A Better Way to Fact Fluency

Score another point for the team against plain ole memorizing multiplication facts. Number sense is where it is at!  Thanks to Jo Boaler at Stanford for another powerful paper on Fluency Without Fear. I can't tell you how many new kids to Mathnasium stare at our ceiling tiles searching for the products of their random times table drill homework.  Parents are almost more fearful of the timed tests than the kids are! Students come to us without strategies and rely solely on trying to withdraw the fact from the recesses of their mind.  Rather, we teach them to use their number sense.  When they have these structures to build their math fact database, the anxiety and fear of timed tests decreases dramatically.

Take 7x6 for my example for upper elementary friends who are still mastering their facts.  If I know 7x5 is 35 (since my 5s are easy!), then 7x6 is just one more 7. 35+7 = 42. Done. I didn't even need my ceiling tiles!  This strategy, along with decomposing numbers, where we distribute a harder fact (like 7s) into easier facts. Using the 7x6 example, I know I can bust up the 7 into a 5 and a 2. Therefore I can take (5x6) and (2x6) and combine the results. 30+12 = 42. Still 42 no matter how you slice it! Again, number sense to the rescue!

For our older students, the problem becomes the numbers extend past 12x12. Middle schoolers often are faced with 17s and 19s, numbers beyond their experience set, so decomposing numbers down to their prime factors helps with reducing fractions, finding least common multiples and greatest common factors. Having full mastery of your multiplication facts will have a dramatic impact on algebra readiness and upper level courses.

High schoolers have even higher expectations of them and need this kind of stuff to be easy so they can conserve brain power for the problem solving.

Jo Boaler is an authority in the math community. I've taken a few online courses with her through Stanford and her perspective is right on with my thinking, which of course aligns with Mathnasium, the Mathnasium Method, and has been wildly successful with Mathnasium's Numerical Fluency program with our youngest learners.  Building number sense impacts the student for the rest of their life and makes the always progressing subject of math an easier subject to understand.

Source:   http://youcubed.org/teachers/2014/fluency-without-fear/ 

What is Procedural Fluency in Math?

Numerical Fluency is an essential part of math success. Kids who do not know their facts often struggle with more complex skills.  Once mastered, Procedural Fluency is next in line!  "I know my facts, but now what??? How do I use them? Which one do I use when?" Often, this shows up late in elementary school or middle school, when the breadth of problem solving strategies have been covered and it is up to the student to begin applying independently.

Can your student give themselves the kickstart necessary to attack a problem? Do they sit there staring at the page not knowing where to start? These could be signs that they lack the confidence to get themselves going.

Procedural Fluency is a student's ability to understand the material with such depth that they can apply the ideal problem solving method correctly and efficiently. I call this building your mathematical toolbox. There are often times that two or three tactics will work, but which is the most efficient? Which leaves less room for error (why turn a two step problem into a five step problem and risk a mistake or two along the way?) and saves time when the clock is ticking.

So how is Procedural Fluency developed? Practice. Exposure. Experience. Modeling by professionals. Through formal lessons in the classroom or with a quality math tutor, students build an arsenal of skills and tactics to move through a problem. They draw on their numeric fluency skills, they choose a strategy that makes sense, and they assess for reasonableness. A student secure in their procedural fluency can often find a second way to solve the same problem to justify their answer.

It is never too late to build a math toolbox! If your child has the numeric skills, but struggles with Procedural Fluency, give Mathnasium of 4S Ranch a call! Our math tutors will provide the instruction and support to help them grow!

To learn more, visit the NCTM website:  http://www.nctm.org/about/content.aspx?id=42833
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Turning Math Errors into Opportunities

Thankfully this year there is a reprieve on standardized testing in California. If there is one lesson learned while I was in Texas during our little testing hiatus last year, do not take this "gift" for granted. The accountability still stands, whether formal or informal. The math material covered in this school year plays a direct role in how successful a student will be next year.  If you are noticing a slide now do all that is possible to stop the trend. As math builds upon itself, the slide will continue if not addressed as early as possible.

With spring officially here, school is in its homestretch and sooner or later some form of end of year assessment will take place.  Encourage your student to learn from past mistakes to increase their success. Some teachers use a type of "Reflection Report" where the students have to categorize the type of mistake made to bring awareness to yourself so you do not go on repeating the same error. Once students have that "ah-ha" moment they tend to avoid making it again in the future. It is often eyeopening for kids to see how their scores were impacted by repeating the same type of error many times in a row.

For your student to benefit from their mistakes, it is best to reference old homework, quizzes and tests and track where points were lost. Did they out and out get the whole problem wrong because they are deficient in a concept?  Did they rush and not really answer what was asked?  Are their facts off? Did they lose a point here and there due to "not reducing" or "labeling" their units? Next time they prepare for a test, any test, have them consider the following:

Concept Mistakes:  This is when your problem solving process is off-course. You may not understand or mix up the steps it takes to reach a solution. You are multiplying instead of adding, you forgot to take the reciprocal of a number, you aren't combining like terms, you needed to convert something first. Do I need to practice more of these types of problems or meet with a math tutor and have it retaught to me? If they struggle with adding or subtracting mixed numbers, chances are a quiz with ten of these problems will not go well.

Comprehension Mistakes:  You are solving for the first part of the problem, but missing the second part in multistep problems. The question asks for which one is NOT but your answer solves for which IS. Make sure you reread the question to make sure your solution has an appropriate answer. Did I solve for the type of unit they are asking me for? Do I understand the vocabulary in the question so I know what I am supposed to do?

Calculation Errors:  Did you forget to regroup?  Did you not take your solution to its lowest terms as required? Were all like terms combined properly? Is my place value off because my writing was not aligned or slightly sloppy? Am I rushing too much?  Many times the kids complete the process 100% correctly (the more difficult part of problem solving) but if their facts are off they will never get the right answer.

These details are the difference between grade they currently have and one that is a level or two higher for middle and high school students. In elementary school it is the difference between getting a 2 on the report card or a 3 or a 4. The details build confidence in a child's mathematical ability.  For younger students in elementary math, their attention to detail leads to prealgebra and algebra success. Algebra success leads to higher scores in more complex math courses students take in high school.

At Mathnasium of 4S Ranch we build a students confidence by working with them on concepts they struggle with or introduce new concepts to broader their math world. We set up good habits from the start that ensure future success so kids go into their classrooms feeling prepared.

Click here for the full article from Business Wire with an interview by Mathnasium founder and Chief Instructional Officer Larry Martinek.
Image retrieved on 3/19/14 from here.

The Saddest Math Picture Ever

I literally felt punched in the stomach when this picture came across my news feed. A viral image taken by a professional photographer of her own 2nd grade child who is frustrated beyond belief over their math homework. Kids with high work ethics put so much pressure on themselves for perfection and have meltdowns when mistakes are made.  This was my son ten years ago.

My own son had plenty of moments like this in the 2nd-3rd grade window.  When we moved from Dallas to San Diego last summer we were both reminded of that period of time. The movers pulled back the big TV from the built in cabinet and there were six snapped pencil halves. My now 17 year old son noticed them first and asked why all the broken pencils were back there. I reminded him of all the temper tantrums he used to throw during homework time. He would go from hard worker to pencil snapper in a split second and throw the pencil across the room. Apparently some of those bits got trapped behind the TV.

We laughed it off since almost ten years had passed, but as a parent I remember calming him down, making him walk away for a while to clear his brain, and at times NOT turning in the homework on time as it was such a negative experience and I needed my kid to feel like a kid and be happy.

It was these situations that led me from stay at home mom to earning my teaching credentials, becoming an elementary school teacher, math curriculum writer, and ultimately an administrator responsible for integrating 21st Century skills into the lessons delivered on our elementary campus. I want kids to understand math. Not just the rules, but the whys. How did those numbers get there? How can I move them more flexibly?

Our math tutors offer quality math instruction that prepares elementary school children for middle school, middle schoolers for prealgebra and algebra, and supports all levels of high school math including advanced algebra, geometry, statistics, precalculus and calculus.

The outburst changes as the kids get older.  Tears and snapped pencils turn into mood swings, bad moods, withdrawn, insecurity of intelligence, and other self-esteem issues.  If you see this nightly, come talk to us and let's see if we can be of help. We identify and help fill critical math gaps, present lessons one on one so it makes sense to the child, and provide homework help so your time with them in the evening is less stressful.

"Less is More" can be Boring to Many

I came across an article highlighting efforts to teach math at an elementary school in rural Florida the other day. I agree whole-heartedly that students need to understand where and when numbers are coming from. I call it "building your math toolbox," and when the going gets tough in the math classroom, students can rely on those nuts and bolts lessons to kick start problem solving.

In the "Less is More" article they shared a day in a classroom where only four problems were covered.  On one, the teacher worked out a division problem that modeled 72 divided by 6 and proceeded to tally mark all 72 "somethings" into six circles.  This is necessary to demonstrated the operation of division, I've used the strategy myself (never with 72, however, as that would take FOREVER, she must love tally marks!) to distinguish two forms of division (when you know the groups but now how many is in the group or when you know how many are in the group but no idea how many groups there are). She is building number sense and experiences like this lead to numerical fluency in multiplication and division facts.

For the students who "get" division, though, that was probably the longest hour of their math lives.  Students with a rock solid math foundation would have picked up the process and procedure early on and were probably anxious to try their own. Only the class was stilllllll counting out 72 tally marks.  Maybe the class could have broke off into smaller problem solving groups or pairs for kids to try some on their own. That wasn't covered in the article, so it is unfair to say it didn't happen, but it does provide a snapshot of when your kid comes home and says they are bored in math class.

Enrichment in math is essential for kids who have the interest, requisite skills, and motivation to learn more.  Mathnasium is the perfect place for this as we build a customized learning plan around your student's abilities. Holes are filled initially (if there are any), but then introducing new concepts follows, and this sets your child up for success as their math options diversity after elementary school. Having a solid understanding of elementary leads to algebra-readiness.

Give a call to learn more and see how our Power Math Workouts will benefit your child long term.  858-312-8888.

The full article can be read:  http://wusfnews.wusf.usf.edu/post/why-less-more-rural-florida-school-preparing-common-core#.UwvdcFJLp4c.facebook

Sunglasses image retreived on 2/26/14 from: http://www.dogpile.com/info.dogpl.t10.4/search/images?fcoid=417&fcop=topnav&fpid=2&q=72+tally+marks&ql=

What Makes Algebra Easier

I can't say these concepts make algebra easy, but definitely easier. Isn't that the goal? To make something completely understandable by having the proper math foundation that each lesson logically flows to the next?  For that to happen, a student's brick wall of math can't have missing bricks!

The National Math Advisor Panel stated way back in 2008 that there are three critical skills that students must master for algebra to go smoothly. They are:

1. Effortless recall and fluency of basic math facts
2. Fluency with fractions and how they interchange with decimals and percentages
3. Certain aspects of geometry and measurement

To become fluent may occur naturally to some, but for others it takes practice.  Having a firm grip on where the numbers are coming from is a start. How do you turn a fraction into a decimal? Or vice versa? Does your student "get" that percents, fractions and decimals are three ways to show something of the same value?  That if we shared a cookie equally, I would get 50%, or 1/2, of .5 of that cookie. That benchmark is fairly easy, but what if there were eight of us sharing a twelve-cut pizza? I would get 11/2 slices, which is 1/8 of the pizza, or 12.5% of the pizza, or .125 of it.  If you know the mathematical process, you should be able to figure out sharing that pizza if there are seven people or 15 people.

Algebra readiness is essential since all prior math leads to algebra and your student's success in the course.  Success in algebra leads to further success for all future math. The pressure to get your child in algebra as early as possible is high but don't let it push your child into a math path they are not equipped to handle. Once they are in it they are in it. It can be a challenging and exciting path, or four years or frustration and struggle.

This summer Mathnasium of 4S Ranch will offer sessions to prepare your child for what lies ahead. Consider our summer sessions which include a "punch card" format to work flexibly with your summer plans.  Get their brain charged with algebraic thinking and practice the essential skills with quality math instructors who make math make sense so algebra is understood from Day 1. We are here to help!

Image retreived 2/19/14:  http://www.a4maths.com.au/userfiles/images/brickwall%20falling%20small.jpg

"Getting" Fractions Leads to Algebra Success

Fractions. We start off learning about them as sharing a pizza or a cookie equally among "x" number of people and it takes off from there. It is said among algebra teachers across the country, that having the ability to work flexibly with fractions (plus have great multiplication skills and a certain number of geometry and measurement skills, but I'll save that for another post) is essential for algebra success. It can be a matter of making or breaking your math path.

So how do we know if our kid is up for the algebra challenge? Are they "algebra ready?" Math standards even call these requisite skills algebra readiness for a reason. You need them to be ready for algebra.  These skills begin as young as third grade and build in complexity, so keeping up with the ramp up is key.

Students should be able to:

• Recognize patterns with fractional parts and be able to "decompose" a fraction to its smallest form (EX: 3/4 = 1/4 + 1/4 + 1/4)
• Find and create equivalent fractions 
• Add, subtract, multiply and divide fractions with common or uncommon denominators

Somewhere along the way, fractions no longer became sharing pizza and cookies, it became probability, ratios, proportions, unit rates, and then comes algebra. Working flexibly with the whole numbers and fractional numbers is critical, but efficiency is just as important. If too much effort is expended on these "nuts and bolts" items, then they begin to slow down the problem solving process.  

If you find your child is not efficient or successful in their fraction sense, they could benefit from Mathnasium of 4S Ranch's program. We build a custom learning plan just for them and their needs and introduce every lesson in a way that makes sense to them. 

Common Core Math Standards can be reviewed here:  http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

When Should You Get a Math Tutor for Your Student?

PBS recently ran an article on their website for parents struggling with when to hire a math tutor for their child.  Sometimes it is a pretty concrete clue: Grades are on the decline. Sometimes it is more of an instinct: Noticing avoidance strategies when it comes to math homework, excuses for why they can't finish, and general negative attitude changes.

When the time comes to making the jump, besides seeking a quality math tutor who is a math specialist, it is important to get to the root of the problem. Why is math getting harder? Was something missed along the way? Where bad habits started that need to be corrected? Is my high school student struggling with pre-algebra concepts but is enrolled in algebra? If your child struggles in one concept, are there other concepts where they could use math enrichment as well?

This makes Mathnasium perfect!  Our center in 4S Ranch fits the needs of anyone reading this article and saying, "This sounds like my kid." We begin with an assessment that identifies areas for growth or advancement. We create a customized learning plan that fits your child and we deliver it with one on one instruction to have the concepts make sense to the student. Once the student is ready, they are given independent time to practice their new strategy on a few problems before meeting with their math tutor and discussing their process a few minutes later.  We help with numerical fluency, number sense, elementary curriculum, algebra, geometry, pre-calculus and calculus help. 

The exchange between students and our math specialists is critical in cementing the math procedure and the student's confidence in tackling the math problem. Common Core math standards require students to communicate mathematically, and through careful questioning by Mathnasium of 4S Ranch's outstanding math tutors, students build their math vocabulary and problem solving abilities.

To read the entire article, you can visit: http://www.pbs.org/parents/education/math/math-tips-for-parents/when-to-get-a-math-tutor-for-your-child/ 

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When is the Right Time to Take Algebra?

Parents come into our center every day talking about algebra. There is a giant push to get kids into the advance math track, but make sure your child is ready to handle all that comes with it: The accelerated pace of instruction, the strong understanding of the requisite skills necessary to be successful, and the impact an undesirable grade has on the high school transcript.

This is a terrific article with the President of the National Council of Teachers of Mathematics addressing "when" to take algebra. It is very good food for thought in making a decision.

http://www.nctm.org/about/content.aspx?id=40258

Image retrieved on 12/6/13 from

 http://www.teachthought.com/wp-content/uploads/2013/05/edshelf-algebra-1-tools.jpg