstrives to enhance public understanding of mathematics” states the MoMath website. “Its dynamic exhibits and programs will stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. The museum’s activities will lead a broad and diverse audience to understand the evolving, creative, human, and aesthetic nature of mathematics.”

MoMath will not open until 2012, however activities such as letting visitors ride tricycles with square wheels along a track with curving terrain are being tested with MathMidway, a traveling exhibit currently at the Museum of Nature and Science in Dallas, TX until May 16, 2011. The exhibit will return to New York City for the World Science Festival Street Fair on June 5, 2011. It will then make an extended stay at New Jersey’s Liberty Science Center from October 7, 2011 through January 22, 2012.

The museum’s founder, Glen Whitney makes the point that the joy of discovering math has been lost to the “tyranny of the curriculum and the almost treadmill of standardized testing.” He goes on to say that there is beauty in the subject. “Math is evolving. It’s an act of human endeavor.”

Here at MetaMetrics, we couldn’t be more excited about the museum.  This will be the only math museum in the United States and hopes to make the point that mathematics illuminates the patterns that abound in our world. We’ve worked hard to show that mathematics is not only necessary, but that it can be fun and accessible for all learners. 

That’s why in 2004 we developed The Quantile® Framework for Mathematics. This practical metric allows educators to measure both student mathematical achievement and the difficulty of math skills and concepts.  The use of the Framework is complemented by a number of mathematics utilities that assist educators and parents by allowing students to access differentiated math resources.  If you haven’t already, I encourage you to take a look.

Conceptua Fractions Adds Quantile Measures

Conceptua Math CEO Arjan Khalsa said it best: “Fractions are tough to teach and equally difficult for students to learn.” The good news is that his organization has responded by providing educators with a valuable resource to help struggling students. Conceptua Math has added Quantile® measures to its innovative Conceptua™ Fractions program, allowing teachers to accurately match students with instructional activities at their readiness level.

Conceptua Fractions comprises more than 400 practice activities spanning grades 2-7. Each activity has a Quantile measure that describes its difficulty level. Educators can compare this Quantile measure with a student’s Quantile measure to determine if the activity meets his or her learning needs, or if the student needs to review some other prerequisite skills or concepts first. Students are likely to have the most success solving problems within a recommended Quantile range of 50Q above and below their Quantile measure.

Click here for more information on Conceptua Fractions, like how it uses visual models, sequenced activities and verbalized feedback to challenge students based on their own learning styles and to keep them engaged throughout the instructional process. The program also offers integrated assessments that allow educators to diagnose student misconceptions, choose remediations and monitor progress as students advance through the core curriculum. Quantile measures for both the complete Conceptua Fractions curriculum and free tools are available too.

Crisis of Confidence: U.S. Teens Worry Over Nation’s Math Ability

A recent Education Week article (subscription required) suggests that our teens may be overconfident in their math and science abilities. Out of 1,000 students surveyed, many reported feeling confident in their math preparedness and 68 percent agreed that math and science skills will be a requirement of most jobs, with 58 percent reporting a desire to work in a related field. However, when asked which country was best at math and science, 67 percent selected Japan or China and only 44% viewed mathematics as important to “solving society’s big problems.”

Intel, the corporation that conducted the study, believes that this study indicates the bar needs to be raised for American students. Shelly Esque, vice president of Intel’s Corporate Affairs Group, said: “We need innovative programs that celebrate not just “making the grade,” but taking the challenging courses that will prepare our students for the careers of the future.”

The Common Core State Standards Initiative is an attempt to align state curriculum standards with the demands of college and career.  That’s been our focus at MetaMetrics as well, and we’ve put together a variety of resources to demonstrate how both the Lexile® and Quantile® measures support the Common Core State Standards’ goal of preparing all students for college and careers.   Going a step further, we’ve also developed utilities that match readers to books of their choice based on their current reading level.  And our mathematics utilities assist educators and parents by allowing students to access differentiated math resources.  If you haven’t already, I encourage you to take a look.

MetaMetrics is an educational measurement organization. Our renowned psychometric team develops scientific measures of student achievement that link assessment with targeted instruction to improve learning.