(Getting Started With Mortensen Math)
I now have enough content on the web that people have told me, "it's a little overwhelming. What do I do?"
Apparently my response which is "Just get started." Hasn't been received well in certain circles. Hence this getting started Page.
I will start with the Mortensen Math Curriculum Starter Kit and move on to with this website later. Simply put, "Crewton Ramone" is unique on the entire internet so just search with ANY search engine for what you want to know. Crewton Ramone algebra. Crewton Ramone Fractions. Crewton Ramone Radicals. Crewton Ramone Completing the Square. Crewton Ramone Pythagorean Theorem. Crewton Ramone fishing & plumbing supply etc. Watch the vids read the pages. What? It's not hard. You need at leaste a combo kit or some base ten blocks/manipulatives.
I stole much of this this from an old hand out that we used to copy and put in the kits. It was written by Brian Templin, and another guy who later committed suicide and shall remain nameless, and proofed by Jerry Mortensen himself. Now I am putting it here with some very unapproved updates, edits and additions.
STARTED WITH THE CSK
Mortensen more than Math
was designed by Jerry Mortensen for all age groups interested in studying mathematics, he took from several sources including the Montessori method where you will find the matching color schemes, teaching techniques like the three period lesson and more. As has been said many times many ways: he stood on the shoulders of giants and saw farther.
Whether you are working with students age 3 or 103, Mortensen Math is
fun, exciting, and understandable. It takes the best from many methodologies and synthesizes them into one uniform method for visualizing and teaching the mathematics. He spent years using this method on students as have I. After about 20 years or so you see what works and what doesn't.
Your first objective is to
explore and become familiar with the materials yourself. Then let
children investigate and play. Observe them as they play. Children
will learn many concepts with very little help from you: same as, longer than, shorter than, one
more than, etc. They may not be able to verbalize these ideas
immediately, but they are gaining experience that will make learning
concepts and facts easy. Just allow them to play. Later you can add more meaning and point out where the symbols come from.
Read the Games and
Activities Manual selecting one or two activities that are
appropriate for your child. Many of the activities can be modified to
be used with older or younger children to build on different
skills, games are limited to your imagination. As you become more familiar with Mortensen Math you will see how the same games can be modified slightly to teach and emphasize various topics.
Make a point of referring back to the Games and Activities Manual for a different activity at least once a week. [Eventually I will have an updated Games and Activities Manual available; for now here is the old one FREE: Series A Games and Activities. You may also want to click the EAT SLEEP MATH tab.]
Most importantly, allow
the student to explore and discover. You will see these two words
prominently displayed on the Mortensen Math workbooks. We want the
instructor to think about directed discovery
rather than giving rules that should be memorized. This can be a very difficult concept for some parents and teachers, and even some older students who have been trained to think math is solely rules and process. There are easily discovered patterns and many rules can be discovered by the students themselves when placed in a math rich environment.
Remember, math is FUN.
(No, really.) Stop working while you and the student(s) are having fun. If you work
at anything too long, it can lose its appeal. We want students to
keep the feeling of fun and excitement, and by "students" we mean students, parents and teachers.
Keep in mind that your subconscious will keep working, even though you stop conscious effort.
You will be amazed at how much will be understood over time. If any material seems to be getting difficult for the child, move to another strand or area. Typically the work will seem easy when you return to it after a few days because your subconscious will have figured it out for you as it were, and with practice the concepts and facts will be available consciously for easy recall. Be aware that the bulk of what we call "learning" takes place in the sub-conscious mind. The sub-conscious mind "thinks" in pictures not symbols, hence the blocks and emphasis on "DRAWING." This is why we have such astounding success teaching students of all ages and skill sets.
GETTING STARTED WITH PRESCHOOL AGE CHILDREN
After free-exploration with the materials and some directed play, young children may start in the Smiley Face Books. Start with Counting Book One . You may then have the child do the first 2 to 4 books in this strand before moving on to any of the first few books of Addition, Subtraction, Multiplication, and Division. To be clear you do not need to do finish a strand of Addition before moving on to Subtraction or Multiplication, in fact you could go directly to Division do a few books there and then pick another topic at random. The emphasis here is on "What is the question (problem)?" and then matching the sketch to the appropriate symbols. (Use the "Three Period Lesson" (also see below) and in the Level l Manual pp 3, 15-17, it will be useful when you start working with the concepts in the books.)
The only skill needed for
working in any of the books is the ability to count to nine. After
completing Book 3 or 4 in each of the areas, we suggest you start in
Use Addition Facts Mastery Books for understanding, practice, internalization and reinforcement of addition facts. Repetition is the mother of skill. Play games and have fun, there is the emphasis but you will have to practice so that the facts are easily recalled. Refrain; however, from drudgery and drill work. Be careful with worksheets. Return to the Smiley Face Series when appropriate for identification and visualization of problems. The Smiley Face Books are an easier workbook format for children when starting a new concept. They do not require fine motor skills. Children can learn math without being able to write numbers the same way they can speak English without knowing their ABC's or how to write them.
REMEMBER TO USE THE
HANDS-ON MANIPULATIVES AT LEASTE 50% OF THE TIME.
50% should be a minimum until they get much older. Also remember to draw pictures then move to symbols.
Develop concepts and
understanding with the manipulatives, then use the workbooks for fun
practice. Just do a few pages at a time and work concurrently in the various strands. You don't need to finish one set before you move on to the next. That said your child may enjoying a certain strand and go further because they find it fun and enjoyable. I knew one student that went through all the Lvl 1 Measurement books and then all the Lvl 2 Measurement books and some of the Lvl 3 before going back and finishing smiley face multiplication. This has been a barrier to entry at public schools and schools that want to do everything the same way for every student.
There is no one "best" way to do it. You will hear Crewton Ramone say they best way is the way you like best. Remember: you are unique just like everyone else. Each student in a class can go through this method their own way and when they are "done" they won't just score well on standardized tests, they will score higher than they have seen any group score on a test and then cause investigations into cheating, such is the disbelief of the system.
GETTING STARTED WITH
CHILDREN AGES 5 TO 8
Most children, at this
age, will still enjoy working with and benefit from the Smiley Face Books.
They will work quickly through the books and then will usually look for more
challenges. Move on to Level 1 Books as you see this interest develop, and as the students move through and complete the Smiley Face Books. Note that these books are for added practice but the students should make up, draw and record many problems on their own that are not contained in the books. When they can make up and then solve their own problems with ease and you can devise "challenging" problems for them (keeping in mind degree of difficulty) which they can solve you will be on the road to attaining mastery. The "trick" is in getting started with a firm foundation.
I heartily recommend the Smiley Face Books for everybody including adults and especially teachers. They were made by Jerry and illustrate the concept of degree of difficulty beautifully. I will often make older students just thumb through them just so they can see the procession. They breeze through the books at first but usually slow down right around book 8 or 9 and spend a little time on book 10. Many will skip the Smiley Face Books for older students altogether. If you have this resource I recommend using it. For some they will opt for Lvl 1 and 2 instead of Smiley Face which they correctly assume are for younger students, if they have students who are 7 or 8. Money is a consideration, currently the books are not cheap. Just keep in mind they are useful for students of all ages although they are designed for the younger students.
Many will start in Level 1 with students who are 5 and up, but keep in mind age is not always the determining factor, you can use level one with younger students also. Students may be working in several Lvl 1 books and several smiley face books ALL AT ONCE. The five strands (Arithmetic, Algebra, Calculus, Measurement, and Problem Solving) are designed to reinforce each other. Math is a language and you will see that contrary to some people's biases the students do not get confused when working in many strands at the same time, they actually get a better understanding of how it all fits together so beautifully.
Students will move from strand to strand with ease. One method is to have the student
work in one strand Monday, another Tuesday, etc.
Another procedure is to have the student do one or more pages in each strand every day.
One day a week might be used for supplemental materials (i.e., Games and Activities, Addition or Multiplication Facts Mastery Books, Smiley Face Books). A rule of thumb is that young children should not get more than three books ahead in any one strand. This is by no means a hard and fast rule. DO NOT discourage the child if they are having fun and show an interest in whatever topic it is. Encourage them to use other books too and be sure to have them make up their own problems that are not in the books as they go along.
Play games, build towers and walls, do the cartwheels and other games to promote the fun learning of basic addition facts. Make math fun. Keep it fun. Focus on one sum at a time and master all 45 addends. Use the Addition Facts Mastery Books as fun written discovery and practice not as drill and drudgery. Remember that these are used to supplement the core program.
The Level 1 Teaching Manual is written in a slightly different format than is customary. The manual starts with an overview of several Algebra books and contains several important concepts and techniques. There is a brief overview of the concept being taught. Then there is a (different) specific example shown along with sample dialogue. The strands are arranged alphabetically for your convenience.
As children work in Level 1 have them return to the Smiley Face Series as appropriate, just because you finished a book or strand doesn't mean you can't return to it later. Indeed you may need to return to them several times over the years. It isn't ever going to be "one and done." We suggest using them as an introduction to larger multiplication and division problems and addition/subtraction problems involving regrouping.
GETTING STARTED WITH CHILDREN AGES 8 TO 10
If you haven't already read the preceding information, please do so. Many older children will benefit from the Smiley Face Series, Addition and Multiplication Facts Mastery Books and the Games and Activities contained in the Series A Manuals and elsewhere on this website and on the blog. You may note that currently the Mortensen Company is out of Series A Manuals. They are out of print, but my kits still include them because Crewton Ramone is cool like that.
Many parents will have
older children work through all the books just to become familiar
with the program. Another approach is to present the concepts and
work a few problems in each strand of the first few books until mastery is shown. You can
then increase the number of problems to be done as the books become
more advanced. Again have the children make up their own problems. At this age, the children will probably do all of the
Algebra, and most of the Calculus and Measurement books. It is best
for the student to start completing a book or two before they begin
working with totally new concepts.
Having older students become familiar with concepts and working with or checking the work of younger students gives them the opportunity to internalize basic concepts. Having students teach each other is optimal. Older students teaching younger students is the most obvious case (or older siblings teaching the younger siblings) but be aware that sometimes the younger students can teach older students and children who have gone down one strand can then help teach it to a fellow student who hasn't gone down that strand yet.
Cooperative learning and children being given some general direction but also the ability to explore and discover for themselves is what you are striving for, again this is problematic in public schools where segmentation, rules and process, and memorization rule the day. Everybody must do the same thing at the same time. Look around, when it comes to the mathematics, how is that working out?
GETTING STARTED WITH OLDER STUDENTS (11 TO ADULT)
As with all ages of math
students, we would like you to start at the beginning to see how the
concepts and methodology develop and fit together. However, we realize this may not be
practical or enjoyable for all people who are getting started with Mortensen Math.
Instead, choose a topic that sounds fun or interesting and start there.
You may not need to do every problem, but do attempt some in every book. You might not write in the first several books at all; however, you will see a need to participate as you progress. Smiley Face Multiplication and Division introduce older students to a fun, new way of looking at these operations and should not be overlooked. You may want to use page protectors or some form of sheet protector and write on those instead of writing directly in the books so you can use them over and over again. As the students get older they may want to copy some problems out of these books and into their own journals or math note books.
I was going to re-write this but I will leave it like it is:
"You will first use the
hands-on materials/manipulatives while following the illustrations in
the books. Then you will use mostly drawings to solve the problems.
You will then start to see the pictures in your head and can then
just deal with the standard mathematical notation.
As you continue, you will want to use the manipulatives with each new concept. This is the design of the program. We want you to use the blocks in each new area and then gradually move to the abstract."
Instead I will comment: When getting started with any new concept, always start in the concrete no matter what age they are. Then as much as possible move to drawings and then to the symbols. Sometimes you have to go from the concrete directly to the symbols but be sure to go back and make sketches or drawings. My own sons are at the point where they can see the problems in their heads. They look like little geniuses when I ask them to square root x² + 8x +16 and they do it orally with no blocks drawings or symbols...just words. They are looking at a picture in their minds. At the time of this writing they are 5 and 7.
"Using the blocks to do problems that you can already do on paper with traditional methods allows you to discover your own understanding. You'll be amazed at what you will learn.
Remember, math is FUN. Just because you are older does not mean that everything will be crystal clear as soon as you look at it. Give it some time. You will be re-training many of your mental images of mathematics. Allow your subconscious to work for you. Give yourself space and time. It will come!"
Here are a few PDFs you:
Some old articles about Mortensen Math.
Scope and Sequence of the Books.
Judy Townsend on "why" Mortensen Math
Progress Charts For Mortensen Math Books
Be sure to buy some gold stars. Kids love gold stars. There are two pages you can print. One for Smilely Face and the Facts Mastery, and one for the 5 strands of Level 1 which you can use for the other levels too since the strands are the same in each level.
Teachers and Homeschoolers will like the scope and sequence and perhaps the perspective of a Montessori Teacher with regard to why Mortensen Math is a superior way to teach mathematics. Those curious can get a glimpse of the former greatness that was Mortensen Math, check out those articles.
Mortensen more than Math
AS YOU WORK WITH THE
MORTENSEN MATH PROGRAM THERE ARE THEMES THAT YOU WILL SEE REPEATED OR
THAT ARE VALUABLE VERBALIZATIONS. This list is included as a
reference and review. Not all of the themes will make sense the first
few times that you read them. Some are important in using the higher
level books. All of these are crucially important concepts and you will find understanding them adds deeper understanding for your students. You will also find some of them are deceptively simple and more understanding will be added as time and lessons go on.
Very simply: What is math?
• What is math?
Math is the study of numbers.
• What do we do with numbers?
We count with them.
• Before we can count we must know what "one" is.
• Before we can count we must have the same kind.
• We never count past nine. When we have nine and get one more, it makes one of the next largest kind.
• Number have two parts, the "how many" part and the "what kind" part
• Imagination not memorization.
IMPORTANT CONCEPTS AND VERBALIZATIONS
For more click the "concepts" tab.
• "What is the
question?" is more important than "What is the answer?"
• What are we counting?
• Addition, subtraction, multiplication, and division are just fast ways to count.
• Multiplication is counting a number a number of times.
• Division is just counting how many times one number is contained in another number.
• We use the rectangle to facilitate counting that is we use the rectangle to make counting easier.
• When we need a "Hero," call on "Zero."
• If it's no fun, get back to one. (Level 3)
These last to are useful in all problem solving and "advanced mathematics.
• Hero Zero
• No fun get back to one.
THREE PERIOD LESSON
This is so important you will find it several times on this website. Clue.
1. THIS IS .....
Identify for student
2. SHOW ME .....
Student points to (holds up) selects
3. WHAT IS? ....
KEY PHRASES THAT DEVELOP CONFIDENCE AND UNDERSTANDING
Use these when the problem is done correctly as well as incorrectly.
• How do you know?
• Will you show me (her/him)?
• Check by using the manipulatives.
• Can you think of another way to show (do) it?
• What is the same? What
And, of course, Remove the NO from the lesson.
Go Home From Getting Started.