Thursday, August 20, 2015

3 Ways to Support Your Child's Early Number Development

About two weeks ago I was taking an early numeracy class, I asked if anyone would be interested in a post sharing what I learned about helping young kids develop a sense of number. While nobody responded on that post, one reader did express interest on Instagram! That was all I needed to pump out a post sharing some of the things I learned about helping young children develop a sense of number.

One of the most powerful things I learned in my class was that with young children, it's really important to let their ideas come first. The second an adult tries to "teach them" how to think about number, the less sense things start to make for young kids--which really hit home with me because I felt that way as a child. The fact of the matter is that mathematical ideas are all around us. Ideas of counting items, fair sharing, arranging items to fit others, etc are all around us. Children actually grow up learning a lot about number and math from the world around them and most children actually have some really great ideas and ways that they've made sense of number, comparative relationships, sharing, and more. It's really important to explore your child's thinking with them. The more you understand what they're thinking, the better you're able to support them from where they are--versus telling them how to think. (Chances are, if you struggled with math, you might start to see how your struggle might have actually been influenced with someone not taking your ideas seriously to start and instead saying, "That's wrong--do it like this!"--You want to avoid that at all costs with children.)

teaching kids to count


Opportunities to count actual objects will increase your child's understanding of number and help them develop skills to become successful. Simply reciting "1, 2, 3, 4, 5..." isn't enough--they need opportunities to engage in different ways to count. There are five counting principles that children need to master by kindergarten to set them up for success with counting and working with numbers. The suggestions below target all five counting principles (one-to-one correspondence, s..order, cardinal rule, item irrelevance, and order irrelevance.) 

*Count objects--ask child to count and encourage them to name the amount they counted-How many cars are there? 1, 2, 3, 4, 5. So how many cars are there? 5.
*Count backwards. For students to understand the order of number, it's really important to have them count forward and backward. In addition, make sure that rhythmic counting (chanting the numbers) is supported by lots and lots of opportunities to count things
*Count two different kinds of objects in one bin/basket--for example you might have some blocks and some toy cars. Put a few of each in a bin/basket and have your child count all of the objects. Some children will count the blocks separately and some will count them altogether. Ultimately, when you ask children to "Count the items in the basket" you will want them counting them all. Some won't do this right away--that's fine, they just haven't developed a sense of item-irrelevance yet (the type of item does not change the amount of items in a collection). Keep giving them an opportunity to count and model correct counting. 
*Give your child objects to count and then change the order and ask them to count. Some children will count the same number, others will see a change in the order as a change in the number. Continue giving them opportunities to count and change the order--and model for them how to count once the order has been changed. 

I learned this in a K-3 class a few years back and am in love with the idea. We all subitize-which means we see a collection of units and we're able to name an amount--like numbers on a dice. Often we can do this with larger patterns, too. We start to see three separate dots as a unit and then we can combine those units, "I see six because I see three and three." 

what is subitizing

Presenting young children with opportunities to subitize is very valuable and allows them to make connections between different numbers. There are lots of ways to help children subtitize. You can use big dice (I found the ones in the picture in the dollar section of Target) or you can even create your own patters with dot stickers on paper plates--they store easy and are large enough and durable)

Some tips for subitizing:
*With really young children, start with small numbers 1-5
*As children get older introduce more combinations and larger numbers
*Present the pattern and then take it away before asking how many there were.
*After the child has named the amount, you can present the pattern and ask how they knew. Encourage them to start using language to explain their mathematical thinking (SUPER valuable), "I saw two and then one more and I knew that was three." (They might struggle with this at first, so model it for them by showing them how you knew. You can then ask, "Did you see it that way or did you see it differently? Even if they see it the same way, have them explain it.)
*A few minutes a day would make a big difference. 

Making ____
While subitizing involves looking at a combination of units and naming a value, you also want students to take individual units and combine them (compose them) to make a given value. For example, you might encourage a small child to find all the possible ways to "make 10" or even "make 5." 

You can support this by giving them the set amount of objects and then giving them a scenario. If I have ten blocks and two baskets, what are all of the different ways I can split the blocks up between the two baskets? Never just let them show you, always encourage them to explain. You'll want them to try as many possibilities as they can. You can do this with any number set. Schools/educators tend to focus on 5's and 10's but it's importatnt to allow them to explore ways to compose all kinds of numbers.

This experience not only leads to an understanding of addition and subtraction, but supports ideas in algebraic thinking as well. (You only know the total, but you don't know the addends--thinking openly like that at a very young age is powerful). 

This will also support children as they develop a sense of flexibility with addition and subtraction facts later on. Using derived facts is a great mathematical tool that allows children to become flexible and fluent with numbers. That means that if a child knows how to double numbers (6+6, 3+3, 4+4, etc.) and knows how to make ten--s/he can access different addition facts using the doubles and making ten strategies. (For example if I child is presented with a problem of 4+3--s/he could use 3+3=6 and one more makes 7 as a way to think about the problem. Another example would be 7+4--if the child knows that 7+3 makes ten, then 7+4 is one more so it would be 11.)

In my class last week, the focus was on early numeracy--PreK-3rd grade was the grade band focus of the class. Yet, we worked through multiplication and division of fractions. Those things aren't covered explicitly in those grades--obviously--yet so many of the things that we learned to support early number development build the foundation for being able to understand the multiplication and division of fractions--it's crazy. All I can say is--start early, give lots and lots of opportunities to count and work with numbers, and take your child's ideas seriously--start with their thinking--you'd be amazed at how far that will take you.

Your children and your children's teachers will thank you later!

Did you struggle with math as a child? Do you have apprehensions about your child understanding/succeeding in math as they enter school? (I'm really passionate about math education--specifically Common Core Math and mathematics reform in education--I'd love to do more posts if there is an interest). 

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