Wednesday, February 16, 2011

Guest Post: Matthew Mandelbaum on Multiplication

Today I'd like to welcome Matthew Mandelbaum, who is sharing with us today a few thoughts on  teaching multiplication.    We're just beginning this subject in our house, so I'm excited to get off on the right foot!

Multiplication: The Third Grade Rite of Passage
It’s now time for all third grade families to gear up for the rewarding gift of multiplication. Are you ready? First, don’t panic.

By Matthew G. Mandelbaum, MA, MSEd, PhD Candidate, Learning Specialist

Winter’s cold temperatures create ample time for indoor learning. As the snow makes its frequent appearances, so too starts the new semester’s upward push towards learning new skills and building upon the successes gained since September. With the right tools and approach your child can learn to conceptually understand multiplication and know her facts cold, without anyone experiencing struggle, tears, or frustration. Here are 7 steps for making the multiplication learning process enjoyable, engaging, effective, and efficient for your family. Start now and by the late spring, as the flowers blossom, so too will the rewards of all of your efforts.

Step 1. Examine your own feelings about math. Parents often have strong feelings about math based on their own experience, which they can unknowingly transmit to their children. How do you feel about the subject? Are your feelings influencing the way your child feels about it? If negative, can you approach the topic with a new perspective and an open mind? Can you see math as a challenge that is intriguing, a puzzle to be contemplated? Your orientation will influence your child’s.

Step 2: Examine your child’s feelings about math. Never let your child say she’s bad at math. This misconception will impinge on her willingness to put forth effort. Move the focus away from perceptions of ability to the degree of effort she is putting forth. With supportive environments at school and home, the child can always improve her effort. By praising effort, your child will continue to take risks to succeed at this massive undertaking of learning multiplication.

Step 3: Be sure that you and your child are focusing on conceptual understanding to build a strong foundation in multiplication. No one wants a house of cards. Your child will benefit from truly understanding the why’s and how’s of multiplication and its relationship to addition and grouping before simply memorizing multiplication facts and multiplication tables. Only focusing on the latter will yield less than satisfying results over the long-term.

Step 4: As conceptual understanding builds, provide your child with an organizing framework for learning facts. Brute force memorization is not as helpful as an organized structure. Moreover, you want your child to be able to actively construct the knowledge and build independence over time. Products should augment curriculum from school and from supplementary work. They should provide ongoing activity, sustain interest, be motivating, and offer feedback so the student feels she is making progress.

Step 5: Choose great products that edit themselves out of the equation forging a sense of mastery and efficacy on the part of the learner. Products should serve as homework help, a supplementary activity, and offer games so that there are multiple ways of interacting with multiplication. These tools should help solve numerical and word problems, so that the student feels like a mathematician actively engaging in discovery; someone doing “real work”. Such an orientation provides feelings of hope, curiosity, love of learning, and investment on the part of the child who can see herself as eagerly on the quest for knowledge. Sounds like a better plan than struggle, tears, and frustration, right?

Step 6: Allow the student to engage in the process of discovery to develop mastery experiences. Products should afford the student the chance to experience knowledge first hand to construct meaning with active awareness; not passive acknowledgement. Look to create the Ah-ha moments where connections among information are crystallized and students have deeper understanding, where they can explain exactly what is going on with their learning in a manner that makes sense to them and others.

Step 7: Provide means for students to take in information, metabolize it and be able to recall, and use it flexibly. Multiplication knowledge is more than just facts. It is the understanding of a system of numbers. Students should be able to have the system in place in a mental construct. They should be able to draw upon that system for fact knowledge and for active problem solving. Students need tools to get the system into their minds. Products like JumpingJoey’s NumberLine Multiplication and Division Book are perfect for learning multiplication and division with understanding. They foster independence, critical thinking and problem solving, are easy to use, work with existing curricula or on their own, and can be utilized in a multitude of ways as the student progresses through the learning process. Moreover, with practice, the tools help the student internalize the learning to develop self-reliance and self-efficacy that raises achievement.


Matthew G. Mandelbaum is the founder of PsySoEd Dynamics, LLC in New York City and is the creator of JumpingJoey’s NumberLine, the innovative multi-sensory arithmetic learning system for Pre-K through Elementary. In this case of multiplication using JumpingJoey’s NumberLine, knowledge becomes a coherent mental number line, with which the student can use flexibly to solve a range of problems. As a father of a young girl, he’s even more committed to making math for all and fostering academic success and achievement for children.

Copyright 2011 Matthew G. Mandelbaum All rights reserved.

1 comment:

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