"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 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.

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, 1^st grade, 2^nd grade, and 3^rd grade).

A question we get at ShillerLearning is, “How long should this math lesson take my child to complete?”

With a personalized approach to education, there is no “right answer” to that question. For example, some children get a concept right away; others need lots of repetition over several days, even weeks.

“How Long Should a Math Lesson Take?” A Montessori Homeschool Approach

Every child and activity is different. Some children get an activity’s concept right away and need no further practice to have it stored in their brains forever. Yet they insist on repeating the activity anyway. These children may not need further practice, but they enjoy the play associated with an activity they are good at. So let them explore, for five minutes or for two hours, until they are finished. If they can work without you right there, that is OK too.

Such active interest on the part of a child is a good sign; the child wants to repeat the satisfaction that comes from achieving a successful completion of an activity. What may seem like repetitive actions to a parent may actually be the child putting closure on the activity, and a child may become anxious if the activity is taken away prior to closure. Closure may also occur when the child – or you - becomes frustrated. When frustration occurs, you may say, “let’s put this activity aside for now, we’ll come back to it later.”

When a child asks to repeat an activity from last week, last month, or even last year, happily comply with the request. Your child will let you know when he or she is ready to move on.

On the other hand, there could be times when you wish the child would be more enthusiastic about repeating an activity that he or she did not fully grasp. When the child (or parent) becomes frustrated or restless with a particular activity, just mark that activity as one that needs more attention next time; we recommend circling the activity number and marking it in your Completed Work Tracking Sheet – and move on. (You can read more about the tracking sheet and other learning management tools.)

For a child to grasp principles fully, the decimal system activities in particular need to be repeated often. For example, one decimal system activity may be repeated once or twice each week for several weeks. Addition and multiplication tables also require several weeks to complete.

Among ShillerLearning's innovations is the Incremental Spiral Method™, which ensures that bite-size activities cover syllabus topics clearly and thoroughly at each age. Because topics need to be revisited regularly - as in a spiral with increasing levels of difficulty and abstraction - children don't learn addition or all aspects of a square or circle all at once. As a result children learn both math and self-confidence at the same time.

This technique was inspired from a study in which two groups of children each had five minutes to work on the same memorization problem. One group had one five minute session; the other group had five one-minute sessions interspersed with one minute sessions of a simple and unrelated activity. The latter group had significantly better results – despite having spent exactly the same amount of time on the problem. That’s why activities on related subject matter tend to be spread throughout the lesson books.

ShillerLearning’s goal is for students to speak and write mathematics clearly, accurately, and concisely based on a solid understanding of mathematical concepts. We find that this personalized approach to the “How long should this math lesson take?” achieves that goal.

Here at ShillerLearning, we are available to support you and your child in your homeschool math journey. We invite you to call 888-556-6284 or message/email with your questions. We are passionate about helping your kids learn - and love - math!

"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.