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. 

Master Fractions and Set the Stage for Success, As Featured in The Wall Street Journal

Algebra Readiness begins in elementary school. Three essential topics in elementary school mathematics are 1) numerical fluency, which includes the effortless recall of addition facts and the times tables stemming from mental math strategies for computation, 2) foundational understanding of the nature fractions, and 3) the basics of problem solving. Mathnasium was recently featured in The Wall Street Journal and highlights our unique and effective approach to teaching fractions. Read the full article here.

As students move into middle school, work with fractions expands to embrace rational numbers (common fractions, decimal fractions, percents, ratio and proportion, and negative numbers). At the same time, student’s problem solving horizons broaden to include multi–step word problems, both routine and non–routine.

Successful mastery of these elements sets the stage for success in Algebra, the rest of high school math, and college. If any of these areas are under developed, the road ahead is fraught with danger.

Visit a Mathnasium Learning Center and see where your child stands.

- Larry Martinek

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 School Refresher

Did you know your student could lose anywhere from two to two and a half months worth of math knowledge over the summer months? By enrolling your student at Mathnasium now, they can move ahead in their class and continue to learn new things.

Refresh their (and your) knowledge with key terms from the Mathnasium Glossary below.

addition counting “how many altogether.” The process of forming a whole.

complement “the rest of it.” the remaining part with respect to the whole.

counting the process of determining quantity (how many, how much).
denomination the collective name of a group of similar things (apples, dogs, inches).

division counting “how many of these are there inside of that.” The process of separating a whole into equal parts.

fraction the result of breaking a whole into equal parts; one or more of those equal

group one or more of the same thing (1 apple, 9 dogs, 5 inches, 8 things).

half the first fraction. A whole divided into two equal parts; one of those parts. “Two parts the same.”

interval the distance from one number (or unit) to another. The space between two numbers.

Law of SAMEness It is only possible to add and subtract things of the same kind, things with the same name, the same denomination (an apple plus a banana is not a “banapples”).

mathematics the study of wholes and parts, and the relationship between them.

matrix literally, “mother.” That which gives form, origin, or foundation to something enclosed or embedded in it. A place of origin and growth. Related words include environment, framework, womb, structure, model; enclosed, enveloping, surrounding.

measurement the determining of quantity.

multiplication counting “in equal groups.” The process of forming a whole from equal groups.

part a component of the whole. A fragment, fraction, section, portion, region; a piece broken off.

percent literally, “for each 100,” “parts per hundred,” “how many for each hundred.”

proportion literally, “according to amount.” The relation of one part to another or to the whole; relative size. Comparison, analogy, balance, symmetry.

ratio a comparsion of two numbers by division.

subtraction counting “how far apart two numbers are” and “how much is left.” The process of removing a part(s) from a whole.

whole undivided. The one composed of the many. That which can be broken–down into parts. All of the quantity under consideration.

zero the number that counts none. That which has no parts.   

- 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 

18,000 Students looking forward to a Summer of Algebra, Angles, and Arithmetic

For most kids, summertime means swimming, sports and sun. But for 18,000 students around the country, the summer months will also be filled with algebra, angles, and arithmetic.

Yes, math.

Mathnasium is anticipating its largest summer enrollment ever this year, with 18,000 students ranging from elementary level to high school expected to take math classes at its franchise locations across the country. The reason? Many students – and their parents – are looking to prevent the notorious summer slide, during which kids lose math concepts and skills developed during the prior school year.

“Much like the muscles athletes use in competition, a student’s math muscles have to be exercised to remain in top form. Research has shown that during the summer months, students literally lose up to 2½ months of computational math skills developed during the year. However, 18,000 students across the nation have decided to fight the summer slide this year and work out their math muscles at Mathnasium. When school starts again in the fall, they’ll be well ahead of the game,” said Larry Martinek, Chief Instructional Officer at Mathnasium.

Summer math students typically spend two to three hours a week at their local Mathnasium franchise locations, working from a customized curriculum designed to mesh with their skill levels and needs. The sessions include specially developed math workouts and math games sessions designed to both motivate and educate.

The sizable enrollment in the Mathnasium summer classes demonstrates the importance of math skills to many areas of academic achievement at all educational levels, as standardized math testing is often used to determine advancement, class selection, and placement. Importantly, summer math at Mathnasium is equally applicable to students who need to address deficiencies in their math repertoire as well as those who wish to progress further than their normal classwork allows.

“I’m expecting about 70 students to sign up for summer math this year, which equals nearly half of our enrollment during the academic year. These students are committed to math for a variety of reasons, with some looking to fill gaps and others wanting to take advantage of the summertime to move ahead. One thing they all have in common is the desire to have a little fun but at the same time be challenged, and that’s something I hope all our students come to understand. Math can be both fun and exciting – and it’s something that everyone can learn,” said Alan Flyer, Owner of the Mathnasium franchise in Roslyn, N.Y.

Mathnasium’s summer math programs are being offered at Mathnasium’s more than 400 franchise locations across the U.S. and abroad.