We do immersions at our Living Education Retreat. One subject. 45 minutes or so. One well-versed teacher. 10-20 'students' a.k.a. adults wanting to learn how to better teach that subject and so pretending to be the students. It's a rich experience in which to participate.
The ever-lovely Richelle immersed a group of us in the teaching of multiplication tables. Math is a subject that always made me cringe in school. Richelle says she was the same way. Love that we have that in common! She began schooling her sons, and in the process noticed some things happening in their learning process that catapulted her into loads of research on the best practices for teaching math. She then wrote a book on her findings. Its so interesting, and has been pivital for me.
Here's my narration on our immersion session:
We started out with oral questions like "John had 2 cents and was given 2 cents more. How many altogether?" Then we took out our manipulatives (coins and beans)and answered more questios by showing it with our items. We also constructed a multiplication table for 2's using our coins and worked with the table in a variety of ways while trading pennies for dimes etc.
We did 5 minuets of mental math questions at the end. Brain gym! I can see how doing this daily would exercise a child's mind into strong muscle, agile and adept.
Here's my brief narration from our first math plenary:
Basically, you introduce a child to numbers by working with each number starting wtih 1 so they understand all it's possible combinations while working with items around the room and manipulatives (beads etc.) Then you learn how to write that number before moving on to the next one. It is a gradual progression. Kindergartners should not be doing pre algebra, even if a worksheet makes it look like they understand it! After all, children take their brains to college not their papers. This early phase should not be skipped or rushed. And if you have an older child who missed it, go back and revisit it before moving on in where they are at. I'm going to do this for myself!
I learned that math teaching should be simple but not simplistic using methods that get right to the heart of each concept. I kept thinking the whole time how I wish I would have been introduced to math in this fashion. In the months leading up the the LER, math was one subject I was especialy looking forward to learning more about, because I will be further introducing my son to numbers this school year.
Richelle's encouragement that math is like a beautiful mountainous land, representing truth and inspiring awe made her session a joy to lean forward in my seat and listen to. She was quoting Charlotte Mason and others. Math is the language of art, science and nature. It tells about our Creator. Its order/laws give wholesome limits. Creation answers back to Him and upholds His laws. Galileo said, "Math is the alphabet with which God has written the universe."
Are we having fun? Are the questions I'm asking engaging for my son and his unique peronality? Do I relate it to his life- nails, cousins, worms, legos, money, tractors? Is math drill a fun treat?
Am I letting the ideas strike him? Is he discovering the shortcuts on his own? Do I allow exploration before giving the corresponding math rule? In the books Mason used to teach math she skipped the pages that explained the math rule that corresponded to the lesson until after the students had discovered it themselves. She let them internalize it rather than the teacher feeding the information to them. This is a revolutionary way to teach!
Am I being content to go slowly?
Am I requiring the explanations for why he arrives to his answer?
Are the questions well within his grasp? Do I have the right tension? I loved this idea! To keep the proper tension for math learning means that I am pulling him along like a skiier behind a boat. I need to pull hard enough to keep his head above water so he's enjoying the challenge, but not so hard that he's being splashed in the face and sputtering. I also can't go so slow that we're not moving forward at all. Either extreme will cause problems. This will be a learning curve for me to recognize, but I'm sure I'll get the hang of it as long as I'm carefully aware.
Are we doing mostly oral work? Am I using written work very sparingly? We will use large graph paper in his own special math notebook- cool!
Am I using manipulatives when necessary, but when he's beyond them, do I take them away? This will also be something I will also have to learn to reconize. I imagine my friends with multiple children who have schooled for many years have a good feel for this kind of thing. I should ask them more about what that looks like.
Do I use one manipulative too heavily? Idea: use pennies but call them baseballs. Don't get hung up on one thing or make manipulatives the crutch:
Ray's New Primary Arithmetic and the corresponding teacher guide by Ruth Beechick (also availiable for free here. )
Richelle's Mathematics: An Instrument for Living Teaching book that gives the practical step-by-step for our daily lessons in number. I had my copy cut and rebound spirally for a few dollars at an office store. I can now have it laying flat in front of me leaving my hands free while I am working at the table or on the couch with my son.
I also looked at Olneys- free online math book, similar to Ray's but moving a bit faster.
Mathematics: Is God Silent? Looking forward to a peek at this book for mom to read.
Eventually we'll read Number Stories of Long Ago. I love that it tells how fathers and grandfathers used to tell these stories to the children around the campfire long ago. I imagined getting cozy with quilts and doing the very same thing with my boys on a crisp fall evening, hot cocoa in hand.
I won't need to buy many manipulatives because we already have them at home: beans, pennies, popsicle sticks etc.
I won't be buying stacks of 'kids' living math books' because in reality, this idea is a common misconception as it relates to a true living education. Having that clarification is freeing, though we'll probably check out a few at the library just for fun. (And yes, my son likes to make triangles with his arm on his hips thanks to The Greedy Triangle. We're just normal people here, okay! :)