To update, I did not do a number talk during week 2. I was going to wait until the 4th week to start back up, but I decided to start during week 3, instead. It was brought to my attention that it would be better to build the norm and routine of Number Talks at the beginning of the year (even if new students are added to my classes, etc). After much thought, I decided to begin with a multiplication problem. I chose to begin with multiplication because I felt like the dot talks were thought of as childish by my students. So, I wanted to give them a more challenging, yet accessible problem.
Reflection
The first number talk of the week was 18 x 3. Periods 1-3 had three strategies shared, period 5 had 4 strategies shared, and period 6 had 2 strategies shared. In every class, one student shared the traditional algorithm. I did not push back on that strategy by requiring the students to make sense of it. Rather, I introduced the strategy as the "traditional algorithm" and told the students that this is how we have learned how to do arithmetic in America. I mentioned that this strategy will get more difficult as we increase the difficulty of the problem. I also encouraged the classes to try a new strategy next time we do a number talk. When polling the classes on how many people did each method, the traditional algorithm was by-far the most popular method.
It is important to mention that the traditional algorithm was not the first method shared. Instead, students with other methods shared their methods first, then the traditional algorithm was shared. It seemed like the students felt as though the traditional algorithm was the correct method. Comments were made like, "That is too complicated. Why would they do that?" in regards to non-traditional algorithm strategies. I eagerly welcomed comments regarding wondering why a method worked and there was some enthusiastic discussion in a few classes.
The second number talk of the week was only done in first period. I had them do 18 x 6. I was curious whether the students would try new methods or if they would see a connection between 18 x 3 and 18 x 6. I was disappointed when only 2 strategies were shared (1) traditional algorithm and (2) distributive property. Over 70% of that class used the traditional algorithm and no one shared a strategy linking the previous number talk's solution. I decided to not have the other classes do the number talk because first period did not get through the rest of the lesson. I need to make more time for the number talks so that way I can get through the entire lesson. So, I am going to do 18 x 6 in week 4 and then I might give the class a simpler two 2-digit multiplication problem.
When introducing the number talks this week, I did not use the phrase "quiet thumbs" and I seemed to get more students to participate. However, there were a few students that put down their fist as soon as I wrote the problem on the board. I cannot say why they did this, but it is my goal to get all of the students to do the problem and use the thumb indicator.
Also, I want to get different students to share their ideas. There are already students who regularly share and I want to help all students to feel comfortable sharing their ideas. I think this will improve as the classroom culture develops and the students become more comfortable with one another. However, I am wondering if I could use another strategy to encourage those that are nervous to share while still maintaining the structure of the number talk.
I saw your KSTF poster presentation and plan to begin implementing some number talks in my classroom this year. Thank you and Tara for sharing your stories and introduction to number talks. It has really helped me as I begin to think about how to introduce number talks to students, colleagues, and eventually parents.
ReplyDeleteA couple of questions I have:
1) To clarify, am I correct that you present students with a problem on the board and give them a set amount of time to solve it without any paper/pencil? How long do you give students on average?
2) Do you have a number of strategies already planned out for each number talk? How do you 'end' a number talk? What kind of questions do you pose for students after they present their strategies?
I'm excited that you are planning to try some number talks this year!
ReplyDeleteTo answer your questions:
1) Yes, you present a problem on the board and have students silently think about the answer. We usually have students begin the number talk with a fist on their chest and when they have the answer in their head, they are to put their thumb up to show that they are done. This strategy allows students to take their time and not feel rushed to solve the problem quickly because some students will take longer than others to make sense of the problem. On average, I would say 30 seconds is how long they need. If they need more than one minute, that is a good indication that the problem was too difficult for them. At that point, I would just switch the problem to something a little easier--most of the time when this happens students are relieved to see you change the problem.
2) Usually before the number talk I will think of at least three different strategies that might be shared. For me, this is to practice ways to record the problem. I found that at first this was one of the hardest parts of the number talks as the teacher--trying to accurately and appropriately record student thinking on the board. To "end" a number talk, I usually wait until there are no more strategies that students want to share and then quickly run through each strategy, asking students to raise their hand if they used "_______'s method." This way, if students didn't have an opportunity to share a new strategy, they feel like they can still indicate how they approached the problem. In terms of questions, I usually pose questions which may seem obvious to the student explaining, but that help the class follow along. For example, when a student is describing how they did 29 + 36, and they say, "I added 9 and 6 and got 15." I would further prompt, "where did the 9 come from? What about the 6?" Sometimes I will ask these types of questions to the class as well, as a way to involve other students in the number talk. Other questions I ask include: • “Can anyone explain ___’s method in your own words?” • “Can you see any similarities between strategies on the board?”“Can anyone see how someone might have found ___ as an answer?