Seize the Summer: Perfect Time to Get Ahead!

As we close the book on the 2013 – 2014 school year, at Mathnasium, we’re excited about the possibilities for our students once summer rolls around! Here are a few reasons to seize every opportunity this summer – the perfect time to get ahead.

•  Everything kids do during the summer helps them get ahead. According to a recent study, at summer’s end, students perform one month behind their progress in the spring. Because new school material is at a standstill, everything kids do during the summer to build their math skills helps them get ahead!

•  Summer is also the perfect time to revisit and fortify math foundations. Math concepts build over time, and often, we find that students fall behind because they didn’t fully understand topics taught in earlier grades. While filling in these gaps is a primary objective of the Mathnasium program 365 days a year, without school stress or homework pressure to worry about, kids have even more time to step back and master these skills over the summer.

•  We love helping our students prepare for next year’s challenges. Another summertime perk: more time to get a head start on material they’ll encounter next school year. And the more prepared students feel, the more excited they’ll be about challenges that lie ahead. Third party studies show significant increase in grade level skills after three months at Mathnasium!

Mathnasium’s summer program offers a customized program for your child, flexible scheduling, and many opportunities to make this your child’s most productive summer yet! Call or email us by May 31^st to get an early summer registration discount. For more information, check out our website.

P.S. May is Teacher Appreciation Month! From all of us at Mathnasium, we’d like to say a big thank you to all teachers for giving young learners the gift of knowledge and for allowing us to support their math curriculum.

“If you are planning for a year, sow rice; if you are planning for a decade, plant trees; if you are planning for a lifetime, educate people.” – Chinese proverb

“Education is the most powerful weapon which you can use to change the world.” – Nelson Mandela

Math Test-Taking Strategies to Boost Confidence

Math anxiety can easily undermine the hard work students have invested throughout the year, lowering their scores on standardized tests and jeopardizing their chances to take advanced classes or enroll in the schools of their choice.

But reducing math anxiety, a well-documented phenomenon, can prevent this. Students can reduce anxiety by reviewing the mistakes they make on homework assignments and practice exams. After grouping these errors into three categories, they can easily be remembered as the “three C’s:”

• Concept, understanding the methods needed to resolve specific problem types
• Comprehension, determining exactly what individual problems are asking students to do
• Calculation, solving the problem correctly without making errors or overlooking any critical details

When faced with challenging test questions, students can become gripped with math anxiety.  However, they can address the root cause by reviewing past assignments and practice tests.  Often, the cause lies in difficulties with one or more of the three C’s.  After identifying where exactly a student’s weaknesses lie, adults can help address them.  This allows students to move on from anxiety and perform at the level of their true potential.

As a first step, parents, teachers or private instructors can sit down with students and look at the types of errors made in homework assignments, regular tests and practice exams.  It’s a process that can be helpful anytime during the academic year, especially when students become anxious about math, and is particularly important when it’s time to start preparing for standardized tests.

To address concept challenges, students can be asked to break questions down into a series of meaningful parts, resolve these parts individually, and then put them back together. Children struggling with both Concept and Comprehension can be asked to read troublesome questions aloud.  This helps to strengthen the mechanics of understanding by invoking different parts of the brain. Another helpful approach is to ask students to reframe questions in their own words.

To help students overcome Calculation difficulties beyond rote practice, which is more appropriate in this situation than the others, it’s crucial to make sure a child’s written work is neat and clear.  Neat penmanship makes a huge difference in kids’ ability to think clearly and follow their own good reasoning.

As the day of the test approaches, children should also take some common-sense steps that can be applied to all types of tests, Larry Martinek, chief instructional officer at Mathnasium notes.  First, avoid last-minute cramming by learning to pace yourself and structuring a daily study plan.  Make sure to eat a healthy, high-protein breakfast the morning of the exam.  Then, in the testing room, STOP and close your eyes.  Take a moment to inhale deeply.  When you exhale, open your eyes and envision the test with an “I can do” mindset.

Studies have shown math anxiety to impact up to half of all students in various ways.  However, with the proper approach, it can be effectively addressed and need not be a permanent hindrance to performance. 

Breaking Down the Question Barrier

Children need to be exposed to the forms of mathematical thought as well as to the details. What is missing in most instruction is the timely unfolding of these basic forms of mathematical thought. The use of consistent, familiar forms clearly depicts the underlying structure and helps eliminate confusion and uncertainty.

 

Without the structure provided by the Question Forms, classroom instruction often disintegrates into the usual collection of details—facts, operations, and procedures—that have characterized unsuccessful mathematics education for decades. All students (“at–risk,” “at–level,” and “talented” alike) benefit from having new material in mathematics presented as reoccurring manifestations of the same set of basic ideas with which they have already become familiar.

Let’s start with questions in the “single-form” format. Each is a breakdown of the format of questions based on one single concept; this allows your student to lay down a base to build a foundation on.

Counting, Grouping, Intervals: 
Count from _____ to _____ by _____s 

     Count from 2 to 16 by 2s...from 1 to 15 backward by 2s.

Denomination and SAMEness:
 What is another name for _________? 

     Name 2 numbers that add–up to 15...to 25...to 75...to 100.

Subtraction and Addition:
 How far is it from _____ to _____?

     How far is it from 5 to 11?...from 13 to 20?

Order: 
_____ is greater than/less than/equal to _____ .

     Name 3 numbers that are between 7 and 10.

Multiplication:
 How much are _____ groups of _____ ? 

     If you see 8 eyes, how many people are there?...16 eyes?...100 eyes?

Division:
 How many _____ are there in _____?

     How much is 1 + 1?...2 + 2?...4 + 4?...8 + 8?...16 + 16?...(continue as far as you students can go mentally.)

Fractions and Fractional Parts:
 How much is _____ (fractional part) of _____? 

     Half of what number is 7?...is 1?...is 12?
How much is half of 8?...of 12?... of 18?... of 200?...of 1,000?

“The Whole is equal to the sum of its Parts”: _____ (whole) = _____ (part) + _____ (part) 

     A cook bought two bags of apples. One bag of apples weights 15 pounds and another weighs 10 pounds. How much is left after the cook uses 17 pounds of the apples for pies?

Percent: 
_____% of _____ is _____. 

     How much is 50% of 6?...of 20?

Ratio:
 _____ is what part of _____? 

     Is 7 half of 14, or is 7 twice as much as 14?

Change and Variation:
 As _____ gets bigger/smaller, _____ gets bigger/smaller. 

     Does it cost more to buy 5 apples or 10 apples? Why?

Proportion: 
_____ is to _____ as _____ is to _____ . 
     Does it cost more to buy 5 apples or 10 apples? Why?

- Larry Martinek

Back to Basics: The Essence of the Mathnasium Difference

Principles of Math can come across confusing to students, especially when they are bombarded with multiple rules and confusing practices. Mathnasium focuses on introducing new subject matter with a consistent and knowable approach, allowing students to build upon a foundation of knowledge while understanding and adding new principles.

To begin Early in a child’s learning, values are expressed in groups of 10s:

• 10 pennies make a dime.

• 10 dimes make a dollar.

•   10 “one-dollar” bills make 1 ten dollars, and 1 ten–dollar breaks down to 10 “one–dollar” bills

• 100 pennies make a dollar.

• 100 dimes make ten dollars.

• 10 hundreds make a thousand.

• 1,000 thousands make a million.

Some things ”make sense” to cut in half: a candy bar, a piece of wood, numbers... Other things don’t: people, pennies, cars... To diagnose the correct approach, assess the subject matter. Use the examples below as guidance.

• If twice as many people as you expected come on a picnic, then you will need twice as much food.

But, if you are baking bread, twice the regular heat will not get the job done twice as fast.

• When you double the number of pieces, the size of each piece is half as much as it was. (This is the inverse relationship: when one thing goes up, the other goes down.)

Contrary to its reputation, Math is not all numbers, in fact, word prefixes play a large role in setting the numerical value. Take these examples:

• “mono–”means 1: The monorail at Disneyland runs on 1 rail.

• “bi–” means 2: A bicycle has 2 wheels.

• “tri–” means 3: a Triceratops has 3 horns.

• “qua–” means 4: a quartet has 4 players

• “dec–” means 10: a decade is 10 years

• “cent–” means 100: percent means “for each 100”

• “mil–” means 1,000: a millennium is 1,000 years—a mile is “1,000 paces”


Finally, I touch on a few points of knowledge for your student (if this is for parents, “parents have kids… teachers have student) that will assist him or her build the base for understanding the previously dissected, whole and parts method.

• A quarter of an hour is 15 minutes (not 25).

• There are 4 quarts in one gallon. A “quart” is a quarter of a gallon.

• Whole basketball and football games have 4 quarters.

• Four quarters make a whole dollar.

• One half dollar is the same as 2 quarters.

• Half-time in a basketball game comes after 2 quarters.

These basic understandings set the cornerstone for laying the foundation of knowledge to continually build and evolve your student’s mind, the Mathnasium way.

The Whole Equals the Sum of its Parts

Word problems can be tough even for the math-minded. The challenge lies in correctly converting words to the numbers and symbols of an equation. One method that helps is the concept that “the whole is equal to the sum of its parts.” Start with these three questions:

• What is the whole in this question? Is its value known or unknown?

• What are the parts in this question? Are their values known or unknown?

• What is the relationship between the whole and its parts? Which remains constant in the question? Which changes? How does it change?

By figuring out what are the parts and what is the whole, we can decide whether we need to perform a synthesis (“building up”) or an analysis (“breaking down”) to solve the problem at hand.

Synthesis:
If the whole is unknown, then the task is to build it up from its known parts:

• If the parts are equal, we multiply.

• If the parts are not equal, we add.

In other words, affirming that “the whole is equal to the sum (total) of its parts.”

Analysis:
If the whole and one or more of its parts are known, then the task is to find the remaining part(s) by breaking down the whole, using the known part(s):

• If the known parts are not equal, we subtract.

• If the known parts are equal, we divide.

Basically, “Each individual part is equal to the whole minus all of the other parts.”

By identifying which category the problem falls under, we can designate a relationship and determine the plan of attack; this is called the whole-part method. Below are a few examples of the method in action.

Ex. #1:

A box contains some marbles. 6 of the marbles are red, 5 are green, and 14 are orange. How many marbles are in the box?

In this question, the whole (the total number of marbles) is unknown. Since the parts (the number of red, green and orange marbles) are known, we can use the Key Synthesis Concept to find the whole:

total # of marbles = (# of red) + (# of green)+ (# of orange) = 5 + 6 + 14

= 25 marbles.

Ex. #2:

A train traveled 200 miles at an average speed of 50 miles per hour. How long did the trip take?

In this question, the distance traveled is the whole and is known. In each hour the train traveled an average of 50 miles, so:

time of trip = (distance traveled) ÷ (average rate of speed)

= 200 miles ÷ 50 miles per hour = 4 hours.

Ex. #3:

Another sandbox contains 100 pounds of mixed sand, 15% of which is brown sand. The rest is white. How much white sand must be added to make the mixture only 5% brown.

In this question, there are 15 pounds (15% of 100) of brown sand. As we add white sand, the whole (the total amount of sand) changes, but the amount of brown sand remains constant (at 15 pounds).

What we want is “15 out of the (new) total” to equal “5 out of 100” (5%, the desired outcome).

We can ask the following equivalent questions,

“15 is to what number as 5 is to 100?” or
“5 out of 100 = 15 out of what number?” or “5/100 = 15/what number.”

All of these methods yield the same answer: 300 pounds. Since the box already has 100 pounds of sand, 200 pounds (300 – 100) must be added.

The whole-part method allows us to identify the first step of a word problem bringing us one step closer to the solution and making math make sense.

- Larry Martinek 

The Importance of Telling Time in a Digital Age

Most students today grow up with tablets, cell phones, and laptops at their fingertips. These tools can aid learning, but they can also encourage laziness. With the Mathnasium Method, students are taught to use their brains, not their iPads. I’ll demonstrate this by using an example of how kids can learn to tell time.

By second grade, most students can count by 1s, 2s, 5s, and 10s, up to at least 200. We can make it easy for them to “tell time” by expanding this to include counting by 15s, 20s, and 30s, as well as counting by 10s starting at any number (7, 17, 27...).

When you stop and think about it, all points on the clock can be reached quickly by counting various combinations of 30, 20, 15, 10, 5, and 1.

When students are taught these counting skills before they deal with clocks, learning how to tell time is a very straightforward process. Without these skills, it’s quite a chore.

Here’s a way to teach students these skills:

• Counting by 10s starting at any number goes like this: start at 23: twenty–three (23), thirty–three (33), forty–three (43)... as though you are just counting by 10s, except that you say the three. So, counting by 10s starting at 37 becomes thirty–seven, forty–seven, fifty–seven...

• Counting by 15s can be done by counting by 10 and then counting by 5: 15 + 15 = (15 + 5) + 10 = 20 + 10 = 30. 30 + 15 = (30 + 10) + 5 = 40 + 5 = 45. 45 + 15 = (45 + 5) + 10 = 50 + 10 = 60.

• Counting by 20s is almost the same as counting by 2s: 0, 20 (twenty), 40 (forty), 60 (sixty), 80 (eighty)...

• Counting by 30s should be presented after the child can count by 3s. Counting by 3s is similar to counting by 2s. Counting by 2s can be explained as, “Say the number, skip the next number, say the number...” Then counting by 3s becomes: “say a number, skip the next two numbers...” Now counting by 30s becomes: 0, 30 (thirty), 60 (sixty), 90 (ninety)...

With the help of parents or teachers, telling time can be introduced to a student as early as kindergarten. The sooner students learn to count quickly using the above methods, the sooner they’ll be using terms like “quarter till” and “half past.”

- Larry Martinek

The reviews are in - Math speaks volumes!

Everyday we strive to reach students through the Mathnasium Method from our very own Larry Martinek.  When our students excitedly show us their great grade, add their test to the Brag Board, or even get an answer correct during practice, it makes the process that much more rewarding.

Courtesy of @lapkoi!

Larry and the Importance of Higher Education

Learning Objectives: PSAT Math Success

Most high school kids take the PSAT. Scoring high on it is both an indicator of good SAT performance and an opportunity to earn a National Merit Scholarship. It pays to treat the PSAT seriously. It just so happens, though, that doing well on the math portion of the PSAT may have more to do with having a good foundation in the subject than having advanced, harder-to-obtain skills.

A study performed by the Journal of Neuroscience found a positive link between basic, single-digit math calculation and success on the PSAT. An MRI scan showed that students with high activity in the left area of the brain, which focuses on simple mathematical exercises, had higher PSAT scores. Although the PSAT and SAT are designed to measure advanced high school-level skills and concepts, this study shows that doing well on the PSAT can be as simple as possessing basic math reasoning (and using a little memorization).

Mathnasium offers a Numerical Fluency program which assists students of all ages who don’t have a complete grasp of computation with single-digit numbers. We define fluency as the effortless recall of number facts, for example, counting by 6s, 7s, and 8s, as well being able to effortlessly calculate “7 + 8 + 9.” Mastery of exercises like these ensure that students have the mental math skills that leads to success on the PSAT and beyond.

Mathnasium’s customized lesson plans and individualized attention make sure that dedicated students attain Numerical Fluency, paving the way for success on the PSAT and beyond.

- Larry Martinek 

Larry on the subject of Math Anxiety

The bell rings and everyone takes their seats. The teacher passes out the test and, with sharpened pencils, everyone prepares to turn the page and begin. The student next to you flips open the first page and seems to begin answering questions with ease. Time seems to speed up, nervousness kicks in, and you stare at the first test question but forget how to complete it, even after having studied the material over and over. Panic rises and before you know it, the hour is done, the test is over, but the innate fear of it all hasn’t subsided. Parents, this is what we call “math anxiety.”

Numbers on a page not only confuse some children, but can also potentially give them full-blown anxiety. This “math anxiety” is intense and feels similar to stage fright. In many cases, math anxiety comes from a student’s memorization of the correct procedure and routine to solving a problem, as opposed to developing a core understanding of the problem. When this happens, children quickly forget what they’ve learned, and anxiety sets in.

As parents we want to eliminate as much stress and offer as much support to our kids as we can. Working with teachers and outside resources is one the best way to get your child comfortable with math content. It is extremely important that you let your child know that just because they don’t understand something the first time doesn’t mean they won’t understand forever.

One way to sharpen these skills and avoid math anxiety is through math instruction outside of school. It is a false misconception that extra help is only for children falling behind in school. Additional lessons and preparation is not only beneficial for kids struggling with the material, it also benefits those students who understand the material and want to strive for further concept and skill development. We want to see our kids keep up with the curriculum, not just try to catch up with daily lessons.

One of Mathnasium’s core math lessons helps our students with Computational Fluency and this includes effortless recall of number facts with addition, subtraction, multiplication, and division. These core skills and principles are extremely valuable for building a strong foundation of basic math aptitude, which will carry forward through grade levels.

We will make sure our students are able to:

Be fluent in adding single digit numbers, something they will be able to do quickly and efficiently with practice

Count from any number to any number, by any number; this will aid them with more advanced math problems

Use Mental Math, for example:

• How much is 5, three times?

• 99 + 99 + 99

• 301 – 195

• 4 x 26

• 1,000 ÷ 16

• 7% of 300

• 6 ½% of 150

All of the above skill sets are crucial to the core understanding, and ultimate advancement, of the math knowledge necessary to compete in the global economy. At Mathnasium, we work to eliminate “math anxiety” and replace it with “math confidence.” From this confidence comes long-term success in math.

- Larry Martinek

Larry's Math Mediums

“Once you learn math and continually use it, you forget how you learned it to start with.” -Larry Martinek 

What do your kids want to be when they grow up? A ballerina? Or an astronaut? Or “just like Mike”? Growing up, kids idolize their favorite singers, actors, and athletes, but kids might not understand that their heroes weren’t born gifted. You and I know that they worked incredibly hard. Fortunately, this means that many dream professions can be attained with extensive practice. Practice math every day and that goal to become an astronaut will take your child very far.

Working on math skills outside of the classroom is crucial to developing a well-rounded grasp of how math is used in the real world. Just as basketball players and musicians do drills, practicing math concepts and skills over an extended period of time can be immensely rewarding. When your child sees that math is utilized everywhere in everyday life, the importance of math as a subject worth practicing will be obvious.

Here are a few ways you can practice math with your kids and prove the practical significance of the subject:

1. Have your kids help out in the kitchen – Preparing food or baking offers a great opportunity for kids to practice with fractions by measure dry and liquid ingredients.

2. Let kids figure out the change for a $10 bill and a $20 bill when they go shopping with you

3. Let them help trip planning - Sources like Google maps help children visualize distances and calculate travel times.

4. Watch the game together – Sports like football are full of statistics and calculations. Watch the game and talk about how these math skills are necessary, even in the world of sports.

5. Set up a hot chocolate stand – Allowing your child to handle and count currency in real-life

At Mathnasium, we use our proprietary Mathnasium Method to teach skills and convey the importance of math. It’s a tried, true, and perfected method that uses a variety of mechanisms to cement learning just like we suggested above. Here they are:

Mental

Questions like “99 + 99 + 99” And “3/4 of 20” are best done mentally. Strong mental math skills help students develop confidence which is the heart of the both self-esteem and a willingness to explore math, in addition to being a much more efficient way to handle many situations. Many of our centers host free Multiplication Madness nights, a fun and motivating way to keep your children’s skills sharp.

Verbal

Direct Teaching and the Socratic Question are verbal modes of delivery. Also, asking students to explain how they got their answers is a verbal experience that can convey understanding.

Visual

A significant number of Mathnasium worksheets contain pictures that help students to focus on the critical attribute(s) of the question at hand.

Tactile

When appropriate, our instructors use manipulatives (coins, dice, cards, scales, clocks, fraction circles, etc.) to guide and reinforce students’ thinking.

Written

Mathnasium teaches all of the standard algorithms for addition, subtraction, multiplication, and division, as well as when written procedures are preferable to mental ones, and vice versa.

Mathnasium lessons involve a combination of these methods to provide an integrated math lesson that not only teaches, but builds confidence and self-esteem. In addition, our Brag Boards on Facebook and Twitter allow Mathnasium locations to showcase the hard work and success of their valued students. Thank you for your interest in how we make math make sense to kids, and how you can too.

Larry’s Math Do’s and Don’ts

In December 2004, the Wall Street Journal reported that American kids are “Economic Time-bombs” because they are not learning enough math to be the good problem solvers the nation demands. With this in mind, how are your children performing in math? 

Most American children lose ground to students all over the world who are preparing themselves for success in the future, which includes, like it or not, a lot of math. And why is this happening?

Unfortunately, this is because year-after-year students are put in classes for which they do not have the prerequisite knowledge necessary for success.  Under these conditions, it is difficult, if not impossible, for teachers to ensure that students are acquiring the number sense in elementary school and the solid pre-algebra skills in middle school needed to be successful in Algebra and the higher math classes required in high school and college, regardless of their choice of majors.   To ensure your child is on track, I have created some simple Do’s and Don’ts. Do’s:

• Do “math” with your children just as you read with them
• Do make sure your children get their math homework done in a timely fashion
• Do meet with your child’s math teacher from time to time so you know what is going on beyond the report card. Work with your child’s teacher to set realistic goals for current school year and for the future.
• Do check to see if your child (one major tip per grade level):
  • Second Grade: Is “fluid” with single-digit addition and subtraction.
  • Third Grade: Can find half of even and odd numbers.
  • Fourth Grade: Know times tables “by heart.”
  • Fifth Grade: Can order fractions using benchmark numbers.
  • Sixth Grade: Is able to mentally calculate percents using “friendly” numbers.
    • 7% of 300 = ? are “friendly” number, whereas 7.132% of 321.097 = ? ain’t so friendly!
• Seventh Grade: Is able to convert fractions to decimals to percents.
• Pre-Algebra: Can effortlessly add and subtract positive and negative numbers.
• Algebra: Is able to solve simple equations “by inspection.”

Don’ts

• Don’t let your negative experiences in the math classroom influence your child’s education.
• Don’t let your child use a calculator until he has developed genuine Number Sense.
• Don’t let your child be put in a math class that he is not ready for, that is, a class where he does not have the prerequisite knowledge necessary for success in the class.

  Following these Do’s and Don’ts will not solve everything, as students need to continuously nurture their math skills and Number Sense with practice. However, use these as guidelines that will help steer your child in a strong direction.