intentionality – Early Math Counts https://earlymathcounts.org Laying the foundation for a lifetime of achievement Tue, 11 Jul 2017 15:51:44 +0000 en-US hourly 1 183791774 Math Sentences https://earlymathcounts.org/math-sentences/ https://earlymathcounts.org/math-sentences/#respond Thu, 24 Jul 2014 14:30:36 +0000 http://www.mathathome.org/blog1/?p=2923 We write math sentences from left to write and use mathematical symbols and words to communicate a mathematical problem (or situation). Once children are in grade school they will read and write math sentences for years.  So how do we prepare them for this eventuality?

I bet most of you already use math sentences with your children all of the time.  When you ask a child to set the table for snack and she comes back to report that she has finished, you might look over at her work and notice that there are 2 chairs that don’t have a place setting.  Rather than telling her that she needs to get 2 more place settings for the empty chairs, you probably say something like,

“Hmmmm. It looks like the table is almost set but not all the way.  How many plates did you put out and how many chairs are there?  So there are more chair than plates.  How many more plates to you need to make sure that every chair has a plate?”

You might also use a math sentence when you are taking attendance.

“If Johnny and Sara are absent,

how many children are absent?”

or

“There are 6 boys and 4 girls at school today.  How many children all together are at school today?

The main point of difference between how older children approach math sentences and how younger children approach them is that older children are reading them and answering on paper.  Younger children are exposed to math sentence because the adults verbally present them and then support them as they calculate the answers.

Most 3 years olds are not going to be able to add 6 and 4 in their heads.  The way that they will get to the answer is through scaffolded interactions, perhaps between themselves and the adult or between themselves and other children.   After posing the question about how many children are in school today, the teacher should then allow the children to try and come up with their own strategies for solving the equation first and the let them try to see if it works.  If, after a couple of attempts, it is still unclear, the teacher can provide a strategy, i.e., “Let’s count all of the children together, both the boys and the girls, to find out,” and then point to each child as s/he is assigned a number.  Remember to stress that the last number you say is the total.

Try and think of number sentences as more than simply asking questions or making statements about math and number, and more as a “plan of action” for including more math opportunities into your interactions with your children.  This intentionality will force you to consider ways to present the problems and then support the children as they figure out the answers.

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Speaking of Math Manipulatives https://earlymathcounts.org/speaking-of-math-manipulatives/ https://earlymathcounts.org/speaking-of-math-manipulatives/#comments Mon, 09 Jun 2014 10:59:53 +0000 http://www.mathathome.org/blog1/?p=2808 Is it enough to have wonderful math manipulatives, organized and available for children to play with, or do we need to be more systematic and intentional with the materials we present as well as in the way we present them?

I’ve been writing about math manipulatives on Mondays for 2 years, but I thought it was time to step back and remind everyone, myself included, that there is a space between “free-play” and “teacher-directed” activity that is at the heart of purposeful math education for young children.

No, it is not enough to put beautiful sets of hand carved wooden Tangrams out in  baskets so children can explore them.  Yes, they should initially investigate the Tangrams on their own and discover their attributes as is developmentally appropriate.  However, intentional math teaching should follow-up the children’s independent play and discovery.  I know that you think very carefully about the materials you present to the children as well as the timing of when you present them.  You consider the children’s ages and stages, as well as their previous experiences when planning.  You think about the Zone of Proximal Development and set up the opportunities accordingly.

The next step is to think about how to use these amazing manipulatives to expose and teach early math concepts.  For example, Unifix Cubes are often placed in baskets on tables during free play.  Children choose them, or they don’t ,and when they do, I often see sustained engagement.  However, what I don’t often see, is purposeful activity using the Unifix Cubes as a tool to teach math.  That is what they are designed for.  This requires planning on the part of the teachers that asks them to consider how to develop an activity (or activities) using the manipulative, less as an open-ended toy, and more as a tool for teaching math.

The next time you set out your baskets of Unifix Cubes, plan an activity using them.  Create pattern cards so the children can copy the patterns using the cubes.  Create a measuring activity so the children can measure different lengths.  Have the children sort the cubes into color-coded baskets.  Ask the children to make their Unifix Cube tower taller, or shorter.  Take their open-ended play to the next step.

Intentional use of math manipulatives is the goal for their use.  Keep thinking about ways to use manipulatives in your “purposeful” teaching.

 

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Intentionality https://earlymathcounts.org/intentionality/ https://earlymathcounts.org/intentionality/#respond Tue, 10 Jul 2012 11:00:17 +0000 http://www.mathathome.org/blog1/?p=210 Young children develop ideas and concepts about mathematics quite naturally.  They think about size, shape, quantity, order, and speed throughout the day as they play and explore.  We, as teachers of young children, need to tap into these natural curiosities and make mathematics intentional.

Intentionality is acting with knowledge and purpose.  It is the opposite of chance- it is planned and thoughtful.  In order to become intentional about math teaching, we need to understand math the way we understand literacy.  The more knowledgeable we are about out content the more we will be able to act and react with purpose.

How are you intentional about your math teaching?

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