Tara: Week 2

Reflection on the week:

This week I decided to continue number talks with addition problems. I chose addition because after experiencing number talks a little bit last year, I realized how difficult multiplication was for them and thought that starting with addition would be a good way to help them build their confidence with number talks and sharing their ideas. Additionally, because I have so many ELL students, it was also a way to continue to have them build their communication strategies as well as work really hard to listen to each other. I thought that addition might be a better choice for this because there was a higher likelihood that they would understand what their classmates did and how it was being described. 

For my first number talk of the week, I did problems of the family: 19 + 31. Below are some screen shots of 

the different classes' strategies. What I found was very interesting! In two of the four classes, the traditional algorithm did not come up by students who were describing their methods. However, in these two classes, I decided to introduce it because I wanted to see if anyone used it. As I introduced it, I began by saying that this is often the way that we learn how to do arithmetic. However, algorithms are meant to be steps that we follow, but are often difficult for us to understand how and why they work. Also, when get into bigger problems, algorithms can confuse us because it is difficult to keep track of all the different numbers if we don't understand where they are coming from. I also said that it is a strategy, and if they used it, that is okay! 

But, I also said that I am going to push them to understand and try other methods as well. When I went through each of the strategies to ask students to raise their hands if they had used that method, there were quite a few people to raise their hand for the traditional algorithm.

In the other two classes, the traditional algorithm did come up and in both cases I did not put emphasis on the method, but did describe the same thing about algorithms and I did in the other classes. Additionally, I pushed the students who were describing how they used the traditional algorithm to use words like "I carried the 10" not "I carried a 1" and "I then added 10 + 20 + 10" and not "I then added 1 + 2 + 1." (As seen in period 1). 

In addition to the traditional algorithm however, I saw someone in every class move around the 1 from the second number to the first number, making the problem a little more easy. Another strategy I saw often was adding the ones and the tens separately. In one of the classes I saw someone round 11 to 10 to add it more easily as well. 

Period 4:

Period 2:

 Period 1:

 The second number talk I did problems in the family of 19 +36. Below are some screen shots of the classes' strategies. I saw similar strategies in this problem as well. One thing that I do want to mention however is that  many of the students have begun to share their ideas, even if they are extremely similar methods as those already mentioned. I am SOOO excited by this, and I have made it a point that I want to hear similar strategies as well. For example, even if a method seems the same but students added in a different order, this is different and I let them know that I want to honor that.

Period 3:

Period 1: 

 Period 4:

Questions as I go into next week:

Overall, I was extremely pleased with how the number talks went this week. I have not had any push back from students and have not heard any comments like: this is too easy or this is for little kids. I'm not sure if it's the way that I framed number talks in the beginning of the year or if these students are being nice and playing along, but the students do not seem like it is a hassle for them or like it is a waste of their time. 

Questions I am left with are: How can I keep up their enthusiasm and positive attitudes about number talks?

How can I help students who have not yet participated feel comfortable sharing?

How can I begin to have students build upon other methods they are seeing?

With all this in mind, this coming week I am taking some advice from some wonderful resources, I have decided that maybe I need to get to know a little more about how students are thinking about numbers using other operations as well. So, I'm thinking that I will do a subtraction problem to see how students are thinking about subtraction as well. 

Melissa: Week 1

I am posting late.  My first week teaching and doing number talks in my classroom was last week.  I faced many challenges and a few successes.  To begin, I am teaching 3 "regular" Geometry classes (composed of 10th-12th graders) and 2 "Freshman" Geometry classes.  Basically, the freshman classes are supposed to lead to the advanced math track with the students taking Calculus their senior year.
Introducing Number Talks
I decided to introduce number talks, to my students, as a way to develop their ability to think flexibly and efficiently about numbers.  I told the students that number talks are a way for them to perform mental math in a way that is more efficient (we talked about what efficient means).  I decided to tell the students this because the school I work at does not have a culture of accepting multiple methods in math classrooms.  Math is taught VERY traditionally.  Therefore, I wanted the students to buy into doing number talks, and I believed the introduction I gave was a way of doing so.  
I also gave my students two goals.
1. Actively listen.
2. Really explain what you were thinking.  I told them that it may seem obvious, but we need everyone in the class to understand and be convinced of our methods.
Basically, I am trying to get the students to see the importance in having a variety of strategies and approaches.
Reflection
My intention was to do two number talks in the first week of school.  I was going to start with two dot talks for the same reasons that Tara mentioned.  I wanted the students to understand the structure and to build their confidence to share their thoughts.  I did the first dot talk on Tuesday in every class.  The number of people whose ideas where shared ranged from 2-5 students.  Also, I felt like the students were super hesitant to do "quiet thumbs." A good number of students in every class half-heartedly put their fists to their chests and some refused to.  My guess is that quiet thumbs are not "cool" so the students are hesitant to get involved in something that seems elementary.  Also, the students seemed content to hear a small number of strategies.  I think this may be related to the math culture at the high school.  It has not been emphasized that math consists of different ways of thinking.  This is going to be something that I need to create in my classes.  So, for the second number talk, I only did it in one class.  The results will similar to those I saw on the first number talk. Finally, I have not had a consistent roster in any of my classes.  I receive new students and lose current students every day.  I was told that this will continue to happen until the end of the third week of school. Tuesday of my second week, I completely lost my first period "regular" geometry class and was given another teacher's freshman geometry class.  This has made it difficult for me to establish norms because I have new students every day.  Therefore, I have decided to wait to do number talks until the 4th week of school.  That is when the schedules will be finalized and I will have consistent rosters.  When I start back up during the 4th week I am going to start with a two digit addition problem.  My students number sense seems to be lower than the students at Fremont HS.  They really struggle with negative numbers, basic algebra, etc, so I think number talks will REALLY help my students.  I am excited to fully integrate number talks into my class!!  Oh, and, another teacher observed one of my number talks and she said "It was really neat."  She asked if she could see a pile pattern task I was doing, but she came too early and she got to see the number talk as well.  Hopefully other teachers get curious and want to do them :)

Wow!  That all sounds really negative.  I do think that the number talks went well in a few ways.  First, the students did have different ways of seeing the dots and all of the classes there was more than one student that shared.  Also, the day after the number talk, a student in one of the freshman geometry classes wanted to share his way of thinking about a problem (which was different than another student's way), so I felt like he valued multiple methods.
Questions   
I am wondering how I get the students to buy into using the quiet thumbs.  I explained the reasoning behind doing it, but it did not seem to be enough.  Is it normal for students to resist it right at the beginning?  I want to stick with using the quiet thumbs because I believe it is the best way, but I also want the students to fully participate.
   

Tara: Week 1

This week marked the beginning of my first year of teaching, and additionally the first week that I used number talks in my classroom. I will begin by describing what I did in my classroom, followed by a reflection, and questions that I have going into the upcoming week.

Introducing "Number Talks"

I decided to sell the idea of number talks to my students as a way to build their flexible thinking by seeing and trying to understand multiple ways of thinking and doing basic arithmetic. I gave them two goals over the course of the year:
1) Push themselves to offer their strategies and methods out loud in class
2) Work on actively listening to their peers' methods as a way to help build their flexibility with numbers
I began this week with two dot talks. My reasoning for doing this was twofold. First, I wanted to build their understanding of the structure of number talks, without the added pressure that arithmetic often brings. Secondly, I wanted them to get into the habit of sharing, listening, and trying to understand other students' ideas and thoughts.

Reflection on the week

I have four classes that I am doing number talks in. Three of which are sophomore classes; these students are taking IMP2, Interactive Mathematics Program. One of which is a freshman class, taking IMP1. 

I was surprised at how mixed my classes were in their reaction to this activity. In the first two classes, both my sophomore classes, they participated, but less willingly. I had to wait to have students raise their hands, but I did eventually have students share their ideas. In the next two classes, students were very eager to share their ideas and to help me understand their classmates ideas. There were several times where I was unsure about how a student counted the dots and needed some help from other students. They jumped at the chance to explain to me what they thought their peer was thinking. I was so impressed by their ability to listen and focus during the dot talks. 

I do feel lucky that my students are all exposed to used to listening to different methods and I think they have already begun building the idea that understanding and seeing multiple methods can help you understand topics even better. So, I am hoping that number talks can reinforce that idea and help them gain more practice understanding, communicating, and thinking in new ways. 

Below you will see pictures of the blackboards for the first dot talk.

Period 1 (10th grade):

Period 2 (10th grade):

Period 3 (9th grade):

Period 4 (10th grade):

Questions as I go into next week

How can I maintain the enthusiasm of my 3rd and 4th period classes as we go into doing number talks with arithmetic?

How can I try and further the sharing and enthusiasm of my first two classes? Also, are they too nervous to share? Or, have they not bought into the idea of number talks? 

Additionally, the native language of over 90% of my student population is Spanish. Could this be affecting some students' willingness to share their ideas?

I think I want to start with addition next week, but am still having trouble deciding on which problem to begin with. I don't want to give them a problem that is too hard, because then it may further shut students down or curb the enthusiasm of others. On the other hand, I am afraid if I make it too easy, they will think it is too childish. 

Right now I am definitely leaning towards giving them an easier problem because I want everyone to be able to access it, and I don't want them to feel bad if they struggle with it. I'd rather it be too easy and then move to a more difficult problem if they are comfortable with it.