Multiplication by Osmosis
Multiplication by Osmosis
The title says it ALL!
By definition, osmosis is easy...unconscious:
"the process of gradual or unconscious assimilation of ideas, knowledge, etc."
Wouldn't you like this for YOUR child?
Learning multiplication facts are often a cause of concern for parents, and their memorization in 6-9 is a gateway to the higher maths of the 9-12 classroom. In this workshop, participants will receive an overview of how multiplication is taught from the first plane up through adolescence.
Multiplication is in some ways a gateway in the Montessori maths curriculum between the more concrete, hands-on phase of the 3-6 and 6-9 classrooms to the more abstract, advanced maths concepts of the 9-12 and adolescent classrooms. Parents sometimes see the memorization of multiplication facts as a sign of how well their child is learning maths in their Montessori classroom. Children who enter Montessori classrooms later, without experience with the concrete manipulatives, may struggle to memorise their facts abstractly. This two-hour workshop looks at how multiplication is taught from Cycle 1 through Cycle 4 in several strands.
Numeration and the concept of multiplication are learned with the bead chains and bead bars in 3-6 and 6-9, which leads into squaring in Cycle 3 and more advanced work with Powers of Numbers in Cycle 4. The memorization of simple multiplication facts is also learned in 3-6 with the Finger Charts, with special mention made of the commutative and distributive properties. Students who enter Montessori without experience with these materials often need more direct, rote methods and several of these (such as the clave rhythm) will be covered in the workshop. The operation of multiplication with large numbers is learned with materials that gradually introduce more abstraction, including the Stamp Game, Small and Large Bead Frames (the repeated addition model of multiplication), the Flat Bead Frame and the Checkerboard (which gives an area model of multiplication). This strand leads into Cross Multiplication in 9-12 and the studies of area and volume.
The concepts of multiples and factors are introduced with the Multiples Tables in 6- 9, and this leads to a study of prime numbers in 9-12. The whole multiplication table is introduced in 6-9 with the presentation of the Numerical Decanomial, which solidifies the child’s grasp of their multiplication facts. The Decanomial is taken a step further in 9-12 with the introduction of algebraic terminology, and this leads into more advanced work with algebra in Cycle 4. As Dr Montessori said, using the hands is the fastest way to abstraction with conceptual understanding, and with these materials multiplication facts are learned almost by osmosis! The integration of maths with other subjects (such as history) will also be covered in this session.
Goals and Outcomes:
Participants will come away with an appreciation of the various ways that multiplication is woven into the Montessori maths curriculum. Parents will appreciate how the learning of multiplication facts is addressed in many varied ways with different manipulatives at various ages in the second plane in particular.
Mark Powell taught for 22 years in Montessori 6-9 and 9-12 classrooms in the Boston area and the San Francisco Bay Area. He was also Technology Coordinator at St. Paul’s Episcopal School in Oakland, CA. He was a teacher trainer with the Center for Montessori Teacher Education, New York for twelve years. Mark has a M.Ed. degree (specialising in Conflict Resolution) from Lesley University in Cambridge MA, and also MA and QLD State teaching credentials. He has published two dozen articles on Montessori education in Montessori and other education journals, and wrote a chapter in the 2008 book A Place for Play edited by Elizabeth Goodenough. Mark has designed many classroom materials, several of which are now sold across the United States and internationally by companies such as Hello Wood and Nienhuis Montessori. He has delivered workshops at American Montessori Society national conferences and has consulted for dozens of Montessori schools across the U.S. and in Australia and New Zealand. He returned home to Queensland in June 2016 and taught at the 9-12 level for another four years before leaving the classroom to join the national peak body, Montessori Australia, as Director of Education Services.
Frequently Asked Questions
Thanks for considering Multiplication by Osmosis!
The title says it ALL! By definition, osmosis is easy...unconscious: "the process of gradual or unconscious assimilation of ideas, knowledge, etc." Wouldn't you like this for YOUR child?
Helping your children get those multiplication facts committed to memory will really up their game in all sorts of math...and Mark explains in detail in this workshop. It's never to late to help your child