Learning and Collaborating

This post was originally posted on my classroom blog for parents. I thought it might be of interest to readers of this blog, too. 

Graphing
On Friday one of our math activities was to create a graph of the number of letters in our first names. I decided to use this as an opportunity to reinforce my lesson that we are all always learning and that we can all figure things out. To do this, I decided to have us create the graph using the graphing feature of Haiku Deck. I told the crew that I did not know how to do this yet but that together we would figure it out. We began by gathering our data (number of letters in our first names) and then set out to figure out how to create a graph in Haiku Deck. We had to experiment with several of the buttons or features to figure out how they work. We had to start over at one point when we decided that our graph would work better with a different orientation. Lots of math was involved in our discussion because we had to find the minimum and maximum values of our data as well as how big the intervals would be. But we did figure it out. The only thing we couldn't do was add labels to each axis of our graph. (I think this is because this is presentation software and they try to limit the amount of text on a slide.)

At this point someone in the crew suggested that we put our graph picture on the camera roll of the iPad and then import it into ShowMe and add the labels there. This was a great idea but I showed them that Haiku Deck didn't have import to camera roll as an option. They all just looked at me wondering why I couldn't figure this out. They said again, just put it in the camera roll and I still didn't understand what they meant. Finally someone remembered that the language they were looking for was to take a screen shot. Brilliant. They were absolutely correct and were connecting our prior learning about taking screen shots to this lesson. We took a screen shot and it was instantly added to our camera roll. (This is when we lost our internet access so I went in later and added the labels to our graph. I used Skitch - which they know how to use, too - instead of ShowMe to add the labels because I wanted to show them how professional it can look with the labels typed instead of handwritten.) Below are pictures of the two graphs - with and without labels.

The best part of this whole lesson is that they saw that I was still learning and that we all worked together to figure out how to create the graph we wanted. I want them to become life-long learners who are willing to jump in and try to figure things out. This lesson was a great example of using all of our 4Cs - creativity, collaboration, critical thinking and communication. These are the lessons that make my day.

Reaching Understandings

Students who struggle in math often lack number sense.

As students build their number sense, mathematics takes on greater meaning. Mathematics becomes more about reaching understandings than following rigid sets of rules. With strong number sense, children become more apt to attempt problems and make sense of mathematics. It is the key to understanding all math.

                                                                      -Jessica Shumway in Number Sense Routines (p.8)

These words tell exactly how I feel about math and math teaching and learning. The phrase "reaching understandings" is just where our focus should be in math. All too often we go straight to "following rigid sets of rules" and this is where we lose students. The "rules" are complicated and meaningless to most students. We need to be helping students explore their own ways of solving problems rather than memorizing sets of rules.

I compare this to reading instruction. What do we really think matters the most in reading instruction? I think most of us would agree that comprehension or making meaning of the text is our ultimate goal. We have learned that focusing only on the rules (phonics, etc) in reading can and usually does lead to readers who tend to be word callers - those who read words correctly but don't understand what they are reading. We know that we need to focus on the meaning of the story being read along with using some decoding strategies. Often the most successful decoding strategies are based on using meaning - thinking about what the story is about, using background knowledge, using context clues, using picture clues, etc. We need to do a blend of meaning and rule following in order to become readers, but we always need the emphasis to be on meaning.

Having number sense and "reaching understanding" in math is similar to comprehension in reading. We may need a blend of rule following and understanding to become mathematicians, but the emphasis should always be on understanding. Always. While not a popular argument, students will be able to use calculators and computers to do those tasks that fall under the "rule following" category, but they will still need to be able to decide what makes sense in a given situation or if the "answer" that they get from their calculator or computer is reasonable. When students have number sense and deep mathematical understandings they will not only be able to decide if an answer is reasonable but they most likely won't need a tool to help them with the computation very often.

I am passionate about this and have been working to make shifts in my math teaching to ensure that students have time to develop deeper mathematical understandings. Thankfully, there are many books out there to help (written by other passionate math teachers). The picture below shows some of the books I have read that have influenced my thinking. I would highly recommend them all. Who or what is influencing your mathematical thinking right now?

Number Talks by Sherry Parrish
Math Exchanges by Kassia Omohundro Wedekind
Number Sense Routines by Jessica Shumway
Teaching Student-Centered Mathematics by John A. Van de Walle

New Books Arrived Today!

My new (to me) math books arrived today. They will complement my current collection of math books nicely. I can't wait to start reading. I still have to wait a little while for Opening Minds by Peter Johnston but it should come soon.

Math Workshop ~ Follow Up

It is way past time to reflect back on how moving to a math workshop is going in my classroom. Overall, I am very happy with how things are going but I have to admit that things are not going exactly how I planned. Isn't that often the case, though?

I had planned to start slowly and begin meeting with one small group each day towards the end of our Math time but that turned out to be more difficult than I expected. I was always so involved with working with individuals that I lost track of time and didn't have time to meet with my new group. I think I was having trouble changing how I used my time each day. I couldn't break out of my normal math routine. So I had to come up with Plan B.

Plan B was to do Everyday Math on Monday through Thursday and then spend all of my math time on Fridays meeting with small groups to do Math Exchanges type work. This is going very well. My class and I really look forward to Fridays. We do three rotations during which I meet with 3 different heterogeneous groups of 4 students. My Educational Assistant (who also happens to be a certified teacher - I know- how lucky am I?) also meets with 3 groups during these rotations, too. This means that we are able to meet with almost all of our students every Friday. We rotate through the groups so that we eventually see all of the groups.

While this is going on, the students not meeting in a group with one of the teachers do other math activities. We have various centers that they can choose from including computers, Everyday Math games and other math games. We have a parent volunteer who comes in and helps manage these centers and answer any questions that might come up. So far it is running very smoothly.

The best part for all of us is the discussions that we have when meeting in the small groups. The kids just jumped right in and were willing to tackle tough problems together right from the start. One of our most recent problems was:

Jill has 10 cookies to share with her friends Mary Beth and Dee. How many cookies will each friend get?

As the first group and I read the problem together, one student immediately started shaking his head saying this won't work. The other students ignored him at first and counted out 10 blocks to begin dividing up the cookies. It didn't take long before the conversation started. They couldn't figure out what to do with the "leftover" cookie. Each group that I met with had the same issue and then had such wonderful discussions to figure out what to do.

Some groups simply refused to cut the cookie into pieces. They just left that cookie out even when I questioned them and tried to get them to look for other solutions. One student said that cookies just crumble when you cut them so you should just leave that cookie out.

Another student used the fact that the names I used in the story were teachers from our school. She decided that I should just give the extra cookie to my daughter, Abby.

One student (the student who was shaking his head when we read the problem) counted out the blocks and saw the leftover cookie and immediately cut it into 3 pieces.

One group quickly decided that the leftover cookie had to be cut into 3 pieces but had lots of discussion about how to cut it in a "fair" way. They drew lots of variations that they decided weren't fair (or "fare" as they spelled it). Finally someone in the group thought of cutting the cookie like a "peace sign" and they were all satisfied that this would be fair.

The discussion in our small group times are very lively and the students learn so much. I, too, learn so much about them as mathematicians. Another great thing is that this type of thinking and sharing is spilling into the rest of our math time during other days of the week. This will help as we try to transition to more of a workshop feel every day of the week. Below are some examples of kids thinking about a problem that was trying to determine which number is bigger, 23 or 15 and then they had to determine how much bigger. This student made each number in tally marks to compare them

and this student counted up from 15:

The exciting thing is that the students are much more willing to write and draw out their thinking as well as share their ideas with each other. There is still lots of work to do and I want to make all of my days have more of a workshop feel but I have to take it step by step.

First Steps ~ Moving Towards a Math Workshop

I recently finished reading Math Exchanges by Kassia Omohundro Wedekind, and experienced an awakening of sorts. I have met with two colleagues (who have read or will be reading Math Exchanges) and we are now ready to start making some changes to our math blocks to better meet the needs of our students. I have many ideas running through my head and so to help me organize my thoughts, I am just going to create a list of things I plan to change and/or try.

Before I begin, I should probably say that my school is an Everyday Math school. I do like Everyday Math but I often wish I had more flexibility with my time and I feel that my students need a deeper understanding of number sense and more problem solving. These are both present in Everyday Math but I think my students need more. I generally follow the Everyday Math program fairly closely but I want to have more of a workshop feel than I currently do. Everyday Math lessons follow a predictable format: mental math and reflexes, a whole group lesson, practice which can include independent work, partner work and games which is similar to a workshop model. After doing some thinking and talking with my teammates we decided that we can use most of these parts and create more of a workshop feel on our own. So we will still use Everyday Math but will begin to tweak things more and more as the year progresses.

Below are some of my ideas of things that I want to try and/or change.

• The first thing that I plan to do is to be more open to "going with the flow" of ideas that come up naturally in any math related discussion. I will not keep one eye on the clock and worry about "getting finished" on time. I will follow the students' thinking and have them share more with the rest of the class. This will help foster that workshop feeling that I am trying to create.
• The next thing that I want to add is to begin to use what Kassia Omohundro Wedekind calls Mathematician Statements. These statements are just lists of things that mathematician do. Some examples include: Mathematicians ask themselves questions and Mathematicians persevere. This will help to develop the workshop culture by labeling the actions that mathematicians do as they solve problems.
• I also plan to add small group meeting times or Math Exchanges to our day. I'll start with meeting with one small group each day towards the end of our math time. These groups will be heterogeneous and will change over time. My goals for the small group meetings are to be able to work more closely with students because they are in a smaller group, to have more time for students to share their ideas with each other, and to be able to gather data about how each student approaches problems and what they know and can do. I also hope that students will feel more comfortable sharing their thinking in a smaller group. 
• Another way that I plan to add more math to my day is to do some math during our morning meeting. I have two books that I am planning to use to help me with this. They are Doing Math in Morning Meeting by Andy Dousis and Margaret Berry Wilson and Number Sense Routines by Jessica Shumway.
• I will also use many of the ideas in Number Sense Routines to add to the mental math portion of the Everyday Math lesson. I have ten frames that I made years ago and haven't used much lately at all. I can't wait to dust them off.
• I also made many games that I read about in a book by Constance Kamii years ago. (I can no longer remember the name of that book.) I plan to use these along with other activities like counting collections (from Math Exchanges) to provide choices of things for students to work on while I meet with my small group each day.
• Keeping notes on student strengths and next steps will also be part of my small group time each day.
• Finally, I want to take Kassia Omohundro Wedekind's advice and teach my students to live like mathematicians. I want us to notice the math that is all around us all the time and to take the time to bring it up and talk about it.

So this is where I plan to start. I still hope to continue to move towards a more full-blown math workshop but I am starting here and will continue to revise as we move through the rest of the year.

Note to Self: This post is getting long but I wanted to add this note to myself about things to add to our math workshop later. Remember to think about how number talks can fit in and to add technology as one of the choices - things like explaining your thinking in a Voice Thread or in an app like Show Me or Screen Chomp on the iPad. Those can also be future posts.

Awakening

I have recently been experiencing an awakening of sorts. I teach first grade but that hasn't always been the case. I started my teaching career in middle school. I taught sixth grade my first year of teaching and then I was moved to eighth grade teaching Math and Algebra. I have to say that this wasn't my choice but I also must say that I ended up loving it. I taught middle school for 9 years and really became a "math person". I loved teaching math and helping students try to really understand math. I lived, breathed and dreamed math.

Fast forward to the present (skipping over several years of teaching 3rd, 4th and 5th grades) and I am where I have always wanted to be. First grade. One big difference between teaching middle school and elementary is that in elementary school you must focus on so many different content areas. I have to admit that I haven't been living, breathing and dreaming math while teaching first grade. I have really been focused on literacy. I have been working hard to create reading and writing workshops where I can meet with small groups and confer with individual students. I love doing this but recently something has been happening with my math teaching.

This summer I ordered a couple of professional books about teaching math and then after school started, I heard about another book, Math Exchanges by Kassia Omohundro Wedekind. I ordered that, too. I couldn't find the time to read them but the changes in my thinking were triggered. I started to really think about my math teaching and began to try to remember the things I truly believed about math and how students can best learn math. I knew that I needed to make some changes in my math teaching - especially in the area of having students think for themselves and solve mathematical problems. Then came the Math Exchanges blog tour and I jumped in. It was the final push that I needed to actually begin to read the books I had and get started with my changes.

While reading Math Exchanges, I started noticing student thinking more often in math and asking students to share their thinking - something that used to be second nature to me but that I had let fade away in first grade. One day we had a spontaneous discussion about whether zero was even or odd and I was hooked. I loved how my students were so excited to try and figure this out. They had a very heated but polite discussion about zero and eventually came to an agreement that zero was even based on the patterns they could see on a hundreds grid.

I have been able to finish reading Math Exchanges during my Fall Break and I have so many plans to change the way things work in our math block.  I still have more reading and learning to do but I can't wait to start making little changes each day - more to come about those changes in the next post. Thanks Kassia for spurring this math "awakening" in me.