Operations for Breakfast

Daily routines (arriving at school, washing hands, eating breakfast, lining up) provide opportunities to get children talking about their ideas. In the following clip, Ms. Torres engages her 3- and 4-year old preschool students in an informal conversation about number and operations during breakfast time. Watch as she invites children to talk about the apples that Samantha is going to eat.

Teacher's Voice: Supporting participation through drawing on children’s home language 
On this day you can see that David was picking up on what we were talking about, but we asked how many were left he answered “una!”  So in his case (in this informal setting) I chose to respond to him in Spanish. Samantha on the other hand was trying to use English, so I responded to her in English. It comes back to that you really have to pay attention to your children and get to know them to see what they're trying to convey.                           -Dolores Torres, preschool teacher

Questions for reflection

• What mathematical ideas emerged during play?
• What was Ms. Torres’ role in supporting children’s sense-making and varied ways of communicating?  
• In what ways were the children given space to participate?  
• Where could you look for opportunities to “mathematize” play in your work with young children?

Discussing Monkey Bars during Transition Time

Here's another example from Ms. Torres' 3- and 4-year old preschool classroom. During a transition between different parts of their daily classroom routine, Ms. Torres' students want to share about recent experiences on the monkey bars. Watch as she builds on children's stories with purposeful questions to enrich the mathematics within this informal space.

Questions for reflection

• How would you characterize Ms. Torres’ role in enriching the mathematics during this informal space?  
• What math ideas were highlighted during this interaction?
• In what ways were the children -- Emanuel and Julien (the main speakers in this video) as well as others-- given space to participate and engage in the math?  

Debbie and Brayton Set Up a Garden Party

Finding opportunities to enrich and extend the mathematics from children's play is an intentional focus for Ms. Franchi, who teaches 4- and 5-year olds. Watch as she engages Debbie and Brayton, who have been playfully setting up a backyard garden party next to the dollhouse.

Questions for reflection

• How did play support Debbie and Brayton's interactions with each other and with the math?
• Ms. Franchi asks a vareity of intentional questions to enrich the math. What questions does she ask, and how does each question support mathematical reasoning?
• What other questions could Ms. Franchi have asked, and why? How would each question build from children's ideas, words, and actions?

See full transcript of this video here.

Patrick Counts Keys

The learning doesn’t stop after children have counted their collections (see Counting Collections Overview for more information about this activity)! Children will often count or organize their collection in a different way. Teachers can also ask questions that provide opportunities for children to begin to think about the mathematical operations (addition, subtraction, multiplication, division) in the context of the collection they have just counted. The goal is not for children to learn the formal names or symbols for the operations, but rather to begin to think about how different actions might change the amounts in their collection. Making sense of these actions and relationships in context provides a foundation from which to build understanding of the operations. See Supporting Counting to Problem Solving for more details about engaging children in this way.

Watch as Patrick counts his collection of keys.

Questions for reflection

• What happened?  Be as detailed as you can.
• What mathematical ideas does Patrick get to work on with his teacher?  What is he able to do?  
• Can you describe his strategies for solving each problem?  
• What other kinds of questions could you ask Patrick about his collection of keys?  

Leo organizes cubes by color

Many children, when asked to count a collection of objects, will choose to organize or sort their collection according to some attribute, such as color or size.  These occasions can provide wonderful opportunities to build from the child’s ideas about what is important or interesting about their collection. See Supporting Counting to Problem Solving for more details about engaging children in this way. 

In the clip below, Leo decided to organize his wooden blocks by color.  Watch as his teacher, Ms. Gaxiola, observes and then follows up on Leo’s thinking.

Questions for reflection

• What did you notice in this clip?  
• What mathematics does Leo understand?  How do you know?  How were we able to learn this?
• What else would you like to learn about Leo’s mathematical thinking?
• Ms. Gaxiola asked Leo, “Which of your groups has the most?” and then, “How do you know it has more?”  What other kinds of questions could you have asked Leo about his collection?