# Helping Parents Understand How Children Learn Number

Recently a parent of a kindergartener sent us an email expressing some concern that her child (Julie) was working with two digit numbers but hadn’t received any place value instruction. The parent was helping her daughter “answer” the lessons and she was concerned that DreamBox might have an instructional sequencing problem. This gave us a wonderful opportunity to put the parent at ease, help her understand how young children learn number concepts, and coach her on letting her daughter do the lessons herself.

Young children are like sponges, and it’s fascinating to watch as they soak up the world. They are in a “making sense time” of learning, meaning that first the learning is “mimicing”, then they develop relational understandings, and finally they own the learning because they can apply it in new situations.

However research shows us that this is not a linear model of learning. Learning is fragile in young children; they go in and out of this pathway before they get to consistent application and own the knowledge and skills.

This is especially true when it comes to developing mathematical understanding. DreamBox is an adaptive learning environment designed to support a child’s fragile learning path to knowledge and application. We begin the young child with developing number concepts and number sense. The big ideas for this step in Julie’s development are:

• Counting by telling how many things are in a set.
• Numbers are related to each other through a wide variety of relationships.
• Numbers have different values when connected to real objects and measure. For example, 5 elephants is a big amount, but five crayons is a small amount though the same number; 12 minutes is not much more than 10 minutes, but it is a lot more than 30 seconds.

Along with these big ideas, we want to help Julie develop number sense which means having a good intuition about number and their relationships. Number Sense develops gradually as a result of exploring numbers, and visualizing them in a variety of contexts.

Early counting starts with mimicing of the sequence. Then a young child learns to count understanding a one to one relationship, and develops ideas about quantities so they see the relationships of more, less and the same. This allows Julie to see numbers as “groups of” (as in counting by 2’s, 5’s and 10’s) and her counting starts to become more fluent and efficient.

This leads the child into what some refer to as the “pre-place-value relations with 10.” They count easily to 10, can group and count with ten, but they are not using place value and are really not ready for the “tens and ones” conversation other than to mimic what they hear. In this stage, we still want them to see larger numbers, to count them using one to one correspondence, to identify where they fit on a number line, and to count them using groupings like 5s and 10s (like the mathrack example you mentioned); but for the child, the understanding is not at a readiness for place value.

So when you see DreamBox using larger numbers, this is what is happening. For us as adults who do have place value knowledge, it seems like place value is being taught and that place value would make it easier to answer the questions but this is not the case. With this in mind let me go to how DreamBox sets up the learning path for Julie and how that learning path can get interrupted.

With each click of the mouse DreamBox is subtly adapting Julie’s learning path based on her answer and her strategy to get to that answer. DreamBox knows that a young child’s learning is fragile so there is a very deliberate back and forth going on. We don’t want to push Julie beyond the point of her understanding but rather challenge the edges of her understanding so she moves along at her own pace. If a parent coaches the child so she gets a right answer or uses a more efficient strategy, DreamBox responds not knowing that the child didn’t really understand what was presented to her.

We adjusted Julie’s learning path to a more appropriate level for her.  Julie’s mom to going to encourage her to spend time on DreamBox, acknowledge her efforts, and talk to her about her “adventure” and what she learned today.

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