Changing the Equation

We’ve written before on Change the Equation, a non-profit, CEO-driven organization dedicated to addressing our innovation problem and committed to driving  “the U.S. to the top of the pack in science and math education over the next decade”.  Good thing too.  Only 43 percent of U.S. graduates in 2010 were prepared for college work in math.  And Scholastic’s Math Hub reports on a new study from the Gates Foundation and Harris Interactive noting that many students report feeling unprepared for college courses in STEM (science, technology, engineering, and math) areas.  That’s too bad, because as Math Hub documents, the US will have over 1.2 million jobs in STEM related fields by 2018.

We applaud the recent work of the Obama administration, and organizations like Change the Equation, for their efforts to prepare students for careers in math, science, and technology.  But parents will have to do their part as well.  It’s critical that parents foster an appreciation of math and science in their children.  The effort to keep students engaged in year round learning starts at home.  As Malbert Smith recently wrote:

What we really need is for parents to create an environment at home that supports academic achievement.  To accomplish this shift in parental expectations and involvement, we will need to conduct a comprehensive and concerted campaign of education and support of parents.  Through PTAs, PSAs, teacher conferences, pediatrician visits, community meetings, library sessions, and many other outlets, we need a crisp message for parents on what they can do to promote their child’s achievement.  The critical importance of school attendance, of devoting space and time at the home for homework,  of turning off the TV and reading, and the use of public libraries, to name just a few, all need to be part of the message.

Those are just basic steps, of course.  It’s our hope that schools and districts will do more to increase instructional time and work to keep students engaged in math activity even over the summer months.  Parents will have to do their part as well by attending to their children’s work and ensuring that their children have the opportunity to complete their assignments. 

STEM related occupations are one of the fastest growing career clusters.  For the U.S. to remain competitive, it’s vital that schools and districts bolster their focus in mathematics and science and that students embrace STEM disciplines as the gateway to college and career readiness.

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.

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.

Math Doesn’t Suck

If you’ve been struggling to find strategies to motivate  teens, and especially young girls, to stick with math, check out these books by Danica McKellar:

McKellar is best known for her television role as Winnie Cooper in The Wonder Years, but she has added New York Times best-selling author to her resume with the publication of her books about math.  McKellar attended UCLA where she graduated summa cum laude in mathematics in 1998 and has made it her mission to show girls that they can succeed in math—that it is OK, and even cool to be good at math.  Through her books and her personal life as an actress and mathematician, McKellar hopes to break the stereotypes that have “trained girls from a young age to believe that math is too hard, too boring and just for boys, and that if they are smart, they can’t be popular or beautiful.” 

The real-world examples of how mathematics can be applied to various aspects of our lives helps make the math McKellar discusses relevant to teens. A few chapter titles from Math Doesn’t Suck provide a glimpse into why McKellar’s books are so appealing:

  • How Many Iced Lattes Can These Actors Drink?: Multiplying and Dividing Fractions… and Reciprocals
  • How Much Do You and Your Best Friend Have in Common?: Common Denominators… and Adding and Subtracting Fractions 
  • Sale of the Century!: Converting Percents to and from Decimals and Fractions

Her clear explanations of mathematical concepts make these books easy to understand.  Fans range from those who struggle with math to those who just want fun examples of how math concepts can be applied to various topics.

Math Education:Formulating the Problem

Math educator, Dan Meyer  (video) has argued that today’s math students have a profound impatience with irresolution.  That is, many math students employ a ‘plug and play’ approach to solving math problems, one where the formula is obvious, only the particulars have changed, and they can simply plug in the numbers for an obvious solution.  Meyer uses a number of textbook examples demonstrating that each word problem is essentially the same – a perfectly formulated problem that requires only the application of the formula for resolution. 

Building on Einstein’s observation that, “…the formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill,” Meyer has taken a much different approach with his math students.   Meyer’s approach is much more conversational  and focuses on the formulation of the problem, an approach, in Meyer’s words, in which ‘math serves the conversation’ – not the other way around.  (more…)

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.