The secrets to getting an A in algebra by Logan Reames appeared first on Cincinnati Math Tutoring.

]]>Many students seem do well in math until they reach the 8^{th} and 9^{th} grade and experience algebra. Algebra is a very different class compared to the type of math students have experienced before and requires a higher-level abstract thinking that many students initially struggle with. It may take some time for students to adjust to this level of thinking but if the students can master the 5 concepts below they will be able to breeze through algebra. Having a strong algebra foundation then will propel the students to be success in the higher-level math classes and into college. After the student masters these 5 concepts below they should have no problem acing their math class.

**1) First and most important concept – Know the Basics**** **

This is by far the most important skill need to be successful in algebra. Many students go into algebra without the imperative beginning skills that should of have been mastered in the lower in the graders. These skills include:

If a student starts an algebra class without these prerequisite skills it makes impossible to fully understand the new concepts. Many times these students are spending all of their effort trying to work through the arithmetic of the problem and are completely missing the algebra concept at hand. If a student is struggling with these prerequisite skills it is almost always advise that a student takes a remedial pre-algebra class before jumping into an Algebra I class. Read more about the dangers of algebra too soon.

**2) Be able to solve linear equations and understand the reasoning and process.**

Solving linear equations is an important skill that comes up in every subsequent math class and has many utilities to it. One important thing to note is that students must understand the process and reasoning and not just mimic what the steps. Many times students get in the habit of solving simple problems in their head by guess and check with reason but never take the time learn the process. Students then get stuck when they reach more complex problems, which become extremely more difficult to solve in their head. An example of this is 2x + 5 = 9, which many student are able to solve in their heads as x = 2. They do not take the time to learn the process of subtracting each side by 5 and then dividing all the terms by 2. Many students can make this guessing method work until they reach a problem like 7x – 4.5 = 20 where that answer is going to be a fraction. If the students did not learn the process there is a very little chance that the student is able to solve this problem. It is also very important for students to also understand the concept that when you apply the same action to both sides of the question it will not affect the value of the problem.

**3) Know the different methods of solving a system of linear equations and know when to effectively apply each system.**

In algebra class students are taught many different ways how to solve a system of linear equations but students often struggle knowing the advantages and disadvantages of the different methods and when to apply them. Students learn how to solve system of linear equations by graphing, elimination and substitution. It is important that students master all of these methods and understand that how they are all related and give the same solution to the problem. Even more important student should understand which method is most effective for the current application.

**4) Master Exponential and Logarithmic functions and expressions**

This is the first time many students experience exponents and logs. It is important for students to master all arithmetic operations when workingwith exponents and logs because this is the most important skill set that will come up in higher-level math. As well as mastering the arithmetic operations students should grasp a strong understanding of graphing these functions through transformations. Students most know how to graph the basic functions of and and be able to use transformations to graph more complex functions and their inverses. As well as being able to graph these functions students need to be able state the domain and range of each of the functions.

**5) Understand everything there is about Polynomial and Quadratic Functions/Equations.**

When working with polynomials students need to understand the algebraic representations of the functions. They need to be able to find the roots through factorization and rational roots theorem. In addition to understanding the algebraic representation they also need to understand graphic representation including graphing parabolas given its parameters and its x-intercepts. This is the most complex concept that students see in an algebra class because it requires a lot of prerequisite skills being put together at one time. If the student is just missing one of these prerequisite skills it makes the process extremely difficult to complete.

If the student is able to successful master these five skills they should have no problem with receiving an A in their algebra class and being prepared for higher-level math classes. If you student is having trouble in their math class you can visit one of our Mathnasium locations here to receive help from our expert math instructors.

The secrets to getting an A in algebra by Logan Reames appeared first on Cincinnati Math Tutoring.

]]>What is the ACT? by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>The ACT is a standardized test that has been around for decades, and nearly every college goer has taken it multiple times. However Most people remain clueless as to what it actually is. This article is designed to help clear up that mystery. It will explain how the test is structured, scored, and administered as well as some nice facts that will help prepare you to take the test.

The American College Testing exam, or better known as the ACT, is a standardized exam used to gauge a student’s aptitude with entering college. It was first administered in November of 1959 to act as a competitor to the more common SAT test. The ACT originally tested four core subjects consisting on Math, English, Social Studies, and Natural Science and it stayed that way until 1989 when the Social Studies portion was changed to Reading with a subsection on Social studies and Natural Science was renamed Science Reasoning. Currently the test covers the same four core topics plus an optional writing portion that was added in 2005. This was done to keep up with changes in the SAT.

This bring us to how the ACT is graded. In each core subject you are given assessed an integer score between 1-36 with a 36 being a perfect score, and if you take the writing portion it will have a similar score between 2-12. However your writing score does not affect your composite score, which is the average of you four core scores. So for example say you scored a 22 in Reading, 24 in English, 27 in Science, 31 in Math and a 7 in Writing your overall composite score will be a 26, the average of 22, 24, 27, 31. Do keep in mind, even though the writing portion doesn’t affect your composite score some colleges require you to have taken it. According to Princetonreview.com the national average ACT score is a 21.

Finally armed with all this information about the ACT you are left with one last, and very important, question. Where/When do I take it? Most students take the test in their Junior/Senior years of high school. This gives them more flexibility when it comes to needed to take the test again or whether or not they need to take the SAT vs. ACT etc. The test is offer every year in the months of September, October, December, February, April and June at a designated tested center. This could be a local High School, Career Technology Center, or College. Registration must be done 5 weeks prior to the test date and can easily be done at ACT.org or with your school guidance counselor. Here are some of the upcoming test dates:

If you still have questions concerning the ACT or any standardized testing feel free to contact Mathnasium (click here) for more information.

What is the ACT? by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>What is Dyscalculia? Recent Research by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>There have always been plenty of students who struggle with mathematics, however in recent years research and studies have shown that this may be due to a neurocognitive disorder called dyscalculia. Dyscalculia is a neurological disorder that prohibits the brain from understanding basic numerical and arithmetic concepts.

According to the National Center For Learning Disabilities (NCLD)–“Dyscalculia refers to a wide range of lifelong learning disabilities involving math. There is no single type of math disability. Dyscalculia can vary from person to person. And, it can affect people differently at different stages of life.”– ncld.org

One can

“Dyscalculia is like dyslexia for numbers.

But unlike dyslexia, very little is known about its prevalence, causes or treatment. People with dyscalculia experience great difficulty with the most basic aspects of numbers and arithmetic…50-60% of people with dyslexia do have difficulties with maths. Not surprisingly, difficulty in decoding written words can transfer across into a difficulty in decoding mathematical notation and symbols.

For some dyslexic pupils, however, difficulty with maths may in fact stem from problems with the language surrounding mathematical questions rather than with number concepts – e.g. their dyslexia may cause them to misunderstand the wording of a question.

Dyscalculia and dyslexia occur both independently of each other and together.-British Dyslexia Association (Dyscalculia, Dyslexia and Maths)

According to a study published in the journal *Science **(Dyscalculia: From Brain to Education)*, dyscalculia is estimated to be prevalent in 7% of the population. Many people learning of this math disability find it interesting that it can be as common as dyslexia. However, it is also very frustrating given that it is much more difficult to diagnose and far less understood. Therefore it is important for parents, teachers, and educators to inform themselves and find valuable sources of authority information on the subject. With that in mind, Mathnasium of Cincinnati will continue to publish information about dyscalculia as it becomes available.

Even though dyslexia and dyscalculia are very similar, dyscalculia is fairly newly discovered compared to dyslexia. Dyscalculia was first suggested in 1974 by researcher Kosc, which is almost 100 years after Oswald Berkhan identified dyslexia in 1881.

Another reason why dyscalculia is less understood is that research and studies on math disabilities are far less common compared to the number of studies conducted on reading disabilities. It has been shown that studies on readings disabilities out number the studies of math disabilities by 14 to 1.

One of the reasons for the large discrepancy is that that many people put a stronger emphasis on literacy compared to numeracy.

Daniel Ansari, a cognitive neuroscientist at University of Western Ontario states* “People freely admit at dinner parties that they are poor at math, while few would admit that they are a poor reader.”*

The social emphasis on literacy has driven studies in reading disabilities and has left studies in math disabilities to lag behind. Because of this many student with dyscalculia go through school without being diagnosed.

Dyscalculia can vary greatly depending on the person but is usually broken down into the two major areas, visual-spatial difficulties and language processing difficulties. Visual-spatial processing deals with organizing visual information in patterns and understanding how these patterns relate to each other. This makes it difficult to follow multi-step problems such as long division and remember simple concepts like which direction is left and right.

Language processing difficulties results in having trouble with making sense and processing what a person sees and hears. Some young children with language processing skill have difficulty processing numbers symbols to real world scenarios such as seeing the symbol “3” and understand it is the same thing as three dogs or three apples. Both of these difficulties affects a person very basic number fluency and makes it very difficult for them to master higher mathematical concepts.

A trained professional can test a student to see if the student has a learning disability. These test consist of the student being interviewed on a large range of math skills on concepts. This test is usually completed using pencil and paper but the trained professional must fully understand how the student understands and uses number sense to correctly diagnose a learning disability.

There is currently no formal test for Dyscalculia however there are a variety of screenings and resources available…

**Panamath:** Justin Halberda and Ryan Ly from John Hopkins University created an online test to identify students with dyscalculia (to the right). The program tests the student’s ability to quickly ascertain and compare quantities, also know as number sense. The program shows a screen of blue and yellow dots for less than a second the user then must state whether there were more yellow or blue dots. A student who has poor number sense has a high chance of being diagnosed with Dyscalculia. The test is available for free at www.panamath.org

**Dyscalculia Screener:** Professor Brian Butterworth, the primary contributing author contact from the above sited Science Journal “*Dyscalculia: From Brain to Education”, has *developed a useful diagnostic screener for teachers. More information can be found at the GL Assessment website at www.gl-assessment.co.uk

What is Dyscalculia? Recent Research by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>How to study for a Math Test by Sam Thompson appeared first on Cincinnati Math Tutoring.

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There are many ways to prepare for a math test. We would like to discuss time-tested techniques for getting an A^{+} on that next Math test! Are you ready for some techniques that you (or your student) can use to nail the test each and every time? We’ll delve into why you shouldn’t “cram it all in” the night before, and we’ll teach you some of the best strategies and the best places to get your information. Well, let’s dive in to “How to Study for a Math Test”!

Today, students that are getting into more advanced math classes are putting off studying until the day before an exam. So, why not just cram for the big test, the night before the big test? It’s about 2 things, practice, and retention. Think about this in terms of a runner who’s just signed up to race in a marathon. If this “runner” has only trained the day before the 26.2-mile race, imagine how ready they are for the marathon the next day. First of all, they are probably exhausted from training the day before so vigorously. Secondly, how well do you think they will perform in the race after training for only one day? And more importantly, if they somehow do manage to eek out a “victory”, imagine how well their bodies are really “trained” to really handle that marathon….OR, did they somehow just barely live to survive another day? In Math, knowing that concepts build upon each other, runners, just like test takers must train for the marathon. This is similar to the Math Exam that a student is about to take. A student needs to prepare a few weeks in advance to excel in that math test so that just as important as doing well, the student retains the knowledge they have learned, so that they can build upon those new found skills. Cramming puts the information in SHORT TERM memory, When you cram, you put the information in recall for only a short time . If you cram, the question you have to ask yourself is, are you feeling lucky? Is your short term memory good enough, and will it hold out? Better not take that chance. Better to put that information in long term memory, and have that information forever, by studying over a long period of time, right? Here’s why not to Cram for a test and the benefits of short term vs long term memory.

Now, let’s talk about resources. Generally, a math teacher usually provides a study guide in advance so the students can look over the material and get a good feeling of how the test will be constructed. To prepare for the test a few weeks in advance, a student can look over each section every night before going to bed. This is one of the best guides as to what kind of problems the student should be practicing. Next, the math book is chock fool of problems the student should be practicing. And the student needs to know what type of problems to be working. Homework is a great guide for that.

So, once you know what types of problems you should be doing, let’s talk about doing those problems. Students should of course be doing their homework problems that the teacher assigns. The familiar saying “practice makes perfect” applies to any level of math. If a teacher assigns all the odd problems, why not give yourself more practice by doing a few of the even problems on the difficult problems? Many times textbooks will have formulas in the beginning of the section that a student needs to memorize. This is essential when student are beginning Algebra. Students need to *rework* example problems that their teacher gives them in class. Just copying down a problem off the board does not mean you understand how to solve the problem. Students need to understand what was done in these example problems, as generally the teacher will change the problems on the test, so students should be able to do any problem like the sample problem, no matter what numbers are in the sample problems. This is why, at night before going to bed, students need to look over the class notes and understand **how** the teacher solved a problem.

The next step is to make a practice exam for yourself after going over the material on the study guide the teacher gave out. The practice exam should be done approximately two days before the test. If the teacher did not give one out, you can create your own study guide. Generally or you are having trouble creating a practice exam there are two options that I recommend. The first is to go to the end of the chapter is your textbook and take the publisher’s chapter practice test. The second option is to find a study partner and work together. If you are feeling confident and your friend is not, studies show that teaching the material to a friend actually benefits you because you are getting more practice doing the teaching. Learn by Teaching!

Your final steps to earning that A+ on the test is to review the material the day before the test. Before dinner, take about an hour to rework some problems of every type that may be on the test. Review the formulas that will be on the test as well. You have contributed six to eight hours of studying for this math test, what to do now? The night before the test, go do something fun that will relieve your brain from math. Working out or going to play some basketball, just pick something you like that’s physical and gives you some exercise and relieves your brain.

Now it’s the day of the big assessment. First of all, don’t skip breakfast, and eat plenty of carbs and fatty foods the morning of the big day. Many kids skip breakfast the big day and its detrimental to brain function when you’re thinking about food instead of math, your brain is literally starving. Studies show kids who eat breakfast score an average of 17.5% better on mat tests if they’ve eaten breakfast.

That’s almost 2 grades better! So, if you follow nothing else from this post, follow this advice and eat breakfast! All your hard work will pay off when you enter the classroom to take the test. One hour before the test, look over the material one more time and while doing this stay focused. This is the last time you visit the material before taking the assessment. All this studying now has given you confidence to do well on the test. There are multiple ways to study for a test. This has just been a great way for many students. Many times students cram for a test the night before and do poorly on the test. Take advantage a few days before the test and review all the material the teacher has presented you. Math is a subject that you will use the rest of your life. We hope you use these tips to nail your next test. Looking for more resource papers like this? Check out our math resource blog!

How to study for a Math Test by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>Borrowing and Carrying or Regrouping? by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>Why Words Matter in Math

Some kids understand it better one way or the other, but the “new” way of regrouping is not the way that many of us adults were taught. *So, let Mathnasium help be a resource for you as your kids learn the “Common Core” methods.*

Consider the following 1st and 2nd-grade Common Core Mathematics Standards:

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as …making ten (e.g., 8+6=8+2+4+10+4=14); decomposing a number leading to a ten (e.g., 13-4=13-3-1=10-1=9)…

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones-called a ‘ten.”

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

2.NBT.5 Fluently add and subtract within 100 using strategies based on place value…

2.NBT.7 Add and subtract within 1000…using strategies based on place value…understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens , ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Parents and teachers will recognize that these standards apply to place value and regrouping, or, as many of us learned, borrowing and carrying. Does it make a difference if we call the process regrouping or borrowing (subtraction) and carrying (addition)?

The difference could be in the sense that a student makes of the addition or subtraction operation. Once while substitute -teaching in a first -grade class, I was asked by a student if the assignment involved “sticks.” Intrigued, I asked him to show me what he meant. He then proceeded to show me how he, “carried the stick over the ones” in the following problem.

13

+19

Of course, what he was really doing was regrouping the resulting 12 ones into 1 ten “bundle” (composing) and 2 ones, leaving the ones in the ones place and regrouping the ten to join the other two tens.

In this problem

123

-89

we regroup the 1 hundred, 2 tens and 3 ones into 11 tens and 13 ones (decomposing-110+13=123). We aren’t borrowing anything (don’t you usually return something you borrow?), we are rewriting the minuend (top number), regrouping (decomposing) the hundreds and tens.

Some may argue that it’s purely semantics; it doesn’t matter what we call the process as long as a student can master it. But for a student having trouble making sense of place value and regrouping, the words borrowing and carrying may not hold as much meaning. The idea of rearranging an addend or minuend to accommodate the operation and calling it what it is, regrouping, may make the steps of the process make more sense.

Since many of the Common Core Standards *are* forcing kids to Regroup instead of Borrow and Carry, we are seeing many kids come in with a lack of understanding of what they are “doing” when they are “drawing the pictures”. They are going through the motions of drawing the pictures, but they don’t really understand what they are doing. At this critical time in a student’s development, we urge parents to make sure their children really understand WHAT their children are doing by challenging them in new and inventive ways. For fun and creative examples, visit any of our 3 locations…start at Cincymath.com.

Helping your students to make sense of math, whether they excel or need extra help, is our passion. To see if math is making sense for your student, check out questions – Mathnasium.com or click on a grade-specific checkup.

Borrowing and Carrying or Regrouping? by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>How to Develop Proportional Thinking in Kids by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>So, get your pencils sharpened and paper ready!

If 5 inches on a map represents 22 miles, how many miles are represented by 9 inches?

There are varying reactions when students or parents are presented with this problem, ranging from, “I was never good at math,” or, “I know we did that in school, but I don’t remember,” to, “Just set up a proportion.”

What does it mean to set up a proportion? What is proportional thinking?

Recently, a student taking a pre-assessment answered this question with 198 miles. Evidently, he multiplied 22 (miles) by 9 (inches). Often, students with limited number sense will simply choose numbers from a problem and manipulate them with a random mathematical operation.

Students versed in proportional thinking would know almost instantly that 198 miles is much too large. The 20 Elements of the Mathnasium Program constitute a student’s number sense. A group of these elements that apply in this situation stipulate that the student:

#10…understands the nature and use of multiples

#15… develops a sense of scale

#19…(has) critical thinking skills

A student with good number sense might reason,”5 inches is 22 miles. 9 is close to 10, which is two 5’s, so 9 inches should represent a little less than 44 miles (two 22’s). Or, “22 is close to 20, so each inch represents a little more than 4 miles (there are four 5’s in 20), so 9 inches would represent a little more than 36 inches.” Obviously, by either reasoning pathway, 198 would not be a reasonable answer. If this question appeared on a multiple choice assessment, the ability to estimate, keeping in mind the scale given, might be all that is necessary to choose the correct answer.

If the answer was to be calculated, element 15 again comes into play:

#15 (The student) understands proportional thinking…and develops a sense of scale.

If the ration of inches to miles is 5:22 or 522, the scale is the same for a length of 9 inches. So, we can set up a proportion (two ratios that equal each other because they have the same scale):

522=9x

Cross multiply:

5x=198

Divide both sides by 5:

5×5=1985

x=39.6

So, our student’s reasoning, that the answer is a little less than 44 and a little more than 36, would help him to see that not only is his answer correct, but that the initial answer of 198 just doesn’t make sense.

Most students who claim to hate math are just tired of being confused and frustrated. When math makes sense, students’ confidence soars as their problem-solving skills develop. If you’d like to check your number sense, go to Middle School Math Grade Level Check Up | Mathnasium.com

How to Develop Proportional Thinking in Kids by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>Improve Your Child’s MAPS Test Score – Resource Guide by Sam Thompson appeared first on Cincinnati Math Tutoring.

]]>Since many of our parents have been contacting us at Mathnasium asking if we can help improve their students’ score on the MAPS (Measures of Academic Progress) test that determines if a child is selected for the Honor’s and accelerated track for Math in many school districts, we have decided to put together this resource guide. Many kids Practice MAPS Tests at home before the actual test, but keep in mind that Students must score at least 95% on these tests to get into these advanced courses. Is your child on the borderline to achieve that score? This guide may help you with navigating the getting that last few percent to get to the top. First, a little background on what MAPS is.

This “MAPS” test is aligned with the Common Core Standards that Ohio schools have adopted for the 2013-2014 school year. Unlike the OAA (Ohio Achievement Assessments), MAPS does not determine how much information has been learned at a particular point in time, but rather one individual student’s progress. Each student completes MAPS testing three times per year.

Many kids ask, why another test!? Well, the MAPS test is designed to provide feedback that is used to specifically to modify the teaching and learning activities during instruction. MAPS tests are assessments designed specifically for learning. They are customized to the individual student, similar to Mathnasium’s method. You may be asking yourself, what exactly do the MAPS tests measure?

MAPS tests are given to students in kindergarten through 10th grade. The tests are a very thorough evaluation, covering everything from Problem Solving, Number Sense, Computation, Measurement and Geometry, all the way through Algebra and Functions, and Data Analysis for the more advanced grade levels just like Mathnasium. Those happen to be all the concepts that Mathnasium is currently teaching. The Mathnasium program is all about Number Sense.

A person is said to have Number Sense when he/she can count from any number to any number, by any number, split any number into halves, fourths, thirds, tenths, and hundredths; and compare any two numbers by subtractions and division. The way that the Mathnasium curriculum is designed will positively and directly affect any child’s ability to score well on a MAPS test. A Learning Center, like the one the Mathnasium that I own, will can raise a child’s score on the MAPS test!

Some parents say, “I don’t understand how how MAPS work.” They can be a bit tricky. Some schools have put together guidelines to help parents and students figure out what to make of the test. Once great school that has put together a great guide to MAPS Activity is Sycamore Schools MAPS REVIEW. Not only does the Sycamore Site have great resources like the Practice MAPS Tests (some of them free MAPS practice tests) They’ve put together a fantastic resource for parents, including an orientation, study-guide, and other resources for the test. [Keep in mind that the study guide provided there is decent, but only a guide. Nothing is a substitute for the 1-on-1 learning interaction you get at a TRUE Mathnasium Learning center! (See Bellow)]

So, are you the kind of Parent that’s ready to Improve Your Child’s MAPS Test Score, more than just a simple online resources? Truly ready to take it to the next level? Well, don’t take our word for it that Mathnasium is a great place to Improve Your Child’s MAPS Test Score, read the couple of Testimonials below.

The following testimonials tell how Mathnasium is proven to boost test scores and give the children the confidence they need to succeed.

One parent reached out to us from Mathnasium (Blue Ash, OH) after his child, Liam, came to the program. Liam was able to accelerate into the honors Math program and even get a 98% on the MAPS test, siting Mathnasium as the reason. The parent stated, “Liam was promoted to the Honor’s Math class. Mathnasium(R) gave him a boost in his math skills and we saw improvement in his test scores.”

Another parent reached out to us after their student of Mathnasium (Mason, OH) was able to excel and enter the Honor’s Program at Sycamore and Mason.

Do you have a student that’s ready for that “boost” in their math skills? Is your student ready to get to that next level or even further? At learning centers where we pride ourselves on our student’s successes where we make math make sense, you child will be a success!

If you want to improve MAPS scores, contact a learning center near you to make it happen! Contact Mathnasium

Improve Your Child’s MAPS Test Score – Resource Guide by Sam Thompson appeared first on Cincinnati Math Tutoring.

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