# Under New Ownership

Dear NewtonMathTutors Parents,

I’d like to introduce myself. My name is Roger Lui. As new owner of NewtonMathTutors.com, I’d like to welcome you to our Math Resource site for Boston-Area parents.

I have over 27 years of experience in the field of education, both as a tutor, teacher and as a curriculum leader, with a strong emphasis in mathematics. I have worked with a wide range of grade levels, from elementary school to high school. I received a BA in Mathematics from Harvard University and a Masters in Education from the University of California at Berkeley, with a double major in elementary education and secondary mathematics education.

As a high school teacher, I have also coached debate and creative writing, and I have led literature discussion workshops. In my many years as a tutor, homeroom teacher and advisor, I have gained experience in coaching students to develop effective study skills and analytical strategies.

I love tutoring because it gives me an opportunity to design an individualized program and approach to meet each child’s unique learning style, strenghts and weaknesses. My emphasis is on detailed diagnosis to identify any learning gaps or weaknesses in prior knowledge, on boosting foundational understanding of concepts and on fostering a student’s self-confidence and ability to learn.

I have lived in the Boston area for thirty years and understand the specific challenges of the Massachusetts math curriculum. I hope you will continue to benefit from NewtonMathTutors.com and introduce your friends to the wealth of resources available here.

–Roger Lui

# Addition Tally Marks

**I was working with a 2nd grader yesterday on addition.** Instead of having kids memorize the addition table, we encourage them to use number sense. Example, most kids are good at adding doubles, 6 + 6, 4 + 4, etc.. (from playing Monopoly?). So we encourage them to see 6 + 7 as 6 + 6 + 1, or* 6 Double + 1* instead of memorizing 6 + 7 = 13. Kids who learn addition this way still end up ‘memorizing’ the addition facts table, but along the way, build a stronger number sense and mental math skill.

**So Christina, Grade 2, was practicing adding doubles plus 1:** 5 + 6 = ____; 7 + 8 = _____; and so on. I was observing her and noticed that she would pause first, look far into the distant blue yonder, then write down the answer. It was slow, but the answers were accurate. I was pleased with myself that she was applying this doubles plus 1 technique so well. But after watching her do this gaze-into-the-blue yonder thing for every problem, I couldn’t resist asking her.

**Me**: “Christina, when you look up into the distance, what are you thinking?”

**Christina**: I am adding.

**Me**: And what are you saying to yourself or seeing in your mind when you are adding?

**Christina**: I see tally marks. And I add them one by one.

**Me**: Does it give you a headache? If I have to see more than 3 tally marks in my head, I get a all muddled up.

**Christina**: Not me. I can see 20 tally marks, no problem.

**Me**: Wow, that’s quite a skill. Hey, want to know how I do it since I’m so bad at seeing tally marks in my head?

And I proceeded to demonstrate the doubles + 1 technique, and have her mimick it a few times. She finished the rest of the work sheet without the blue-yonder gaze.

**This encounter made me realize that sometimes we explain a math concept,** we think the child gets it because the answer looks right, but he/she really doesn’t. Instead of telling you, this big know-it-all adult, that what you are saying doesn’t make sense to her, the child coninues to resort to old comfortable, though less-effective techniques of getting to the answer. This may also be why in a big classroom setting of 20, 25 kids, children can fall behind without the teacher noticing.

**How to avoid these situations?** Simple, just ask the child to explain their steps back to you by asking questions like below:

Q. Nice job, how did you solve that?

Q. That answer is correct! How would you explain to a friend how you did that?

Q. What do you see in your head when you were thinking about that problem?

Q. Can you think aloud? I’m interested to hear how you think about this.

Q. Pretend I’m your friend, and I just don’t get this. Can you help me?

# Math teaches you to think

It’s back-to-school time. Teachers now have websites where they post their curriculum, homework assignments, and their intended-to-inspire thoughts about the subject. I’ve browsed a number of Math teachers websites and found some good ones:

*. The thinking that must go on when you do math helps in all your other subjects. When you are “doing math” you are practicing thinking. Math is weightlifting for the brain. Yes it can be dreary and repetitious. At times, it can be incredibly frustrating. But the struggles you’ll experience as you work your way through the math textbook serve to strengthen your mind. There no greater discipline, no better way to train your brain.”*

**Math teaches you how to think***It’s not punishment. Homework is given so YOU can practice something you’ve started to learn in school. When you can do something by YOURSELF, then you know that you’ve really learned it. HW is given 4 to 5 nights per week and is due the next day. If it is complete you get a check(100%), if its incomplete(more than half done) you get a check minus(70%) and if you didn’t do it (less than half done) it’s a zero. Hw can be handed in the next day for a check minus(70%). ~ Mr. Leonard Monsoon, Day Middle School, Newton, MA*

**What’s the purpose of homework?***, always make an attempt, no matter how hard it is” ~ Mr. St. Claire, Day Middle, Newton MA.*

**TRY**# Dyscalculia – Math learning disabilities

**Have you heard of Dyscalculia?** It’s a learning disability like Dyslexia, but for math. Dyslexia has become a household word, but Dyscalculia? Even my computer thinks it’s a typo.

**Math learning builds on itself.** Children with dyscalculia have difficulty learning the meaning of numbers, what we call number sense. Parents may remember these children having trouble with tasks like sorting objects by shape, size or color; recognizing groups and patterns; and comparing and contrasting heights, weights, sizes when they are very young. Learning to count, recognizing and matching numbers can also be difficult for these children.

**When they start school, they struggle to remember and retain** basic math facts (i.e. addition facts, times tables). Word problems are challenging to them as they have trouble figuring out how to apply what they already know to solve math problems.

**Like most learning disabilities, Dyscalculia varies from person to person** and affect people differently in school and throughout life. Among those with dyscalculia, some can develop math phobia, or a fear of math, because of bad experiences with math, being embarrassed in math class, or simply because of poor self-confidence in the subject.

**Parents naturally want to know how to help** their children if they have Discalculia.

**First, get a professional diagnosis. ** Many children lack practice in math, or have difficulty concentrating (ADD, ADHD) in class which affect their ability to succeed in math, but the fix for that is very different from the approach dyscalculia kids need.

**Second, recognize that it does not correlate to intelligence.** Children with dyscalculia often live with the belief that they are stupid – and they may be told so by parents and teachers too. They may portray difficulty in memorizing their multiplication tables, add up, or subtract, and in fact numbers may make no sense to them at all. They may not be able to tell time easily on a non- digital clock, tie their shoe laces or read music notes. If these children don’t get help, and they end up shutting themselves from math, yes, they will grow up and find themselves not being able to participate in many intelligent conversations about sales discounts, restaurant tips, investments, economic trends, and cooking (lots of fractions!) – but that’s not because they are not intelligent, it’s because they closed the window on learning math.

**Third, provide them more individualized learning environments** where the instructor can tweak the way math is taught to them. This is not possible in a classroom of 25 to 30 kids. Dyscalculia kids need more individualized instruction – if one way of explaining fraction addition doesn’t sink in, the instructor can attempt another way, or switch to manipulatives for example, and not be tied down to the class clock and 30 other kids. When the instructor teaches a child, it’s to, for, with that child only. While the child is working on practice drills to reinforce the learning, the instructor can check on other students.

When teaching children with dyscalculia, it’s crucial that the teaching makes sense to them. Memorizing, flash cards are not as effective because they have a hard time retaining the information. Read about our student Lance, you know math makes sense to him when he starts taking it so personally : I demand a recount.

# I’m not planning to be a mathematician!

**Does your child ask you why they need to work so hard at math if they are not planning to be a mathematician?** How do you answer your child?

We get asked that a lot, sad to say by girls, more than by boys. Here’s how the discussion goes. Share yours in the Comment section below.

**Student:** “Why do I need to study so much math? I’m not planning to be a mathematician when I grow up.”

**Instructor:** So what are you planning to be when you grow up?

**Student:** I don’t know, but definitely not a mathematician.

**Instructor:**: Especially because you don’t know, you’d better keep working on your math.

**Student:**: Why?

**Instructor:** Because you want to leave your options open. What if you decide to be an Olympic gymnast, an entrepreneur, a football coach, a neurosurgeon, a pre-school teacher, a bounty-digger, a chef, a TV producer – you can bet your money they rely on math everyday.

**Student:** But you can just hire someone to do the math.

**Instructor:** And that’s what many people do. That’s why, if you know math, you’ll always have a job.

Even an actress, like Danica McKellar (The Wonder Years) needs math. If you have a middle-school daughter, give her Danica’s book: Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail. It is sprinkled with testimonials of her friends, how they felt about math, what their careers are now, and how important math is in their work.

*“We’ve seen girls perform similarly [to boys], but what we have seen also is that in high school, when we arrive and give them surveys about how they feel about math . . . they score worse. They feel more frustrated and anxious than boys,’’ *said Ivon Arroyo, a research scientist at the University of Massachusetts Amherst who is working on the software being tested at Turners Falls, called Wayang Outpost.

*“That may make girls not persevere as much in the harder problems.’’*

**Encourage your daughters to do well in math so they really can be anything they want to me. ** And don’t forget, share with us how you answer your child when he/she asks you why they need math.

# Problem of the Week – June 8, 2010

**Grade 1 to 3
#1 Question :** Sally has to be at school at 8:15 am. If it takes her 25 minutes to get ready, 10 minutes to eat breakfast, and 15 minutes to get to school, what time should Sally wake up in the morning to make sure she gets to school on time?

**Grade 3 to 5
#2. Question**: Every Friday the students in Mrs. Hull class get a chance to win a homework pass using a spinner. The spinner contains the letters F, I, J, Q, S, and the numbers 2, 6, 9, 11, 15. To win a homework pass a student must spin either a vowel or a prime number. What is the probability of a student winning a homework pass each week?

**: If two monkeys can eat two bananas in two minutes, how many monkeys will it take to eat 18 bananas in six minutes?**

6 – 8th Grade

#3 Question

6 – 8th Grade

#3 Question

**Algebra and Higher
#4 Question:** A square has a side length of 8″ . An isosceles right triangle with legs that are 8″ has its vertex at the center of the square. What is the area of overlap of the triangle and the square?

**Answers:**

#1 Answer: 7:25 am

Note: We assume that the time that Sally should wake up gives her the minimum amount of time she needs to get ready.

#2. Answer: 3/10 or 30%

#3 Answer: 6 monkeys

Note: Since it takes two monkeys to eat two bananas in two minutes, it takes one money two minutes to eat one banana. So in six minutes one monkey can eat 3 bananas. That means it will take 6 monkeys to eat 18 bananas in six minutes.

#4 Answer: 16 inches2

Note: Because the vertex angle is a right angle at the center of the square the legs of the triangle iintersect adjacent corners of the square. This means the overlap is a fourth of the area of the square. 64 / 4 = 16.

# I Demand a Recount!

It’s Math MCAS prep time here at my house and a 4th grader friend of my daughter’s was tackling this problem:

The multiple-choice question asks the student to select a reasonable conclusion based on the data above.

The student studied the question, then said, “I don’t like this. It makes boys look bad. I demand a recount!” My initial reaction, as his instructor, is to get him to focus on the question and answer it, not turn it into a debate. I got more flustered when he proceeded to take a pencil and extend the dark bars:

But thankfully, I stopped short to appreciate what’s actually happening. This kid really understands this graph. In fact, he internalizes the data from the graph to the point of getting upset about what it’s saying. That is true understanding. That’s more precious than the ability to pick the right multiple choice answer.

When math becomes relevant, when math makes you mad, when math is more than symbols and digits, when math talks to kids, that’s so awesome!

# MCAS Math Success – Excellence or Habit?

**We just went through MCAS diagnostic week.** Students take a 40-question mcas math diagnostic assessment to help us gauge how prepared they are for the Math MCAS and what areas we need to work on.

**The MCAS questions are more than just arithmetic computation problems.** Almost every question is a word problem. Take this one below:

**Many students not used to these type of word-intensive question** structure get bogged down with the reading and miss the math. To excel at the MCAS, a student should go over hundreds of MCAS questions until turning words into math becomes a habit.

**That goes for math learning in general.** It’s one thing to learn a concept. It’s another thing to keep practicing on it until it becomes a habit. You know something about habits? It’s on cruise control. Habits have stronger staying power in exam rooms, it’s less vulnerable to anxiety. You see this in the Olympics all the time. Muscle memory they call it. Ask an Olympic figure skater how much thinking she does on the ice during that 3-minute performance. Zilch. It’s all muscle memory. She’s practiced her routine so many times that it just plays out instinctively.

**That’s what math skills are.** It comes with a lot of practice. But that kind of practice will pull a kid through in tense situations like MCAS exams, or in the near future SAT exams. You hear parents talk about ‘test anxiety’. They claim their children really know the material, but just ‘doesn’t test well’. Is that so? Before you put another label on your child, how about prescribing the same workout of successful athletes ? Practice. Until they can add fractions of unlike denominators half asleep, until they can rattle off without thinking that 4/5 is 80%. Until they hear alarm bells when they see answers that don’t make number sense. Then see if they test well or not.

**Where to find hundred of MCAS Math questions? ** Go to : http://www.mcasmathprep.com . You can even pull up questions by category so if your student struggles with Fractions/Decimals, or with Geometry, you can find past year MCAS Math questions related to those topics.

We are what we repeatedly do. Excellence therefore is not an act, but a habit. –Aristotle

# A step down: Federal education standards

By Ze’ev Wurman and Sandra Stotsky | Boston Globe, March 13, 2010

**THE OBAMA administration plans to make states adopt proposed national academic standards** as a condition for receipt of federal education grants. The problem is what the administration has proposed is not near the quality of what the Commonwealth already has. [ Editorial: This is true, Massachusetts (MCAS) and North Carolina have the most difficult tests? ]

**High academic standards are the foundation of Massachusetts**’s landmark education reform success. They set goals for students to reach in each year of elementary, middle, and secondary school. The standards are rigorous, but Massachusetts students have proven year after year that they are up to the challenge.

**The latest draft of national English language arts and math standards **looks very different. The prestigious National Math Advisory Panel identified algebra as the key to higher-level math study and recommended that more students should be ready to enroll in Algebra I by eighth grade. But it is unlikely that these standards could even support the teaching of such a course in ninth grade. [ Editorial: The Algebra-too-soon phenomenon - when kids have not been equipped with the skills, thrown into Algebra prematurely is damaging to their attitude about math. Kids write themselves off as not-wired for math when they just have not had the necessary pre-Algebra prep. ]

…

**While the Commonwealth’s standards steadily move to higher levels **of academic content from K-12, the draft English language arts standards move along a yellow-brick road to an empty set of skill-based “college and career readiness’’ benchmarks. The content consists mostly of non-binding lists and titles included in the appendices. In math, the standards end somewhere short of Algebra II. [Editorial: Newton North and Newton South High School go all the way up to Math AP (Advanced Placement) Calculus CD.]

**Ripple effects of the common core standards would be felt** throughout public education in Massachusetts. New standards require new assessments to test mastery of them, and that would spell the end of MCAS. [Editorial: Plus the extensive resources required to train our school teachers to prepare our students for the new tests.]

**Ominously, Stanford education professor Linda Darling-Hammond** is overseeing the assessment side of the national standards effort. Rather than focusing on academic achievement, Darling-Hammond has long touted using student portfolios and other forms of assessment like “those that have been used in leading-edge assessment systems . . . such as those in Connecticut, Kentucky, Maryland, Maine, and Vermont.’’

**“Have been’’ are the key words here**. Connecticut scrapped its former standards and assessments in favor of ones that look more like Massachusetts. Vermont and Kentucky also gave up on student portfolio assessments because they proved unwieldy, unreliable, and too expensive.

I**t takes time to develop and implement quality standards.** The common core standards would be implemented just a year after the process was initiated. Only three weeks will be allowed for public feedback before the standards are finalized. It’s easy to understand much of the support for national standards, dubbed “no vendor left behind.’’ The standards development committee includes an inordinate number of folks from major testing companies. But state policy makers should think long and hard before scrapping the nation’s best standards in favor of an untested substitute. [Editorial: To their point, the developed countries that do very well in math have national standards. Countries like Singapore, Sweden, India.]

**The Commonwealth and its municipalities foot the bill** for over 90 percent of state K-12 public education expenses. While it’s natural to be tempted by federal dollars during trying fiscal times, it’s important to remember that education will still be a state and local responsibility when that money runs out.

Massachusetts invested years of effort and billions of dollars to develop a set of standards that are the heart and soul of the nation’s most successful education reform. Let’s not give them up for a set of so-called Common Core College Readiness standards that wouldn’t even get our children into college.

Article Source: Boston Globe, March 13, 2010. Authors: Ze’ev Wurman, a high-tech executive in Silicon Valley, who helped develop California’s standards and assessments in the mid-1990s. Sandra Stotsky is a member of the MA Board of Elementary and Secondary Education.

# Guess-and-Check vs. Algebra

I have a 5th and 7th grader. At the dinner table last night, I asked: If Tom takes 2 years from his age and gives it to Mary, Mary’s new age is twice Tom’s new age. If Tom takes 3 years from his age and gives it to Mary, Mary’s new age is three times Tom’s new age. How old are they?

My husband immediately said, ‘classic algebra’. The 5th grader went, ‘I don’t know Algebra, I’m going to use Guess and Check’. My 7th grader has started algebra so he started setting it up with variables T and M.

I just sat there and continued eating my dessert.

Would you know it, the guess-and-checker got the answer first. The algebra solver plodded along, got a negative answer, changed his setup, rechecked the negative and positive signs and eventually arrived at same answer.

Start doing ‘algebra’-type problems with your kids before they learn algebra. Simple problems like: *Tom has $10 more than Joe. Together they have $120. How much does Tom hav*e? Problems like that prompt non-algebra students to use their number sense. Ok, $10 is not a lot, so they have close to the same. Half of $120 is $60. Let me try $50 for Joe. Tom has $10 more, that would make it $60. Total’s only $110. So Joe must have a little more to total up to $120. That kind of mental exercise for your child’s ind is like what going to the gym is for your body.

Here’s another algebra problem a 3rd grader should be able to do: The sum of 2 numbers is 20. The difference of those same 2 numbers is 10. What are those 2 numbers?

When your child starts algebra, his math muscles will be primed and ready to use unknown variable to help him do what he has been doing, just a lot more efficiently. x, the Unknown, will be a very good friend indeed, instead of an intimidating stranger.