Singing Banana (James Grime) recorded this video at the Mathematical Association annual conference dinner, 2011. I’ve shared it before, but that was over a holiday weekend, so many of you may have missed it. It relates, in a way, to our PUFM lesson this week.
Enjoy!
Photo by Chrissy Johnson1 via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
Our decimal system of recording numbers is ingenious. Once learned, it is a simple, versatile, and efficient way of writing numbers. … But the system is not obvious nor easily learned. The use of place value is subtle, and mastering it is the single most challenging aspect of elementary school mathematics.
Ironically, these challenges are largely invisible to untrained parents and teachers — place value is so ingrained in adults’ minds that it is difficult to appreciate how important it is and how hard it is to learn.
— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers
In other words, we take place value for granted. I know this was true of me when I started teaching my kids. Every year, their textbooks would start with the obligatory chapters on place value, which seemed to me just busywork. I began to appreciate the vital importance of place value when I read Liping Ma’s book and saw how the American teachers were unable to properly explain subtraction or multi-digit multiplication.
Place value is the heart of our number system, the foundation on which all the rest of arithmetic must be built. Because of place value, “The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.”
Photo by Iain Watson via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
Many things in mathematics need to be understood relationally — that is, in relationship to other concepts. But some things just need to be memorized. How do you know which is which? A homeschooling friend pointed out that one thing children definitely need to memorize is the counting sequence from 1-100 and beyond. While there are some patterns that make counting easier, one does just have to memorize which “nonsense sounds” we have attached to each number.
Another sort-of counting that young students should master is subitizing — recognizing at a glance how many items are in a small group. Children do this instinctively, but we can help them develop the skill by playing subitizing games.
[Aside: In writing this blog post, I ran into some nostalgia. Back when we first did these PUFM lessons, my daughter Kitten was only a toddler. I wrote, “I’ve tried to do lots of counting with my youngest, who hasn’t quite gotten beyond, ‘…eleven, twelve, firteen, firteen, nineteen, seven,…’ The numbers tend to start appearing randomly after she gets past 10.” Ah, memories.]
[Photo by geishaboy500.]
It began with a humble list of 7 things to do with a hundred chart in one of my out-of-print books about teaching home school math. Over the years I added a few new ideas, and online friends contributed still more, so the list grew to its current length of 26. Recently, thanks to several fans at pinterest, it has become the most popular post on my blog:
Now I am working several hours a day revising my old math books, in preparation for publishing new, much-expanded editions. And as I typed in all the new things to do with a hundred chart, I thought of one more to add to the list:
(27) How many numbers are there from 11 to 25? Are you sure? What does it mean to count from one number to another? When you count, do you include the first number, or the last one, or both, or neither? Talk about inclusive and exclusive counting, and then make up counting puzzles for each other.
Can you think of anything else we might do with a hundred chart? Add your ideas in the Comments section below, and I’ll add the best ones to our master list.
This is wonderful! I am definitely not a crafts-person, but I can’t wait to make some of these. If I can just find my daughter’s pony beads….
From Cindy at love2learn2day, who got the idea from a math conference workshop by Kim Sutton.
Krista at the LivingMathForum wrote, “We’ve used these for several years. My son even made a bunch of them a few years ago and sold them at a homeschool resource fair. We always have one in most of our board games to help younger children add up their die rolls. I find them relaxing for some reason, just moving the beads along the cord, and my son will sometimes sit and listen to me reading, etc., and just manipulate the beads.”
You can use these math activities to play with your counting rope:
Photo of Lex times 11, by Dan DeChiaro, via flickr.
We are finishing up an experiment in mental math, using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.
Take your time to fix each of these patterns in mind. Ask questions of your student, and let her quiz you, too. Discuss a variety of ways to find each answer. Use the card game Once Through the Deck (explained in part 3)as a quick method to test your memory. When you feel comfortable with each number pattern, when you are able to apply it to most of the numbers you and your child can think of, then mark off that row and column on your times table chart.
So far, we have studied the times-1 and times-10 families and the Commutative Property (that you can multiply numbers in any order). Then we memorized the doubles and mastered the facts built on them. And then last time we worked on the square numbers and their next-door neighbors.
Photo of Miss Karen (and computer) times 3, by Karen, via flickr.
If you remember, we are in the middle of an experiment in mental math. We are using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible. So far, we have studied the times-1 and times-10 families and the Commutative Property (that you can multiply numbers in any order). Then we memorized the doubles and mastered the facts built on them.
Photo of Javier times 4, by Javier Ignacio Acuña Ditzel, via flickr.
If you remember, we are in the middle of an experiment in mental math. We are using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible. Talk through these patterns with your student. Work many, many, many oral math problems together. Discuss the different ways you can find each answer, and notice how the number patterns connect to each other.
So far, we have mastered the times-1 and times-10 families and the Commutative Property (that you can multiply numbers in any order).
Photo of Eeva times 6, by Eric Horst, via flickr.
The question is common on parenting forums:
My daughter is in 4th grade. She has been studying multiplication in school for nearly a year, but she still stumbles over the facts and counts on her fingers. How can I help her?
Many people resort to flashcards and worksheets in such situations, and computer games that flash the math facts are quite popular with parents. I recommend a different approach: Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together?
We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.
The Engineer was away on a business trip, and Kitten and I were in the mood to veg out on YouTube, so I hunted for some golden oldies. We used to watch Square One TV faithfully, back when my eldest was in first grade. I can’t believe they haven’t released this show on DVD!
We found recordings of my two favorite songs (“Nine, Nine, Nine” and “8% of My Love”), but the picture quality was horrible. This video was the runner-up:
Denise Gaskins' Let's Play Math 