Wednesday, November 28, 2012

Tara: Weeks 10-12

10th grade

During these next few weeks, I continued with multiplication for my 10th grade students, but crossed into double-digit numbers and even some triple digit multiplication. 

It was interesting to see how the students reacted the first time I put up a double-digit multiplication problem. You could literally hear sighs in the classroom! However, as I continued to do them, I got less and less push back on the difficulty. What I found is that the students who offered their answers were able to transfer strategies from the earlier number talks to these more difficult multiplication problems.  

One struggle that I still have is that I believe a few students are really struggling with their basic math facts and this is seriously inhibiting their ability to participate in the number talks. I can think of at least 5 students who do not have their basic multiplication facts memorized (like 6x8). I'm not quite sure how to have them still participate fully during this time and at the same time continue to push the other students in the class to think more deeply about multiplication. 

Another thing that I ran into during these number talks was that students were not distributing when they were breaking up numbers. For example, the number talk 15 x 13. There were some students who wanted to break up the 15 into (10 +5) and the 13 into (10+3) and then they wanted to multiply. However, they were not distributing when they multiplied so they were only performing these operations: 10 x 10 + 5 x 3. 
This brought up a good discussion in each class and I was able to introduce the area model for them to see why we had to distribute. 

Below are some of the number talks with two digit multiplication. 
1st period:
2nd period:
4th period:
1st period:

4th period:

I am planning to stay on multiplication throughout the rest of the semester, however am transitioning to using money to have my students think about bigger numbers. For example, I will do problems like $1.99 x 6.
I am hoping that they will use strategies they have already seen to think about these types of multiplication problems and I am hoping they will also come up with new strategies because of the different context of money.

Sunday, November 25, 2012

Melissa: Weeks 11 and 12

I started to see a little more success during these weeks.  There was more participation from students that do not typically share.  The students seem to be gaining confidence and there were even positive remarks from the students.

First Period: All Freshman Geometry.  This class was given to me several weeks into the school year so we are still working on providing other methods besides the traditional algorithm.

Second Period: 10th-12th grade Geometry.  This class is one of my more challenging classes.  The class is predominately male and it is not "cool" to have high academic status.  So, assigning competence  has proved itself to be challenging.  Specifically, David F. has very interesting and valuable ways of thinking, but he tends to act out.  So, I was pleasantly surprised to see David volunteer his method.  Luis and Guadalupe rarely volunteer their ideas during whole class discussions, as well.  And, Garrette regularly shares and he has high academic status, but he was not listening during the number talk and he shared Guadalupe's strategy.  Hence the "Not paying attention" note.

5th Period: 9th Grade Geometry.

 6th Period: 10th-12th Grade Geometry.  This class' culture is very similar to my second period's.  Again, I was pleasantly surprised by the students that shared their thinking.  Valentin is an EL senior student that seriously struggles in math.  While he did show the traditional algorithm, I was happy that he was the first one to share his ideas.  Amanda is also a senior and she has an IEP.  And, Denzell is a junior that has high social status.  I haven't done number talks with this class because they are my most challenging class.  I have six students with IEPs in this class and the classroom management has been a constant struggle.  After this number talk, several students mentioned that they had never thought about "borrowing" like Denzell and Amanda did.  Most of the students did the traditional algorithm when I polled them, but they were very enthusiastic about seeing the other strategies.  After this, I decided that this class needs to do number talks just as much as the other classes.  And, when I did a number talk the following week, more students raised their hands for methods besides the traditional algorithm.

Looking forward, I am going to start percents.  I am anticipating more challenges, but I am going to remain positive.  Because the high school I work at serves a very rural and low income demographic, I am still thinking about how I am create a number talk that will build on their experiences (like we did last year with the milkshakes - my students do not go off campus for lunch and the town they live in is in the middle of the desert so there are not really any common restaurants that I can use).  I am going to talk to another teacher to see if there is something he thinks I can use.  I will update on how it goes!

Monday, October 22, 2012

Melissa: Week 10

Before I begin my reflection on Week 10 I want to talk about what happened during weeks 5-9.  I inconsistently did number talks during those couple of weeks.  There were a few weeks where I did not do a number talk at all or other weeks where I did a number talk in one class and not in others.  I wish there was a good reason for why I did not do them, but there isn't.  I think a lot of the reason is because of time.  During those weeks, I had the number talks on my lesson plan but ended up not doing them.  I guess I did not make it a priority.  Also, I felt like my students did not see the benefit and had negative attitudes about number talks.  So, I saw it as another challenge I would have to deal with in the period.  Rather than facing the challenge and trying to overcome it, I guess I ran away.  However, I still see great benefits in number talks and I want my students to enjoy them so I did one number talk last week (109 + 26).  I wanted to give the students a problem that all students would feel successful on, but that was enough of a challenge for the students that have been successful earlier.

In all of the classes, the traditional algorithm was the most used strategy.  However, it is not a strategy the students choose to share in front of the class.  When polling the students on which strategies they used, the traditional algorithm gets the most hands.  However, there are many different methods students use that break numbers down and are flexible ways of thinking.  Because I had a long lapse between doing number talks, I am not surprised at the amount of students that still do the traditional algorithm.  In the same vain, I noticed that the same students are the ones to volunteer.  However, more students raised their hands to share out the answer and I did get a couple new kids to share their strategies.  The main issue I faced was that students did not seem to see the value of hearing other people's strategies.  The students I work with are mainly motivated by getting a "grade" for work they have done.  In general in my class they will ask, "Are you collecting this?  Are we going to get a grade?"  They only want to do work if they will get a grade for it.  So, it is hard to motivate them to participate and be involved in things that are not graded.  Going into this next week, I am going to continue on with addition because the students are still not confident sharing and I want more students to try other methods besides the traditional algorithm.  I am going to consistently do number talks, regardless of challenges that may arise.

Sunday, October 14, 2012

Tara: Weeks 4-9

Wow! As the first quarter of teaching wraps up for me at school, I have finally had some time to sit and reflect further on number talks.
I have been consistently doing them anywhere from one time to three times a week depending on our schedule. I have had several challenges and several successes during the past 5 weeks and I want to share some of these now.

Number Talks with Addition

I have taken my number talks in two different directions depending on my classes. As I have discussed before, I began with addition problems, mainly focused on problems that could employ strategies such as rounding, moving numbers flexibly (for example 19+ 34 is the same as 20 + 33), and breaking down numbers into tens and ones.

Here are some highlights of the boards from some of the number talks with addition. I spent 6 weeks doing addition with my students. By the end, students were getting much more comfortable using strategies besides the traditional algorithm and were bringing up the same methods during each number talk. On the other hand, I would say only about 60% of my students have shared their strategies. I have been pushing new students to  try and explain their methods, but it seems like the same students are constantly wanting to share. This is still a challenge that I am facing and I hope that I can work towards pushing these quieter students to eventually share their ideas.
9th grade class:

10th grade, Period 2

10th grade class, Period 1

10th grade class, Period 4

10th grade classes--Multiplication Number Talks

In my 10th grade classes, I decided to take my number talks in the direction of multiplication. I decided to do this for a few reasons. First, in these classes we are doing a unit on area and volume and I thought that doing problems with multiplication could fit nicely into making number talks fit a little more closely with the curriculum. This coming week I plan on introducing the area model for multiplication as I think that it can connect some of the things we have learned about area with the number talks. 
Secondly, I decided that multiplication would be a nice transition from addition--it can be a little more challenging, but I was hoping that students would be able to use some of the strategies that they had for addition with multiplication--primarily seeing numbers as tens and ones and being able to break up numbers to make the problems more simple. 

So far, I have seen students using strategies such as those mentioned above and have been impressed with students' thinking about the multiplication problems. In my first set of number talks on multiplication, not one student mentioned the traditional algorithm, although I'm sure some students still used this method and it has come up several times since then. I presented the problems such as 

Below are some of the boards with the number talks with multiplication. 

10th grade class, period 1

10th grade class, period 2

So far I have not used multiplication problems with two double digits and that is my plan for this coming week. I think that this will lend itself to introducing the area model for multiplication as well. 

9th grade class: Percentages

For my freshman class, I decided to do percentage problems with number talks. The reason I chose this is because they are currently in a unit on probability. I thought this would be a good way to strengthen their idea of percentages and flexibility in working with percentages. Additionally, when we did percentages last year at Fremont, my students seemed to be scared of percentages initially, but I think that my students definitely had a breakthrough in thinking about percentages during these number talks. I am excited to see how my current students are thinking about percentages and if they have a similar experience. 

My freshman were pretty nervous when they first saw me put up a percentage problem and there were many groans around the room. However, I think that some students have really started to catch on to some of the strategies of their classmates. I had one number talk where 5 different students shared their ideas (see below). Again, a challenge is still getting all students to participate in sharing their thinking. I have not yet done a pair share with my students and I think this is something I want to try this week. Or, another idea would be to have them record their own strategies and collect them so that I can see how individual students are thinking about these problems as well. 

Below is one of the number talks done with percentages:

Monday, September 17, 2012

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.

Tuesday, September 4, 2012

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. 

Monday, September 3, 2012

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.

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.