3 Key Solutions to Math Success

"True understanding of the child's needs requires that we focus on the uniqueness of each child rather than group them under broad categories of common behavior." - Larry Shiller



3 Key Solutions to Math Success

Society values math skills.

According to the Bureau of Labor Statistics, a solid math education can mean a 350% increase in pay.

Yet even with unfilled jobs in our economy, NASA estimates that two million jobs in technology are going unfilled by American workers because they are unqualified.

The U.S. has an ongoing math crisis. Fortunately, there are solutions that do work!

 

Here are a few key solutions to the US math crisis:

 

1. Get rid of grade levels

Huh? How could we do that? But think about it: students don't learn in grade chunks; they learn - and master material - at their own pace. Segregation is bad - any kind of segregation. We have grades because once we grew beyond the one-room schoolhouse, it made life easier for bureaucrats. That's not good enough: Let's get rid of grade segregation. Ideally, education should nurture a child's intrinsic motivation to learn, create, and do satisfying work. An educator should guide the child to progress through the curriculum as concepts are mastered (and can be built on), rather than, “Time to move on!” Knowing the 3 possible outcomes of a lesson will guarantee that a student successfully moves on without regard to grade. Montessori schools the world over have been liberated from grade levels, focusing instead on personalized education, for over a hundred years. That's also happening now at the Ridgeview Charter School in Colorado and hundreds of other schools across the US - and it's a success.

 

What about labels?

2. Don’t rely on labels and categories

In a well-meaning attempt to help more students, we create categories such as LD, ADD, and ADHD, and define processes for each.

In fact, every student should have a label: His or her name.

Wait, don't we need those labels in order to better serve our kids? Yes, diagnostic labels serve an important role in bringing support services to students. However, they also can have unintended side effects. In trying to group children under categories of diagnosis, we group together children who are actually quite different from one another. And in doing so, we underemphasize their important differences. Parents can become frustrated when their child is not fitting into the diagnosis mold.

True understanding of the child's needs requires that we focus on the uniqueness of each child rather than group them under broad categories of common behavior. 

Let's use our great American marketing muscle to target each student individually - and to let students fulfill the American dream by providing an environment that lets them reach their own potential, not some bureaucrat's idea of their potential.  

 

3. Multisensory math education

A typical homeschool curriculum engages about 30% of the brain. By and large there are no kinesthetic or auditory lessons, and the use of manipulatives is limited. Unless a student takes to abstract thinking right away, the odds are good he or she won't be good at – or like – math.

Your child completes a lesson correctly - say it was a visual lesson that requires looking at a picture and doing a simple calculation. The child then successfully completes several drills on the same material. Does that mean your child has mastery and a full foundational understanding of the topic covered?

The problem is that this lesson and drill only reached 30% of the child's brain. The rest? Not getting this concept! Now, imagine four lessons on the same concept - one each for visual, tactile, kinesthetic, and auditory neurons. Now the child's brain is being engaged 100% - to its fullest potential - and connections are rampant. Only then will a child truly have mastery.

Without a complete multisensorial experience children lose the richness that comes from absorbing the same material from all learning styles: visual, auditory, tactile, and kinesthetic. Only then will a student form a rock-solid web and foundation of knowledge and ability. The sensorial materials enable the child not just to memorize, but to gain conceptual understanding.

 

Whether your child is average, gifted, ASD, a combination of those, is a current or former Montessori math student, or not, is a pre-k math student or in junior high, make sure that the math program for your child includes a multisensorial approach like the one used by ShillerLearning.

 

Need help with multisensory math ideas? The 20-page Fun with Fractions Activity Pack homeschool freebie is full of multisensory fractions games and math activities. Complete the form below to download yours today!

Larry Shiller

Larry Shiller is President of ShillerLearning, whose mission is to help every student fulfill their potential. Shiller has degrees from Massachusetts Institute of Technology and the Harvard Business School and is the author of Software Excellence (Prentice-Hall).

A father of three, Shiller is active in non-profits and his hobbies include working with local startups, music (Shiller is an accomplished violinist who - when not helping children learn math and language arts - performs in the NYC tri-state area), tennis (Shiller's team made it to the USTA national finals in his skill bracket), Quoridor (Shiller is a former USA Champion), backgammon (Shiller is the Voice of Backgammon, doing commentary on backgammon tournaments worldwide), table tennis, and flying (Shiller holds a private pilot's license).

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2 Math Manipulatives That Will Solve Your Math Problems

"What the hand does, the mind remembers." - Maria Montessori

 



Research shows over 7% of students experience severe learning disabilities in math. Countless more struggle because of the way the language of math is spoken to them. You might as well be speaking Greek. Our goal at ShillerLearning is to make math understandable for every child with hands-on, exploratory learning – learning by doing.

Is your child struggling with math or would you like to avoid your child having math problems in the first place? The decimal material (also known as base ten blocks) paired with Montessori number cards are a game-changer for students young and old. I wonder how many parents, who themselves struggled with math as children, would have had an easier time learning (and even loving) math if they had worked with these tools.

 

As Dr. Maria Montessori so eloquently stated, "What the hand does, the mind remembers."

 

Together these hands-on tools make the decimal system and place value visually obvious and number sense easy to acquire – something with which many students struggle. These easy-to-use manipulatives and accompanying activities set your child up for math success and banish the tears and frustration. They provide a concrete introduction to the decimal system in an amazingly understandable way and can be added to any math instruction.

What are they?

The decimal material physically represent each place value category. There are unit cubes (1 cm x 1 cm x 1 cm), ten rods (1 cm x 10 cm x 1 cm), hundred flats (10 cm x 10 cm x 1 cm), and thousand cubes (10 cm cubed). Used in sufficient quantity, these math manipulates not only help children visually quantify each place value amount, but instruct in and provide learning by doing for inequalities, multi-digit operations (addition, subtraction, multiplication, and division), exchanges within operations (borrowing and carrying), skip counting, and more.

The decimal material is introduced using the Montessori three-period lesson – a simple, but effective gap preventer that ensures the student understands the concepts and materials being used. The ShillerLearning YouTube channel features videos on the three-period lesson, as well as doing operations with the decimal material and number cards.

First the units are used to introduce and strengthen the recognition of quantities one through nine. The materials are then paired with number cards to learn the symbols – the numerals – 1 through 9.

The number cards help children recognize the numerical symbols for each place value category of the decimal system. One of the fringe benefits of the number cards for students with special needs is that they empower students to work with numbers without having to be able to write numbers. The number cards consist of four sets of cards for the first four different categories of numbers in the decimal system (base ten). The smallest sized cards are numerals 1 – 9 (units/ones), increasing in size algorithmically for place value with numerals 10 to 90 (tens), 100 to 900 (hundreds), and 1000 to 9000 (thousands). The cards are color-coded for place value in green, blue, and red with the color pattern repeating for each new place value family - everywhere a comma goes. If we were to create cards in higher place values, the color pattern would continue. Ten thousands would be blue and hundred thousands would be red.

With success achieved in numbers one through nine, students are ready to learn place value into the thousands! As they work with the material, they also discover that if we count beyond the number nine in any decimal (place value) category, we continue counting into the next highest category.

Abstract, sometimes difficult concepts become hands-on, concrete, interactive. This introduction and exploration of numbers is unparalleled in creating a solid number sense and understanding of place value – the cornerstone of a solid math foundation.

The magic continues as you work with operations: addition, subtraction, multiplication, and division. Students learns 4-digit static addition (addition without an exchange, commonly referred to as carrying), doing in the concrete with the materials and number cards what they will later do on pencil and paper. Once that skill is mastered, they learn to play the exchange game where various quantities of a place value are combined; when ten is reached, it is traded in the materials bank for the next place value, adding that to whatever is left over. Now the student is ready for dynamic addition – addition with an exchange (addition with carrying).

Here is a peek at 4-digit addition with exchange. The following is a summary of activities that are scripted in the ShillerLearning Math Kit I, Lesson Books 1 and 2.

 

◼ First, the problem is constructed on the work mat with the number cards and addition sign.


◼ Then, the decimal material (base ten blocks) for the first addend are laid out with the number cards.

Repeat for the second addend.



◼ Now we do in the concrete exactly what the student will do later abstractly with pencil and paper. First, bring down the units (ones) and lay the 9 number card below them.


◼ Next, we bring down the tens. In this case, we have 13.


◼ We trade 10 of those tens in for 1 hundred flat, keeping the remaining 3 tens.


◼ We show that the hundred flat goes above the hundreds column, just like they will do abstractly with pencil and paper.

That floating one on the paper which is confusing to many students is no longer mysterious. They have experienced exactly what it represents.


◼ Then, you guessed it, bring down the hundreds, lay out the 500 number card, bring down your thousands, and lay out the 3000 number card.  

Finally, the problem is read as a whole, overlapping the cards as you read it: 2192 plus 1347 equals 3539.

A ruler may be used as the equal sign bar as shown on the right.

Here is a video that pulls it all together with a different example.



You will be amazed at how quickly young children achieve conceptual understanding as well as success in performing operations – preventing math struggles from occurring. The activities are also a powerful remediation for older students struggling with math for a variety of reasons and crucial support for students with special needs. These are two math manipulatives that will promote the success of every student in homeschool math.

The decimal material and number cards are available separately and can be added to any math program. They are both included in Math Kit I (covers pre-k, kindergarten, 1st grade, 2nd grade, and 3rd grade). To celebrate the new set of ShillerLearning color-coded decimal material, save $20 until October 31st. Because without them, math can be scary.

 

Antoinette LaGrossa

Veteran homeschool mom of five, Antoinette LaGrossa has been homeschooling since 2001. Having experienced her family’s frustration with multiple math programs, Antoinette understands the struggle that can come with teaching math. Everything changed in 2004 when she tried ShillerMath. She quickly joined the ShillerLearning team and has been supporting home educators for almost two decades - sharing hands-on learning tips, encouragement, and practical experience from homeschooling five very different children. Antoinette speaks at conventions across the country and is host of ShillerLearning’s Tuesdays@2.

 

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Language Arts Kit A (PreK/K-G1)

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Multisensory Math Hacks to Incorporate into your Homeschool Classroom

Multisensory Math Hacks

for Your Homeschool


Multisensory math is something we love here at ShillerLearning. Counting, learning place value, exploring geometric shapes, and all types of mathematics become more fun when partnered with interactive activities. Not only do kids learn math more effectively with a multisensory approach, they enjoy learning and become lifelong learners. Multisensory learning engages with visual, tactile, kinesthetic, and auditory lessons. Here are some ways to incorporate multisensory math into your homeschool classroom:

  • Building: By using blocks and other building materials, children can make clear visual representations of the problems they are trying to solve, create shapes, and more. The classic children’s building blocks are some of a child’s first encounters with math and some of the best ways to make math fun and more concrete.
  • Touch: Handling manipulatives (fun, colorful objects for learning), tapping out numbers, and creating tactile points for numbers are all great ways to incorporate the sense of touch. It’s also fun to create manipulatives out of things that have interesting textures such as modeling dough, quinoa, or putty.  
  • Counters: Unit cubes (included in Math Kit I and Math Kit II), small pieces of food, blocks, beads, or any other small object can be used as counters. This is especially beneficial with younger children learning 1:1 correspondence, solving math problems, and counting. We use the unit cubes as support for math facts in the Math Facts Boot Camp live classes. When learning place value, the unit cubes are paired with ten rods, hundred flats, and thousand cubes. As students advance in their math skills, unit cubes can be used in geometric modeling and creating numeric modeling plans. Never underestimate the benefit of a counter!

  • Music: Some children learn incredibly fast through song. Music like the 50 ShillerLearning math songs helps reinforce concepts through catchy songs kids will enjoy. (And music isn't just for math; there are over 50 language arts songs - including a song for EVERY letter of the alphabet and fun activities to go with them.) Learning to play and read music can also help children with math skills when they’re older!
  • Movement: Incorporating math into outdoor games, using dice, dominos, or a ball to practice math facts, dancing to math music, and counting steps or objects while walking are all ways to get the body moving and grasp math concepts. Sometimes even just a simple movement break in between lessons helps reinforce a concept and improve focus.
  • Drawing: Drawing out a problem (such as 5 stars + 2 stars = 7 stars), making shapes and illustrating word problems engage different parts of the brain and build different neural connections.
  • Images: Using visual materials such as pictures, graphs, tables, and images will reach visual learners as well as help reinforce concepts in another way.

 

If you find yourself trying to present a concept to a child that they seem to be struggling to grasp, try approaching it from a different angle using one of these multisensory techniques. If you need help generating ideas or tips feel free to call or email us or ask in the ShillerLearning Customers  Facebook group. We also post multisensory math ideas and tips on the ShillerLearning Facebook page.


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Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Amanda and her family reside in an Airstream parked in Washington State. She loves Washington's outdoor opportunities. When not homeschooling, she also blogs, works as a virtual assistant, and loves creating hand-lettering pieces.


What is the Best Reaction When One Has Failed to Solve a Math Question?

What is the Best Reaction When One Has Failed to Solve a Math Question?


Photo Credit @mythreedovesschoolhouse

 

Solving a homeschool math problem is only interesting and endorphin-releasing when it’s hard.

Solving a math problem requires an approach. If the approach is obvious and correct, the problem is easy. So hard problems don’t present an obvious approach. Elegance is not typically an adjective used to describe a successful approach that’s not obvious because you’re not likely to pick the best approach first: things are messy.

The beauty of math is that you can brainstorm all kinds of crazy ideas about how to proceed and you can actually try them out until one works. If you did this in real life, you’d probably get arrested.

As Thomas Edison realized, every failure is a step towards success. So one never fails to solve a math problem: you just haven’t solved it yet.

Two kinds of (intermediate) failures may result:

1. You think a dead-end is an obstacle. Until you realize it’s really a dead-end, you bang your head against the wall. But that’s not all bad: some useful things come out of that. When you finally realize it’s a dead-end and not an obstacle, you’re ready for a different approach.

2. You think an obstacle is a dead-end. You, therefore, try other approaches. When none of those works out, you begin to think, “Hey, maybe that wasn’t a dead-end, maybe it was an obstacle.” And you struggle until you make a breakthrough and solve it.

young boy solving a math problem at the table

Photo Credit @ofnumbersandstars

 

Self-awareness and the ability to let your negative emotions (frustration, anger, etc.) drive positive action will eventually result in success.

Encourage your child to ask for help when needed along the way, not letting his or her ego get in the way of seeking help from others. By constantly seeking advice from his peers, Albert Einstein ensured his theories were by and large bullet-proof (at least through the present).

If you’re a student, the best homeschool math curriculum - special needs students, gifted, and average learners included - doesn’t just show you what approaches work best; it teaches you how to think to come up with the best approaches.


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Larry Shiller

Larry Shiller is President of ShillerLearning, whose mission is to help kids learn and fulfill their potential. Shiller has degrees from Massachusetts Institute of Technology and the Harvard Business School and is the author of Software Excellence (Prentice-Hall).

A father of three, Shiller is active in non-profits and his hobbies include working with local startups, music (Shiller is an accomplished violinist who - when not helping children learn math and language arts - performs in the NYC tri-state area), tennis (Shiller's team made it to the USTA national finals in his skill bracket), Quoridor (Shiller is a former USA Champion), backgammon (Shiller is the Voice of Backgammon, doing commentary on backgammon tournaments worldwide), table tennis, and flying (Shiller holds a private pilot's license).

Tips to Know When to Teach Fractions to Kids

When to Teach Fractions to Kids


I’ll never forget the joy in my son’s eyes when he shouted out- “Mom! Four quarters make one dollar, now I get this fraction thing!” It’s that moment of realization and understanding we absolutely love as homeschool parents. The moment when we realize our kids ARE getting it and we CAN thrive at home educators.  

 

For many children, making the connection between all those slices of pizza being the same as one whole pie is easy. Until you write it down on paper and take away the word pizza.

 

Or the child who can easily grab half a sandwich… but then stares at you like a deer in the headlights when you ask them to find the ½ written out.

 

It can be hard to translate real life into numbers on a paper- or even visual representations.

 

Homeschool parents are often frustrated by fractions. They see their children interacting with the “real life” examples and struggling to translate that over. Or parents worry the concept will be too difficult or confusing for their children. These are legitimate concerns.   Yet they shouldn’t stop you from teaching this important skill. We’re here to give you tips not only on when to teach this basic math skill but how to teach them in a way that won’t bring any tears or frustration.

The Best Way to Teach Fractions to Homeschoolers

 

The team at ShillerLearning discovered there was a gap in the fractions curriculum available to home educators. We saw this gap across all teaching modalities, especially among the Montessori-based home educators. Nothing truly hands-on existed for parents. We heard again and again from parents with no idea what to do. Our hearts broke for kids who cried over boring worksheets that didn’t make sense.

 

Something had to change

 

We created our Fractions Kit for exactly this purpose. It’s an open-and-go, 100% multisensory and engaging curriculum. You’ll discover it’s modeled just like our popular Math Kits I and II. We’ve used the same Montessori-inspired language, lesson structure, and manipulatives to bring this important basic math concept to life.

 

No more boring worksheets. Your children will use colorful pieces, real materials from home, and more. They’ll not only learn what a fraction is but why they matter. Your students will learn how to identify them in the real world. With joy and ease, they’ll complete equations, learn about denominators, and more. You will love not having anything to prepare but opening a book. Students will love learning and have a blast doing it. We’ve even heard from families whose children choose to work on this kit in their free time because they enjoy it so much.

When Should I Introduce Fractions??

 

Most children are ready around 2nd grade. However, fractions can be introduced from the time your children are very young. Give concrete examples in real life anytime you’re able. Count coins with them so they can see how 4 quarters, 10 dimes, 20 nickels, and 100 pennies all = 1 whole dollar. Cut up their sandwich and name the quantities. Discuss the percentage of sales and which fraction they match up to. If they have real-life situations in their brains already, they’ll be less intimidated.

 

Here at ShillerLearning, we don’t believe in putting an age limit on when children should be learning something. Isn’t part of what we love about the Montessori Method that children learn on their own pace? We have young children working in our kit, all the way through teens. We’ve even had a few adults work through the kit to help fill in gaps in their own education!  

 

If you don’t give age ranges, how do I know when to start my child on the kit?

 

This is a question we’re asked all the time. It can be confusing to not get a cut and dry answer. For most children, fractions are added in Kit I along with Book 2 or 3. Sometimes families will wait until they’re done with Kit I, others add the kit in alongside Kit II, Book 4. The overwhelming majority introduce fractions at Kit I Book 2 or 3.

Options and Tips for Introducing the Fractions Kit:

  • Give your student a choice when they’d like to do fractions and how often.

 

Your student may want to work once a week on fractions, drop their current book, for now, to focus exclusively on fractions, rotate the kit book in at their leisure, or complete the entire book after book 3. These are only a few suggestions, your student may choose when they’d like to work on them

  • At least through fourths needs to be introduced by the end of the second review test in book 3. Your student will need this information to move on to the next section.

 

  • Foundational knowledge of division can be helpful, but not necessary

 

  • As you progress through the Kit, you’ll eventually hit a point where you need to have completed specific lessons in our Math Kits to proceed.  

 

The Kit will last for several years! In general, it’s not something that’s worked all the way through because of this.

 

Want some additional help with this foundational & basic math skill? Love “real life” learning, games, crafts, etc? Make sure to grab our FREE Fraction Activity Pack for additional lessons. You’ll find lessons designed for all ages- toddlers through teens. As always, they’re full of the best of Montessori-inspired games, crafts, lessons, works, and more.

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See Inside Our Montessori-Based Kits

Math Kit I - PreK to 3rd Grade

Language Arts A - PreK to 1st Grade

Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.


Enhance Your Math Lessons with these Fun Montessori Pi Day Activities

Enhance your Math Lessons with these Fun Montessori Inspired Pi Day Math Lessons


My High School math teacher had all the digits of pi wrapped around the upper portion of the classroom wall like a border. Any student who had memorized them all by the 14th of March got bonus points in the class. Only a few kids were able to accomplish this feat. My teacher celebrated by bringing in pies and having a fun “pi-day” in class.

You can incorporate Pi-Day into your homeschooling as well.

Here are a few ideas to get you started planning your "Pi Day" School Day:

 

  • Talk about what Pi is: Bake a pie- math, reading skills, and snacks! What more could a homeschooler want??

 

  • Cylinder works,

 

  • Pi-digit matching,

 

  • Fractions with circles (our Fraction Kit is a great option for this!),

 

  • Use a compass to make different size circles,

 

  • Measure out 3.14 inches or feet of string,

 

  • Have pot pie for dinner,

 

  • Number writing practice writing the digits of Pi,

 

  • Read about famous mathematicians,

 

  • Research how it got the name “Pi”,

 

  • Take a field trip to a local pizza place and get a lesson on spinning the perfect pizza pie,

 

  • Check out Pi day activities at your local library,

 

  • Read the book Sir Cumference and the Dragon of Pi,

 

  • Practice making the Pi symbol in rice, sand or with our grain set,

 

  • Make the Pi symbol out of playdough or clay,

 

  • Find Pi with a variety of circles!

Here are a few lessons from our math curriculum you might want to use on Pi day as well:

 

Math Kit 1:

 

Book 1

Lesson 2- Shapes

Lesson 10- Shapes Matching

Lesson 15- Comparisons Among 2

Book 2-

Lesson 42- Subtraction With Circles

 

Math Kit 2:

 

Book 5

Lesson 10- Diameter and the Chord

Lesson 113- Angle Degrees

Lesson 114- Protractor and Radius

Book 6

Lesson 84- Planes

Lesson 85- Circles and Spheres

Lesson 118- Measuring a Circle’s Circumference

Lesson 119- Circle Circumference and Pi

 

Happy Pi Day!  


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See Inside Our Montessori-Based Kits

Math Kit I - PreK to 3rd Grade

Language Arts A - PreK to 1st Grade

Amanda Osenga

Amanda is a former Montessori teacher, now homeschooling her dear son - an only child. Her family resides in an Airstream parked in Washington State and loves Washington's outdoor opportunities. When not homeschooling, Amanda blogs, loves reading, and creates hand-lettering pieces.