Pythagorean Day

You may have heard of Pi Day (March 14) to celebrate the ratio of a circle’s circumference to its diameter or e day (February 7) to celebrate Euler’s constant, but have you heard of Pythagorean Day?

Pythagorean Day occurs when the digits in the date satisfy the Pythagorean Theorem. Recall that the Pythagorean Theorem states that in any right triangle with sides a and b and hypotenuse c, it is true that a² + b² = c². This year, Pythagorean day is August 15, 2017 because the digits 8, 15, and 17 satisfy the Pythagorean Theorem: 8² + 15² =17².

Now that you know, how will you celebrate Pythagorean Day? Here are some fun ideas:

  • Throw a triangle party! Make and eat triangle-shaped foods, decorate with triangles, and play games such as seeing who can list the most Pythagorean triples.
  • Watch a short video of a conceptual demonstration of the Pythagorean Theorem.
  • Make your own proof of the Pythagorean Theorem.
  • Listen to a fun song about the Pythagorean Theorem.

The next Pythagorean Day will not happen until December 16, 2020 (12² + 16² = 20²). Have a happy Pythagorean Day!



Creating Positive Math Experiences for Learners

A recent article described how anxiety toward math can hinder mathematical progress. As parents and educators, how can we reduce or eliminate math anxiety through creating positive math experiences for learners? We’ve come up with some ideas.

1. Focus on math as a process rather than math as a single answer.
Many students view math as finding a single answer, where getting the right answer is good but getting the wrong answer is bad. When learners feel concerned with finding a single correct answer, they can develop anxiety toward math. In reality, math is a process that requires making conjectures, finding examples or counterexamples, trying new ideas, and collaborating. One way to help learners view math as a process is to ask learners questions such as “how do you know?” or “can you prove that?” rather than immediately confirming whether an answer is correct. Praise learners for their ability to explain their mathematical thinking, even if an answer is incorrect.

2. Ensure learners have material with an appropriate level of challenge.
If material is too difficult for learners, it can cause learners to feel anxious or discouraged. Choose problems with multiple entry points and provide learners with various tools to help solve such as manipulatives, graph paper, or colored pencils. Knowing a learner’s Quantile measure can also help educators choose materials with an appropriate level of challenge.

3. Avoid using math as a punishment.
Many of us have probably had a teacher who assigned extra math problems when the class was misbehaving or a parent who made us do schoolwork when we didn’t complete a chore. When math is used as a punishment, it leads learners to associate negative feelings with doing math rather than feelings of accomplishment, intellectual curiosity, and joy. Find creative ways to use math as a reward instead of a punishment, for example by spending one-on-one time playing a math game with a learner or allowing a learner to use special technology such as a tablet for the purpose of doing math.

4. Remain calm.
Parents and educators may feel anxious themselves about math, and learners can sense this feeling and replicate math anxiety from adults in their lives. If you feel math anxiety as an adult, try to remain calm when working with learners. It may help to review materials on your own first, prior to working with students, to give you a chance to review concepts before explaining those concepts to a learner.

What are some ways you create positive math experiences with learners in your life?

Velocity Norms for Academic Growth

Shuttleworth (1934) suggested that growth standards for stature should be expressed in terms of progress rather than status. Tanner (1952) provided a theoretical framework for the development of clinical standards for growth and advocated velocity standards. Bayley (1956) made the first effort to produce standards for height that took account of tempo. Her paper foreshadowed the landmark paper by Tanner, Whitehouse and Takaishi (1966) on longitudinal standards for height velocity and weight velocity. Incremental growth charts for height and weight have since been produced for use in the United States (Baumgartner, Roche & Himes, 1986; Roche & Himes, 1980).

Have you ever heard of growth velocity norms for academic growth—i.e., the growth rate of reading ability or mathematical understanding? There are three reasons you haven’t, which persisted for most of the 20th century: (a) the absence of sufficient longitudinal data on which to base investigations of academic growth; (b) the analytical methods available to educational researchers who wished to study growth; and, (c) challenges of educational measurement (e.g., dimensionality, lack of scale comparability and common units across instruments). Yet, I submit at the dawn of the 21st century, these obstacles have been overcome.

The most recent two reauthorizations of the Elementary and Secondary Education Act (ESEA) required states to assess reading and mathematics in multiple grades. States have been accumulating data for more than a decade. So, longitudinal data are now feasible for reading and mathematics.

Rogosa, Brandt and Zimowski (1982) advocated the use of longitudinal data collection designs gathering more than two waves of serial measures on the same individuals, accompanied by an analytical methodology focused on the individual growth curve. In their landmark book, Raudenbush and Bryk (2002) included a chapter on formulating models for individual change. Singer and Willett (2003) gave book-length treatment to the modeling of individual change. Perhaps the most enabling resource for the educational research community was Singer’s (1998) article demonstrating how to implement multilevel (including growth) models using one of the most widely available general-purpose statistical packages.

Finally, near the end of the 20th century, a new scale was developed for measuring reading ability. Its significant advantage over previous scales was a new kind of general objectivity, attained by calibrating the scale to an external text-complexity continuum and double-anchoring the scale at two substantively important points, much as temperature scales are anchored at the freezing and boiling points of water (Williamson, 2015).

Combining longitudinal data, multilevel modeling and state-of-the-art measurement scales from The Lexile® Framework for Reading and The Quantile® Framework for Mathematics, Williamson (2016) premiered incremental velocity norms for average reading growth and average mathematics growth. Based on an individual growth model, the incremental velocities reflect the long-term developmental growth of students in a well-established reference population (n > 100,000). Now, it is possible to refer the reading or mathematics growth rates of students observed during schooling to a clearly defined population of growth curves derived from serial measures of students whose reading ability and mathematical understanding were systematically assessed over time.

Baumgartner, F. N., Roche, A. G., & Himes, J. H. (1986). Incremental growth tables: Supplementary to previously published charts. The American Journal of Clinical Nutrition, 43, 711-722.
Bayley, N. (1956). Growth curves of height and weight by age for boys and girls, scaled according to physical maturity. Journal of Pediatrics, 48, 187-194.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd  ed.). Thousand Oaks, CA: Sage Publications.
Roche, A. F., & Himes, J. H. (1980). Incremental growth charts. The American Journal of Clinical Nutrition, 33, 2041-2052.
Rogosa, D. R., Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurement of change. Psychological Bulletin, 92, 726-748.
Singer, J. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 24(4), 323-355.
Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.
Shuttleworth, F. K. (1934). Standards of development in terms of increments. Child Development, 5, 89-91.
Tanner, J. M. (1952). The assessment of growth and development in children. Archives of Disease in Childhood, 27, 10-33.

Summer Math Challenge Kicks Off on June 19th!

On average, all students, regardless of socio-economic status, lose approximately 2.6 months of grade level equivalency in their mathematical repertoire over the summer months each year. This means students can enter a new school year in August or September having lost about a third of the ground they covered the year before. Fight the summer slide, and keep math skills sharp with the Quantile Summer Math Challenge, a FREE math skills maintenance program based on grade-level standards that help prepare students for college and careers.

For the past several years, MetaMetrics has tried to help stave off the erosion in learning that can occur during the summer months with the Summer Math Challenge. Last year, almost 20 State Department of Educations and over 26,000 students across all 50 states signed up to take the challenge. This year, we have expanded our successful program to include those students who have just finished 8th grade. Now, the program is targeted to students who have just completed grades 1 through 8 and is designed to help kids retain math skills learned during their previous school year.

The Summer Math Challenge lasts for six weeks. The challenge focuses on one math concept per week, so as to help the student remain sharp but not feel overburdened during the summer. From June 19th through July 28th parents will receive daily emails with fun activities and links to educational resources. Activities will be grounded in everyday life and be engaging for both parents and children. This program also helps parents to understand that they do not need to be math experts to talk about math with their kids! When the program ends parents can print an award certificate to celebrate their child’s summer math accomplishment! To learn more, visit

Late Elementary, Middle and High School Educators Needed For Reading Research Survey

Are you an educator who works with struggling readers in late elementary, middle school or high school? Are some of your students reading at levels three years or more below what is typical for students at their grade level? We are interested in your feedback on reading materials often used with students reading at lower levels. We want to hear from you!

Please indicate your interest in being part of our current study (and possibly future studies) by completing the short survey found at

New Advanced Lexile Professional Development Workshop

Take your Lexile Professional Development to the next level! We are excited to announce our newest Lexile workshop, The Lexile Framework in Action: Making Curriculum Content Accessible to ALL Students.

This full-day, advanced workshop will guide curriculum coaches, content specialists, classroom teachers and media specialists in the development of units of targeted text and resources. Our facilitator will lead the group in using resources already in place to support instruction that will target all learners. Current state standards, district curriculum pacing guides and recent student Lexile® measures will provide the foundation for developing customized lesson plans.

We also offer numerous other Lexile workshop options including half- and full-day introductory sessions. Learn more about this new offering and view our full range of workshops at

Interested in training on the Quantile Framework for Mathematics? Visit to learn about our Quantile Professional Development workshops.

Summer Learning Tools From MetaMetrics

Fight summer slide with free tools from MetaMetrics!

Visit Lexile “Find a Book” to submit your Summer Reading Pledge and download our Summer Reading Log. Use the log to track a child’s reading throughout the summer break. Search our database of over 270,000 titles for books within a child’s Lexile range. Enter the child’s Lexile measure, and then narrow the search by selecting topics of interest. You can also use “Find a Book” to check the availability of books at local libraries or purchase titles from major booksellers. When school starts again, share the reading log with the child’s teacher to show his or her dedication to reading.

Keep math skills sharp with the Quantile Summer Math Challenge, a FREE math skills maintenance program based on grade-level standards that help prepare students for college and careers. The program is targeted to students who have just completed grades 1 through 8 and is designed to help kids retain math skills learned during the previous school year. The Summer Math Challenge lasts for six weeks and focuses on one math concept per week. From June 19th through July 28th parents will receive daily emails with fun activities and links to educational resources. When the program ends parents can print an award certificate to celebrate their child’s summer math accomplishment! To learn more, visit

Games Playlist for Students

Soon, we could see teachers prepare a learning games playlist for their students. In March, a DC based startup unveiled a free web service called Legends of Learning that would help teachers assign educator-vetted games to the classroom.

Vadim Polikov, the creator of the web service calls it, “Spotify for learning games” after the online music streaming service that provides users with unlimited songs and playlists they can create. Polikov grew up with classic games such as The Oregon Trail and Civilization, but has come to the realization that most games now do not align with academic standards or teach material that is appropriate to students. Educational games can also be too long to be played in the length of time of a class session.

With Legends of Learning, teachers can create a playlist of short five minute games up to longer forty minute games with over 500 titles. Science games can be played now, but titles will be available soon for English and Math (Grades K-12). Gameplay will also be tied to virtually all state academic standards.

Teachers will also have their own online dashboard which will show the progress of each student. “What we’ve focused on is making this for teachers and, really, by teachers,” says Polikov.

From article in ASCD SmartBrief March 28, 2017

See the Quantile Framework in Action at NCTM

Are you attending the National Council of Teacher of Mathematics Annual Meeting and Exposition this week in San Antonio? Take this opportunity to learn more about the benefits of the Quantile Framework for Mathematics. We’ll be visiting the conference and meeting with some of our partners whose products utilize the power of the Quantile Framework.

Quantile partners exhibiting at the conference include: Big Ideas Learning, The College Board, Curriculum Associates, Houghton Mifflin Harcourt, Imagine Learning, McGraw-Hill Education, Mentoring Minds and Origo. We hope to see you there!

New Partnerships Increase Use of Quantile Measures

A series of new partnerships have greatly expanded the reach of the Quantile Framework for Mathematics. In the last year, Quantile measures have been added to Pearson’s aimswebPlus and Istation’s ISIP Math. Quantile measures have also become available through state assessments in Kansas and to the 15 member states of the Smarter Balanced Assessment Consortium. These new partnerships are in addition to the numerous state level assessments and assessment products that already report student mathematical ability in Quantile measures, including Kentucky’s K-PREP, North Carolina’s NC READY, Curriculum Associates i-Ready, HMH Math Inventory and Imagine Math. Also this year, new materials and textbooks from Pearson, McGraw-Hill, Origo Publishing and Big Ideas Learning have been calibrated to the Quantile scale, adding to the dozens already featuring Quantile skill or concept measures.

Quantile measures accurately match students with instructional materials by measuring both mathematical capability and the complexity of mathematical skills and concepts on the same developmental scale. There are two types of Quantile measures: a measure for students and a measure for mathematical skills and concepts. The Quantile student measure describes what the student is prepared to learn next. The Quantile skill or concept measure describes the difficulty, or demand, in learning that skill or concept. Both measures are represented as a number followed by the letter Q (e.g., 640Q) on the Quantile scale. Quantile measures can improve mathematics teaching and learning by helping educators target instruction and determine if students are on track to pass year-end assessments and succeed in college and careers. Visit for more information about the Quantile Framework.

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.