Productive Failure

“If at first you don’t succeed, try, try again.” Babies learn to walk in this way. Preschoolers learn to button, tie, and zip to dress themselves in this manner. However, the idiom can now apply even after children enter school. In the article, “How ‘Productive Failure’ In Math Class Helps Make Lessons Stick,” Katrina Schwartz explains that productive failure is not just the idea that persistence pays off. Rather productive failure is an effective teaching strategy that involves “careful lesson design, a strong classroom culture and an instructor trained in getting results from small failures so his or her students succeed when it matters.”

The idea is that teachers are trained to develop math tasks that students will not be able to solve but that evoke a students’ prior knowledge relating to the task. Teachers also receive training to gain deeper content knowledge to assess student ideas and misconceptions as well as learn how to set the classroom environment to foster failure as a natural part of learning and not an embarrassment.

The Quantile Framework can help teachers to develop tasks that promote productive failure. Using the tools available on Quantiles.com, teachers can select activities to both develop challenging tasks and tasks that ensure prior knowledge. Here’s how:

  1. Go to Quantiles.com.
  2. Click “Use the Quantile Framework” at the top of home page.
  3. Select “Math Skills Database.”
  4. For the State Standards search, select the state in the dropdown list.
  5. Select the grade level or name of the math course in the Course dropdown list.
  6. Select the specific standard in the Standard dropdown list. Click “Search.”
  7. A list of Quantile Skill and Concepts (QSCs) targeted to the standard will appear.
  8. Click a QSC to view more details including its Knowledge Cluster. The Knowledge Cluster provides insight into Prerequisite, Supporting and Impending Quantile Skills and Concepts.
  9. To help create challenging tasks, click a QSC number for a Supporting or Impending QSC to see free challenging resources.
  10. To access resources to build prior knowledge, click a QSC number for a Prerequisite QSC to see free resources calibrated to a prerequisite skill or concept.

To learn more about productive failure, read the research of Manu Kapur, Professor of Psychological Studies at The Education University of Hong Kong.

Teaching Math with Storybooks

By reading and discussing stories with children, you can gain some insight to how they think. Herbert Ginsburg, a professor of psychology and education at Teachers College Columbia University suggests that reading and discussing math storybooks with your child can help set the stage for meaningful mathematical achievements in school.

Certain books, such as counting and shape books are centered on learning math. However, there are also many books that have embedded mathematical ideas in the stories. For example, when Goldilocks sees Baby Bear’s bed and realizes it is too small, she compares the size of the beds to the bears. By doing this, she then realizes that there is a simple correlation between the two: the smaller or larger the bear, the smaller or larger the bed.

Storybooks deal with mathematical information informally with patterns, spatial relations, measurements, addition, subtraction, multiplication, and division. When reading books with your child ask questions about what’s happening in the story, make predictions of what will happen next, and try to find the embedded mathematical skills.

The following ideas may promote your child’s math learning:

  • Read books that you both find interesting.
  • Talk with your child about what is happening in the story.
  • Use mathematical language to describe and explain events in the book, (this square has four sides and they are all the same length, this is the biggest, which weighs the most) this should also keep your child engaged.
  • Think about your own math experiences and if they are negative, try not to transmit those feelings.

Reading stories is a wonderful way to help your child understand new mathematical skills. To help you along, we have math literature guides on Quantiles.com that can be used to introduce new mathematical skills. Literature guides are provided as a resource for the Quantile Skill and Concept (QSC) they are associated with.

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Ginsburg, H. P. (2016, February 2). Finding the Math in Storybooks for Young Children. KQED News. Retrieved from http://ww2.kqed.org/mindshift/2016/02/02/finding-the-math-in-storybooks-for-young-children/

 

New Tool: The Lexile Analyzer Editor Assistant

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We’d like to share a newly released Lexile analyzer professional tool, the Lexile Analyzer® Editor Assistant™. In response to the rising demand to produce text to specific reading levels, we developed this tool to help you do just that.

The Lexile Analyzer Editor Assistant has many exciting features including an enhanced interface to help more efficiently and effectively develop leveled text at a particular Lexile level by allowing you to combine the analyzer within your working document for quick and easy analysis of your text.

The Lexile Analyzer Editor Assistant can be licensed from MetaMetrics for a variety of usages such as:
– Determining the Lexile measure of a particular text
– Targeting content to receive estimated Lexile measures
– Rewriting and editing text directly within the tool while receiving Lexile measures on demand

Learn more about the Lexile Analyzer Editor Assistant by viewing our overview video.

 

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!

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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.

For more information, please visit https://goo.gl/mer2mp. Each teacher whose classroom participates in the study will receive a $75.00 Amazon gift card.

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

Another Vote That Parents Can Support Mathematics Instruction

Jason Zimba shared the struggle of helping their children on weeknights in spite of the busy schedules of the family members in his article “Can parents help with math homework? YES”. His article is encouraging for the hopeful parents who really want to help their children with their academic progress with his indications that such activities as flash cards, games, or just checking homework is a positive gesture to instill for the children the importance of success and gratification when they work hard in their studies.

As mathematics educators, others might think it is effortless for us to prepare activities, listen to our child’s methods for solving problems (even when we would do the problem differently), or sit down and check the answers in the homework. But I can testify as a mathematics educator that it all takes time, which I don’t have an abundance of, to prepare games, flash cards, puzzles or to check homework. In addition, it is also a struggle for us to listen, without interruption, while a child is explaining a process for solving a problem, particularly when the method is different from our own.

To help to expedite some of these responsibilities that might save the parents time and promote the child’s understanding of the math is to have the child prepare the flash cards. Certainly as parents we can check the cards, but the child can make the corrections and begin to memorize the material while working of the flash cards. Puzzles and activities in the child’s homework might get some creative juices flowing if the child is encouraged to make up a similar activity and then explain the rules to the parents. The child will begin to understand how important it is for directions or definitions to be clear. Some of this places the responsibility for developing and learning the material on the child.

But let’s not restrict the enjoyment of mathematics to homework assignments or puzzles that came from the classroom. Our jobs, games, and hobbies often involve mathematics as well. Sharing with the children where activities such as carpentry, sports, preparing spreadsheets, knitting, or cooking involves understanding measurement, fractions, formulas, proportions, statistics, or sequence characteristics. Families who play board games or card games are promoting logical or inferential thinking, as well as counting, probability, counting money, geometric relationships, or using percent. Teaching and sharing the function of mathematics in these pursuits will instill an appreciation and enjoyment of mathematics’ role in everyday activities.

Certainly our children need our support and sometimes instruction to complete homework and projects for school. We try to make reading fun by reading to our children or sharing enjoyable books. Science is often fun with minimal lab activities in our kitchen or backyard. Enjoying mathematics is in many places. It is just a matter of recognizing when we are using the math and sharing those moments with our children.

Bridging the Gap Between High School and the Work Force

While the focus on college and career readiness in our education system is not a new idea, and while progress has been made, students overall are still not adequately prepared for life after high school. According to research published last year by Achieve — a nonprofit education reform organization dedicated to raising academic standards and graduation requirements, improve assessments, and strengthen accountability — roughly half of all high schoolers report gaps in high school preparation and the working world.

High schoolers are not the only ones shouldering the consequences of this lack of preparation though. Employers across the country are agreeing that there is a disconnect between the skills that graduates have and the skills that they need. Common themes are lack of “soft skills” such as effective communication, team work, punctuality, etc., as well as a lack of knowledge in critical STEM areas such as basic math and science prerequisite skills. Scott McLemore, technical workforce development manager for Honda North America, Inc., has experienced this in his industry first-hand and discusses how, “There is a severe shortage of people entering the manufacturing field, so much so that it could eventually result in millions of jobs going unfilled due to either a lack of interest, or a lack of the required skills.”

So how do we go about building this bridge? One promising solution is through partnerships between high schools and institutions of higher education. An excellent example of this is P-TECH, a public high school in Brooklyn, NY. These partnerships have been made to meet the growing demand for job candidates with STEM skills. Through this model, students spend six years taking both standard high school courses and classes specifically focused on a certain profession. These credits can amount to an associate degree as well as an industry-specific certification upon graduation. The goal is to have students earn college credit sooner while simultaneously gaining hands on experience. The result of this has been nothing short of optimistic. For example, in 2014 the four-year high school graduation rate for early college students in New York was 86.9 percent, compared with the citywide average of 68.4 percent, and of 205 seniors who graduated this past year, 57 earned an associate degree.

Happy Holidays From MetaMetrics!

As the holidays and the end of the year approach we’d like to take a moment to reflect on 2015. It’s been an exciting year for us here at MetaMetrics and an exciting time in the world of education. We have been happy to watch as our two core products, The Lexile Framework for Reading and The Quantile Framework for Mathematics, continue to expand both domestically and globally.

While we we can boast of many achievements this year, some of our proudest moments include the debut of the Lexile Career Database and the Lexile by Chapter Guides; increased participation in the CCSSO Chief’s Summer Learning Challenge and the Summer Math Challenge; numerous research publications and many new product and publishing partnerships.

This holiday season, we invite you to join us in supporting First Book. First Book provides new books to children in need throughout the United States and Canada. With over 135 million books distributed so far, First Book is making huge strides towards solving ton of the biggest challenges faced in the development of literacy—access to books. Please join us as we help to spread some joy and holiday cheer with the gift of books. 

From our family to yours, we wish you a very happy holiday season! For a few laughs we invite you to view our company holiday video and learn about our newest “product”, The Giftile Framework for Giving.

New Lexile Resource: The Lexile Career Database

We’d like to share our newest Lexile resource, The Lexile® Career Database. The Lexile Career Database is a new tool to help identify the reading ability necessary for career preparedness. It contains Lexile® measures for over 250 careers (to date) as well as important descriptive information for each career. The database is a result of years of research examining the text complexity of a variety of reading materials in various domains of the post-secondary experience.

The Lexile Career Database uses a common scale for readiness across all careers and is an excellent new resource to address the emerging emphasis on career readiness. With The Lexile Career Database, educators and students can identify the reading ability needed for a desired career and use this information to inform goal setting. It is the only metric available to compare and describe reading demands of careers.

The careers featured within The Lexile Career Database have been identified as Bright Outlook Occupations by O*NET, the premier online career search database designed for the U.S. Department of Labor. Bright Outlook Occupations are careers that are expected to grow and/or emerge in the next few years and offer large numbers of new job openings.

The Lexile Career Database is now available for integration into Lexile partner products and services. To learn more about licensing the Lexile Career Database click here or view our recent webinar The Lexile Career Database: Discover the Reading Demands of Prospective Occupations.

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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.