We Thought We Should Mention

As the new Common Core State Standards are being implemented in math classrooms around the U.S., middle school educators are facing two challenges:

1. Keeping middle school students interested in learning

2. Meeting the rigor of the new standards

Here’s a little hope for math teachers: A recent survey of middle school students by Raytheon Co., indicates 7 out of 10 students like math!  The survey also indicated that Math is the third most popular subject just behind gym and art.  That’s good news.    Another finding in the survey sheds light on how students prefer to learn new subjects.  48% of students prefer hands-on learning, while  37% of students report preferring to learn with computers.  Dead last in order of preference is lecture from a textbook. 

Fortunately, the Quantile Framework for Mathematics provides teachers easy access to hands-on, computer based, free resources to help spark student interest in learning mathematics.  These resources are aligned with Common Core State Standards, and all 50 state curriculums and are available in the Math Skill Database and Quantile Teacher Assistant.

Additionally, these easy to use tools offered at no cost to educators allow for differentiating instruction to meet the needs of all students without the difficulty of navigating through endless math websites. Dr. Malbert Smith and Jason Turner, in a recent white paper wrote, “As the rigorous Common Core State Standards in Mathe­matics move from the adoption stage into the implemen­tation stage, it is imperative that classroom educators be given the tools and resources that will allow them to move beyond whole-class instruction and begin to differentiate for math students at every level.”  The Quantile website simplifies teacher efforts to locate and utilize relevant materials because these resources are attached to each Common Core standard.

As the implementation of the Common Core standards becomes a reality the Quantile website can be a vital tool in the classroom.  In addition to the tools mentioned for the teacher, the free tools offer a meaningful way to differentiate math instruction for all learners and to link students to resources in a way that can be engaging and fun.

Because a high number of parents report feeling intimidated by math concepts we can assume that uncertainty and unease translates into a failure to routinely discuss math skills and concepts with their own young children.  Even parents not steeped in the technical details of reading comprehension and literacy development often spend time reading with their children; and informal literacy activities, e.g. asking a young child to sound out a word, look at an illustration for context clues, or pick their favorite book are a regular part of many parent’s nightly routines.  So it’s not surprising that math discussions and activities often get left behind.  As this recent article by Annie Paul makes clear, failure to introduce young minds to mathematical concepts at an early age can have serious impact on the student’s readiness to learn math skills later in life:

But speaking to them about numbers, fractions, and decimals? Not so much. And yet studies show that “number talk” at home is a key predictor of young children’s achievement in math once they get to school. Now a new study provides evidence that gender is part of the equation: Parents speak to their daughters about numbers far less than their sons…

The frequency of number talk in the children’s homes had a big impact on how well the youngsters understood basic mathematical concepts such as the cardinal number principle, which holds that the last number reached when counting a set of objects determines the size of the set (“One, two,
three—three apples in the bowl!”). A subsequent study by Levine found that the kind of number talk that most strongly predicted later knowledge of numbers involved counting or labeling sets of objects that are right there in front of parent and child–especially large sets, containing between four and ten objects.

Paul goes on to offer a set of helpful suggestions for introducing ‘number-talk’ early on in a child’s development and urges that parents attempt to incorporate number talk at least as often as they talk about words and letters:

• Note numbers on signs when you’re walking or driving with children: speed limits and exit numbers, building addresses, sale prices in store windows.
• Ask children to count how many toys they’re playing with, how many books they’ve pulled out to read, or how many pieces of food are on their plate.
• Use numbers when you refer to time, dates, and temperatures: how many hours and minutes until bedtime, how many weeks and days until a holiday, the high and low the weatherman predicts for that day.
• With older children, math can become a part of talking about sports, science, history, video games, or whatever else they’re interested in.

We couldn’t agree more.  Mathematics has received far less attention than literacy at both school and at home.  It’s our hope that parents will recognize the importance of numeracy and that lessons that important must start at home.

This recent Education Week Teacher article, “Survey: Teachers Place Little Value on Standardized Tests” prompts the consideration of the purposes of standardized testing in the United States. A recent report published jointly by Scholastic and the Bill & Melinda Gates Foundations states that only 28% of educators believe the state-required standardized tests inform or gauge student achievement.

Additionally, survey respondents worried that many students fail to take standardized test seriously and therefore, do not perform as well as they do on quizzes and test administered during classroom instruction.

It’s important to point out, however, that standardized testing can actually be used to inform instruction if those assessments have been linked to The Lexile^® Framework for Reading and The Quantile^® Framework for Mathematics. When standardized tests are linked to these frameworks student score reports can identify their levels of ability, monitor growth over time, and inform instruction that in a way that allows educators to target student ability levels for both reading and mathematics.

The Lexile framework offers a developmental scale that teachers can use to match text to a student’s reading ability. The Lexile Find a Book site offers an abundance of book titles with Lexile measures so that parents and teachers can match the material appropriate to the student’s interest and reading ability level. The Quantile framework is another developmental scale that teachers can use to match student’s mathematics ability to the difficulty of mathematics topics at the introductory level. These various topics in mathematics can be found at the Quantile website where most major skills and concepts have been aligned to state standards.

If standardized tests are linked to The Lexile Framework for Reading or to The Quantile Framework for Mathematics, the assessment allows educators to differentiate in meaningful ways.  If you haven’t already check out these valuable resources, be sure to take a look.

Every mathematics teacher wants to be able to help their students learn more math and learn math better.  The typical mathematics classroom contains a diverse range of students who differ in their readiness to learn.  Quality mathematics teachers seek new strategies to reach their students and help them grow.

Differences in learning occur for a variety of reasons.  Some students may have academically encouraging homes.  Some students may have academic learning disabilities. Other students may have physical differences.  And just as with physical growth, some students may simply grow in their mathematical abilities at different rates. 

Regardless of the reason, mathematics educators often strive to find tools and resources to help meet individual student needs and differentiate instruction.  Handheld, mobile technologies may offer just the means to do that.  As this recent article from SmartPlanet, details there are new opportunities for the visually impaired learner using “haptic” technology. 

Haptic means relating to the sense of touch.  Through a research project at Vanderbilt University, an android app is being developed to help learners who have difficulties with their vision to learn mathematics – a subject where visual data such as graphs, charts, and symbols are relied upon for communication.

Many learn better through doing rather than speaking or hearing. Mathematics can be difficult to teach to these learners.  In addition to assisting the visually impaired, such technology may open the door for the kinesthetic learner.  With handheld devices becoming downright commonplace, this seems like an opportunity with a lot of promise.

MetaMetrics recently released a policy brief on the mathematical education issues now facing our nation’s students.  Written by MetaMetrics President and Co-founder Malbert Smith, and Director of Professional Development,  Jason Turner,  A Mathematical Problem: How to Help Students Achieve Success in Mathematics Through College and Beyond examines what it means to be college and career ready in mathematics and the dire consequences of being unprepared for the mathematical demands of life after high school:

Many U.S. students graduate unprepared for the challenges they will likely face in college and careers. This unpreparedness not only portends significant academic challenges, but increasingly dire consequences at both the individual- and macro-economic levels. At the individual level, students may find themselves unable to compete academically and miss out on employment opportunities in some of today’s fastest growing career sectors. At the macro level, poor mathematics performance suggests an alarming outlook for our country’s competitiveness in the international arena.

We encourage you to read this policy brief as it details more than just the problems we face — Smith and Turner also discuss the solution. The Common Core State Standards provide a map for getting students college-and-career-ready. Forty-seven states already adopted these standards. The next phase is implementation. How will educators apply the Common Core State Standards in the classroom? Smith and Turner discuss the wealth of free resources available at http://www.quantiles.com/, one such resource is Math@Home. We welcome you to explore The Quantile Framework for Mathematics and learn about all the online tools it has to offer.

Want to subscribe to our policy briefs? Visit www.Lexile.com and click on Register in the top right corner. Be sure to check the box next to News Releases!

We’ve written before on the efforts of Khan Academy - a free, online classroom that is available to anyone with an Internet connection.  Khan Academy offers thousands of video lessons on everything from specific mathematical concepts to explanations of the mortgage loan crisis.  Because Khan’s videos are easily accessible, students (and parents) are able to take advantage of its ‘always-on’ access to review videos in their own time. 

Khan’s work has gotten the notice of educators across the US and a number of Foundations and educational organizations, including the Bill & Melinda Gates Foundation, are looking to capitalize on Khan’s approach to individualizing education:

Each student’s math journey shows up instantly on the laptop Mr. Roe carries as he wanders the room. He stops at each desk, cajoles, offers tips, reassures. For an hour, this crowded, dimly lighted classroom in the hardscrabble shadow of Silicon Valley hums with the sound of fingers clicking on keyboards, pencils scratching on paper and an occasional whoop when a student scores a streak of right answers.

The software program unleashed in this classroom is the brainchild of Salman Khan, an Ivy League-trained math whiz and the son of an immigrant single mother. Mr. Khan, 35, has become something of an online sensation with his Khan Academy math and science lessons on YouTube, which has attracted up to 3.5 million viewers a month.

Now he wants to weave those digital lessons into the fabric of the school curriculum — a more ambitious and as yet untested proposition.

This semester, at least 36 schools nationwide are trying out Mr. Khan’s experiment: splitting up the work of teaching between man and machine, and combining teacher-led lessons with computer-based lectures and exercises

The most promising aspect of Khan’s work is that it harnesses technology to promote individualized instruction.  We’ve written before on the importance of blending technology platforms with instructor interaction to promote differentiation, or even individualization for each student.  By providing a platform that monitors each student’s progress and then responds with more instruction for students who are not ready to move on or with new concepts for those that are, Khan is upending the more traditional assembly-line model of the classroom, allowing teachers to monitor student progress and respond to struggling learners, while allowing proficient students to move forward.

Not it appears that Khan is getting the chance to put his model to the test at larger sites and with more classrooms:

In the past, math class at the Summit schools was always hands-on: the class worked on a problem, usually in small groups, sometimes for days at a time. But getting an entire class of ninth graders to master the fundamentals of math was never easy. Without those, the higher-level conceptual exercises were impossible.

That is where the machine came in handy. The Khan software offered students a new, engaging way to learn the basics.

Ms. Tavenner says she believes that computers cannot replace teachers. But the computer, she recognizes, can do some things a teacher cannot. It can offer personal feedback to a whole room of students as they work. And it can give the teacher additional class time to do more creative and customized teaching.

“Combining Khan with that kind of teaching will produce the best kind of math,” she argued. “Teachers are more effective because they have a window into the student’s mind.”

Khan’s efforts are worth noting.  Khan’s work is inspiring and is likely just the beginning of the work that can be done with virtual classrooms.  We’ve incorporated Khan’s work into our own tools on the Quantile Framework for Mathematics website.  In Math at Home, for example, students can select textbook chapters and lessons and search for supplemental material by which to review their primary lessons.  In many cases, they will find a variety of Khan videos available to help review core skills and concepts.  If you haven’t already, be sure to take a look.

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.

Tip of the hat to Scholastic’s Math Hub for posting this piece on the state of technology in math education.  Though many math educators report still relying on a basal textbook, many more are employing a variety of digital resources to help reach struggling math students:

On average, math teachers reported spending more than one full class period per week using digital tools or content, and many spent significantly more time utilizing technology. Specifically, among teachers who report using digital content or tools during more then 26% of class time (high digital use), the highest percentages are remedial math teachers and grades 6-8 math teachers. The most commonly used digital tool is interactive whiteboards. Teachers considered interactive whiteboards to be the most important supplemental material in addition to textbooks. This demand for whiteboards is a change from 2008 when interactive whiteboards were not even part of the survey. Math teachers and educators value the “faster reporting” and “detailed student/class information” generated by computer-based programs, features that traditional textbooks and workbooks cannot provide.

What many math educators have discovered is that moving from whole-class instruction to differentiating for struggling students requires going beyond the textbook to solutions that harness technology to adapt and respond to a student’s learning trajectory.  Technology of that sort can take multiple forms, but some important features include the ability to individualize for a student’s needs, provide supplemental resources, and multiple explanations for math skills and concepts.  As many educators now understand, one size does not fit all when it comes to math instruction; and ensuring that students graduate ready for the mathematical demands of the post-secondary world entails matching student math ability to the level of the lesson. 

At MetaMetrics, we’ve attempted to harness technology to supplement and strengthen student math ability through Math at Home.  Math at Home serves as a portal for matching students to targeted math resources across a variety of mediums.  Because each student has a different preferred learning modality, Math at Home offers online resources, video tutorials, skill practice sites, literature guides, games, and hand’s-on activities – a wide variety of resources to keep students engaged in math activity.  But Math at Home is more than a mere portal.  There are plenty of activity portals widely available.  What distinguishes Math at Home from other student portals is the Quantile Framework.  Math at Home uses the student’s Quantile measure to establish the student’s math level.  The list of available resources differs for each student and is based on their Quantile measure, or math level.  Additionally, Math at Home utilizes a large database of textbooks to match students with resources of their choice based on their current textbook lesson, but at their own math level.  If you haven’t already tried it, be sure to take a look.

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.

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.