This page is incomplete, many links are missing so use the side bar to navigate. Dig around there is a ton of info on the site even though it is in it's infant stages. You have a kit and want to know how to use it? You've come to the right place.
50% of this method is based on Montessori...at leaste. Another 48% came from Jerry Mortensen taking the ball and running with it so to speak. The last 2% (being generous) is from yours truly. Like so many of my students I have discovered a lot of math methodology and teaching techniques that most likely ALREADY existed.
Two hundreds...dancing by the fire. 100 + 100 = 200. Any little kid can understand that.
I discovered them for myself but I didn't invent them per se. Like Columbus discovering the New World...the Indians were already there. While I spent time in Idaho, I must say Jerry was Masterful at directed discovery: I had questions he wouldn't always answer them, but tell me to go fool around with the blocks and come back when I could tell him the answer. Other times we'd draw in the dirt...or go to the VJ Mortensen Company World Head Quarters (a small warehouse in a small industrial park in CDA) and play with blocks. Usually answers came very quickly...because you can SEE it.
I also like to joke that I have forgotten more math than most people know: that's not too far from true. I've gone down some strange and fantastic roads chasing my 1st Mistress. My 1st Mistress is the Matematics...ask anyone, particularly my "exes"...that's so puny I can't stand it. I crack myself up. But I digress again.
In addition to Mortensen Math, I have taken a couple other methods that were symbol based and applied them to the blocks so you can SEE WHY the "tricks" work. I am sure I am not the first person to do this. Now, I am in the process of making one cohesive methodology. The guy that started "Math-U-See" has already done a lot of this out of necessity, filling in gaps Jerry Mortensen left.
Jerry had/has a wealth of knowledge but he failed to write it all down. Much of the training I got was like learning an oral tradition. I can't find it anyplace else written down, I have come to the conclusion that some of it really was original thought out of the mind of Jerry Mortensen. Particularly the parts relating to the calculus, and some of the parts that show percentages...
Frankly, some of it is only written down in notes I took during seminars where Jerry Mortensen was presenting, something that became rarer and rarer over the years, or during times when he would come and do a little segment at one of our "International Teacher Trainings" (teachers would comes across the boarder from Canada) where I was presenting most of it and he would come and spice it up. He would always pull something new out of his butt mostly for my benefit...and to show me who was boss (lol) just when I thought I pretty much knew the whole methodology.
Jerry distilled the mathematics down to what we like to call
The Five Basic Conceppts.
Eventually, I have will have video on this site of me presenting not only the five basic concepts, but many other lessons which always come back to one or more of the five concepts. Simplify, simplify...or slim-piffy as one of my favorite math students would say.
The image at left is classic Mortensen Math, showing expanded notation. and a simple problem any 5 year old can build, count and understand. 13 x 12 is one big red one, five blue ones and six green ones. As usual the second part of this where you "split and shift" is left out.
We call that number 156, one hundred fifty six. All we do is count.
If you use your imagination and a three period lesson, now we can rename the blocks. Instead of the big red one being "one hundred" we'll call it x2 (x-squared), the blue ones are now x's instead of tens but the units are still units. Little kids love algebra for a host of reasons and often ask for it by name during tutoring sessions.
Any little kid can take x2 + 5x + 6, factor it by counting the sides or multiply it by building it across (x + 3) and up (x + 2) like you see here. When I work with little kids they see blocks and drawings first and then later we add the symbols. By then the symbols make sense. Jerry Mortensen always made it clear that the concepts needed to be presented at the child's level, using language they could easily understand. If the child didn't have the vocabulary you'd make sure and develop the vocabulary, and make sure they could relate the symbols to the blocks and drawings.
Later when we evaluate the expressions for various values of x, little kids just get out the blocks and count. I used to get little kids to stay after their sessions were over and show the teen-agers how easy it was to factor quadratics. You would be amazed at how much motivation and attitude adjustment this would create...especially if was a 9 year old girl and a 16 year foot ball player.
Talk about leveling the playing field! OMG I crack myself up.
Rapidly a crude drawing like this has lots of meaning, and we can describe it with symbols. If we are in base ten that's 11 x 11 = 121. 112. In algebra thats (x + 1)2 = x2 + 2x + 1.
We can see that it is a square number and we can see from the pattern that we are doing multiplication. For new comers this will take a bit of time to get used to.
Just keep in mind like any language you won't learn it all at once and the more you expose yourself to it the easier it becomes to understand. Some people "know math"and this gets them terribly excited because now they can see it.
Others take a bit if time to make sense of it because they "know math" and as one engineer said on the first day of a three day seminar, "blocks ain't math." But by the time it was all over he was quite enthused because he understood how he could teach his daughter math and maybe even make it fun. He had already discovered that turning up the volume didn't help and often resulted in tears.
Jerry Mortensen always made sure everybody got on the same page. From the most advanced to the beginner...and he always did it by starting in the concrete...using three period lessons, because as he would say, "it's no use if you don't know the names of the blocks or what the symbols mean" He also enjoyed being entertaining: putting on a dog and pony show to teach math and by being patient. Something I am still developing..."I have students not patients..."
Here is a pdf called "Mortensen Instead" Judith Townsend on Why She Replaced Montessori Math Material [in her school.] By Judith Townsend. You may find it interesting.
Judith Townsend is an AMS certified elementary teacher and has trained extensively in the use of the Mortensen math manipulatives and methodology. She lectures and provides seminars for teachers and parents in the US and Canada. She is an elementary teacher at the Princeton Montessori School and a teacher trainer at PCTE in Princeton, NJ.
Look for more informational pdfs like this here soon...
"Nice to meet you, where's your father?" ~First thing Jerry said to me upon our first meeting.
"Math is not a spectator sport." ~Jerry Mortensen
"Teachers are not there to educate your children. Teachers are there to assist you in the education of your children." ~Jerry Mortensen
"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen
"Mortensen Math is like a big super rich triple chocolate cake: the first piece is delicious, the next piece is good, pretty soon you don't want a third piece...don't try to cover too much in your seminars. Next time they come back they'll be ready for another helping. Know when to quit." ~Jerry Mortensen.
Find out more! Go here for a FREE one hour overview on how to teach math using manipulatives, specifically using Mortensen Math with me, Crewton Ramone.