Math Lit: Probability, Measurement, and Graphing

Math and story books may seem as though they belong to completely different disciplines, but they can work together to teach mathematical concepts that some students find difficult. The stories and pictures are engaging for kids, helping them to stay focused on the principles at hand. Also, the stories provide children with a familiar, more concrete platform for understanding concepts that are both foreign and abstract. Below are some great titles which can make the tricky concepts of probability, measurement, and graphing easier to swallow. Parents and teachers may want to use these books as introductions to new material, or as a way to reinforce concepts that have already been taught using more traditional methods.

Probability

Most children are fascinated by the concept of probability once they become aware of it, though statistics is not typically taught until the very end of high school. The understanding that many events are not completely random represents a big milestone in a child’s development, and as children learn to play simple games involving coin tosses, spinners, cards, and dice, probability becomes an important principle in their lives.

To help kids move beyond the kind of probability they’ve learned by tossing coins, children’s literature comes to the rescue with a variety of fun and informative storybooks. For teaching simple statistics, The Reading Teacher* recommends A Very Improbable Story by Edward Einhorn, It’s Probably Penny by Loreen Leedy, and Caldecott Medal winner Jumanji by Chris van Allsburg. Odds are good kids will love learning with these stories!

Measurement

Using a measuring tape or ruler seems pretty basic, but for some children it can be a real challenge, particularly when inches are subdivided into fractions. The concept of length can be difficult for kids to wrap their heads around, in part because many of them don’t have a lot of experience measuring things themselves.

More practice is obviously called for, but parents and teachers may want to consider reaching for storybooks to teach children the fundamentals behind measurement. For teaching linear measurement, a recent article in The Reading Teacher* recommends Inch by Inch, written by legendary children’s author Leo Lionni, The Fattest, Tallest, Biggest Snowman Ever by Bettina Ling, Much Bigger Than Martin by Stephen Kellogg, and The Inch-High Samurai by Ralph F. McCarthy among others. Books like Mr. Archimedes’ Bath by Pamela Allen help explain other types of measurement.

Literature may lend meaning to measurement that kids didn’t see there before, and the selections above are a few examples that really measure up!

Graphing

A book about Rene Descartes, the French philosopher and mathematician who gave us the Cartesion system of coordinates, hardly seems destined to be a child’s favorite. Yet The Fly on the Ceiling by Julie Glass is clever and engaging enough to keep kids entertained while they learn about the theory behind graphing on a coordinate plane.

The Reading Teacher* recommends several other titles for teaching students about graphing through storybooks, among them Fair is Fair by Jennifer Dussling (bar graphs) and TigerMath: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda (various types of graphs).


*Bintz, W. P. et al. Using Literature to Teach Measurement. (2011). The Reading Teacher, 65(1), 58-70

Friday Favorites

SchoolBook
The School Book pages of the New York Times are an excellent "go to" resource for what is going on in the world of New York City education. They include links to helpful guides and websites, a school search feature, and articles, blogs, and conversation threads about current issues.


Education Week
We liked the article in the May 23rd issue of Education Week about how introverted children may be overlooked by their teachers -- and how their more thoughtful nature can be an asset in other situations, such as taking standardized tests.


Inside Schools
We have recommended the InsideSchools website before (a project of the Center for New York City Affairs at The New School), but haven't mentioned their presence on YouTube, where they have posted excellent instructional videos on how to choose a school and special education services. In the complex New York City public school maze, these video guides help provide clarity. For a sampling, check out the video below about specialized high schools in New York City.

Photo: Josh Pesavento/Flickr Creative Commons

Behavioral Therapy and ADHD

Scientific American has reported on findings from the recent Experimental Biology meeting in San Diego that look at the relative effectiveness of cognitive and behavioral therapies versus medications in helping children and young adults with Attention Deficit Hyperactivity Disorder (ADHD). 

Included in the research reported at the meeting were findings by Dr. Claire Advokat of Louisiana State University, who looked at college students with attention difficulties and found that it was not medication, but good study habits, that determined several parameters of college success, such as grades. Dr. Advokat noted, according to the Scientific American report, that this does not mean that medication had no effect for these students, but that it may help students develop good study habits, which then improves student performance. 

Other researchers at the Experimental Biology meeting included Dr. William Pelham of Florida International University, who noted improvement in children's ADHD behaviors, such as classroom disturbances, when their parents received training in behavioral tools and in managing their own stress. Dr. Pelham has also conducted studies suggesting that children with ADHD who receive low doses of medication combined with behavioral therapy do better than children receiving only medication or only therapy. 

While there is much work to be done, none of the researchers whose findings were discussed in this article by Scientific American suggested going back to the days before ADHD medications became available and only cognitive and behavioral therapies could be offered; they generally agreed that it is important to explore the relative uses of all available modes of treatment. While medications generally work more quickly and are more cost effective than longer term behavioral therapies, they can have side effects. The real question that remains is what works best for each individual child and young adult in the long run.

Changes in Medical Education

Two recent articles in The New York Times focus on how medical education is changing. Both reflect the trend away from the traditional path of four years of hard science courses in college, followed by four years of medical school, where coursework continues to focus strictly on science based topics.

One move away from this is the growth in post-baccalaureate pre-med programs, where college graduates who have not taken the necessary science courses, or who are out in the working world but want to switch to a career in medicine, can prepare for medical school. According to the Times article, more than 15% of new medical students have gained admission after completing such programs and there are now 135 post-baccalaureate programs listed with the Association of American Medical Colleges (AAMC). These students may have studied poetry, history, or psychology in college and may have had work experience as teachers, artists, or marketers. They can bring a very different perspective to their medical education and their interactions with their patients.

Another trend involves changes to the medical school curriculum itself, towards what the Times piece calls "heart and soul and social science." The AAMC is making substantial changes to the Medical College Admission Test (MCAT) in an effort to look for strengths in areas other than just science, with the goal of admitting individuals to medical school who bring a broader skill set -- including the ability to connect to their patients, not just to analyze test results. Beginning in 2015, the MCAT will include sections on "Psychological, Social and Biological Foundations of Behavior" which are designed, according to the MCAT website, to recognize "the importance of socio-cultural and behavioral determinants of health and health outcomes." In addition, another new section called "Critical Analysis and Reasoning Skills" is intended to help identify applicants from diverse backgrounds. Students entering college this coming fall will be the first group to take the new MCAT when it is put in place in 2015.

Dr. Yellin's work as a consultant to the Office of Student Affairs at New York University School of Medicine and his extensive experience performing evaluations of medical students lead him to observe that whatever changes may occur to medical school admissions and curriculum, the academic demands of medical school will continue to be an issue for future physicians."Like other strong learners," he notes, "medical students will not get very far in their studies or careers without an understanding of how they actually learn and without developing a repertoire of strategies. Often, learning strategies that have worked for them in other environments don't work for them in the demanding setting of medical school. They need to develop new strategies for the extraordinary demands of the medical curriculum and that requires them to understand how they learn, since even very successful students will have stronger and weaker areas in their academic skills."

Photo: Alex Proimos/Flickr Creative Commons

The Scoop on Schools: Resources for School Selection

Some families, especially those who are well settled in suburban school districts, don't give much thought to school selection. But for others, including families in large cities with numerous school options, or those who are considering moving or enrolling their child in a private school, solid information on schools is of critical importance.

For New York City families who can have choices of public schools available at every level, an excellent starting point is the school search feature on the website InsideSchools. Located on the home page of the site, this feature allows you to search by school name, number, or geographic location. The individual reports on each school are generally the results of visits to the school by members of the InsideSchools staff, sometimes multiple visits over a period of time. In addition, comments by parents and others often highlight issues that can be important to families trying to decide if a particular school would be a good fit for their child. The site also includes news and information on the often complex process of applying to New York City public schools.

Outside of New York City, an excellent option for researching schools is Great Schools, a national nonprofit whose funders include the Gates, Walton, and Robertson foundations. The site lists over 200,000 schools and allows families to search using a variety of parameters. This site includes all kinds of schools -- public, private, and charter. There is guidance on how to choose a school, including such issues as how to choose a school when moving from a distance. The site also has sections for homework help and parenting issues.

For families who want a private school setting, the website of the National Association of Independent Schools has a Parents' Guide that includes a school search feature that allows searches by such parameters as specialized sports programs (equestrian and crew among several dozen others) and schools that offer International Baccalaureate programs.

Next Steps for College-Bound Students with Learning Difficulties

High school seniors have generally made their college decisions and are focusing their energies on end of year activities such as proms and graduation. But for students with learning disabilities and other issues which can impact their learning, there are important things to do between now and the start of college to make sure that they are set for success in the fall. 

This is the time -- after you have been admitted and have accepted a place as a freshman -- to make sure your accommodations will be in place when you arrive on campus. For those students who have been accepted to specialized support programs at their college, there will probabably be a great deal of outreach to you to make sure your paperwork is complete. You will have had to submit current documentation of your learning or other disability as part of your application, and one of the benefits of these programs is that they will help to make sure you will receive all the accommodations you require. 

If you are like most students, however, it is your responsibility to communicate with your school's Office of Disability Services (ODS) to make sure your documentation is up to date and complete. There is still time to arrange for the kind of documentation your school requires to validate your entitlement to accommodations. This documentation can range from a full neuropsychological and educational evaluation (such as those we do here at The Yellin Center) to medical documentation of an ongoing physical condition. Every college has guidelines that clearly describe what they require and forms for you to use to submit your documentation. Get them from the college's website as soon as possible and make sure you submit the required information to the ODS without delay.

Once the documentation is complete, you need to speak to the ODS staff to arrange specific accommodations that will meet your individual needs. Are you used to a particular kind of text-to-speech software? Will you need extended time for your exams? A quiet exam location? A note-taker? Colleges are required to provide accommodations for you that will "best ensure" that you are able to access the campus, your classes, and the curriculum. But that doesn't always mean that you will get every accommodation you seek or that you will get it in the form you are used to using. You need to make sure that your documentation clearly outlines how your disability impacts your academic and residential life and what "academic adjustments, auxiliary aids and services, and modifications" (from the language of the Americans with Disabilities Act) will be necessary because of this.

Keep in mind that once you are granted accommodations you still need to take several steps to put them in place. You will need to pick up the forms documenting your accommodations from the ODS, provide a copy of the form to each professor, and then follow up before each exam to remind the professor that you will be needing accommodations for the exam. Remember, unlike in high school, the responsibility for obtaining accommodations and having them implemented falls on you. By starting early and keeping the lines of communication open, you will be able to start classes in the fall with all the supports you require for success.

Photo: Briles Takes Pictures/Flickr Creative Commons

Vocabulary Knowledge Scale

Memory is a strange animal indeed. Recent research suggests that people have difficulty differentiating between what they know and what is familiar to them unless they are specifically prompted to do so. Dr. Yellin likes to share a story about a conference about memory he attended in which the lecturer asked the attendees how many of them knew how a toilet worked. Most of the hands in the room went up. The lecturer then asked how many of them could explain it step by step. Nearly every hand went down. This is the difference between familiarity and mastery: Just because our memories have encountered a concept before does not mean that we understand it thoroughly.

The first step in transitioning from a recognizer to a master of a concept is to determine where the gaps are, and sometimes that realization takes some outside prompting. This issue is particularly prevalent in the issue of vocabulary. Many students will say that they know a word’s meaning only to be unable to define it when asked. Chances are they’re not being cheeky; their brains are just confusing familiarity with mastery. To help students combat this, a vocabulary scale can be a great tool. 

The scale is made up of four levels:

Level 1 – I can define that word and use it in a sentence.

Level 2 – I’ve heard that word before and know the gist of it. I may be able to give you some examples or use it in a sentence, but I can’t come up with a solid definition.

Level 3 – I’ve heard that word before, but I have no idea what it means.

Level 4 – Huh? I’ve never heard or seen that word.

If an adult working or talking with a student suspects that a student does not know a word, s/he should ask the student to determine which level the word is for them using the scale. Sometimes, simply discussing a Level 2 word is enough to help students construct a definition for it. Words from Level 3 and 4 should be taken in context, and preferably in the context of other sentences as well, deconstructed, and looked up.

The vocabulary scale is not intended to instruct students in vocabulary, per se. It can, however, make students more self-aware of their levels of word knowledge, making it even more powerful than any curriculum.

Photo: Horia Varlan/Flickr Creative Commons

Remembering Maurice Sendak

While reading the New York Times obituary of Maurice Sendak this morning, your blogger could not help looking up from the kitchen table, above which an illustration from his book In the Night Kitchen has hung for many years. His work was part of the fabric of our children's lives, well beyond his best known work, Where the Wild Things Are.

Sendak had a complex nature. "I don't write for children. I write and somebody says, 'That's for children,'" he told Stephen Colbert in an interview this January. His stories and characters were strange looking and sometimes scary -- and yet children could identify with them.

His brillant collaboration with Carole King in the musical Really Rosie, which was performed off Broadway and made into a television special and eventually into a DVD, took four of his stories (Chicken Soup with Rice, Alligators All Around, Pierre, and One Was Johnny), which were collectively known as the Nutshell Series, and brought them vibrantly to life. In a houseful of small boys, Pierre "who would only say 'I don't care'" was a well-loved cautionary tale, and our sons had the words to all of the story-songs memorized.

If you or your children haven't yet had the pleasure of delving into Maurice Sendak's world, you may want to give some of his books a try. They are not standard children's fare -- but then, as Sendak noted, they weren't really written for children.

Photo: Kate Hiscock/Flickr Creative Commons

The Role of Memory in Decision Making

We've all heard the expression "learning by doing." But just how does having done or experienced something in the past actually help shape our decisions and behaviors later? 

Scientists at the University of California, San Francisco, have looked at brain processes in rats to better understand how humans build on their past experiences in making new decisions. Dr. Loren Frank and his team blocked the neural pathways -- split-second electrical bursts in the memory areas of the brain -- that enabled the animals to "replay" their past experiences learning their way through a particular maze. Earlier studies had suggested the role of mentally reliving past experiences as key factor in making new decisions, such as how to approach a new maze configuration. But it was necessary to isolate this brain function to understand its importance to learning and decision making. When this function was blocked, the rats were unable to link their previous experience with the maze to their current situation and their performance in the maze deteriorated. 

“It appears to be these ripple-like bursts in electrical activity in the hippocampus that enable us to think about future possibilities based on past experiences and decide what to do,” Dr. Frank stated to the NIH’s National Institute of Mental Health (NIMH), which helped to fund the research. "Similar patterns of hippocampus activity have been detected in humans during similar situations.” This "awake mental replay" is related to the way that sleep helps to consolidate memories in humans and is also related to day-dreaming. It seems even when we think we are disengaged, our brain is busily at work, consolidating what we have learned and readying us to apply it to a new situation.

Image: Derivative work: Looie496 [Public domain], via Wikimedia Commons

Science and Science Fiction Reading Ideas

Science can be one of the most fascinating subjects a student can study. Kids love learning about the way the world around them works and appreciate the practicality of science. Science taught from a textbook, however, can be a dry topic indeed. Trade books can pep up science instruction that young people find tough to get excited about, however; and there are many fantastic offerings available. To ensure you’re supplying your young readers with the best of the best, check out favorites picked by the staff at the Smithsonian and the National Teachers of Science Association.

But not every child enjoys reading books about science. Why not whet kids’ appetites with science fiction instead? Great conversations can be had about whether or not the futuristic ideas in a science fiction novel are currently feasible, or what would need to happen for them to exist.

A quick Internet search for “children’s science fiction book list” yielded many great lists, some complied by various libraries around the country, others by news media and awards committees. One outstanding source for excellent science fiction titles for children of all ages is the Golden Duck Award list, though of course this list should not be considered exhaustive. Some stellar young adult titles, like The House of the Scorpion by Nancy Farmer (National Book Award Winner for Young People's Literature, Newbery Honor Book, Printz Honor Book) and Feed by M.T. Anderson (National Book Award Finalist) are notably absent. Still, it’s a great starting point for those unfamiliar with the genre’s offerings for young readers.

With this variety of genres and topics available, it should be easy to convince even the most skeptical of students that science rocks!

Photo: Lokesh Dhakar/Flickr Creative Commons

Extended School Year

As the academic year moves along, many students are beginning to think ahead to summer and to a break from school. Even though the weeks of vacation can mean that the first part of the following year will include a review of skills that got a bit rusty over the summer, this isn't a major issue for the vast majority of students. 

For some students who are receiving services under the Individuals with Disabilities Education Act (IDEA) however, the summer break may pose a significant challenge to fragile educational progress. For these students, an extended school year (ESY) may be the solution. The IDEA is silent about extended school year services, but the subject is dealt with in the regulations that implement the law. These are quite general, and simply note that such services should be provided if the child's IEP team determines that they are necessary for that student to receive a Free Appropriate Public Education (FAPE). The regulations further note that such services should not be limited to any particular classification of disability or to any type of services.

Our colleagues at the Wrightslaw website have recently addressed this issue and note that the criteria for an extended school year vary from state to state. Here in New York, for example, extended school year services, sometimes called 12 month services, can be provided by an IEP team only "to prevent substantial regression. Substantial regression would be indicated by a student’s inability to maintain developmental levels due to a loss of skill, set of skill competencies or knowledge during the months of July and August." Other states have different standards, so the first step to deciding whether to seek an extended school year should be to check the specific laws and rules that apply to your state. For most students with learning difficulties, an extended school year is neither necessary nor obtainable from the public school system. This doesn't mean that students can't work on their academic skills in summer school programs, at camp, or otherwise -- just that such educational services will not be formally provided and paid for by the public school district.

Photo: Stephanie Precourt/Flickr Creative Commons