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/ 

Is Your Child "On Board" with Improving in Math?

One of my favorite quotes is the famous Henry Ford one, "Whether you think you can, or think you can't - you're right!" It's all about attitude. A recent study defended that it is possible to change your success level in math by changing your attitude. Students who continue to think they can't do it, will likely prevent future academic advances in the subject.  

While we certainly have a balanced mix of kids who struggle with math with the kids who visit Mathnasium of 4S Ranch for math enrichment, we see progress every day. Struggling students who are "on board" with the reality of their math situation, know it isn't going to fix itself overnight. There is an investment of time and practice, and possibly even some remedial lessons to build that foundation.  Once those parts become easier, the next level is easier. Slowly but surely, progress is made, grades go up, confidence is built, and more!  If you have a good math base, the lessons in school become easier to follow, you can structure questions for your teacher in such a way that you learn more concretely (instead of "I don't get it." try, "I see where I had to do ______, but what I don't understand is why I then do ___.")

Two tips to get your child "on board:"

• Get them to believe that the work will pay off once the investment is made. Kids who don't believe they can won't bother trying.
• What is their motivation?  If it solely is for better grades, that is great, but statistically speaking greater increases come from kids who are interested in the subject. At Mathnasium we say "Kids don't hate math, they hate being confused and intimidated by math. With understanding comes passion. And with passion comes growth - a treasure is unlocked."

Read more: http://www.businessinsider.com/being-good-at-math-is-not-about-natural-ability-2013-11#ixzz3EisyIWCd

Image Retrieved 9/29/14:  http://www.lorensworld.com/wp-content/uploads/2013/01/128000814379780740_tqmONAO5_c.jpg

How English Impacts Math

I found this study to be very interesting.  Stereotypically, math success associated with certain nationalities, especially with Chines and Japanese students, has always been the norm.  As researched here, the language itself could be giving young students the kick start all kids need to make sense of numbers and how they work and build.

It has been recognized that the simple language parameters used by some countries limits confusion or misconceptions caused by a number's name.  What exactly does "eleven" mean?  Isn't it really just a ten and one more?  Some languages use that to set the base with the English translation simply "ten-one." It even puts the ten first (as it would be in place value) before the number in the ones place.

Much of common core, and certainly the proprietary Mathnasium curriculum, translates numbers from fifty-five to 5 tens and 5 ones so students can regroup easier, multiply easier, and more. It's called decomposing a number and it makes harder numbers and complicated processes less hard.

The biggest "take home message" I read in this is that early numerical fluency sets any kid up for success, especially as the math gets more complex.

To see the article, please visit: http://online.wsj.com/articles/the-best-language-for-math-1410304008#printMode

Teachers are Always Students

One of the things I love most about being involved in education is that you never stop being a student yourself.  Our focus at Mathnasium of 4S Ranch is always on what we can do as instructors to make math make sense to our students.

Last week I had the privilege of spending the day with Larry Martinek, the creator and Chief Educational Officer of Mathnasium.  He shared great strategies in working with Common Core and providing that extra something that makes kids feel successful every visit!

Many of his comments tied back to early numerical fluency and the roadblock it presents to further math success. This summer Mathnsium launched a program exclusive to Numerical Fluency and making those numbers come more automatically by using a strategy that slowly becomes effortless.
We also discussed the importance of students being placed in a math class appropriate to their abilities upon middle school - algebra readiness is what it is called in the education world. While we cannot make specific recommendations, much of our data collected through our diagnostic testing is sound evidence if a student is on the right path based on their skill set and if additional progress is necessary to improve classroom grades and understanding.

Larry hasn't let the substantial growth of the Mathnasium brand break his focus on why we do what we do.  Every ounce of his being is dedicated to the curriculum that he and his team create for our students. It was a great day for inspiration!

Time Tested Curriculum! Improved again!

Katie Couric does a great job of breaking down Common Core. In her video for Yahoo! she addresses the goals/objectives of its existence, and how while the standards are national, the implementation is local. With this comes the growing pangs of trying and testing lessons that will drive the rigor while limiting confusion.  As a former math curriculum writer myself, we spent summers rewriting quality lessons so that teachers could more easily and clearly deliver them to students.  Often we would abandon a lesson because it was counter productive to the cause (too cumbersome, too wordy, not enough hands on).

http://news.yahoo.com/video/now-common-core-012638311.html

What I love most about Mathnasium is that our curriculum is sound.  With thirty years of experience in developing and refining our curriculum, it has become timeless.  While we support Common Core wholeheartedly, we realize sound math is sound math. You can't learn B before A, if H isn't making sense then lets revisit G. Mathnasium hasn't rested on its already successful laurels. Our track record of success is outstanding, and yet this summer a revised curriculum launched to make math instruction more meaningful to our students!

I feel so lucky!

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
Clip Art retreived on 8/30/14 from: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9nG-Pu03lq-aLheYIj9keGjuqFc5CUomLhzrryn37GH2kymlHw8DJ2bBnrryZ1xnWgcLrum7N7UjI1EouVv6wSnWpmh-e-KwxH-lwnzXU6ecuIZH2guOaRUS3SSDzof4qmvVsy4_5-vXn/s1600/Math-problems-dyscalculia2.jpg

Reasonableness

With all the years I have been in education, whether from the side of a homework helping mother of two, the teacher for 3rd, 5th and Special Ed kids, elementary administrator, and as a math curriculum writer I don't think a day has gone by where the phrase, "Is this reasonable?" hasn't left my mouth.

So many times kids get so wrapped up in what it is they are doing that they don't stand back and ask themselves, "Is my answer reasonable?" Sure you have an answer, but go back and make sure it makes sense. This year, make this the new standard in your student's math life. The Common Core math standards require kids to explain their process and problem solving.

My favorite lesson in third grade was what I called "The Magic Brownie Pan." Students were given a bunch of information about a girl who baked two tray of brownies with a a dozen brownies in each. Four friends came over. Half had two brownies and half had three.  How many brownies were left?  There is a lot of data in the question. First of all, you need to know what "dozen" and "half" mean. You need to figure out how many brownies there are in the first place before you figure out how many are left.  Inevitably a few kids will give me an answer greater than 24 brownies, maybe they added all the brownies to all the kids to how much each kid ate.  I would joke about it not being a Magic Brownie Pan that miraculously bakes more brownies as kids are eating them. Those brownies are gone! Forever! There will be less than what was originally there, but how many exactly and how do we know we are right? What is our strategy?

Encourage your student to always check for reasonableness. The earlier they condition themselves for this type of scrutiny of their work, the greater the payoff down the road! For elementary math students, this will be key in becoming algebra-ready (also called pre-algebra) and success in higher level high school math courses.

If you need the support of math specialists, come to Mathnasium of 4S Ranch where our customized learning plans teach your student math skills, kids can get homework help, and math confidence is built.

National Honesty Day is Today

I didn't even know such a day existed such a day existed, but today is National Honesty Day. Apparently it was created to balance out the fact that the month is kicked off by April Fools Day.  So a few "honest truths" about math. I learned these after taking a Stanford course last summer:

• There is no such thing as a "math person" or a "non-math person." 
• Mindsets concerning math can be changed, but it takes time and effort, so those that consider themselves "non-math people" need to know they have the power to makes things different
• Mistakes in math are learning opportunities - sticking to it and powering through a tough concept may come with bumps and bruises, but ultimately makes for a better mathematician
• Boys are not better at math than girls. Girls are just as capable.

So if math is "hard" for your student, or if you are fearful of projecting your "non-math person" identity onto your child, know it can be turned around.  Will it necessarily be easy - No. I have to be honest about that. The reality is, a student's future is highly dependent upon the opportunities they seize earlier in life, so working hard and "getting it" in elementary school leads to opportunities in middle school. Solid middle school performances opens the doors to advanced math and AP classes in high school which translate into getting into a four-year college, or even a select university, in the major of your choice. 

Parents Helping with Homework Could Hurt Them

My morning routine always includes a news update from the Today Show. I will admit it is not exactly the hardest hitting news each day, but I love their balance between human interest and global segments. This morning they discussed The Broken Compass, a new book trending in American about how providing too much help, or helping too often, can actually negatively impact your student.

The book analyzed surveys of American families taken by the US Department of Education over the past thirty years. The ideas of parents "taking the reigns" or "taking over" during homework time, thus not allowing the child to do most of the work, dominates and is considered to be counterproductive to the cause.  The goal would be for the kids to do as much work as possible, with you as a support system, so they can independently complete tests and quizzes successfully when in class (and away from the overhelping parent).

The Today Show joked about their own personal experiences in helping their own elementary kids with homework, but who can honestly say they have not uttered these same words at the end of a long day: "Let's get this over with" or the frustration you feel when something so clear to you isn't clear to your child,  "It's right in front of you! The answer is right there!"

At Mathnasium of 4S Ranch, we provide the support system at homework time. Students will work with an instructor on a sampling of problems, and once they show understanding are released to complete some work independently. This builds confidence in the concept. Instructors then return to check over work and reteach if necessary.  When kids walk out our doors they know they were the ones doing the work, not us, and their success in the classroom improves.

Math Help: Don't Become a Math Mummy

At this time of year it is easy to go into panic mode and pull out all the stops for getting your child "over the line" when it comes to their math class.  I have parents who come in daily looking for a quick fix when it comes to getting math tutoring or math homework help.  Please be careful in finding that silver bullet to make all the math problems go away; it pretty much doesn't exist.  If math has been following a downward trend line the past couple of years, it is necessary to go bad and rebuild. If it took months and years for this problem to escalate, it won't take a month to get back on track.

Chances are if they are struggling there is a reason. Putting a bandaid on a concept works for the short term, but too many bandages holding together a math student is heading for trouble. The student will start to look like this dude - scared, confused, panicked, and unprepared.

First of all, address the problem before it gets out of hand.  If you are already at crisis point, make the necessary investment to gain those concepts currently missing.  Sometimes you have to take those two steps back to move one step forward.  Quick fixes don't address the deep down issues preventing success. Setting reasonable expectations and having patience to let your child learn for mastery, not in a race-like situation, is key for long term success.

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.