Valuable, Tailored, Free Information from College Board

If you are about to prepare yourself or your child for the SAT, it is critical to check one source first.  Any student who has taken the PSAT/NMSQT has access to a free College Quick Start account with the College Board.  This information is vital, because it contains all of the questions and their answers from the test, along with the correct response and an explanation of why each was the best answer. 

The Quick Start account also has hundreds of tailored practice questions, based upon the student’s weaknesses on the prior test. 

My College Quick Start Link

According to College Board, “Students can access their accounts starting in December when paper score reports are received. To sign in, students need:

  • The access code printed on their PSAT/NMSQT score report
  • A College Board student account (Students who do not already have a College Board account will be prompted to create one. It typically takes less than two minutes to create a free account.)”

This is absolutely vital information that every student needs as they begin SAT preparation, and it is information that needs to be shared with any potential tutor, so that the tutor can focus on areas of demonstrated weakness, saving money and time.

SAT Study Books

SAT Question of the Day

This is a great link for students preparing to take their SAT tests!  If you go to the following link, you will get a SAT practice question each day from the company that administers the SAT.  After you have clicked on your best response, you will be able to see the correct answer and why it is the best one.

SAT Question of the Day link:

My tip:  Remember, sometimes these tests have two good answers.  You always need to pick the best answer, so make sure you are not picking the first good answer you see and moving on to the next question before you have looked at all the possible choices.

Second tip: When choosing SAT study materials, choose the Official SAT testing materials from the College Board.  They are devising the tests, so they are the best authorities on what you will find on these examinations.  Their official book has full length SAT tests that you can use as practice.


Understanding the New Mathematics Standards and Testing

New Mathematics Standards and Testing –


There is a lot of confusion about the new Common Core state standards adopted by most states in the nation and its accompanying testing.  The latter half of the following article (scroll down about 14 paragraphs) has quite a bit of good information for parents about how the testing will change:

The key points are that these new standards and the testing being developed will have a diminished emphasis on students demonstrating that they know rules and procedures.  Students will have complex, real life word problems to solve, and they will also have to explain how they arrived at their answer. 

This is not to say that students will not need to learn the rules and procedures, but they will learn the rules by using manipulatives and pictures to solve cognitively complex mathematical problems and derive the rules in groups.  Then, there will be a class discussion that will take place in which the teacher leads a discussion about the rule or procedure the students have derived so that students understand conceptually the most efficient procedure (these are the common rules and procedures from standard mathematics that everyone learns).  Only then will students begin to use the newly-derived rule to solve more mathematical problems with the efficient algorithm they have derived and work to build their speed and fluency with the new procedure.  This is the same way in which students in Singapore learn mathematics.  Students in Singapore consistently prove on international mathematics testing that they are the best mathematics students in the world.  They consistently are far more advanced in their skills than students in the United States, who fair poorly on conceptual and real world applications of mathematics (Van de Walle, Karp, and Bay-Williams, 2013).

The implications for parents are a few:

1) Your child may begin to struggle with the new mathematics instruction for a while.
2) From my discussions on forums for teachers of mathematics, it is clear that some teachers are adamantly resisting the change.  The problem is that their students will not do well with the new testing.  Basically, students will now need to not only learn the rules and procedures of mathematics, as we all did as children, but they will be expected to understand mathematics on a deeper, more conceptual level that will help them solve 21st Century problems (BTW… Good Common Core teaching practices do not throw out knowledge, speed, and fluency practice of the rules and procedures. That is a fallacy).  It may be wise to have a discussion with your child’s mathematics teacher in order to find out how they are adapting to teach the new standards. 
3) Since the vast majority of mathematics tutors in America are not trained in teaching conceptual mathematics and having students solve cognitively complex mathematical problems with discussion in order to derive the standard rules and algorithms (Most simply tell students the rule and have students solve problems based upon the rule they just taught the student), their methods are less helpful than in the past for helping struggling students get back up to speed in classes where Common Core mathematics instruction is beginning to take placeParents need to shop carefully for mathematics tutors.  The days of hiring the local mathematics wiz and being able to count on good results have gone.  Parents need to ask potential tutors how they teach mathematics and how their instruction has changed in light of the Common Core standards.

Currently, I am providing three mathematics tutorial options using Common Core standards teaching techniques for parents of students grades 5 through 8.  I have a fractions tutorial for $25 an hour that you can either schedule through Google Helpouts:
or through my calendar, if you prefer to pay via Paypal:

For a limited time (until I have three students committed to these and until August), I am also offering free fractions, geometry, and pre-algebra lessons twice weekly for my graduate certificate program.  Information on the free, twice weekly lessons are here on Google Helpouts:

In either of the three choices, we will always begin a lesson with a problem that students solve with manipulatives or pictures that help them learn a mathematics rule, formula, or procedure.  Then, we will have a discussion about the rule and how the student believes such problems can most efficiently be solved.  After I guide students to the most efficient rule or procedure, students will be provided ample opportunity to use the new rule and develop speed and fluency with its use in solving real life problems.  I will also incorporate mathematical games and mental mathematics instruction, such as estimation strategies and instruction, in order to help students develop the key skill of checking to see if their answers make sense.

The Next Step in Middle School Mathematics Remediation


If you followed my last post, you know that the first step in mathematics remediation is to check to see if your child has memorized his or her basic mathematics facts.  If you use the link above, you will be able to find links for the practice of each number table for multiplication.

The next step is obviously that your child also needs to be able to perform multi-digit multiplication and long division without difficulty.  If anyone needs for me to find some links to helpful websites for this, please let me know!

The next step that is critical is that your child needs to be able to fluently work with fractions.  This is another large cause of many children having problems with mathematics in middle school, high school, and beyond.   Van de Walle, Karp, and Bay-Williams (2013) stated that students not fully understanding fractions keeps them from succeeding in algebra and higher mathematics.

Fraction skills need to be built one upon the other.  Many students have quite a bit of trouble with fractions, because they were not taught fractions in a concrete manner first, then moved on to operations with fractions.  For example, the 4th and 8th grade NAEP national testing found that only 41% of eighth graders in the U.S. could place three fractions in simplified form in correct numerical order (Van de Walle et al., 2013).

Researchers such as Johanning (2011) are finding that middle school students often have learned procedures, but do not have a basic number sense of fractions and their size.  Students who learn mathematics as a collection of procedures without understanding the conceptual underpinnings of fractions in a concrete manner cannot estimate in order to determine if their answer makes sense.  They are less able to answer real world problems that involve fractions.  The new testing being developed will place a greater emphasis on real world problem solving with mathematics.

Many parents, finding their child is having problems with mathematics will turn to a “math wiz” to help their child.  This may or may not be helpful.  If their trained teacher was not able to help them, this must cast doubt on the local “math wiz” being able to help them either!  Unfortunately, adults in the U.S. have mostly been taught mathematics as a group of procedures.  Many of us admit to not really understand the concepts behind the procedures.  Many adults state that they, “… never really understood math.”

The types of lessons that I teach begin with students using either manipulatives (fraction bars, fraction strips, pies, number lines) or pictures that they draw.  They will solve a real world problem that will help them begin to understand why the rules for operations of fractions work (For example, why do we not add the denominators when we add fractions?).  Using manipulatives and carefully chosen problems, I move students to understanding of why these rules work through problem solving and discussion.  Then, students work to improve their understanding and move from the concrete and the conceptual to abstract problem solving with the traditional procedures and algorithms using carefully chosen problems.  In this manner, students understand the procedures they are using and why they work.  I also emphasize estimation skills, so students are always being asked, “Does this answer make sense?  Why?” Then, we utilize games in order to build speed of computation.  This is how the National Council of Teachers of Mathematics (n.d.) advocates that mathematics be taught, based upon mathematics education research.


Johanning, D. I. (2011). Estimation’s role in calculations with fractions. Mathematics Teaching in the Middle School, 17(2), 96–102.

National Council of Teachers of Mathematics. (n.d.). Principles and standards for school mathematics. Retrieved from

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication. 


fracation bar

Does Your Middle Schooler Have Problems With Mathematics?

Does your middle schooler have problems with mathematics?

The first step is to check something really easy.  Any parent can quickly and easily check this and the problem can be remediated over the course of a few weeks without tutors.

Give your child a quick multiplication table quiz.  This may shock you, but one of the biggest reasons that children begin to fail in higher mathematics, which they begin to explore in middle school, is that they do not have their mathematics basic facts, such as their multiplication tables, memorized (Van de Walle, Karp, and Bay-Williams, 2013).  Without these facts, mathematics is a slow and painful process and seems out of reach for students.

If you find this is the case for your child, do not wait.  Mathematics needs to be learned in a hierarchical manner: one skill builds upon another.  The longer it goes on that they do not know their basic facts, the further behind they will get.  The best way to approach this problem is with carrots and sticks as needed and to have your child commit several minutes each night to studying one table at a time.  I have provided the first link for you for random practice with the 2s and 3s below.  I will make a page that will provide links for practice of all of the tables up through 12.  My suggestion is to have the goal of one table (5s, for example) per week, or two if possible (such as during the holidays).  Quiz them at the end of the week.  Each week, quiz them on some of the prior tables as well.  The tables need to be learned automatically and quickly.

Here is a link for practice of just the 2s:

And the 3s:

Look on the right-hand-side of this blog page over the next week, and I will put the rest of the links for this practice of the other tables on one page for your convenience.


Free Challenge Problem Group for Pre-Algebra Students

I have created a free challenge problem group on Edmodo for students who would like to explore Pre-Algebra.  There will be a new problem each week, along with discussions between students.  Often, you will discuss the problem with each other online, in order to help each other figure out the answer.  Each problem will be solved with manipulatives, like fraction bars and pie charts, so you will really understand mathematics on a deep, conceptual level.

If the members of the group would like, I can create more problems each week, in order to extend your learning.  I will also often provide online resources that will give you some more practice and will suggest games that you can play with the other members of the group via Google Hangouts.  I would like to have six or more students join the group.  I am doing this as part of the requirements of a graduate certificate program.

In order to join, please place a request by using my contact information, or by using the “Join” URL for the Edmodo group:


Free Mathematics Tutoring in Pre-Algebra

Free Mathematics Tutoring In Pre-Algebra

  • This is an offer for three students who need some remedial work with Pre-Algebra issues, such as fractions (where we will begin), geometry, and beginning algebra issues.   I need three students who could benefit from review of fractions, geometry, and algebra such as presented at the Pre-Algebra level.  We will use manipulatives, like fraction bars and pictures, to make the problems more real and will play games once you work with the other students to figure out each rule for fractions with your manipulatives.  This will help build your computational speed in a fun manner.  These lessons are for a graduate certificate course I am taking.
  • This is not for on-the-spot tutoring.  Every lesson will be carefully designed and move in a progression of skills.  Students need to be wiling to commit to two or three 55 minute lessons per week through August.  All three students will meet with me at the same time.  All lessons are free.  The students need to be in the seventh grade or above and need help with fractions and other Pre-Algebra topics.
  • There is one catch, there will be a sample problem that I will have you try to solve as a group each week that may be harder than the rest of what we are doing.  You must simply give the sample “challenge problem” your best effort each week.  That is all I ask.  The problems are required by my graduate program.  The challenge problem will only take about 15 to 20 minutes during one lesson each week.  This is the only catch; the sample problem is a bit harder.  It is just to see what students can do at your level.  I also have created games to make the learning fun and to help build up your speed in computations, once you have learned the concepts.
  • Mathematics tutoring – Elementary through Pre-Algebra.  I utilize guided problem solving with manipulatives and concept-based lessons that will make mathematics both enjoyable and very real.  Then, I will move you to the most efficient procedures to solve the problems.  This is Common Core Mathematics instruction.  You will need to understand mathematics on this level for the new testing being developed.
  • You will need a headset with a noise-cancelling microphone for the appointments, a quiet room in which to do the lessons,  and a computer with a printer and scanner hooked up, because I will send you files of mathematics manipulatives, like fraction bars.   I have found that Google Hangouts needs a computer that runs Vista or newer.
  • Please only contact me for the lessons described above.  If you are looking for other types of free lessons, please do not waste your time or mine.  If you are interested, do not set an appointment yet.  Please contact me via my contact information for this blog.  We will need to find a time that all three students and I can agree upon, so we will be setting our schedule in a Hangouts group each week.  Please state in the message other contact information (you will need a Google account and contact information, because we will use Google Hangouts as the VOIP), the grade level of the students, and something to let me know that you are agreeing to a commitment of twice weekly, 55 minute lessons as well as the one challenge problem per week.
  • Once I have three students, the offer ends, and I will keep a waiting list, if someone needs to drop the group.
  • I look forward to working with you and making mathematics fun and understandable.

Multiplication By Twos Basic Facts Online Practice

This is for my students who are working on basic multiplication facts.  Here is a site you can work on this week, in order to be ready for the multiplication by twos quiz on Friday:

Leave the two boxes checked on the main page, so you can check your answers, then press “Begin. ”  Practice for a while each day.  Mathematics is so much easier, when you know your basic multiplication tables!  Enjoy!


Only 43% of 2013 Seniors Taking the SAT Scored at a College Ready Level

Here is a link to an article in The Atlantic with the dismal results on the latest 2013 SAT scores:

Please read my articles below and to the left, if you want to learn some strategies  as your son or daughter prepares for the SAT.  Clearly, one fact emerges that the students who demonstrate by their SAT scores that they are college ready are those who take advanced courses in high school – Trigonometry, Calculus, and Pre-Calculus along with Honors or AP classes.

I would add, based upon current research such as cited by Van de Walle, Kamp, and Bay-Williams (2013), that U.S. mathematics scores have been traditionally lower than those in some Asian countries (most notably Singapore), due to the continued emphasis on procedural skills, without much deep understanding of content.  In the United States, we have mostly been taught procedural  mathematics, with little  emphasis on the underlying conceptual knowledge.  Thus, students learn how to make computations with little understanding of how to utilize these skills in real world mathematics.  The landmark mathematics treatise, “Adding It Up” (National Research Council, 2001), stated that, as in anything, there needs to be a balance between conceptual knowledge and procedural fluency.  Otherwise, students will be able to mimic the sample problem the teacher places on the board and dutifully solve more problems of the same type that day; but, overall, they tend to have difficulty at a later date ascertaining when to utilize the procedure taught when solving real world problems.  More evidence that our current state of mathematics instruction based upon procedural knowledge alone does not benefit our citizens is the fact that many adults state, almost proudly, “I never did understand math,” or “Math was always hard for me.”

I have begun to offer Pre-Algebra lessons in addition to reading and writing remediation and ESL instruction.  The classes (usually with three students) will begin with a mathematics problem, but I will not provide a formula to help in solving the problem.  I will help remind students of what they already know and give them mathematical manipulatives to use as well as provide tips and hints on a means of solving the problem.  An example of such a problem would be to provide students with cut-outs of right triangles and graph paper before students have learned the Pythagorean Theorem and have students use their prior knowledge of how to find the area of a rectangle to help them figure out the formula for solving right triangles (I urge you to try this at home!  It is easy to see that the right triangle is one half of the area of a rectangle, making it easy to see why you multiply the 1/2 times the base times the height, because the base and the height of the right triangle are simply the length and width of the rectangle).

After the students have come up with a solution to the problem, we will have a discussion about the problem and how they solved it and look at other problems to see if the “solution” they discovered will work for other problems.   I have students take notes about their problem solution and maintain a mathematical notes folder that contains words, images, and symbols to help them remember their solution.  Then, I will have the student solve more problems of this type, in order to gain the procedural fluency  that they need to solve mathematical problems quickly and efficiently.

The manipulatives we use will include cut-outs, graph paper, and vitual manipulatives that they will have access to whenever they would like to use them.   Note: In addition to the cut-out manipulatives, the virtual manipulatives I now use are online.  I am in the process of finding the iOS and Android virtual mathematics manipulatives that can be downloaded, so a student can utilize them even when they do not have Internet access.

Finally, the Atlantic article about the 2013 SAT scores did not break down the scores by SAT category, but I would also remind parents that a key determining factor in reading success is wide reading.  Has your child always picked up a wide range of books, reading daily and consistently?  If so, and especially if they are taking advanced courses in high school, they are likely to be poised to receive a high score on the SAT Critical Reading and Vocabulary sections, because they will have a far greater vocabulary than their peers who are not wide readers.   Please see my articles on the SAT Reading and Writing Preparation to the left (or below), if you would like to find out more.

If you are interested in scheduling an appointment for an online reading or writing remediation, SAT preparation, Pre-Algebra, or ESL lesson, please see this link for information:


National Research Council (NRC). (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Retrieved from record_id=9822&page=115

 Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publications.

(Note: There is a problem in formatting references in WordPress.  I apologize for a lack of requisite hanging indents and the strange change in the font!  I may need a WordPress tutor!)

What Services Should You Expect from a Qualified SAT Reading Tutor?

There is a lot of money being made in the SAT preparation industry.  Two large companies dominate the industry.  Some parents spend tens of thousands of dollars for SAT Reading and Writing test tutoring services for their son or daughter, but the results from these major companies are less than stellar.  They often promise gains of a certain number of points on each exam.

Please read this article here before you read the rest of my article:

It contains information and links to two studies conducted 10 years apart, one in 2009, that show only about a 30 point overall rise on the total SAT scores for students who took a preparation program.  Some of these companies and tutors will claim that you will gain 100 points and more.  The research shows that this is fallacious.

The reason is that the best preparation for the SAT is everything that your child did from elementary school onward.  In terms of the writing and reading sections, students who are not fluent readers on grade level with large vocabularies will suffer.  The best preparation of all is to begin the process in elementary school with some very basic things that all parents can do.

Please see this post for more information:

So what can be done (for the SAT Reading test and Vocabulary section) when a student is in high school and has had a less than stellar school career so far?

  1. The tutor should be qualified to test the student’s reading for grade level equivalent, fluency, and comprehension.  This can easily be accomplished in less than one hour.  They should know how to spot reading disabilities and fluency issues and provide remediation.   The student and parent need to be apprised of the results of the testing and a strategy for the subsequent lessons.
  2. The tutor should spend one lesson teaching test taking strategies.
  3. The tutor should then proceed to provide any remediation work, such as fluency lessons, provide lists of higher interests/lower level books to boost the reading level, and conduct any remediation for reading disabilities in the course of reading instruction.  This work is highly engaging.  Students can progress 2 to 3 grade levels doing fluency work twice a week for a few months.  In my work remediating reading for middle school students, I found this to be something most struggling readers needed.
  4. Concurrently, the tutor should provide lists of higher interest/lower level books at the student’s current grade level.  They should read daily for at least a half an hour.  The tutor should also provide an article in an informational magazine at the student’s current reading level, so that the student is beginning to get work in both fiction and non-fiction reading.   The tutor should introduce unfamiliar vocabulary and help the student learn how to use word parts (prefixes, roots, and suffixes) to determine the meaning of unknown words.  This is a powerful strategy for vocabulary improvement!  The non-fiction article should be discussed at the beginning of the appointment.  These, BTW, can be a great source of SAT Writing topics!
  5. As the student arrives at fluency with full comprehension (a key!) at their grade level equivalent, it is time to begin teaching students about the types of questions they will encounter in this section of the test, and begin to have students read articles on grade level and answer typical questions that they will be given on the SAT.

Any SAT tutor or preparation company that directs the student to study lists of vocabulary words, does not initially test the student’s reading skills, or fails to teach the students how to use word parts to determine the meanings of words is not fully preparing the student for the SAT. If no skill deficits are found, lessons can proceed from point 1 above to point 2 and then point 5. When the student is reading articles and successfully comprehending and answering questions such as posed on the SAT test and knows how to use word parts to determine the meanings of unknown words, the lessons can end, and students should continue to read widely (especially informational text on grade level), using their new found skill of using word parts to help them determine the meanings of new words.

Use this information as a guide when you interview a potential SAT Reading preparation tutor or tutoring company. This will save you a considerable amount of money and time. It is a waste of time to do things that will not produce much of a gain, but improving fluency and comprehension (for those students that need the remediation) and teaching test taking strategies, word attack skills, and practice with the types of reading and questions to be found on the test will produce the greatest gains. This will also help your son or daughter succeed in college. The greatest reason that students drop out of college is that they do not have the reading skills for the incredible reading load that they will experience in college.

I would be happy to tutor your son or daughter via Skype. My contact information can be found here: