- What is Math on the Level?
- WWhat grades are covered in Math on the Level?
- What is Mental Maturation?
- Why is Mental Maturation so important in learning math?
- My child seems slow at mental maturation. Does this mean he or she won't be good at math or isn't smart?
- What do you mean by long-term memory and short-term memory?
- Why does Math on the Level get learning into long-term memory?
- Are 5 problems a day really enough to learn math?
- Do I have to make up the math problems?
- What if I want to use more than 5 practice problems a day?
- Why don't you use workbooks?
- I like the Math on the Level approach, but how is it different from traditional methods?
- Why doesn't Math on the Level assign a grade level to each math topic?
- Will my child learn as well as if I used textbooks?
- Is there a placement test? How do I know where to start my child?
- But I don’t think I’m good at math. How can I teach my child?
- Can Math on the Level be used with children who aren't homeschooled?
- What should I buy to help my older child who is struggling with math?
- Can I use Math on the Level to tutor my child?
- Will it adequately prepare my child for my state's standardized test?
- If I'm not sure about Math on the Level, what should I do?
- Does Math on the Level work with Common Core Standards?
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Math on the Level is a complete, flexible math curriculum for the whole family that is designed specifically for teaching at home, taking advantage of the many learning opportunities that are not present in classrooms. The curriculum emphasizes practical, real-life applications as a primary way to teach math, adapting the instruction to each child's maturation level, and an individualized review approach that spreads practice out over time so the knowledge is retained for the long term.
Math on the Level was written by homeschoolers to equip parents to teach any concept to their children from preschool through pre-algebra.
Practical: math is taught through normal family activities.
Flexible: math instruction can be as formal or as informal as you desire.
Individual: the curriculum lets you teach to your child's actual abilities – even the review is designed specifically to each child's level of need.
Simple: the teaching guides make it easy to teach math.
Versatile: a number of different approaches are provided to address different learning style.
Math on the Level also makes math easy to teach. Since it was written from the perspective of a homeschool mom, it is very "mom-friendly" and addresses both the challenges and opportunities of teaching at home.
The curriculum covers pre-school through pre-algebra for the whole family, so after completing the program, the child is ready for Algebra 1. Since each child proceeds at his or her own speed, the age (or grade) at which this occurs depends on the child . Typically, children start Algebra 1 some time between the 8th to 10th grade. However, those who are quick to learn math can be ready earlier.
Math on the Level has no grade levels. Instead, the curriculum equips parents to teach what their children need to learn at a pace that adapts to each child. Those who learn quickly are not held back, but those who need more time are not pressured beyond their ability. The curriculum helps you identify and fill these gaps, in the child's math knowledge, and the 5-A-Day review system provides sufficient practice to ensure the math knowledge is retained.
Unlike other curricula, Math on the Level doesn't require teaching all children using the exact same grade-by-grade sequence. The four teaching guides cover every concept taught before Algebra 1 (the "scope"). We also have ordered concepts according to complexity, starting with simpler, pre-K topics and progressing to more advanced concepts. We also provide a "suggested sequence" to use as a guide. However, the curriculum is designed so each parent can choosel the actual teaching sequence and set the pace based on the needs of the family and the ability of each child.
What is mental maturation?
Mental maturation is a term used to describe the development of the brain and its ability to handle information. Children go through stages of mental development just as they go through stages of physical development. Children mature at different rates, both physically and mentally, which is why it is best to give individualized instruction rather than placing all children on the same one-speed learning track.
The maturation may be the main reason a child is struggling to learn a new concept. Researchers have identified several stages of mental maturation that affect the child's abilty to learn. Here is an example. One maturational stage is the ability to understand what is called "reversibility." Children who don't understand reversibility may look at a row of pennies and the same pennies heaped in a pile, and say that the long row has more than the pile, even though they saw the same pennies moved from the row to make the pile. It doesn’t matter if the pile is spread out again like a row or heaped again into the pile – the child will still say that either the row or the pile has more pennies. At this development stage, the child cannot comprehend that going back and forth between the two arrangements doesn't change the amount. Later on, the child's mind will mature to a stage where this concept is understood.
If a child who doesn’t understand reversibility is taught fact families (i.e. that 3 + 1 = 4 and 1 + 3 = 4), he or she may learn the two math facts, and may even learn to go through the motions of switching the first two numbers, all without really understanding why he or she is doing it. Each fact will be learned as a separate piece of information, and the child won’t understand the connection between them.
Teaching children when they are mentally mature enough to understand the information will help them make sense of the math they learn, which makes it easier and much less frustrating for both the student and the parent!
Not at all. Consider the physical development of children; it is obvious that different children mature physically at different rates, and those who reach developmental milestones first are not necessarily the ones who are the most athletic when grown. The child who speaks early may not end up being the one with the best verbal ability as an adult.
In the same way, the rate of mental maturation does not predict how smart a child is or what kind of math skills the child will have. However, if children become frustrated and discouraged from being forced to learn math concepts before their brains are able to understand them, they may give up before the maturation kicks in, and their math ability may never be developed.
Long-term memory refers to a way of keeping information in your brain for a long time. Short-term memory is information that stays in your brain for only a short period of time. We retain our home addresses and phone numbers in long-term memory, but when we look up the phone number of a store, we probably will store that in short-term memory, retaining it only long enough to dial the number. It is then forgotten.
There are many aids to storing information in long-term memory, but generally what we use and experience regularly over a long period of time is more readily retained for the long term. However, when a student crams for a test, information is generally put into short-term memory.
One of the best ways to get learned information into long-term memory is through repetition over a long period of time, which is the approach used by the Math on the Level 5-A-Day review system. This unique approach provides a straightforward way for your child to practice everything that has been learned at a pace based on the child's ability but at least once every three weeks throughout the curriculum. With this continual review over time, all concepts are retained better than using the typical short-term drill. If at any time a concept is forgotten, that will be discovered within a few weeks rather than waiting until the next year. When the child has difficulty remembering a topic, you compensate by putting it on more frequent review.
It is important to distinguish between teaching math and reviewing math. The 5-A-Day process is not how you teach new math concepts but how the child reviews what has already been learned. When you teach a new math topic, you will provide as many problems as are necessary to make sure the child understands the concept. A new math concept does not go onto the child's Review Chart until he or she has learned it. During the teaching portion of the lesson (whether done with paper and pencil, through Math Adventure activities, or in unit studies), you use as many practice problems as are needed to help the child learn the concept. This does not mean that you give the child a page of problems to solve on his or her own. Rather, you demonstrate the new skill to your child and together go over as many practice problems as are needed. Unlike the 5-A-Day independent reviews, you will be working with the child to make sure he or she learns the new concept.
After the concept is learned, it goes on the child's Review Chart and is scheduled for daily review for as long as needed to reinforce the child's understanding and skill with the concept. Then, it gradually is moved to less frequent practice, with the goal being to keep the child sharp with the skill. With the 5-A-Day system, every concept the child has learned is practiced at least once every three weeks, with the pace determined by the parent specifically for the child. This way, 5 problems a day are sufficient to review the math concepts in a way that promotes long-term retention with no gaps.
No, but you can if you want. The four Math on the Level teaching guides provide a supply of practice problems with full solutions for every concept in the curriculum. You can use these problems when you teach and copy them on the child's 5-A-Day review papers. Of course, like the rest of the curriculum, you can also make up your own problems or use other resources.
The Concept Chart lists all concepts and shows you where to find the teaching ideas and the practice problems (located in the back of each teaching guide).
Math on the Level is designed to be a flexible program that can be adapted to your needs. If you want to give your child more than five problems a day, you certainly can. However, most people will find that five daily problems work well.
This question often comes up when there are more than five concepts being reviewed. When that occurs, it is a simple matter to choose a problem that combines more than one concept. The curriculum shows you how, and each page of practice problems includes information about concepts that are easily combined.
Some topics will replace other, simpler topics in the 5-A-Day review. For example, once the child is reviewing multiple-digit addition, there is no longer any need to keep practicing single-digit addition. The Concept Chart tells you when a concept is replaced by another concept or is dropped.
Workbooks are an attempt to teach all children the same way, whereas the Math on the Level approach is to teach to each child's individual learning ability. The real problem with workbooks is they don't adjust to the child. If the child isn't maturationally ready to understand the concept being presented, or else simply needs more time, the workbook doesn't alter its pace – it just keeps going. If the child needs more practice in a particular concept, the workbook cannot adust to provide the needed practice. Most workbooks have a large number of practice problems for the most recently learned concept. This intense short-term review approach is more effective for short-term memory instead of long-term memory. The Math on the Level approach is to provide individualized review, adjusted for each child's need, with continual practice spread out over time. This practical, family-life approach of individualized instruction and review yield far better results than the one-size-fits-all workbook approach.
In traditional methods, the textbook author chooses the scope, teaching sequence, and practice problems, aiming at a mythical "average" child; then, the same teaching pace, methods, and generalized set of practice problems are applied to all children. However, some children will have difficulty understanding the concepts at the pace presented, while others could be given more advanced concepts at a faster pace. Each year's textbooks also include a substantial amount of re-teaching of the previous year's topics, which is necessary to "catch up" those who didn't understand them last year (but that further frustrates the ones who are ready for more).
In the classroom environment, each year the class moves to a different teacher who has limited knowledge of each child's capability. This type of year-to-year discontinuity, combined with the sheer number of students in the class, makes it difficult to provide individualized instruction. Also, it is usually impractical to teach math through normal life activities in the classroom environment or through a textbook.
Math on the Level is designed to fit the home learning environment, which has few to none of the restrictions of the classroom. Homeschoolers normally teach only a handful of children, and there is no reason to cover topics at a pace that is too fast or too slow for each child. The homeschooling parent knows the child and can therefore provide truly individualized instruction, year after year. And unless you force it to be so, the homeschool environment does not have the limitations of the classroom, so teaching through daily life becomes both practical and straightforward.
Math consists of a series of concepts and skills, and the assignment of math concepts to specific grade levels is very arbitrary. In education, we often hear about the bell-shaped curve, which is also called the "normal" distribution. For the population of children which grade-level instruction materials are trying to address, as with a classroom of 20 to 30 kids, this bell-shaped curve indicates that normally there are some who will not understand the topics at the pace they are presented and will be left behind, while others could learn at a much faster pace bit are held back. Maturation is not the same as intelligence, but those who mature more slowly are often made to feel less intelligent than those whose math maturation occurs more rapidly. However, the generalized one-size-fits-all instruction approach, with its specific teaching scripts and uniform lesson plans, places all children on the same one-speed learning track, with the textbook author determining the pace.
With homeschool, your child is a population of one – not a group of 30 – and what is normal for your child changes as he or she matures. Maturation takes place at an irregular pace (in fits and spurs). Therefore, it is best to teach the child what he or she is ready to learn in ways that make math meaningful, and then give continual practice of what has already been mastered so it isn't forgotten. With Math on the Level, you have access to every concept the child will learn before algebra 1. The best pace at which to teach is the one that works best for your child. And with the 5-A-Day system, each child practices every topic he or she has learned at least once every three weeks, and more often if needed, so that nothing is lost.
Math on the Level is an excellent curriculum for homeschool instruction that is based on more than 20 years direct teaching experience both in the public school system (special ed) and in the home learning environment. Although some grade-school children can learn on their own from textbooks, most children learn much better using the Math on the Level approach, because the teaching is directed to their own level of maturational and strengths. The curriculum is provides a strong foundation in math so that the child is well prepared to move into algebra. The 5-A-Day review system helps children retain math better for the long-term while being much more motivating than the intense, short-term review approach with its pages of practice problems.
Math on the Level uses a review process rather than placement tests to assess the child's strengths and discover any gaps in previously learned math. The Getting Started section shows how to fill out the child's Review Chart by assigning 5-A-Day practice problems to review every concept your child has learned. Instead of "just jumping in somewhere," and clearly not "starting all over again," this straightforward placement process quickly and methodically lets you evaluate how well your child has retained the math that has been learned. Because this placement process introduces and uses the 5-A-Day review system, it gives the child early successes with 5-A-Day papers, since the first 5-A-Days will use the easier concepts. By starting this skill review at the beginning of the curriculum, you can be sure to identify and fill in any gaps that your child has in his or her understanding or retention of math, as well as to know where to begin teaching new concepts.
The problem of maturation in math is not new. Many parents who think they are not good at math were really just taught concepts before they were able to understand them, so there are gaps in their math understanding as well. It’s important to realize that as an adult, the brain has now matured to the point of being able to understand the math concepts presented here.
In various subject areas, many adults have forgotten much of what they learned in elementary or junior high school, but they find they can re-learn it quickly as they teach their children. This can work in math as well. As you go through the beginning concepts and teach your child, you will be reading the lessons as well, teaching yourself. The Teaching Guides are easy to understand, and you will find your confidence in math increasing as you and your children learn together.
Math on the Levelis designed to fit the homeschool learning environment, which is uniquely suited to give the individualized instruction and daily life application. As a complete math curriculum, it works best when teaching a small number of children (as opposed to the large classroom environment). However, since Math on the Level covers every topic that is learned from preschool through pre-algebra and has teaching ideas that address many learning styles, it is an excellent resource for any tutoring application or for parents who wish to help their children understand math concepts, whether taught in public, private, or home school.
Another excellent use for Math on the Level is for High School Review. Many children who were taught in a traditional classroom environment will have gaps in their understanding of basic math concepts, either from being taught before they were maturationally ready to understand the concept, or else they forgot the concept because it was not sufficiently practiced. Unless these gaps are filled, the student will have difficulty with more advanced topics (algebra and higher). Using Math on the Level to review all of the lower grade math topics with the Jr. High and High School students provides an excellent way to discover and fill in those gaps, which will be much easier because of the increased maturation of the older students.
It is difficult to provide a general answer to this question, since every situation is different. There are many reasons why a child will struggle with math. This can occur if the child was taught at a pace that wasn't right (maturation issue). The child may have learned the steps to solve the problem without truly comprehending the concept. Also, since math builds on itself, any gaps in the child's retention of math concepts will cause ongoing problems. These gaps can occur if the concept wasn't really understood or if it wasn't practiced often enough to get into long-term memory. Often math frustration can be traced to insufficient command of math facts (the ability to instantly recall addition, subtraction, multiplication, or division of two numbers). There also may be learning issues that make math more difficult and for which a multi-sensory approach (like Math on the Level) would be helpful. Moreover, if the child has experienced significant frustration or failure, motivation can become a major obstacle.
To provide a solid foundation for your child, you need to find out where the gaps are and fill them, regardless of when they were first learned, which is why we offer Math on the Level only as a full curriculum.
Yes! Math on the Level is an excellent resource for tutoring. Often private tutoring in math can cost from $40 to $60 per hour, so it doesn't take many hours to exceed the cost of the full Math on the Level curriculum. The Math on the Level approach will let you quickly identify and fill gaps in a child's understanding and provide a solid foundation in math. The curriculum provides an excellent resource to help your child understand any math concept learned before Algebra 1.
We frequently are asked about standardized testing, usually from a fear that teaching "at the child's level" will not adequately prepare him (or her) for the "standardized test," particularly if some concepts covered in the test have been postponed. Some states require a minimum level of performance on the grade-leveled "standardized test" in order for the parent to be allowed to continue homeschooling. This can be quite a conflict for those whose children mature slowly or have learning difficulties. Since the home learning environment is so beneficial to these children, this concern is definitely one to manage.
With the Math on the Level approach, the parent is equipped to teach any concept, so it certainly is possible to keep pace with any state's standardized tests. However, rushing ahead of the child's actual learning pace just to pass a test is very counter-productive to the child's long-term learning (and is not generally advised). One thing to consider is that standardized tests normally expect children to forget some of what they have learned, which is reflected in the scoring. With the Math on the Level 5-A-Day review process, the child will continually practice all math concepts that have been learned so that nothing is forgotten. Therefore, the child will perform better than expected for concepts that have been learned, which can make up for problems that are missed because the concepts have been postponed.
Another approach to take is to introduce the postponed concepts to the child just before the test, teaching the steps to solve the problem(s) without worrying about true comprehension. That approach may lower some of the child's anxiety during the standardized testing, and you can get back to true teaching for comprehension after it is all over.
If your child is old enough, you might want to explain to him (or her) that maturation is not the same as intelligence. Just as children walk at different ages and grow physically at different rates, which does not reflect future athletic ability, so also children's minds develop and mature at different rates, which doesn't reflect future learning ability. The one who matures slowly may in fact be more intelligent than the one who matures quickly. Sometimes understanding this will help a child have more self confidence.
Math on the Level was designed as a complete curriculum, which is why it is sold only as a 7-volume set. One way to gain confidence in how Math on the Level will work with your family is to join the Math on the Level Yahoo users group. That way you can hear from other Math on the Level users, read posts, and ask questions yourself. Every family is unique, but often you will get great advice and insights from other parents who have encountered a similar situation.
The question of whether a curriculum is or isn’t aligned to “Common Core Standards” doesn’t apply to Math on the Level in the sense that it would for most curricula. Common Core Standards are designed for and apply to the teaching methods and practical restrictions of the age/grade segregated classroom. The Math on the Level curriculum is designed for homeschool instruction of a multi-age family in a home learning environment. The differences are many. For example, rather than specifying a required teaching sequence for all students, Math on the Level lets parents choose a sequence and set expectations for each child based on the child’s maturation and learning ability. Math on the Level also employs real-life teaching methods that are impractical in a typical classroom but are readily available in the homeschool learning environment. Whereas a classroom teacher must use written word problems as a way to connect math to real life, a homeschool teacher using Math on the Level can teach children through real life “word problems” so that concepts are learned through and connected to meaningful experiences.
The focus of Math on the Level is to equip parents to make appropriate decisions for teaching their children in the way they deem best for each child. A parent who chooses to follow Common Core Standards can use Math on the Level by teaching concepts in the order and by the grade level listed in the standards. However, parents who feel the Common Core Standards are not appropriate for their children can choose a different teaching sequence they feel will let their children learn more successfully. Either way, the student will benefit from Math on the Level’s real-life instruction approach and individualized review-over-time system.
Since Math on the Level is not a curriculum that employs a set scope and sequence, we do not plan to change our curriculum to align with a scope and sequence approach. However, because parents and teachers who wish to follow a particular scope and sequence can already do so with Math on the Level, our curriculum can be used by someone who wishes to follow the "Common Core Standards."
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