Sorry I haven't been writing more. There are many things I want to get to here, but there are many things in my way.
I had a conversation with a commenter that resulted in his writing a post to share here. He is selling something, which makes me disinclined to share it; but he is a teacher sharing his connections and story, and attempts to innovate, which I like. I've received no compensation for this. Please let me know in the comments if it is an inappropriate use of the blog, to you.
Jumping Joey's Numberline
Math Facts for Kids or What’s More Important the Answer or the Process?
By Matthew G. Mandelbaum, MA, MSEd, PhD Candidate, Learning Specialist
Two middle elementary students sit together faced with the following problem: A girl has some jellybeans that she wants to share with her friends. With 3 other friends, she has 1 left over; with 5 other friends, she has 1 left over; and with 11 other friends, she has 1 left over. How many jellybeans does she have?
After reading this problem, the two students are left with choices for problem solving. Should they take a trial and error approach? Should they continue to re-read the problem over and over again, in hopes of some insight? Or should they use a tool to help them learn? Seeking to improve frustration tolerance, perseverance, and the value of process, I suggest they use a tool. They turn to JumpingJoey’s NumberLine® Multiplication and Division Book, which they have been using to learn both operations. “It’s not just for learning number facts,” one student says to the other. “Right! Let’s figure this problem out!” he replies. They now re-read the problem with purpose, hunting for clues. “4, 6, and 12 seem important,” one student says. “Because we have to add the girl and her friends. Let’s investigate them as factors.” The students turn to each of the factor’s string of multiples and analyze the collection of number facts. “Do they share a common multiple?” the first asks. “Let’s see,” flipping back and forth through the book’s pages. “Hey, each of them has 48. Look, on the four’s page, there’s 48 (4 x 12) on the six’s page there’s 48 (6 x 8) and on the 12’s page there’s 48 (12 x 4). The common number is 48!” “Cool!” says the other. “If they all share 48 and there’s 1 left over, that means there are 49 jellybeans in total!” “Let’s check: 49/12 = 4 remainder 1; 49/4 = 12 remainder 1, and 49/6 = 8 remainder 1. That is it!” “We did it; we solved the problem! That was awesome!”
They showed a great deal of pride. I asked them if they felt confident with their answer and if they liked the process of using a tool. They said they did, because it made them feel like mathematicians; they weren’t afraid and they did not give up. In this example, a challenging problem using math facts led to an enjoyment of the process, a sense of satisfaction, and a chance to have a mastery experience where the students could take on something difficult and with there own effort, and only a small amount of adult guidance, to develop increased self-efficacy for math.
This is a path towards a sound math foundation, where process leads to performance. However, I often see that in the quest for math achievement, parents can assume that getting the right answer is the most important thing about knowing math facts, when in fact a child’s decision process that leads to the answer is what should be looked at most carefully.
Memory can work a few ways. Either there is a weak association among information or a strong association. Both types can lead to the right answer when the situation is not so difficult. However, when the challenges begin to mount, having a strong association among information will yield to fewer errors than a weak association.
The key to math facts for kids is strong conceptual understanding. Parents looking to help their children grow should seek to have benefits over the long-term in addition to short-term grades on little assessments. In order to reach this goal, parents can supplement scholastic efforts with at-home tools that provide an organized number line framework to promote conceptual understanding, mathematical fluency, plus a strong foundation for learning math facts. We feel that by using a product like JumpingJoey’s NumberLine, students build a coherent mental number line, which they use flexibly to solve a range of problems. This ability is important because, as reported in the journal Psychological Science of the Association of Psychological Science, scientists found that the quality of mental number line in children and pre-adolescents strongly and positively correlates with arithmetic aptitude, math achievement-test scores, and overall math grades.
Math facts are the building blocks for arithmetic, which form the foundation for higher math throughout the grades. It is important for the child to interact with numbers and consider their meaning with deep contemplation, because new topics will be built upon these numbers to form new knowledge. The child will need to relate what he knows to what is being taught. This relationship needs to be processed on a deep level.
When looking to help support a child’s learning math facts, parents can ask questions like “How did you get that answer?” or say “Show me your thinking.” Within this process, parents need to reward their children’s effort instead of their ability so as to build mathematical competence. To support the last goal, parents can choose products like JumpingJoey’s NumberLine that help their children see themselves as capable mathematicians who are actively engaged in the learning process. Such products should be intrinsically rewarding and promote intellectual curiosity.
Arithmetic is a fascinating subject of study. Numbers possess a lot of power. The Pre-K through elementary years are formative in establishing a child’s sense of self as a learner. Throughout these years, students are met with challenges, like learning math facts. Of vital importance, is their ability to persevere despite obstacles so that they may approach tasks with a realistic sense of confidence and openness to what is new.
Einstein said, “Never regard your study as a duty, but as the enviable opportunity to learn to know the liberating influence of beauty in the realm of the spirit for your own personal joy and to the profit of the community to which your later work belongs.” Children deserve to have this orientation towards learning. As parents and educators, we owe it to them to create an environment in which they can think this way. After all, it worked for Einstein, right?
A New York State certified educator in Childhood General and Special Education, Matthew has over 13 years of varied experience working with students of diverse ages in a range of settings from pre-kindergarten to college, in public, private, parochial, afterschool, and tutoring environments. Together with his wife Jamie Cohen, he founded PsySoEd Dynamics® LLC, a company dedicated to developing high quality educational products whose first line of JumpingJoey’s NumberLine products helps students learn math facts and concepts using a fun, multi-sensory approach. As parents of a young girl, they’re even more committed to making math for all and fostering academic success and achievement for children. You can read Matthew and Jamie's Statement of Philosophy for Teaching, Learning and Educational Product Development here.
Copyright 2011 Matthew G. Mandelbaum All rights reserved.