Adjusting Math Terms for the Common Core World

Valerie Faulkner of North Carolina State University argues for a shift in the mathematical language we use.  The Common Core should give us pause and force us to reconsider the terminology and vocabulary we employ in describing certain skills and concepts.  Here are a few examples:

Old Habit (eliminate)                                     New Habit (adopt)

Defining equality as “ same as”                   Defining equality as “same value as”

Calling digits numbers                                    Clearly distinguishing between digits, numbers and numerals

Addition makes things bigger                      Addition is about combining

Subtraction makes things get smaller      Subtraction is about difference

Let’s borrow from the tens place               Use regrouping, trading, decomposing

Multiplication makes things bigger          Teach 3 structures of multiplication

Divison makes things smaller                     Teach the different structures of divisions,

Doesn’t go into                                                 Prepare students for later learning by using accurate language

Saying “and” means decimal point         Don’t create false rules for language using and

Canceling out                                                   Explicitly use and discuss the idea behind simplifying

Referring to “the answer”                           Use the model or the relationships to justify your answer

Guess-and-check as a strategy                 Teach systematic math representations

                                                                                                                             

Old habits die hard, but this is food for thought as many districts get farther into implementing the Common Core.

Identity Confusion: The Problem with the Equal Sign

Henry Borenson explains how we use the = sign in two very different ways.  The first way is operational, for example 10 + 15 = ______.  The second way we use the sign is relational, indicating equivalence between two sets of expressions, each of which includes one or more operations, for example 8 + 4 =_____ + 5.  But in 1999 a study of hundreds of first through six graders only 5%  solved problems like this correctly.

Borenson believes that because of this study we can conclude that the relational meaning  of the equal sign is not something that students find intuitive or self evident. When asked to fill in the answer to the problems above most students said that 12 belongs in the space because the answer follows the equal sign.  The equal sign seems to trigger the operational definition in most students’ minds. Some students thought the  + 5 was just there to confuse them.

Borenson recommends  introducing students in the second or third grade to the idea of balanced equations using concrete objects rather than numbers and the equal sign. Once students get the idea the equal sign can be introduced with the balancing explanation. Studies have shown that if the relational meaning of the equal sign is introduced in this way students are much more likely to grasp both ways.

How to Encourage a Love of Mathematics

Here’s Lisa Medoff from Stanford University suggesting eight helpful ways that educators can build students’ tenacity with a subject that frustrates many of them: math!

  • Empathize. It helps to imagine a situation where you are out of your confort zone and feeling frustrated and agry.

 

  • Know your stuff. Be sure to spend time mastering the topic and walking students through their own self-doubts and frustrations.

 

  •  Use a variety of activities and supports. Get students working in groups with structured, hands-on, real world activities with the teacher circulating to troubleshoot and provide one-on-one support.

 

  • Convey the “growth” mindset. Let the students know that some may have to work at it harder and they will approach the problem differently, but they can all master math.

 

  •  Answer all questions respectfully. Even if the question has been asked before, you might say, “ I am glad you asked me again to make sure you understood.

 

  • Be intentional about homework. Think about how many problems students need to practice, which problems will be most helpful, will help be needed, etc.

 

  • Reframe the purpose of quizzes and test. Make it clear to the students that the test are not to determine how smart the student is but to show how well the teacher taught the information.

 

  • Praise effort and reinterpret mistakes. Students should learn to see success as the result of effective effort and mistakes as a sign that more work is needed.

 

Developing Non-Cognitive Skills

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.

 

Recognizing the Value of Math

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.

One Less Excuse

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.

It’s Just A Game?

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 Peril of Math Anxiety

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.

Not Just for School: Math at Home

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.

The Importance of Early Math Numeracy

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.

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