Have you ever finished working with a child and realized that you solved the problem and are uncertain what the child does or does not understand? When engaging in a problem-solving conversation with a child, our goal goes beyond helping the child reach a correct answer. We want to learn about the child's mathematical thinking, support that thinking, and extend it as far as possible.
BECOME A KID WATCHER! Reflect on their strategies and learn from them.
Warning Signs
1. Interrupting the child's strategy*Do I understand how the child is thinking and will my ideas interfere with that thinking?
*Will the child be able to make sense of my ideas if I interrupt?
2. Manipulating the tools
*Will the child still be in control of the problem solving or will it become my thinking? my control of the pen? my ownership of the problem?
*Will my problem representation make sense to the child?
3. Asking a series of closed questions
*Will my questions be about the child's thinking or my thinking?
*Am I asking a question or providing steps to follow?
*Will the child still have an opportunity to engage with substantive mathematics, or will my questions prevent him/her from doing so?
Alternate moves to take
*Slow down: allow the child to finish before intervening
*Encourage the child to talk about his/her strategy so far.
*Ask questions to ensure that the child understands the problem situation and how the strategy relates to that situation.
*Ask whether trying another tool or strategy would help.
*Warning Signs: Recognize three common instructional moves that are generally followed by taking over children's thinking, Teaching Children Mathematics, Vol. 21, No. 2, September 2014
Questions - - WAIT for an answer (avoid leading ?'s like "Did you count?")
- How did you work that out?
- Show/tell me how that works
- If you did know, how would you do it?
- Tell me more about that
- Prove it
- Why/How do you think that?
- What # did you start with?
The following are great for number talks!
- My strategy was...
- What would happen if...
- I agree/disagree with you because...
- I know a different way...
- How did you...
- I know my answer is correct because...
- I hear you say that...
- Your strategy reminds me of...
- Math Talk Cards, Brittany Beaumont, www.peachy-teaching.com
Images: Tunstall's Teaching Tidbits
As we listen to a child our purpose is to discover the person behind the words. Talk serves the intellectual growth of our students as well as their social and emotional needs. It invites us into their lives and gives us a gauge on their thinking. Talk sheds light on the inner concerns of our students!
Warning: Not speaking and participating in classroom activities is harmful to your learning growth and development.
We verbalize to internalize! Make your talk purposeful!
Benefits of Dialogue
- deeper levels of comprehension
- development of a classroom community
- creates new possibilities
- develops critical thinking skills
- elevates student learning
- development of collaboration
- development of empathy
The four basic ways to engage in purposeful dialogue include:
1. Agreeing: I agree with ___ because...
2. Disagreeing: I disagree with ___ because...
3. Adding on to an idea: I'd like to add to what ___ was saying
4. Clarifying meaning: I don't get it. Would you clarify?
Four Essential Questions for Teachers
1. What do we expect our kids to learn?2. How will we know when they have learned it?
3. How will we respond when they haven't?
4. How will we respond when they have?
Divergent Question: no specific answer, asks someone to think broader about a topic
Convergent Question: ability to give "correct" answer to standard ?'s that don't require significant creativity
We Remember...
95% of what we teach someone
80% of what we experience personally and think critically about
70% of what is discussed by others
50% of what we both see and hear
30% of what we see
20% of what we hear
10% of what we read
Glasser, 1990
Probing: Asking a child how they are solving tasks
For example:
Can you do that another way?
Do you have another way to check that?
I saw you moving your lips and your head, what words were you saying?
How did you work that out?
What did you do to solve that problem?
Show/tell me how that works.
If you did know how to do that problem, how would you do it?
Tell me more about that.
Why does that work like that?
Prove that.
Why do you think that?
How do you know that?
Avoid dichotomous questions such as, "Did you count? Did you start from seven" and questions that embody unwarranted assumptions, "Where did you count from?"
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