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.

To learn more, please view our recent webinar The Lexile Career Database: Discover the Reading Demands of Prospective Occupations and see additional supporting information here. The Lexile Career Database is now available for integration into Lexile partner products and services. Contact our Strategic Partnerships team for more licensing information. 

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Dewey Decimal Day

Happy Dewey Decimal Day! Each year on December 10th we honor the birthday of Melvil Dewey (1851-1931), a respected librarian, educator, and the inventor of the Dewey Decimal System. Dewey first published his groundbreaking library classification system in 1876 as a four page pamphlet. Through the years the Dewey Decimal System (or Dewey Decimal Classification as it is officially named) has been expanded and revised through 23 editions, the most recent iteration, a four volume set, was published in 2011.

The Dewey Decimal System is the most widely utilized library classification system in the world. Over 200,000 libraries in at least 135 countries use it to organize their collections and it has been translated into more than 30 languages. The system is maintained by the Online Computer Library Center (OCLC). Learn more about the Dewey Decimal System including licensing options and monthly updates by visiting the OCLS’s Dewey website.

The Dewey Decimal System assigns a three digit number based on the subject of a non-fiction book, with decimal numbers providing further detail. This allows libraries to organize books in a meaningful way so patrons can locate the books they need and easily return them to their proper location. Before the invention of the Dewey Decimal System, libraries often organized their collections by acquisition date, not by subject. Imagine how difficult it would have been to locate the right books that way! To celebrate Dewey Decimal Day visit your local library and look for some books, start the Dewey Decimal Challenge or even stay in a hotel inspired by the Dewey Decimal System!

The Foundation of Education

So often we get caught up in the negativity surrounding education. Whether that’s funding, adjusting the curriculum, or tragic events. In the midst of this media coverage it is far too easy to overlook the people whose work forms the foundation of our education system: our teachers.

Teachers help shape students, they help mold them, encourage them, spark their creativity, give them things to aspire to. They give students the means to reach goals they didn’t think they could meet, or to have dreams they never thought they could have. Teachers do all this despite long hours, low pay, student diversity, and more. In light of this, NPR has created a series called “50 Great Teachers” to recognize what often goes unrecognized — great teachers. Teachers who make an impact. Teachers who go above and beyond not for their own benefit, but because they genuinely care about the future and development of our students.

This series features everything from swim teachers who focus on earning student’s unwavering trust to a principal who dedicated years of his life to transforming the success rate of senior exams at his school from 12% to 100%. These stories give insight to what goes on behind the scenes in the lives of teachers. It exposes what often goes unnoticed to the public — persistent dedication. It spotlights teachers like Rodney Carey. Carey was a bail bondsman who couldn’t shake the fact that most of the students he was bailing out of jail, who had an upbringing much like his own, were underserved and had scarce opportunities available to them. He decided then to dedicate his life to improving this through teaching. Carey remarks,  “I know that you cannot save everybody,” he says. “But if one of them could just go along, complete his education, go to college, and I see him in the future doing something positive with his life, that makes me think that what I was doing is all worthwhile.”

This series will give you perspective on the uplifting aspects of our schools and hopefully encourage you to look past the negativity and appreciate the positive influence teachers are having on our students, despite numerous obstacles.

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/kzG0mi. 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.

Unpacking the Complexity Within the Text Complexity Measure

By Malbert Smith III, Ph.D. and Matt Copeland

With the recent release of Harper Lee’s Go Set a Watchman, there is renewed interest in her classic, To Kill a Mockingbird. In fact, Brody and Maloney (Wall Street Journal, July 14, 2015) argue that teachers need to rethink how they teach To Kill a Mockingbird in light of the themes in Go Set a Watchman. The timing of this release also corresponds to the five year anniversary of the Common Core State Standards (CCSS). Regardless of where you land on the merits of the CCSS, it has brought a renewed instructional emphasis on the concepts of text complexity and close reading.

With the next generation of standards’ emphasis on increasing the diet of non-fiction and the number and quality of complex texts that are taught, there was concern among some teachers that many of our canonical texts (particularly fiction) taught in middle and high school did not appear to satisfy the text complexity requirement. For example, when one examines the quantitative leg of the text complexity triangle, To Kill a Mockingbird has a measure of 790L which corresponds to the recommended grade level of 4 to 5 in Appendix A of CCSS. However, when one examines the qualitative and reader/task legs of the triangle, the authors of the CCSS in Appendix B adjust the recommended level to grades 9-10 where this novel is typically taught.

Shanahan and Duffett (2013) reported that, like Mockingbird, seven of the ten most popular books taught in middle school and five of the top ten books taught in high school are not challenging enough on the quantitative index. Against this backdrop ELA teachers in middle and high school have been asking whether these classic books can satisfy the requirements of close reading of complex text. And the answer is that these books are outstanding not only on the quality and reader/task dimensions but also along the dimension of quantitative measures of text complexity. In fact, when we dig a little deeper into these individual works, we often find that there is sufficient complexity—even based upon the quantitative index alone—to warrant their inclusion in our curricula.

But beyond the consideration of what works we teach, another important consideration are the instructional practices that we use to deliver that learning to students. Certainly, close reading and the reader and task considerations within the CCSS text complexity model are essential; they provide the framework for thinking through the kinds of instructional scaffolding we might provide to help students be successful. As classrooms around the country prepare to begin another school year anew, helping practitioners to examine the complexity of a text and even the finer grain details of the quantitative index, might be a rich resource for more data-driven instructional planning.

To this end, MetaMetrics is unveiling the beginnings of a new line of research: chapter-by-chapter graphs (such as the one shown below for Mockingbird [Figure 1]) of the Lexile measures of chapters within an individual work. Our belief is that equipped with this type of information instructional leaders can make decisions on how best to focus their instruction time and thereby have an even more profound positive impact on student learning.

Figure 1. Lexile measures by chapter for To Kill a Mockingbird.  Fig1

As one can see in Figure 1, while the overall text complexity measure of Mockingbird is 790L within the entire book, there is substantial variation among the individual chapters of the novel. In fact, of the novel’s 31 chapters, 18 chapters fall above the entire work’s Lexile measure of 790L, while only 13 chapters fall below the 790L mark. And while only one chapter (Chapter 20—part of the courtroom scene) falls within the Grades 9-10 text complexity band, five more chapters come within 100L of that range. From this graph, we believe it is easy to see that there are a number of opportunities to present sufficiently complex text to students and to provide the close reading opportunities and instructional scaffolding our students may need.

Interestingly, when we have asked ELA teachers of Mockingbird to predict which specific chapters of the novel might be more complex than others, they typically predict the same ones that the quantitative measures identify. This would seem to support the notion that many practicing classroom teachers are quite adept at selecting texts that provide sufficient complexity for their students’ learning and understand—even intuitively—where the complexity resides. However, making these realities more concrete in our minds offers us a number of opportunities to reflect upon our instruction.

As an extension of this work, we have gone a step farther and also begun to examine each paragraph within a particular chapter. Just as we see variation among the Lexile measures of individual chapters, we see even more variation among the paragraphs within a chapter. For example, when we examined the complexity within Chapter 13 of Mockingbird [Figure 2], it became clear to us that although the overall measure of this chapter is 1020L—just below the text complexity grade band range for Grades 9-10—there does exist a sequence of about 20 paragraphs that overwhelmingly do fall in the text complexity grade band and, in fact, even exceed that grade band in one instance. The opportunities to engage students in close reading of text at the appropriate level within these 20 paragraphs seem rich on the surface. An examination of the content of those paragraphs—the scene where the young narrator of the novel, Scout, comments on the arrival of her Aunt Alexandra, the relationship Alexandra maintains with her brother, Atticus, and her staunch belief in the importance of family and social traditions—confirms the importance of the passage to the novel as a whole. And, perhaps, becomes even more important now given the narrative presented in Go Set a Watchman.

 Figure 2. Lexile measures by paragraph for Chapter 13 of To Kill a Mockingbird. fig2

As a former high school ELA teacher, I (Matt) now see how examining and unpacking the empirical text complexity measure of books could have helped me greatly in planning for instruction. For example, I see more clearly now where the opportunities for close reading exist within the novel. I would rethink the reading schedule I typically hand to students at the beginning of the unit to highlight these “peaks” of complexity within the work and spend more time focusing my efforts on providing my students—particularly my struggling readers—the instructional scaffolding they need in order to be successful with these chapters. The possibilities seem endless.

If we desire to meet the ideals embodied in the next generation of standards, educators need time, tools, and resources. Even within the text complexity model itself, such opportunities do exist. Our challenge is to harness these opportunities, embrace them, and empower changes to our curricula and—even more importantly—to our instructional practice.

As we think about the needs of our students and re-think some of our curricula and instruction, Scout’s wisdom and insight from the end of To Kill a Mockingbird, when she finally stands upon Boo Radley’s front porch, seem all that much more relevant: “I had never seen our neighborhood from this angle.”

For more information and to view the collection of available Lexile by Chapter Guides, please visit lexile.com/lexile-by-chapter/.

References

Brody, L.  & Maloney, J. (2014, July 14). Teachers’ new homework: a ‘Watchman’ Plan. The Wall Street Journal. Retrieved from http://www.wsj.com/articles/teachers-new-homework-a-watchman-plan-1436917909

Lee, H. (2015). To Kill a Mockingbird. New York: HarperCollins.

Lee, H. (2015). Go Set a Watchman. New York: HarperCollins.

Shanahan, T. & Duffett, A. (2013). Common Core in the Schools: A First Look at Reading Assignments. Washington DC: Thomas B. Fordham Institute. Retrieved from http://edexcellence.net/publications/common-core-in-the-schools

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.