Melissa: Weeks 4 and 5

These past two weeks have been hectic.  But, I managed to do 4 number talks. 

Week 4:  I decided to switch to addition problems part way through the 4th week because the students were not seeing the value of nontraditional algorithm methods.  I figured this may be because they have not thought of multiplication flexibly.  So, I wanted them to have some success with number talks and I wanted to hear from several different students (as opposed to having two strategies for multiplication).  So, I began with 19 + 26.  All of the classes had several different strategies and the attitude towards number talks seemed positive overall.  New students began sharing and students even asked each other questions.

Week 5: I wanted to build off of the momentum from the 4th week, so I had the students try 28 + 17.  This problem gives the same answer as 19 + 26 but it pushes the students a little farther by using 8 and 7.  In fact, in only one class a student shared the traditional algorithm, but they did it a little different.  So, the students seem to be understanding that the the traditional algorithm is not always the best strategy and they are even seeing similarities in each other methods.  Some students have said things like, "His method is almost the same as mine, but I did ______ instead of _______."  I am going to continue with addition and focus the problems on a certain strategy.  Then, I plan to get back into multiplication.  In one class where 2 people tend to be the main "speakers", seven different students shared their methods and I had to have other students hold theirs because of time.  So, I am beginning to see the students' confidence with number talks increasing.

I do not have questions, at this point, but I do have a couple goals for myself:
- I am working on getting different voices, so I have been saying, "I want to hear from someone whose method has not been on the board, yet."
- Quieting the side conversations while a student is sharing their method.  I think the students think my voice is the only one that really matters, so I am working on having the students see value in each other's ideas.

Tara: Week 3

Reflection on the Week:

In my last reflection I talked about how I wanted to get more information about how my students were thinking about many different kinds of arithmetic problems, so I decided to do subtraction problems this week. Due to scheduling at my school this week, I only had time to do one number talk. In my first two classes I decided to give subtraction problems.

The minute I put the problem on the board, I could immediately read my students’ faces—they were not confident and some even chuckled or mumbled curse words under their breath. When the number talk began, I got four or five different answers in each class. In reflecting on this, I am glad that my students feel comfortable providing multiple responses to a problem that they know there is only one answer to. However, I could tell that students were nervous and not confident to share their strategies. When strategies were shared, students had a really difficult time explaining their thinking. Although several students did use the traditional algorithm, many others did not. However, many students somehow got confused in their thinking about subtraction—whether it was taking away too many and not adding some back in at the end, or trying to use strategies that they used for addition, which did not transfer over perfectly for them in this case. I really pushed students to try and make sense of what other students had done in their heads and where their thinking may have gone astray. However, I could tell that my students were not as interested in this number talk as they had been previously.

This happened in both of the first classes that I did this number talk in. However, for the second two classes I decided to go back to addition. I did not want to lose the steam that I had from the previous number talks and I still wanted students to be excited by the math and the number talks themselves. Hence, I went back to addition. The problems that I decided to use were a variation on the previous week’s number talks, except this time using 100s. The problem I used was 109 + 26. This number talk went much better than the subtraction ones. I had more student participation, more student-to-student interaction, and more enthusiasm from my class. I think that while this problem was more difficult for them, and in fact I did get multiple answers for the solution in both classes, it was something that they had been thinking about previously. Because they had previous experience with this type of problem, they were able to follow along and easily figure out where their classmates may have made an error. They did not have to spend time and brain energy trying to understand the problem itself or trying to understand new strategies presented, as in the subtraction number talks , instead they could focus on methods that they had previously seen and why/how someone may have made an error. I am very glad I decided to switch up this number talk because I think that my students were able to get more out of it, and I think I was able to maintain buy in with these two classes.

Questions that I still have:

1)      How am I going to proceed with my first two classes?

 I understand that while my decision to use subtraction may have caused some students to disengage from the problem, I am hoping to bring back addition this week and see how it goes. I am hoping that brining back an addition problem that can employ similar methods as before will allow students to feel confident again with number talks and will help them gain more buy in with them as well.

2)      For my other classes, should I keep going with a string of similar problems to the ones that I have already done?

I think that I do want to continue using similar addition strings, but add in more complexities such as two triple digit number addition instead of a triple digit and a double digit. I think that this adds a layer of complexity in that students now have to keep track of more numbers and decide how they can move numbers more flexibly. I may continue with one more number talk involving a triple-digit number and a double digit number.

3)      Something I am still thinking about and wondering about is how to get new students to participate. I have had many of the same students participate in the number talks in the past few weeks and I want to be sure that other students are able to have their voices heard. I am wondering if I should do a written explanation at some point soon, just so that all students have an opportunity to share their idea and then I can consolidate results and show them how many different methods were used and how many people chose each method.

4)      Another thing that I am still thinking about is how to get students to try methods other than their own. I think that some students have begun to do this but I am not sure about students who do not feel comfortable sharing their ideas with the class and are a little more quiet. I have tried to ask students to raise their hands as a way to show if they used particular methods once they are up on the board, but this is sometimes difficult to tell if that is really the method that they used or if they are just raising their hand to raise it. Also, I have noticed that some students never vote.

5)      I am also thinking about how I can get some feedback from students about his process so far. I think it could be beneficial to see how they are feeling about number talks. In the next few weeks I might provide them with some kind of reflection piece about number talks just to get a feel for how and what they are thinking about the experience so far. 

Melissa: Week 3

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.