Here’s an interesting perspective: Kentucky math teacher, Alison Wright, described how two students in her Algebra II class reacted to a quiz that was returned. One student looked at the test, rolled her eyes, threw the paper on the floor, and complained the test was not fair and should not count. The second student read the comments, reworked the problems to find her mistakes and stayed after class to discuss the test.
After some research Wright came up that a new approach that she is going to implement in her class this year.
· Teach students that wrong answers are a helpful part of the learning process. Many students shut down because they are afraid of having the wrong answer and failing.
· Use cooperative group work as often as possible. By doing this students develop social skills necessary for teamwork while constructing arguments and providing valuable feedback to each other in a nonthreatening environment.
· Use “A” and “Not Yet” as the only two possible grades. Wright believes this will help students that have bad reactions to failing grades.
In a recent Gallup poll Americans were asked “Thinking about all the subjects you studied in school, which one, if any, has been the most valuable to you in your life?” The top three subjects were Math (34%), English/Literature/Reading (21%) and Science/Physics/Biology (12%). This is similar to the results from the August 2002 results where 34% of the respondents listed mathematics as the most valuable subject.
With the emphasis now in school curricular standards on critical thinking, innovative problem-solving and effective communication skills, these results should be no surprise. Many schools are emphasizing the importance of STEM (science, technology, engineering, and mathematics), education and attitudes towards these once-dreaded subjects are changing. Many now recognize the importance of mathematics and science in the preparation for post-secondary studies and career training.
While many Americans believe in the importance of the “three Rs” (reading, writing, and arithmetic) in public schools, the demands of curriculum should be fashioned to promote student focus on logic, reasoning skills, and the ability to report and justify their conclusions. As a mathematics educator, it is good to see mathematics listed as a top priority. With new frontiers in science, technology, and engineering opening up, it is imperative that mathematics and language arts go hand-in-hand as the classroom subjects that need the most emphasis. But overlooking creativity, innovative and logical thinking must also be included in the daily expectations of student inquiry.
Those of us who like to believe we are artistic and creative because we are left-brained or that we are analytical and that we reason logically because we are right-brained may be disappointed to learn that these explanations may be more myth than fact.
With the ability to collect data from neuroimaging in brain scans, scientists have observed that the functional connectivity and networking within brain functions are not concentrated in a specific hemisphere of the brain based upon the type of activity a person is performing. In a study out of the University of Utah, researchers found that there is little evidence that one side of the brain has a stronger influence upon our personalities or interests than another.
In other words, the functional network system of the brain seems to be so interconnected that many personality traits, strategies for thinking or creating, or personal areas of interest cannot be attributed to the stronger lateral side of our “gray matter.” It’s not uncommon to hear individuals use the mythic right-brain left-brain theory to support certain abilities or account for specific deficiencies, e.g. reading or mathematics. This study, however, casts doubt on such claims. In fact, both hemispheres of the brain are tightly connected and are necessary for proper functioning. Remember that next time you hear someone say they ‘don’t do math’ because they’re a right brained person. That reasoning appears to be a fancier, dressed-up version of the idea that they lack the ‘math gene’ or they lack mathematical reasoning as an innate ability. Math and reading, like any skill, can be learned and improve with practice.
We all know kids love video games but how effective are they? A study of 88 second graders that were divided into 3 groups to determine the effectiveness of on line games. One group was to play a game for a 3 week period, while another group had to solve similar math exercises on paper, and the last group had no assignment. The students were given an electronic test before and after the test period. The results showed the students that played the games had a 6% increase in scores, the students that did the paper exercises had a 4% increase in scores, and the group that had no assignment had a 2% increase. In addition, the group that played the games as well as the group that did the paper exercises solved the test 30% faster than the first time, while the group with no assignment was only 10% faster. A parent survey showed that students that played the interactive game described the activity as “fun, exciting, and fantastic” 80% more often than the paper exercise and 60% of them wanted to play more.
This study supports the importance and effectiveness of our own Summer Math Challenge and other resources that are provided on the Quantile.com website. If we can find interactive games that “hook” students we can improve math skills and maybe change the way some students view math. Visit our page http://quantiles.com/ to view the free resources we have available for all students.
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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