Literature That Will Enrich Mathematics

Embracing literature to enhance mathematics instruction in the classroom or at home benefits students by providing a richer and more meaningful perspective of mathematics. Connecting children’s literature with mathematics is an effective avenue for promoting problem solving, communicating in mathematics, and make connections between the mathematics needed in multiple disciplines. The paper “Using Children’s Literature to Teach Mathematics” presented on The Quantile® Framework for Mathematics site offers teachers and parents helpful suggestions for identifying literature that will support mathematics instruction and engage students.

An appropriate book to enhance an effective mathematics lesson should have an authentic context that includes real-life experiences, multi-cultural components, and enjoyable plots that unite mathematics and literacy. A report titled “Making Informed Choices: Selecting Children’s Trade Books for Mathematics Instruction” by S. J. Hellwig, Eula E. Monroe, and James S. Jacobs (2000) offers suggestions for identifying books that will support instruction and create meaningful and explicit connections to engage students. The article offers pointers for choosing appropriate children’s literature with mathematics topics. An appropriate book should:

  • represent mathematics and other information accurately and depict mathematics relationships correctly.
  • presents factual information, uses terminology appropriately, and portrays mathematical principles accurately.
  • includes a format and presentation that are visually and verbally appealing.
  • offers interest and pleasure without overpowering the text with mathematical processes and terminology.
  • provides a context for learners to make meaningful connections between mathematics and personal experiences.
  • easily connects the mathematical process or experience to the resolution of the story.
  • presents concepts in a way that appeals to a range of audiences and abilities.
  • appeals to a variety of interests, cultures, and/or experiences.
  • offers layers of richness beyond the predictable or expected and presents exciting new views or ideas.
  • engages students with a story that layers the unexpected with original insights or surprising events.

The study of mathematics is not just about learning mathematical processes and memorizing facts and algorithms. Mathematics becomes more visible in everyday life when students discuss the uses and advantages of applying math in various situations and recognize the necessity of mathematics in careers, personal budgets, traveling, and even games. What better way to promote those discussions when so many children’s books are available to add fun and interest to topics in mathematics?

Who Schooled the Senate?

By Malbert Smith III, Ph.D. and Andrew Ashley

As in all elections, we tend to divide candidates up with binaries, such as Left/Right, Republican/Democrat, Establishment/Outsider. Yet, another binary we could use is Publicly/Privately educated. As we sit mired in an election cycle where the nation’s public schools, the Department of Education, and the cost of college tuition come under scrutiny, we decided to examine how members of the U.S. Senate were educated in high school. We also looked at the education of the candidates for U.S senate races this cycle who hope to unseat the sitting senators.

Despite many reports on the profession, ethnicity, gender, military service, and age of the 114th Congress, a neglected variable has been how many members attended public or private schools during their K–12 education. In order to shed light on this, we decided to research where senators graduated from high school. In the aggregate we found that 74 senators attended public school and 26 attended private school. The number of senators who attended private school is considerably higher than the national average. According to the 2010 census, approximately 1.3 million students went to private high school out of the 16.16 million students attending high school across the nation. This means that about 8% of the country is going to private high schools, considerably lower than the Senate. And thirty years ago it was similar a trend. According to the 1980 census, 9% of high school students were in private schools. Of the 44 Democratic senators, 29 graduated from public high schools while 15 graduated from private ones. Republican senators have a higher concentration of public school graduates, as 43 Republican senators graduated from public high schools. Eleven Republican senators graduated from private schools.

Some senators even attended the same high school. Senator, and Democratic primary presidential candidate, Bernie Sanders (VT-I) and Senator Chuck Schumer (NY-D) both attended the James Madison High School, a public high school in Brooklyn, New York. Senator Patrick Toomey (PA-R) and Senator Jack Reed (RI-D) both attended the private La Salle Academy in Providence Rhode Island. Though neither set were in high school at the same time.

Of the 16 members on the Senate subcommittee on Elementary and Secondary Education we found that 12 attended public schools. Four attended private schools.

Perhaps more striking than whether senators graduated from public or private high school, however, is how many senators choose to send their children to private schools. Members of Congress are considerably more likely to send their children to private schools than the national average. The Heritage Foundation has monitored congressional children’s education for many years. According to the 2009 report (Burke, 2009), 55% of U.S. senators sent all their children to public school. However, 45% sent at least one child to private school. This is relatively similar among Democrats and Republicans as, in the 2009 survey, 43% of Democratic senators sent at least one child to private school while 47% of Republican senators did so. As Catherine Cushinberry states, as quoted in a recent article in the Atlantic, not being a public-school parent still amounts to a detachment from the laws regarding education one hopes to make.

We expanded our search to examine where the candidates for U.S. Senate in 2016 went to school. While we could not find information on every candidate, as many are newer to the public limelight and their high school education has not yet been reported (and some primaries have not finished at the writing of this article), we were able to glean the education of 24 of the 31 candidates (for 26 senate seats). Overwhelmingly, the candidates have public education backgrounds. Of the 24 candidates, only five candidates graduated from private schools. Of these, Evan Bayh (IN-D) graduated from the prestigious St. Albans School in Washington, D.C. while his father served in the senate for Indiana; Chris van Hollen (MD-D) graduated from the Middlesex School, a preparatory school in Massachusetts where his grandfather taught, while his father served as U.S. ambassador to Sri Lanka and the Maldives; and  Katie McGinty (PA-D), Jason Kander (MO-D), and John Caroll (HI-R) all graduated from catholic schools in their hometowns..

During this quest, we discovered finding information on senators schooling can be cumbersome. Finding information on all 100 sitting senators was difficult and for this reason we did not look into the 435 members of the House of Representatives. We believe it shouldn’t be so arduous to track down this information. As members of the 115th Congress convene in January of 2017 and begin to debate and craft educational legislation, we would encourage them to disclose their K-12  educational experience. The public’s confidence in our elected members would only be enhanced by such transparency.

Math Circles Help Develop Students’ Problem Solving Skills

At MetaMetrics, we get excited when we see enthusiastic students and educators in our community! Just down the street from our offices is exactly what you can find on Saturday mornings: students, parents, and educators working together to solve challenging math problems as part of the Chapel Hill Math Circle headquartered at the University of North Carolina at Chapel Hill.

What is a math circle? A math circle is a group of students of any grade level coming together to share their passion for math through exploring challenging math problems or special topics. Math circles benefit students by providing the chance for them to solve unfamiliar problems in unique ways. In traditional math classrooms, students often learn a new skill and then immediately apply that skill to a set of practice problems. This process does not give students the opportunity to determine which mathematical concept or solution strategy should be applied to a given problem. In math circles, students see problems out of context from classroom instruction, which helps them develop the ability to solve problem, make arguments, critique others’ reasoning, and persevere through difficult tasks.

In the Chapel Hill Math Circle’s beginning group, students in first- through third-grade solve problems such as this one:

A male parrot and a female parrot are talking. The one with a yellow tail says, “I’m a boy.” The one with a blue tail says, “I’m a girl.” If at least one of them is lying, who is who? Explain your answer.

This is an example of the type of problems the advanced group of high school students would solve:

A polyhedron is made up of pentagons and hexagons. How many pentagons must there be? Prove that no other number of pentagons is possible.

These problems are designed to solicit deep thinking and require students to try multiple solution strategies, collaborate, propose and test conjectures, and communicate ideas using valid mathematical arguments. At the end of the school year, the math circle concludes with a Julia Robinson Math Festival, a full day of problem solving, games, and prizes, all related to math!

For more information about math circles, including how to find a math circle near you or how to start your own math circle, visit the National Association of Math Circles at https://www.mathcircles.org/. For more information specifically about the Chapel Hill Math Circle and the corresponding Triangle Math Teachers’ Circle that provides professional development for local teachers, visit https://chapelhillmathcircle.org/. For more information on the Julia Robinson Math Festival, visit http://jrmf.org/.

math-circle

Photo Courtesy of the Chapel Hill Math Circle

Can Pigeons Read?

Reading as we know it comes from two important elements. One is the ability to decode, which is a trait known to humans and how we use language. While some studies have been used to see how well animals can learn this skill, like speaking (the most infamous maybe the work of the Communication Institute of St. Thomas founded by the illustrious anthropologist Gregory Bateson and neuroscientist John Lilly that attempted to teach dolphins to speak to humans), this is often considered a singularly human trait.

The other element is known as orthographic knowledge, or the ability to detect words. It turns out, this may be an ancient evolutionary trait, shared with species as distant as pigeons. A joint team of scientists from the University of Otago, New Zealand, and Ruhr-University Bochum, Germany, determined that pigeons can be taught to recognize certain words. They also could learn to detect patterns to possibly identify words from non-words. Pigeons could learn to detect as many as 58 words. However, pigeons are far less adept at learning vocabulary as other primates, like baboons. Baboons could understand, on average, 139 words, to the average pigeons 43.

In short, to say that pigeons can read is a rather a truthful hyperbole. This amazing research, however, does demonstrate that pigeons and many other species quite separate from us have some of the essential building blocks that allowed our ancestors to create language. Hopefully, further research will illuminate what else such a connection may mean for the development of language.

Celebrate Storytelling in Mathematics

September 25th is Math Storytelling Day! MetaMetrics® offers Lexile “Find a Book” so that educators and families can use student Lexile® measures to make informed decisions about reading materials that both interest children and are at reading levels appropriate for them to understand the material. Likewise, on quantiles.com MetaMetrics offers Math Literature Guides that accompany children’s books so that teachers and parents can use student Quantile® measures to engage children with appropriate topics in mathematics. Because this is the week of storytelling in mathematics, we want to share some Math Literature Guides that serve as samples for a variety of mathematics skills and concepts.

A simple topic for the early mathematics learner is working with ordinal numbers, such as first, second, third, and fourth. A fun book to read is Trouble on the T-Ball Team by Eve Bunting. The Math Literature Guide for this book offers ideas for using ordinal numbers at sports events (third quarter of a football game), in routine events of the day, or when losing the first tooth. In the Math Literature Guide, notice the blue title of the book. This means that when you click the title, you will be taken to the Lexile “Find a Book” page for that book.  On that page in the right-hand column is a drop-down menu called “Find This Book.” Select “World Cat” in that drop-down list to see libraries near your home where you might find the book. You can also select “Barnes & Noble” or “Amazon” to purchase the book.

For children a little older, another more challenging math topic is counting to a million, the subject of the book, A Million Dots by Andrew Clements.  Dots are everywhere in the book and the challenge is to find the dot that is indicated by the number on the page. The Math Literature Guide for this book offers ideas for questions that will encourage children to think critically when comparing such large numbers.

Geometry topics are the subject of many children’s books. One example is Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander. This book includes some plays on words about angles and circles. By fifth grade, students are learning about right angles, acute angles, and obtuse angles. So the Math Literature Guide for the book offers ideas for finding different types of angles in the book and for thinking about where angles are found in architecture, design, and nature.

Mathematics is everywhere in our world but can seem to be invisible unless we take the time to point it out. Reading children’s books that accentuate the uses of mathematics offers insight and appreciation for the role of mathematics in our lives. Talking about the books we read makes reading more fun as well.  Sunday, September 25, is Math Storytelling Day, so take a trip to the library where you will find books that reveal mathematics in unexpected places to kick off a week of pleasure in reading books about mathematics. Read and enjoy!

Story Telling in Mathematics

Many people have fond memories of mom or dad putting them to bed with favorite bedtime stories. I recall the precious memory of a parent reading a fun story just before I snuggled into bed for the night. I also have a special memory of the bedtime hour when my dad was home to tuck me in. He did not read stories to me. He gave me “algebra” problems. From the time I was in third grade and up, he would ask, “A number plus 8 is 15. What is the number?” Now as a grandmother, I play “Mystery Number” with my grandchildren at bedtime. They never fail to follow their answer with “Give me another one, Grandma!”

My bedtime memories were a good combination of mathematics and literacy. The benefits of reading to our children are enduring. Through books, children appreciate experiences of others that often relate to their own experiences, expectations, and dreams. Children’s books can also help to teach the concepts and uses of mathematics.

Math Storytelling Day is coming up! According to their website, September 25 is set aside every year to celebrate the many ways that mathematics is used in our daily lives. “Math Storytelling Day is a great opportunity to get children excited about math through stories and games. Math stories can include logic, patterns, puzzles and numbers.”

A great place to find mathematical resources, such as games, activities, websites, tutorials, and videos is quantiles.com. Parents and teachers can access resources that are targeted to a child’s mathematical ability level based on The Quantile® Framework for Mathematics.  This learning community for teachers, parents, and students also includes helpful articles such as “The Quantile Framework for Mathematics in the Home.” As well as those ideas listed in the article, another simple convenient way to encourage a strong appreciation for the mathematics people use every day is to read books about math topics that inspire children to appreciate and enjoy mathematics.

The website quantiles.com lists children’s books that teach mathematics and offers Math Literature Guides that detail specifics about how to connect mathematics and literature. Each Math Literature Guide includes a series of questions and activities that promote ways for parent to talk about mathematics with their children. One example is the Math Literature Guide for the book Keep Your Distance, a fun and humorous book about measuring lengths with inches, feet, and miles by Gail Herman.

To celebrate Math Storytelling Day this year, the Quantile Team at MetaMetrics will share more book titles and Math Literature Guides about various topics in mathematics. Math storytelling can be an enjoyable experience for parents, teachers, and students as they focus on the ways mathematics is used daily. Stay tuned!

Gold in Math Olympiad

The 2016 Rio Olympic Games finished almost a month ago with the U.S. winning a total of 121 medals, which is almost double that of Britain in second place.  While we are still celebrating our nation’s athletic prowess, we should also be touting our academic success — the U.S recently won its second consecutive gold medal at the International Mathematical Olympiad (IMO). The IMO is an annual competition for high school students held each year in a different country. The two-day competition requires students to complete 3 problems each day in 4 ½ hours. Here is an example problem:

“In Lineland there are n ≥ 1 towns, arranged along a road running from left to right. Each town has a left bulldozer (put to the left of the town and facing left) and a right bulldozer (put to the right of the town and facing right). The sizes of the 2n bulldozers are distinct. Every time when a right and a left bulldozer confront each other, the larger bulldozer pushes the smaller one off the road. On the other hand, the bulldozers are quite unprotected at their rears; so, if a bulldozer reaches the rear-end of another one, the first one pushes the second one off the road, regardless of their sizes. Let A and B be two towns, with B being to the right of A. We say that town A can sweep town B away if the right bulldozer of A can move over to B pushing off all bulldozers it meets. Similarly, B can sweep A away if the left bulldozer of B can move to A pushing off all bulldozers of all towns on its way. Prove that there is exactly one town which cannot be swept away by any other one. (Estonia)”

In the podcast “Count One More Gold for The U.S. — In MathJody Avirgan interviews Po-Shen Loh, the U.S. team coach. Loh, once a team member and now a professor at Carnegie Mellon University, thinks that just as the U.S. Olympics inspires young athletes, the IMO can likewise encourage students to be interested in mathematics. “I think that mathematics is similar to sports in the sense that if you do more practice, you actually get significantly better,” states Loh. “And the big question then becomes, ‘How do we convince people that doing that practice in mathematics is a fun, fruitful, exciting thing to do?’”

Good question, Professor Loh. One way we can encourage fun mathematics practice is through the use of math games. A quick internet search yields hundreds of math game sites. For a more precise approach to finding math games, teachers and parents can use the free resources available on quantiles.com.  At the site, click “Use the Quantile Framework” at the top of home page. Then select “Math Skills Database” and “Keyword Search.” Enter a keyword such as “Operations.”  A list of Quantile Skill and Concepts (QSCs) targeted to the topic will appear. Suppose you want to practice “Order of Operations.” Click the QSC “Use order of operations including parentheses and other grouping symbols to simplify numerical expressions.” Then click” Show 18 Resources” to view the free resources calibrated to that skill. There are several math games listed to help students practice math AND have fun.  

Shakespeare in the Original Pronunciation

To all high school English teachers and Shakespeare fans, a wonderful—-albeit delightfully esoteric—-publication earlier this year may have slipped under your radar. David Crystal, the Anglo-Welsh linguist, has produced the first Oxford Dictionary on Original Shakespearean Pronunciation. While on the surface this may seem like Academic pedantry at best, and utter hogwash at worst, I couldn’t recommend exploring it more. Looking into the original pronunciation of Shakespeare allows us to feel closer to Shakespeare’s world; help us understand rhymes and puns that no longer seem to work (which reminds us of how rude and bawdy original Shakespeare really was); and have a lot of fun just examining how English has shifted. Forty dollars does seem like a frivolous investment just to be able to comprehend pronunciation of the Bard’s player. However, Crystal offers free material and information on how pronunciation works. You can also compare how the sonnets have shifted over time. For instance, you can compare one of my favorite sonnets, Sonnet 130, to the Original Pronunciation. Or see how A Midsummer’s Night’s Dream would have sounded to its first audience.

Here is a video of David Crystal and his son Ben explaining more OP and doing a demonstration of some of accent as they compare parts of the Henry V and Romeo and Juliet.

Vocabulary Matters

Vocabulary matters. From early readers learning sight and high-frequency words to medical students deciphering Latin-based names for the parts of the human body, vocabulary is critical for academic and life success. While students acquire many words indirectly through typical reading experiences and engagement in conversation, research suggests that high-quality direct instruction of vocabulary remains an effective way for students to learn new words. Unfortunately, time limitations and the quantity of potential words preclude educators and parents from providing direct instruction designed to teach all possible vocabulary words.

To address this challenge, MetaMetrics has developed a new technology, Lexile® PowerV, to facilitate the selection of words from a piece of text. Words are selected based on three criteria: challenge level, relevance to the passage, and consequence for later reading experiences. The challenge criteria can be based on either the text complexity (e.g., words that will be hard given this text) or reader ability (e.g., words that will be hard for a particular reader). Words relevant to the passage reflect the key themes of the text based on a corpus analysis of 1.4 billion running words. Lastly, words with high utility (i.e. words that are part of large word families) or have been recognized as important for future academic success are selected where appropriate. For more information about the research underlying PowerV, please see our research briefs Empirical Lexile Measures for Words, Lexile Word Frequency Profiles, and Calculation of Lexile Word Measures Using a Corpus-Based Model and Student Performance Data.

This research initiative has implications for parents, educators, and partners. For parents and educators, MetaMetrics’ Lexile “Find a Book” website provides a portal to PowerV functionality. For select books, PowerV provides targeted vocabulary lists based on either the text complexity of the selection or specific reader ability. The word lists generated by PowerV can be used to inform pre-reading activities and instruction, providing readers with an opportunity to learn critical words before encountering them in text. The utility of these word lists is best illustrated with examples.

Don Quixote by Cervantes has a text complexity of 1410L, and PowerV selected ten words from the book that are important for readers to know, regardless of their individual reading abilities: goatherds, shepherdesses, valorous, earldom, belabored, doleful, covetous, digressions, succor, and chaste. To get a more individualized vocabulary list, a teacher or parent could enter a reader measure for a student. In this example, a reader measure of 1000L was entered and PowerV generated a custom word list that is appropriate for this particular reader: curate, disenchantment, commending, absurdities, lamentations, besought, jousts, renegade, and proverb.

A more contemporary example is Harry Potter and the Sorcerer’s Stone by J. K. Rowling. The first novel in the Harry Potter series has a text complexity of 880L and PowerV identified the words that are important for readers regardless of reading ability: referring, broomstick, defrosting, clouted, unseated, bathrobes, quartets, trances, and alibis. For a fourth grader reading at 600L planning to engage with this stretch text, PowerV identified a custom vocabulary list: chasers, scuffles, piers, bowlers, madam, cloak, boaters, dodges, hushing, and whiskery.

MetaMetrics provides a web service for partners looking to integrate PowerV functionality into their own instructional systems. The service accepts a variety of parameters (text, ISBN, Lexile range, number of requested words) and returns appropriate vocabulary lists. Example usages could include: highlighting of challenge words (if in a digital environment), providing word lists in the front of each book, or pre-reading vocabulary-building activities. For more information about licensing Lexile PowerV, please click here.

Given the importance of vocabulary development for academic success, the word selection provided by PowerV is a critical first step in improving student vocabulary knowledge and reading comprehension. With these words in-hand, parents, educators, and partners all have the opportunity to adopt the instructional approach that best suites the needs of their students. In the end, vocabulary matters.

Lexile by Chapter Guides: Expanded Offerings for a New School Year!

A flurry flutters throughout our nation’s schools as instructors clean classrooms and libraries. Bookshelves are being rearranged. Teachers frantically organize their textbooks and create new bulletin boards. This month, educators gear up with excitement, and refresh their materials (and themselves!) for a new school year. Here at MetaMetrics (developer of Lexile measures), we’re refreshing some of our resources for you too!

Launched last fall, Lexile by Chapter Guides have drawn considerable attention to the utility of Lexile measures in instructional planning. In particular (and as articulated in Tim Shanahan’s blog post this past June), this work helps grades 2-12 teachers think beyond merely using text complexity measures as a way to assign certain texts to students based upon their reading ability. Instead, these Guides help teachers think more about the kinds of instructional scaffolding needed to bridge the gap between the difficulty a particular text presents and the individual student’s unique reading abilities. With a deeper understanding of both the complexity within a book and the reading ability of individual students, educators can more thoroughly explore and prepare for those reader and task considerations in the classroom.

MetaMetrics is pleased to announce that we have added 38 new Lexile by Chapter Guides (LbC) for 33 different titles to our collection. These new Guides are available, along with our previous offerings, on the LbC webpage here. The new titles included represent many books that have been requested by teachers and librarians through our feedback survey; our research into frequently taught full-length works at various grade levels; and also a few that serve to illustrate the importance of this work for instructional planning.

Perhaps most exciting in our new offerings is the inclusion of 16 non-fiction, informational texts. These non-fiction titles (many of which also have discussion guides for teachers collected here) will help provide teachers of science, mathematics, history, social studies, and other content areas access to the same information teachers of literature have enjoyed over the past year.

The planning and preparation that goes on in schools this time of year becomes the foundation for student success over the next many months. We hope Lexile by Chapter Guides are a part of that planning and preparation too. Whether teachers are using these Guides to help them better understand the needs of their instruction, or whether they are sharing them with students to help them anticipate and plan for their own independent reading, Lexile by Chapter Guides are a treasure trove of information that help to spur everyone toward success!

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.