Our 2-year-old, Monkey, loves numbers, and my husband and I are doing what we can to encourage his enthusiasm. For example, a few weeks back I bought a big container of number and letter cookies at Target. When we give him a cookie, we have him try to identify the letter or number on the cookie. He loves it, and so it’s both a game and a teaching moment. We’ve been surprised and delighted at how well he recognizes numbers, but he’s two and far from perfect. This means that my husband and I have to think about how to respond when he’s wrong.

There’s a subtle but real difference between the two conversations below. In the first, I give the answer away. In the second, I give Monkey a chance to come up with the answer himself. I’m communicating very different expectations and providing different learning opportunities.

**Conversation 1**

Mom (holding up a 6 cookie): What number is this?

Monkey: Nine!

Mom: No. That’s close. It’s a six! What number is it?

Monkey: Six!

**Conversation 2**

Mom (holding up a 5 cookie): What number is this?

Monkey: Two!

Mom: Not two. What number is it?

Monkey: Five!

Whether we’re helping with homework or just engaging in conversation, the way we respond to our children in interactions about mathematics can make a difference in their opportunities to learn and their attitude toward math. Our questions can **feed** or **fish**, **prompt** or **probe**, and thereby subtly or even dramatically affect the nature of our interaction.

**Feeding** is when we give our child the answer outright. This can be appropriate with very young children. If Monkey can’t identify a 6, telling him that the cookie he sees is a 6 helps him make a connection between the written numeral and the word. As he makes more of those connections, he’ll gradually become able to identify 6 on his own. However, once a child is older or more fluent in a skill, feeding is less productive because it removes the necessity for thinking.

**Fishing** is when we have an answer or solution path in mind and we’re trying to get our child to land on it. It’s a game of “guess what the grownup wants me to say,” and it’s not very conducive to learning. But it can also sometimes be hard to recognize when we’re fishing. In the second conversation with Monkey, I knew he could identify a 5 and thought I was giving him an opportunity to think harder about what he was seeing. But it could very well be that he was throwing out number words to see which one landed and earned him the cookie.

**Prompting** is when we ask our children questions to help lead them to the correct answer or down a solution path we know they are capable of following. In teaching we use the term “scaffolding,” which is when, with a little bit of help, a child can do something that they are not capable of doing on their own. With good prompting, the child is doing most of the thinking and getting *just* the help they need. Less effective prompting can keep a child from connecting the dots and truly understanding:

Parent: If everyone in our family eats two pieces of pizza, how many pieces of pizza do we need?

Child: I don’t know.

Parent: How many people are in our family?

Child: 4.

Parent: What’s 4 x 2?

Child: Umm…

Parent: What’s 2 + 2?

Child: 4.

Parent: Plus 2 is…?

Child: 6.

Parent: Plus 2 is…?

Child: 8.

Parent: How many pieces of pizza do we need?

Child: 8.

In this conversation, the child could get every answer right without every seeing the logic of the solution method. Contrast the conversation above with the one below, in which prompting is used to help the child follow their own inner logic.

Parent: If everyone in our family eats two pieces of pizza, how many pieces of pizza do we need?

Child: I don’t know.

Parent: How could you figure it out?

Child: Umm…

Parent: How about four pieces. Is that enough?

Child: No. Then only two people could have pizza.

Parent: So how many more do we need?

Child: Um, four?

Parent: Why?

Child: Because we have two more people.

Parent: So how much pizza do we need?

Child: Eight pieces.

**Probing** is when we are asking our child questions *not* to get them to an answer, but to get at their thinking. Probing is often the most effective type of questioning a parent can do, because it encourages a child to be aware of their thought processes and to have confidence in their own reasoning. And probing *without prompting* is really hard to do when your child gets an answer wrong! When a child answers a question wrong, we want to get them to the right answer. But sometimes all a child needs is to think aloud in order to see what they’re doing wrong, and sometimes as a parent we need to know how they’re thinking in order to best help them. Both of these require the parent to just give children space and opportunity to reason on their own.

A note: Young children are not very good at explaining their thinking, but they should be given the opportunity anyway. As they grow older, they will become more sophisticated at explaining their thinking because they have had the expectation laid out, and have had opportunity to practice.

When my children have made a mistake and I ask for them to explain their thinking, they often don’t give much of an explanation, but do pause for a while, mentally recheck their approach, and then come back with a correct answer. To get them to speak more about their approach, I sometimes:

– tell them I would like to teach another child (either one of their friends or another sibling) how to do this and ask them to help me think of a drawing that would help.

– explain my own thinking and ask if they did it the same way or a different way. My kids already have a cheeky independence streak, so they always give me a different approach and then we get to talk about how the strategies relate.

Fishing can be easily turned into something much more, just by asking “how do you know?” Until now, I had never thought to ask this for number/letter recognition tasks, but it seems to me that could be a really cool conversation. How do they know that cookie is a 6?

Lastly, guessing-and-checking is a valid strategy. We make it clear that it is ok not to know an answer, in fact that is an exciting opportunity to learn. However, I’m not the checker when they guess, since that’s no fun. So, what ideas do they have for how to check? Again, imagine recognizing a number cookie. How could they check whether something is a 6? I think you’ll see some fantastic thinking.

Those are some great suggestions for continuing and deepening the conversation (fodder for another blog post, maybe!). And I like what you say about guessing and checking. It’s not the guessing itself that can make fishing problematic – it’s the relying on someone else’s authority and never moving beyond that.