The March issue of Teaching Children Mathematics cited a recent study from Stanford University School of Medicine showing, for the first time, how brain function differs in people who have math anxiety from those that do not. The 2012 study involving second and third grade students that showed signs of math anxiety while they were performing addition and subtraction problems. The study found that the part of a student’s brain that was responsible for mathematical reasoning was less active while the portion of the brain associated with negative emotions was more active. “Until Young and colleagues did this study, no empirical research substantiated the claim that math anxiety can stand in the way of young children’s success in completing problem solving and mathematical reasoning task.”
Even back in 2000 Vanessa Stuart author of “Math Curse or Anxiety” gave her fifth grade students a survey and found that that her students’ anxiety toward math stemmed from a lack of self-confidence of their mathematical abilities. She knew she needed to raise their self-confidence while teaching them math. She found using journal writing, collaborative group work, as well as other strategies helped. She had groups work on problem solving and encouraged students to share solutions with one another. Students helped one another see a variety of ways to solve problems. They became more willing to take risk and share ideas through journal writing. They also shared frustrations and she was able to reply back in the journals without embarrassing her students.
Teachers have been aware of the importance of supporting students’ self-confidence involving math. Now, the results of this study highlight the importance of assessing math anxiety in young children because of its impact on their ability to be successful in mathematical reasoning and problem-solving.
A recent Time article profiled Laura Overdeck is a high-tech consultant that switched to a stay at home mom. She has just launched Bedtime Math a website devoted to creating a new stamp for arithmetic. Lots of people believe they are “not good at math but you don’t hear them say they are not good at reading.” Overdeck thinks that parents should make time for math at night just as they do with reading bedtime stories.
She began by emailing about a dozen friends a word problem with varying levels of difficulty appropriate for preschoolers to upper-elementary students. Her numbers had tripled within a week and nine months later 20,000 people had signed up to receive the free daily emails.
Overdeck said that math is seen as a fun activity in her house and that kids seek out math activities, but she realizes this is not the norm. “Everyone knows they should read a book but nobody knows they should be doing math with their kids,” remarked Overdeck. She thinks it is important to make math engaging and applicable to daily life to connect with children. She does this by involving world situations into math problems in her daily emails. There are several math sites as well as math games that show students math can be fun, so Google some math sites and start early to show your child math can be fun. And be sure to check out our own Math at Home for targeted math activities that students can do at home. And to keep students engaged in math activity over the summer, be sure to sign up for our Summer Math Challenge.
Not surprisingly, what students know about math by first grade seems to be an early indicator of how well they will be able to do everyday calculations later in life. About 1 in every 5 U.S. adults can’t perform at a mathematical level that is expected of a middle school student.
A study from the University of Missouri tested 180 7th graders that were performing lower than their peers in a test of core math skills needed to function as an adult. The results showed that the students that were behind in 7th grade were also behind in 1st grade. Unfortunately, the gap was never filled. Dr. David Geary a cognitive psychologist leads a study tracking children from kindergarten through high school in the Columbia Mo. School system. He stated that the students behind in the early grades are not “catching up” with students who started ahead.
Geary says students need “number system knowledge.” This includes:
- knowing that 3, three, and 3 dots all represent the same quantity
- knowing that 23 is a bigger quantity than 17
- realizing that numbers can be represented in a variety of numerical ways such as 2 + 3 = 5
- 4 – 1 = 5, 5 + 0 = 5, 6 – 1 = 5
- using a number line to show the difference between 10 & 12 is the same as the difference between 20 and 22.
Mann Koepke of NH’s national Institute of Child Health and Human Development has a number of suggestions to help children with math at an early age. For example:
- attach numbers to a noun such as 5 crayons so they can visually see the concept of the number
- talk about distance by asking “How many steps to your ball?”
- describe shapes
- measure ingredients
- discuss what time you need to leave to get to a destination at a certain time
- making change when buying items
- predicting which line in a grocery store will be the quickest
It is never too early to start recognizing how much math is used in daily activities. And whenever possible, it pays to intervene early to ensure student math success.
We recently recommended The Joy of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz. One of the more interesting essays explains some of the mathematics behind interesting phenomena. He offers the architecture of New York’s Grand Central Station whispering galleries as one such example. In the whispering galleries two people can stand at two points 40 feet across the hallway from each other. If one person whispers “sweet nothings” the second person can clearly hear each word, but passersby cannot hear a word.
While this phenomenon seems like magic, it’s actually based on mathematics. The gallery is elliptically shaped (or oval shaped) which means there are two focus points on the floor where all sound waves will bounce from the walls.
One of my favorite examples of elliptical shaped architecture is the National Hall of Statues in Washington, DC. This is where the U. S. House of Representatives held their sessions from 1807-1857. There are two bronze plaques on the floor. If two people stand on those plaques across the hall from each other, they can talk to one another in a normal conversational tone and not miss hearing a word.
The first time a tour guide told me about these two points, I knew immediately that the two points were focal points of the elliptically-shaped hall. But the tour guide also shared that John Adams had his desk sitting at one of those bronze plaques on the floor and pretend he was sleeping. Actually, he could hear every word that was said among the other representatives. This is because his desk was at the point where all sound waves would bounce off the walls and over to the focal points. One of those points was where John Adams was sitting.
So what is wrong with this story? John Adams served as our second president from 1797 to 1801. At the end of his one and only term, he retired and moved back to his home in Massachusetts. While I love the math that is demonstrated in a beautiful and historic buildings, I also appreciate and know enough about U.S. history to realize that John Adams did not serve as a representative in the original US capital in Washington, DC. But I still can’t help but smile when I hear the story, as it so beautifully illustrates how much mathematics influences our world in unseen ways.
The Joy of X by Steven Strogatz is a series of essays that explore the seemingly limitless span and beauty of mathematics underlying so much of our universe. Strogatz’ exploration begins by considering the counting of the Sesame Street characters and extends to the unique and inviting applications of trigonometry, limits, and fractals. But don’t let that scare you. His examples yield insights into the way mathematics influences politics, art, and nature. And, of course, he explores the way science and technology rely so heavily on mathematics as well.
The author takes a delightful approach by using concrete examples in order to illustrate an abstract concept that even the inexperienced and the less mathematically inclined can understand. A reader with a mathematical background will respond to Strogartz examples with such reactions of “I never thought of it like that!” or “I didn’t know that!”
Even if you’re not a math educator, you will find the material enlightening and enjoyable.
MetaMetrics® is pleased to announce that the redesigned Quantiles.com will be released on March 14, 2013. The site has been given an all-inclusive makeover, complete with a brand new look and feel, improved navigation and tablet and mobile compatibility.
The new Quantiles.com will feature:
- A slick, crisp, design
- Tablet and mobile compatibility
- New content and images
- Redesigned tools such as the “Math Skills Database” and “Textbook Search” featuring improved functionality
In addition to these new site features, we are excited to announce “The Summer Math Challenge” a six-week, e-mail-based initiative designed to combat summer math loss. The initiative, based on the Common Core State Standards, will target students who have just completed grades 2 through 5. Parents will receive emails with resources and activities designed to help their kids retain the math skills learned during the previous school year.
We’d like to invite you to witness the unveiling of the new Quantiles.com first hand. Join us March 14, from 3 to 4 PM EDT, and you just might win free pie! Three lucky people who participate in our “Happy Pi Day… Introducing the New Quantiles.com” webinar will receive gift certificates for a free pie shipped nationwide from Porch Pies in Los Angeles, CA. For more information about the webinar, click here. Register today!
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According to a recent article in EdWeek, among 2013 high school Seniors, there has been a 21% increase in interest in STEM-related careers, as compared to 2004. The most significant differences were by gender. Among 2013 seniors who were interested in STEM careers, 38% were males compared with only 15% who were female. Unfortunately, surveys of students in future graduating classes indicated an even wider gap between genders.
The most disturbing element of the recent report is the outcome of the surveys of high school Freshmen. Of those students who reported interest in STEM-based careers as freshmen, approximately 57% lose their interest in fields of science, technology, engineering, and mathematics. The federal government estimates that there will be around 8.7 million positions within STEM-related fields, as compared to the 7.4 million positions that currently exist. In order to meet the demands of the future, it is vital that our educational system maintains and enhances student interest in the sciences, technology, and mathematics throughout their high school career. If students are expressing an interest in these areas early in their high school career, it is certainly an indication that such interest should be sustained and encouraged by their teachers and administrators.
As a mathematics educator, I am pleased to see the budding enthusiasm of high school students for STEM related areas. The challenge now is how best to encourage, support, maintain, and enhance their studies in the sciences to preserve that zeal and excitement and to ready those same students to develop their potential for success in college and STEM based careers.
With the wide availability of calculators on phones, mobile devices, computers, and many other electronic devices, some may wonder if it’s still essential for students to commit math facts to memory. In a world replete with digital assistance is the memorization of math facts still necessary?
Researchers Daniel Ansari and Gavin Price of the Numerical Cognition Laboratory at the University of Western Ontario in London, Canada, and Michèle M. M. Mazzocco, the director of the Math Skills Development Project at Kennedy Krieger Institute in Baltimore, analyzed the links between students’ math achievement and the way their brains processed the most basic problems. Their study was published this month in the Journal of Neuroscience. Interestingly, the study shows that the process in which students compute single-digit math problems may be indicative of how well they perform on college-readiness exams. Students that scored higher appeared to recall answers from memory while the students that were lower performing used an area of the brain associated with processing, indicating they were working through the problem. As Ansari comments, “Perhaps the building of those networks early in development go on to facilitate high-level learning, which in turn allows you to free up working memory”.
This study appears to support the idea that fluency with basic math facts is, in fact, an important skill. There are multiple ways to support the codification of basic math fluency: asking your child to recite basic math facts while riding in the car, while waiting for meals at restaurants, while waiting at the doctor’s office. Siblings can even quiz each other – serving to not only practice math skills, but to signal the importance of academic achievement. All of these passive settings provide clear opportunities to reinforce and codify basic math fluency.
Many curricular frameworks for teaching mathematics tend to be only a list of mathematics topics to be learned, with no clear elaboration of key ideas or organizing principles. Because of this, students may not be taught to integrate mathematical ideas, which causes gaps in their knowledge and limits their understanding. The Quantile® Framework for Mathematics, used in conjunction with the Common Core State Standards for Mathematics (CCSSM), helps teachers identify key connections and provide ways to ensure that students gain a comprehensive understanding of mathematics.
Mathematics is hierarchical and lends itself to learning progressions. Development of mathematical concepts depends on a student’s understanding of prerequisite concepts. Learning progressions are curricular frameworks that provide sequencing and guide teachers on proportional use of instructional time. The CCSSM lend themselves to the development of learning progressions because they provide critical areas for instruction. The CCSSM aligns content across K-12 so new material clearly builds upon concepts learned previously.
The Quantile Framework for Mathematics and its taxonomy provides a unique way to support the implementation of the CCSSM and address individual student needs by reporting both student ability and difficulty of concepts on the same scale—the Quantile scale. The taxonomy of the Quantile Framework comprises approximately five hundred skills and concepts called QTaxons. Each QTaxon is linked to related QTaxons, and these groupings form a knowledge cluster. Knowledge clusters form a tightly woven web that encompasses the mathematics learned from kindergarten through high school. By using information about student mathematical ability, the difficulty of the mathematical concepts, and the relationship among mathematical concepts, teachers can effectively target instruction for their students.
For a more detailed description, be sure to check out our latest white paper: Weaving Mathematical Connections from Counting to Calculus: Knowledge Clusters and The Quantile® Framework for Mathematics
Just last week, I was invited to speak at the CCSSO Rural Chiefs Conference in Kansas City on the topic of “Supporting Math Differentiation in a Common Core World”. While there is much written and discussed on the idea of differentiated instruction, in practice there are limited tools and resources to support math differentiation, a deficiency well-documented in this recent Ed Week article, ‘’Educators in Search of Common Core Resources”.
A theme permeating much of my presentation was the seemingly benign but pernicious neglect of math in our country. By almost any measure, e.g. instructional time, professional development, number of assessments ,instructional programs, etc… math runs a distant second to reading in the amount of instructional attention given. At least part of the challenge we face in addressing our math crisis in k-12 education will require that we remedy this neglect.
In my suggestions for addressing this imbalance I focused on four critical strategies. While the adoption of the CCSS is a huge first step in the right direction, its real success will rest upon how effectively we implement these standards. Along with the implementation of these standards, it is critical that we recognize that math – like any other skill – can be learned. Too often we subscribe, consciously and unconsciously, to the notion that math achievement is an inherent ability, as if math achievement was based on a “math gene”. If we take more of a Carolyn Dwek growth perspective, as opposed to a fixed mind set, we will go a long way toward promoting the idea that math achievement is possible for all of our students.
Secondly, we need to build math tools and resources that support differentiated instruction. Once, when leading a math workshop for a school district, the head of the math department informed me, tongue in cheek, that all math teachers know how to differentiate instruction: “We say it louder and we repeat it”. This RV (repetition and volume) model is likely to only work if the student is hearing impaired. Yet I suspect we have all seen variations of this model, this when we continue to drill a student on a math problem or concept to no avail. Meaningful differentiated instruction is really only possible when we are able to measure a student’s math level and the difficulty of the math concepts and skills on a common scale. This possibility is now a reality with the Quantile Framework for Mathematics. Once you know a student’s Quantile measure you know what math skills they are ready to learn. And just as importantly, one can make sure that the learner has acquired the necessary pre-requisite skills. Unfortunately, we often continue to employ the “RV” model and fail to drill down and provide differentiated content and instruction to meet the unique needs of the learner. (more…)