Last week we had over 80 parents, along with administrators, thinking, doing and talking about math. The event was a School Planning Council meeting sponsored by our district, facilitated by Richmond educator and consultant Carole Fullerton. She has developed an excellent blog, Mathematical Thinking.
She began by asking parents what they wanted for their children. They responded with similar ideas across the room:
• to enjoy and be engaged by math (not to fear math)
• to connect with their learning
• to understand math (not just memorize procedures)
• to be able to use what they know about math to solve real problems
A couple of big ideas that stuck with me:
1. Teach Math from Left to Right
When we do mental math (add, multiply, divide, or estimate in our heads) we tend to perform the calculations using the largest numbers first. For example, if I needed to add 86 books to 73 books, I might think 80+70 = 150 and 6+3 =9, therefore my answer is 159. There are of course, other ways to think of this, but that is one way.
Why then, when we add or subtract numbers on paper do we begin with the ones column and move from right to left? When parents posed this question to Carole, she cited convention. It is simply the way we’ve always done it, but it is not the best way according to Carole. She added it is the only thing we do in this order in English . . . Carole modeled how teachers and students can add, subtract and solve various problems by thinking and working from left to right – just as if we were solving the problem in our heads. The beauty of thinking and teaching in this way is that the mental process mirrors the written process, and facilitates a much stronger number sense.
So back to our example, instead of thinking (and saying to students) first we need to add 6+3 and then 8+7, we are now thinking about 80+70 and 6+3. This is a huge and important shift. (And if we had to carry, we might say or hear students say in a think-aloud, “and carry the 1” when the number in question is actually ten….) Yikes! No wonder I struggled when I was first teaching these concepts.
2. The Equal Sign means “is the same as”
This point may seem terribly obvious to you. However, it resonated with me as a parent and a teacher. As Carole noted, the equal symbol = means “is the same as,” not the answer comes next, or put the answer here. This is an important concept, whether in algebra class or pre-algebra class, such as grade one.
3. Make your Thinking Visible
Carole emphasized the importance of collaboration, multiple pathways to seek solutions and the importance of making thinking visible – a concept that applies to all learning.
Carole shared two key messages for parents helping children at home:
1. Parents are not expected to be fluent with K-12 curriculum. Instead, they should ask good questions:
What does this remind you of?
Can you think of another way to do this?
What connections are you making so far?
What would a similar problem look like?
2. One purpose for homework is to practice skills or concepts learned in class. If your child is struggling with math homework, and you have asked good questions, write a note to the teacher explaining that you tried to work the problems out together and got stuck. The teacher can then follow-up and chances are – you are not alone!
Top photo: Creative Commons from Flickr