Video Reflection: Lesson on Patterns

The purpose of this Lesson on Patterns was for the students to generate and recognize the relationship between numbers in a series that were based on a specific mathematical function. By physically performing the function of "the magic doubling pot," students would be able to see the rate at which the number of coins grew with each repeated doubling.  Ultimately, the teacher wanted the students to express this relationship in mathematical terms such as, for any given number of coins (Cn) put into the magic pot, the number of coins that came out would be equal to Cn + Cn or 2Cn. 

What techniques and strategies are used to orchestrate and promote student discourse and how effective are these strategies implemented?

At the beginning of the lesson, the teacher had the class seated on the rug near the front of the class. During this point in the lesson, the teacher encouraged student discourse through questioning and, once, sharing their thoughts with a partner. When a response was incorrect or not forthcoming, she reworded her question or narrowed its scope. To confirm the students knew what to do for the lesson, she had them repeat back to her their understanding of the assigned task. Students then went on to work in groups. The teacher identified a student resource person for each table in the event there were questions as to what they were supposed to do. Had the students been more comfortable with estimating, this step might have been useful in promoting discourse between students of differing levels of competence. Unfortunately, many students got hung up on this step which demanded more of the teacher's attention than she had anticipated. After the lesson, the students returned to conference on the rug and discuss their findings and misconceptions. The only part of the discourse that seemed to be a necessary digression was the verbal description of large number addition with manipulatives near the end. It was clear from one student's groan that he was losing patience with this part of the conversation as it drifted away from the function under consideration.

What evidence is there that students have learned the mathematics being taught?

From the students work it is clear that students 3, 4 and 5 understood the function taking place when the coins from the pot were put back in to be 'doubled' again. Student 1 may require more discussion to appreciate his misconception, that relationship was an addition of 10 each time. Student 2 seems to have come to understand the error of his reasoning and at least began to correct it before losing steam. In the post-lesson discussion, it appeared that many of the students could express why the misconception of Student 1 was incorrect. I am not convinced whether he could. 

If you were asked to teach this lesson, what changes would you make and why?

I would pose the problem as a dilemma and, through questioning, have the students examine both possible outcomes. From examining the students' work, they appeared uncomfortable making a choice between A and B. Perhaps they did not want to be wrong. Perhaps they sensed that they needed more information to make their decision. If they were generating a recommendation instead of guessing at a result, the students could save face if their 'gut' response proved incorrect. 


The following are some suggested questions: 
"The old couple has asked our class to help make this decision. Should they take the 1000 coins or should they take keep their original five and accept the magic pot? How might we go about finding out?" 
"How many coins would the magic pot need to make for the magic pot to be the right decision?" This question gets the students to at least express what a more favorable number of coins might be. 
"Without doing any math on paper, about how many coins do you think the old couple will have if they use the pot 10 times? How did you come up with this estimation?" (Model this with the students as a group. Accept multiple answers and rationales.)
"The In and Out box table helped us keep track of our data when we imagined putting one, two, or three things in the pot. How might we use the same table to help us solve this problem?" This last question will get the students to explain how to modify their use of the table from the first In and Out Box and express why the numbers in it look so different and, eventually, so large.


Overall Use:


I found watching this teacher's methods, planning and reflections to be an excellent experience and I am so grateful. It was very forthcoming of this teacher to allow her skills to be examined so publicly. I hope to be as brave and skilled myself one day. Having observed her model the process, there is a better chance I will be. My only criticism was that I didn't get a real sense of the flow of the lesson as it was shown in such short snippets. After watching so many vignettes I found it hard to find the passages I wanted to review. I will definitely refer back to this resource in the future.