I'm a homeschool mom, my daughter is 7. She will be in second grade next year. I appreciate the different ways of doing math, rather than just stacking the numbers and adding/subtracting. I'm not sure how to go about teaching it. Any good resources out there for a homeschool parent? Thanks!
This is coming from an educator that isn't fond of common core for various reasons. What I believe is at the heart of common core math tho, is that the "Why?" is important. Math isn't just a series of steps to get to an arbitrary answer that someone says works, but it's a logical method of using order built into numbers to arrive at the correct answer.
My personal philosophy is that students first and foremost need the building blocks to USE to think. Ensure that they know their multiplication tables like their own name! But... once they have that foundation on which to think, give them all the "why's" you can; not just "these are the steps." My 2 cents anyway.
I rather like The Art of Problem Solving's Beast Academy series. It is a complete curriculum, but in a "graphic novel" format, with problem solving emphasis. This can lead into other resources from AOPS for middle and high school. (I was myself homeschooled, homeschool both of my children ages 5 and 8, and am a mathematics professor. In my experience, the perspective of these books will begin to develop the sort of attitude toward mathematics that yields playful and productive discovery, as well as the development of core skills.)
Stacking the numbers, and carrying the tens, works and is understandable to generations of people. You can explain each step as being correct by itself.
I recommend teaching your daughter how to count on her fingers using roman numerals. This will let her see how she can "carry the one". Her four fingers on her right hand are Is; her right thumb is a V; her four fingers on her left hand are Xes; and her left thumb is an L.
Whatever method you teach, you should make sure that every step has a clear meaning, and that it is clear why the expression at that step has the same value as the expression at the previous step. You should make sure that your daughter can explain each step.
1 1 1 1 1 1 537 537 537 537 537 + 547 => + 547 => + 547 => + 547 => + 547 ==== ==== ==== ==== ==== 4 84 084 1084
In the first step, 7 + 7 = 14. She can check this by doing the math on her fingers (using roman numerals). The 4 goes down below, and the 10 is "carried", by putting a 1 above the tens place.
In the second step, 1 + 3 + 4 = 8. (or 10 + 30 + 40 = 80, because all three numbers are in the tens place.) The 8 goes down below. Because 8 is less than 10, there is no need to carry anything from this step.
In the third step, 5 + 5 = 10. (or 500 + 500 = 1,000, because both 5s are in the hundreds place.) The 0 goes down below, and the 10 is "carried", by putting the 1 above the thousands place.
In the fourth step, 1 + 0 + 0 = 1. (or 1,000 + 0 + 0 = 1,000, because this step is for the thousands place.) The 1 goes down below, and nothing needs to be carried further.
Teach your daughter to check her own work.
- Casting out nines is an old-fashioned way.
- Performing the inverse calculation is a complete way -- but might allow making the same mistake in reverse.
Teach your daughter to sanity check her own work.
- Estimating checks the rough size of the answer.
Have your daughter keep a log of her most common mistakes
There are so many mathematical directions you can go. I have found Living Math Forum (a yahoo group) to be incredibly eye-opening. There are about 5,000 members, and questions usually get a variety of answers from other homeschoolers.
How do you want to approach math? There are various curricula available, there are "math readers", there are activities that help kids make sense of the math, and activities that make it feel useful to them.
And how comfortable with math are you?
My answers to you would depend very much on details of your situation and interests.
You also might be interested in my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers.
After three years of intensive work with the new math standards (as part of the writing team for a new, national common core-based mathematics curriculum), my partner and I began consulting for school districts, training their teachers in the very thing you inquired about....HOW best to teach this new math. Almost without exception the teachers we worked with asked one common question..."How can we help our students' parents?" It seemed as though nothing existed (yet) that would work with ANY curriculum to simplify the process of TEACHING it....to basically just help parents navigate these new waters in a way that made them feel confident. After much searching, for a resource we could recommend, we found we needed to create it.
In response to all of the parents and teachers (and PARENTS WHO TEACH!!) we created the "Thinking Math Differently" series of guide books. Each level-specific book will work alongside any curriculum you are using, enabling you to 1. gain your own understanding of each topic and 2. develop your own style of teaching it that will foster deep understanding in your child.
These guides, available on Amazon.com, are a true resource for teaching elementary mathematics! Please feel free to reach out with any specific questions you may still have! Our email address is firstname.lastname@example.org.