## The Quantile Framework By The Numbers

Want to learn about the Quantile® Framework for Mathematics? View our brand new Quantile Infographic to find everything you need to know about the Quantile Framework in one easy to understand graphic. Learn the basic concepts of the Quantile Framework, find out how students receive Quantile measures, where you can find Quantile measured content, and see an overview of the free math resources available on Quantiles.com. View the full infographic and download a printer-friendly version of your own.

While you’re visiting Quantiles.com please take some time to explore all the wealth of information and mathematics resources made available for your use. And don’t forget to sign up for the 2016 Quantile Summer Math Challenge!

## Should Algebra Be Required in Our Schools?

Recently Marilyn Vos Savant, from the “Ask Marilyn” article of Parade Magazine (December 6, 2015), received the question “Do you think algebra should be required in our schools?” Marilyn’s short answer was “Yes.”  Her emphasis lay in the fact that algebra is a branch of mathematics that teaches students logic – how to think rather than what to think.

The mathematics branch of algebra is certainly an exercise in abstract thinking with symbols and structures to represent relationships in mathematics that justifies our operations in arithmetic. With the Common Core State Standards for Mathematics, students are encouraged to manage and work through the reasons many of the algorithms is arithmetic work. These comprehensive methods of teaching arithmetic will contribute to a better understanding of the structure of mathematics and science.

Algebra is a foundation for topics in chemistry, economics, physics, statistics, and architecture. There is a plethora of technology that we use every day that works for us because someone knew enough about algebra to put together relationships to make our GPS, computer, cell phone, microwave oven, and car work for us.

Marilyn’s analogy to studying algebra in mathematics is similar to athletic training that includes various types of exercise equipment rather than always using one machine, such as a rowing machine.  In order to be physically fit, we should be doing kinesthetic as well as aerobic methods of physical training. In like manner, in order to be intellectually fit, many areas of study should be included and algebra is certainly one of them.

Galileo is quoted as saying “Mathematics is the alphabet in which God has written the universe.” Keep in mind that algebra uses the alphabet to delineate numeric relationships, mathematical algorithms, and logic. So it appears that Galileo would have agreed with Ms. Vos Savant that algebra should be required in our schools.

## Grade 4, 7, 8 Classrooms Needed for Mathematics Research

MetaMetrics is seeking participants for an upcoming research project investigating the difficulty of various aspects of mathematics problems.

We at MetaMetrics believe that assessment and instruction should be connected. Providing quality information about a student’s mathematics ability is a key component of one of MetaMetrics’ mottos: “Bringing Meaning to Measurement.” We continue to explore innovative relationships in the development of mathematics assessment through our research agenda.

As such, MetaMetrics is recruiting for our ongoing mathematics item difficulty research initiative. We are specifically looking for teachers of students in grades 4, 7, and 8 willing to administer a short set of mathematics items to their students using our online assessment delivery system.  The goals of the research include examining features that make items more or less challenging for students.

We look forward to working with you on this important study.

## Grade 4, 7, 8 Classrooms Needed for Mathematics Research

MetaMetrics is seeking participants for an upcoming research project investigating the difficulty of various aspects of mathematics problems.

We at MetaMetrics believe that assessment and instruction should be connected. Providing quality information about a student’s mathematics ability is a key component of one of MetaMetrics’ mottos: “Bringing Meaning to Measurement.” We continue to explore innovative relationships in the development of mathematics assessment through our research agenda.

As such, MetaMetrics is recruiting for our ongoing mathematics item difficulty research initiative. We are specifically looking for teachers of students in grades 4, 7, and 8 willing to administer a short set of mathematics items to their students using our online assessment delivery system.  The goals of the research include examining features that make items more or less challenging for students.

We look forward to working with you on this important study.

## More Math at Home, Better Performance at School

Few would argue that our society privileges mathematical and the scientific disciplines over the humanities. Yet, well before studies concluded reading to your children will help them learn phonetic and phonemic awareness parents’ have been reading to their children. How many have done algebraic equations or recited times tables as they settle their children down to bed? Simply, we may all agree on the importance of mathematic and scientific skills in the 21st century, but at home thoughtful and concerned parents continue to just promote linguistic and reading skills.

It might be time, though, for parents to begin encouraging their children in math as with literature. A new study by Talia Berkowitz and other faculty at the University of Chicago— featured in Sciencesheds light on how parental math talk can greatly improve a student’s ability. In fact, just putting aside a few times a week for high-quality math discussion can significantly help students learn.

Of course, one of the reason’s reading is something many parents share with their children is many people have access to books. Reading with your kids is something most parents can do. But math is something many people feel less adept at sharing with their children. Fortunately, MetaMetrics has material to assist! Math@Home is a free resource targeted at assisting parents to develop meaningful lessons matched to students’ Quantile scores. It even offers instructional assistance which parallel many math textbooks assigned to students.

Similarly, many parents may be familiar with the “Summer Slide” in reading. This slide affects mathematical skills as well. To keep Math skills fresh and sharp instead of atrophy, MetaMetrics offers the Summer Math Challenge! The Summer Math Challenge is a free opportunity from June to July to help keep students learning instead of losing math skills over break!

## Math = Logic?

Suppose you’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?

Stumped? Don’t worry, you’re not alone. It’s not a trick question though; in fact the answer is fairly straightforward:

You ask either of them: “If I asked the other person which door is the one to escape, which would he point to?” Then you take the other door.

According to Nicholas Kristoff, a New York Times columnist, those with mathematical training are more likely to figure out this problem. Why is that? Kristoff explains that math isn’t just math — it’s logic. The skills utilized when studying and learning math are the same logistical skills you use for everyday things like brain teasers, statistics, or economics; even if you don’t realize that’s what you’re doing.

Questions like the one mentioned above, however, are often puzzling to Americans. For example, studies show that only 37% of American kids could correctly answer the question below whereas 75% of our Singapore counterparts answered correctly.

What is the sum of the three consecutive whole numbers with 2n as the middle number? (Answer: B)

1. 6n+3
2. 6n
3. 6n-1
4. 6n-3

It is not uncommon to hear stories of America’s poor performance in reading and math on an international scale. While this is a common misconception considering our scores have actually been improving over the past years, some of our counterparts in other advanced countries are indeed progressing more quickly. This is not due to an overall higher intelligence of other countries though. If we revisit the Singapore comparison we can learn that this kind of thinking is not innate. Instead, this logic is taught. Some may be familiar with the concept of “Singapore Math”, a model constructed upon child development theory that relies on student mastery of a limited number of mathematical concepts each year. The end result is that these students have a deeper level of comprehension and are therefore more prepared for problem solving. This enables them to master more difficult topics, like fractions and ratios, at much earlier ages than American students.

So if this is true, why then are Americans “avoiding” math? I’m sure we all know someone, or have been guilty ourselves, of copping out with: “Oh, I’m just not good at math”. But why do we have these outlooks on our math abilities when they can indeed be taught?

The answer may lie in our early foundations in mathematics. Unlike Singapore’s focus on mastery of limited concepts, American mathematics often focuses on memorization and drilling of concepts, such as multiplication. This can result in a lack of understanding about the meaning and function of numerals. And since mathematics continuously builds on itself, if a student doesn’t master the basic foundational concepts they will progress slowly and often fall behind. In fact, a study by researchers at the University of Missouri found that: “Children who don’t grasp the meaning and function of numerals before they enter first grade fall behind their peers in math achievement, and most of them don’t catch up”. This contributes to the alarming 22% innumeracy rate among adults in the United States. This early exposure and mastery of basic mathematical concepts is crucial for future arithmetic abilities.

This comparison is not to dishearten educational efforts in the United States, however. In fact this should encourage the public that the solution may be more straightforward than we imagined. Tools such as The Quantile® Framework for Mathematics can aid in this transformation by providing learners with resources for their individualized mathematical levels. Tools like these can be personalized for each student and provide additional means for gaining mastery of specific concepts.

## Teachers: Help Us Improve the Quantile Framework and Earn \$\$\$ for Your Class

MetaMetrics is currently recruiting 3rd grade classrooms to participate in a study to examine mathematics items. We hope you will consider participating in this study. We will give a \$25.00 Barnes and Noble gift card to each teacher whose classroom participates in the study AND a \$50.00 American Express gift card to go toward a “pizza(teacher choice)” party for the class to thank students and teachers for participating in the study.

Please visit here to complete the short interest information form for your class.   Class participation is on a first-come, first-served basis, so we encourage you to respond soon. Multiple teachers within one school or district will be considered, but each teacher does need to complete the information form.

## Promoting Life-Long Learning in Mathematics

Learning mathematics requires deep-rooted intrinsic motivation, motivation to learn, to problem solve, and to discover the best methods for solving those problems.  When we, as educators, attempt to offer doing well on assessments or being prepared for college algebra as intrinsic motivators, we often find that the results are marginal and superficial.

The role of mathematics educators is to promote reflective practices that promote connections within the realm of mathematics, as well as prepare students for the mathematical elements that are the foundation of so many aspects of the daily lives of citizens, consumers, and workers in their communities.

Mathematics teachers need as much training as possible promote discussion and reflection in their math lessons. Some considerations for best practices include the following:

• Rather than expecting the teacher be the source of knowledge, a mathematics classroom should offer opportunities for the students to explore, collaborate, and make decisions on methods to solve problems. Such guided interaction among the students will add excitement to the development of student problem-solvers.
• Instructional feedback needs to be more than whether the answer is right or wrong. Students need guidance on which elements of the process were misguided, help with identifying the flaws in judgment, and what adjustments need to be made. In solving most puzzles, we need to step back and determine where we are missing some information or going in a wrong direction. Working in the mathematics classroom can offer the similar intangible gratification when the problem is solved.
• Problems can be solved using different approaches. Allow time for students to discuss in whole group activities or in small groups to share the different methods and styles of thinking. In the social studies or science classrooms, many discussions lead to the phrase “I never thought of it like that.” Sharing tactics in the mathematics classroom can certainly lead to such discoveries, also.

In order to develop mathematics classrooms that foster reflection, discussion, engagement, and discovery, math educators should be trained at every level. Teachers without strong insights about the reasons for the various algorithms in mathematics will not have the confidence to promote dialogue that might go in unexpected directions. Even the teachers in the lower grades need to understand how topics in mathematics are interwoven so that “math talk” promotes that connectivity. Students who become engaged in learning become life-long learners. This should be the case in all content areas, including mathematics.

## Adjusting Math Terms for the Common Core World

Valerie Faulkner of North Carolina State University argues for a shift in the mathematical language we use.  The Common Core should give us pause and force us to reconsider the terminology and vocabulary we employ in describing certain skills and concepts.  Here are a few examples:

Old Habit (eliminate)                                     New Habit (adopt)

Defining equality as “ same as”                   Defining equality as “same value as”

Calling digits numbers                                    Clearly distinguishing between digits, numbers and numerals

Subtraction makes things get smaller      Subtraction is about difference

Let’s borrow from the tens place               Use regrouping, trading, decomposing

Multiplication makes things bigger          Teach 3 structures of multiplication

Divison makes things smaller                     Teach the different structures of divisions,

Doesn’t go into                                                 Prepare students for later learning by using accurate language

Saying “and” means decimal point         Don’t create false rules for language using and

Canceling out                                                   Explicitly use and discuss the idea behind simplifying

Guess-and-check as a strategy                 Teach systematic math representations

Old habits die hard, but this is food for thought as many districts get farther into implementing the Common Core.

## Identity Confusion: The Problem with the Equal Sign

Henry Borenson explains how we use the = sign in two very different ways.  The first way is operational, for example 10 + 15 = ______.  The second way we use the sign is relational, indicating equivalence between two sets of expressions, each of which includes one or more operations, for example 8 + 4 =_____ + 5.  But in 1999 a study of hundreds of first through six graders only 5%  solved problems like this correctly.

Borenson believes that because of this study we can conclude that the relational meaning  of the equal sign is not something that students find intuitive or self evident. When asked to fill in the answer to the problems above most students said that 12 belongs in the space because the answer follows the equal sign.  The equal sign seems to trigger the operational definition in most students’ minds. Some students thought the  + 5 was just there to confuse them.

Borenson recommends  introducing students in the second or third grade to the idea of balanced equations using concrete objects rather than numbers and the equal sign. Once students get the idea the equal sign can be introduced with the balancing explanation. Studies have shown that if the relational meaning of the equal sign is introduced in this way students are much more likely to grasp both ways.

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.