Our modules include video interviews or observations to introduce students to children’s mathematical thinking.  Our major method involves Thinking Stories that present short video clips along with a detailed discussion of their significance for understanding children’s mathematical thinking. Magic Math Minutes, such as this one about measurement, are very, very short Thinking Stories. The modules also present corresponding unedited videos—that is, videos that form the basis for the Thinking Stories, but do not offer commentary.   

There are several ways in which you can use the Thinking Stories and/or the corresponding unedited videos in your teaching, in a live class or on-line.  (In the Pedagogy of the Video Clip, for example, I discuss how I used unedited videos in my live classes.) 

1. You can ask your students to read and watch a Thinking Story as a homework assignment, much as you would have them read a journal article, and then not use the unedited video at all. 

2. You can ask your students to review the unedited video before class; you can then review it with them in class; and you can ask them (or not ask them) to study the corresponding Thinking Story after class. 

3. You can ask them to read and watch the Thinking Story before class; you can then review the raw video with them in class. 

4. You can review the Thinking Story yourself before class; you can then review the corresponding raw video with the students during class. 

Each of these methods, I think, is worthwhile under different circumstances; each method may hold different appeal to individual instructors.  You decide. 

Below are some suggested exercises for reviewing specific unedited videos either before examining them in class or before reading the corresponding Thinking Story.  The exercises involve a series of questions that the students should consider as they interpret the video.  Of course, you can choose not to ask some of the questions and/or ask some different ones.  

Anna Counts involves a little girl counting out loud from one up to 99. 

• First, watch the entire video (below) from beginning to end.  Then review it and think about these questions.  When you answer them, be prepared to cite specific video evidence to support your interpretation
• How many numbers do you think Anna memorized?  How do you know they were memorized?
• How do you think Anna managed to say the numbers from 20 to 29?  Did she memorize them?  What other method could she have used?
• Why did Anna place a special emphasis on the words “twenty-nine?” and “thirty-nine”?
• After “thirty-nine” Anna asks, “What comes after three?”  What is that all about?  How do you explain the math idea behind Anna’s question?
• After Anna gets to “fifty,” the adult asks her to count further.  What do you think of this request?  How would you respond to someone who says that it is developmentally inappropriate to ask a young child to count so high?
• How would you describe Anna’s motivation, interest, and affect?
• What would you say about this statement? “Counting to 100 is just a dull memorization task.”

Ben Learns How Many deals with a little boy’s understanding of cardinality—how much.

• First, watch the entire video (below) from beginning to end.  Then review it and think about these questions.  When you answer them, be prepared to cite specific video evidence to support your interpretation
• In Part 1, Ben begins by putting out 5 “apples” (red checkers), without counting out loud.  Then he checks.  What do you notice about his checking?
• The examiner puts them in a straight line and asks Ben, “How many apples.”  What did Ben do in response to that question?  What could he have done?
• The examiner then spreads them out and asks how many there are “altogether.”  Why did Ben count them?
• In Part 2, when the apples are spread out, Ben immediately answers that there are three.  He said later that he counted them.  How else do you think he could have gotten his answer?  
• How do you interpret Ben’s response when the apples were covered by the sheet of paper?  

This Magic Math Minutes video shows Saniya and Mia placing circles on a grid.

• First, watch the entire video (below) from beginning to end.  Then review it and think about these questions.  When you answer them, be prepared to cite specific video evidence to support your interpretation.
• At the outset, the interviewer, Mia Almeda, asks 5-year-old Saniya, “Can you make yours the same as mine?”  Saniya succeeds, making a vertical line.  She succeeds a second time too, making a horizontal line. But when Mia makes the diagonal, Saniya cannot produce a copy.
• Why do you think that she might have had a problem making a diagonal line?  
• What kind of thinking does making a diagonal line demand compared with the vertical and horizontal lines? 
• How would you describe the girl’s reaction to failure?

Ben Learns How to Add deals with a little boy’s understanding of addition.

• Watch the entire video (below) from beginning to end. Then review it and think about these questions. When you answer them, be prepared to cite specific video evidence to support your interpretation.
• The hiding game. At the outset, the interviewer hides some chips under a pink piece of paper and then puts more under it.  Ben was asked to show how many were under the paper.  
• How did Ben solve the problem? 
• What did he have to know to solve it?
• What do you notice about his language?
• What does this video say about his understanding of addition?  
• The pirate game.  At the outset, Ben is very excited to learn that he will play a new game in which he was required to “predict” the number of chips in the bag.  Please answer the same questions as above:
• How did Ben solve the problem? 
• What did he have to know to solve it?
• What do you notice about his language?
• What does this video say about his understanding of addition?  

Patterns and Algebraic Thinking involves Brian and a sequence of towers with blue and white connecting cubes.

• First, watch the entire video (below) from beginning to end.  Then review it and think about these questions.  When you answer them, be prepared to cite specific video evidence to support your interpretation.
• At the outset, the interviewer asks Brian to make the 4th tower.  How do you think he managed to make it?  What must he know in order to make it?  
• The interviewer asks Brian to describe what the 5th tower would look like (before he actually makes it).  Do you think his description was accurate?  How did he know there would be 5 blue blocks?
• How did Brian figure out how to make the 8th tower?

Bella and the Cubes: A Measurement Mystery involves measuring using connecting cubes.

• First, watch the entire video (below) from beginning to end.  Then review it and think about these questions.  When you answer them, be prepared to cite specific video evidence to support your interpretation.
• The interviewer asks Bella, “How many cubes do you think you would need to measure how long that is?”  How did Bella figure out that she needed 6 cubes?
• Next, the interviewer asks Bella, “So how many cubes long is the orange stick?”  What do you think of Bella’s answer?  What does it say about her understanding of measurement?