Is There Beauty in Math?

Beauty  in math.  Back in July, I selected  the word beauty  to begin my journey  with my fellow colleagues  in Math Rocks. When I chose the word beauty , I was not really sure how  those two words would relate to each other or how  beauty in math would  look.  After being a part of Math Rocks for the past seven  months, I  have discovered that math and beauty go together  in many different ways.

One way that I feel that I found beauty in math was through the process of fostering curiosity .  Through the Math Rocks group, I was introduced to Number Talks.  With the introduction of number talks in my room, the students have become deeper thinkers and analyzers. They  have also become comfortable with experimenting with  different strategies to solve problems.  So rather than passively receiving  strategies from me, they have become the owners and presenters of ways to problem solve.  In addition, they have learned to  appropriately challenge and question their classmates about their thinking.  As  we have continued this process throughout the year, the students  are excited for this time of the day and are eager to share . I love that  they  eagerly await this time each day.

In addition to fostering my students curiosity , I feel that throughout this process my own curiosity has been fostered.  Each time that we have met as a group, I have walked away with  new things that I want to try  in my classroom . I feel that this group has challenged my own thinking about math  and also challenged me to try new things in my room . Through this,  I feel that I have been more curious about the thinking that goes on in the minds of my students during math.

I  have always felt that fostering relationships with students and colleagues has been a strength of mine.   Using Number Talks has been another way to build strong relationships in the classroom.  In particular, students have become more willing to share their thinking aloud  without fear and the students have learned to use  appropriate language to agree, question or challenge each other without it becoming a personal attack. I  feel that this has taught them a skill that they  will be able to use throughout their life and in all different types of relationships.  In addition, I feel that  I have been able to foster relationships with the other teachers in the group. It has been amazing how much each person in this group  has brought to the group. I hope that we will continue to stay in contact and share ideas that we are using in our rooms that have been both successful and unsuccessful .

I am thankful that I had the opportunity to participate in this group. It has sparked my curiosity . It has allowed me to meet and learn from some amazing teachers in district. Finally it has allowed me to see beyond what I must teach and see the beauty in  math through the  eyes of my students.

 

The Open Middle Experiment

Well with all things that we try , there is always the chance that it may fail. When I was thinking about an open middle problem and how  I could create one to fit the unit  we were working on, I thought decomposing a composite figure will allow students the opportunity to find their own way to decompose the shape into a way that fits their thinking .  Below is a picture of the problem that I used :

I began by asking students to think about all the ways they could decompose the shape. Most responses were to draw a line  and create a 2×2 at the top. After that they were really unsure if there was another way to do it . With some encouragement, some students made a line  down to separate and make a 2×5 and then a larger one. After making them I asked them to consider whether there was one way that would make the area of both decomposed shapes closer to the same size.  in hind sight,  I wish I would have made a shape that would have encouraged the students to decompose in different ways.  It was however interesting to listen to their conversations. I do feel on some level  this was a failure on my part in the sense  I did not create a problem that allowed the students to have  a wide range of thinking but it was also successful because it did encourage my students to have some great math conversations.  Below is some of their thinking.              

The Adventures Of Number Talks

Though I consider myself nothing but a novice, I have found Number Talks to be one of the most interesting and exciting parts of my day.  Each day I am learning more and more about my students as thinkers and they are becoming more and more willing to share their thinking.  For the lesson that I am going to share,  I chose the problem  49 -28.  I chose this problem because I wanted to see my students decompose the numbers to subtract. I was also curious to see if any of my students would use rounding  to help them solve this problem.  When I was thinking about, I expected that many of my students would solve with  number line as that is what they have gravitated to most of the time.  Below is my plan : 

 

This is how my students solved the problem.:

As I expected several students shared that they used a number line. I found that Lilli really struggled to not want to do algorithm but was able to walk me through the steps.  When Rachel shared, she  said she go rid of the 9 and the 8 and made it  40 – 20 and then had to put the  9 and 8 back in and subtract. Though it is not recorded when then had a class discussion of what would happen if we made it it 50 and 30 and that led to a discussion about how do you put those numbers back in when doing subtraction. They all thought that it was easier to round when you added . The student that said  29 changed his thinking but he did share that he made it 40 -20  but then just brought down the nine and did not think about the 8.

 

What is next ? I think that I will continue to use numbers where they can work to  have students to adjust one number to make subtraction easier as many of them thought it was difficult to  figure out what to do with the number they changed.

So far, I have had students  open up and say that they are willing to change their thinking which has been awesome. At the same time however, I still have a few students who are not sharing and I would really like to find a way to reach all of them.   I do love  the number talks and I am excited to see how this thinking will transfer to their own problem solving. I really like that the students are doing the teaching to the other students. I would like to improve in my recording and in also making a chart of their strategies.

 

 

 

Trying my hand at something new. Estimation 180

I selected estimation  180 to try with my class. We had just had a few lessons on estimating and I thought it would be great to introduce this sight so that they could see that estimating is something that happens  in the world around them all of the time.

I must state up front  that in the midst of doing this activity , I forgot to take any pictures to document what we did. I will  be doing this site again and will add an additional blog and some pictures.

I started will day 6 as it was the  cup full of almonds and I thought that this would be a good starting point for them to make reasonable estimations.  As students began to discuss what they observed, I was surprised with how reasonable their  estimates were . The majority went extremely high in the too high and said 100 . This allowed for a good discussion about what would be  a reasonable too  high number.  As for too low again the number stated was o or 1 .

When it came to discussing how many almonds there actually were , the estimates went from a low of 15 to high of 45. Many students came to the board and tried to could one by one, others saw the almonds in layers and others said they based their estimate on what they new about  a package of almonds.

I am looking forward to using this regularly in the classroom as  It  sparks such a great discussion  between the students.

Finding dislike, fun, challenge and beauty in my classroom – Math Rocks Mission 8

I have  energetic faces that arrive at my door everyday.  Sometimes they lose some steam during math but for the most part they are still energetic and excited during math.  I was excited to do the survey to see what they were really thinking about math  . Here were there thoughts about the subject

Math is fun   10 out 21 indicated math was fun  . Their reasons were

•  it makes me smarter
• you can add, subtract, multiply and divide
•  you get to multiply
• numbers are cool
• We get to play math game

Math is beautiful   2 out of 21  . Their reasons :

• there are so many numbers and signs and different ways to do  things.
• problem  solving  is unique

I like math because it it challenging  6 out of 21 . Their reasons :

•  it makes me think
• it works my brain
• I like challenges
• the problems are hard

I don’t like math   3/21  . Their reasons:

• Math tricks me a lot
• The problems are confusing
• I still count on my hands.

I found this to be insightful as some of the students answered in a way  I would not expect based on how they participate or complete work in class.  I enjoyed doing the survey and plan to do it again  at the mid year point.

Life in Portable 1B

Well it is hard to believe that only a few days ago my room was a quiet portable with  desks and chairs just waiting to be filled.   With limited space in a portable,  I have to make the best use of each space.  In my pictures, you will notice that  I did not take many of my walls as they are fairly empty at the beginning of the year and what goes on there is created with and for my students. That being said,  I try my best to  make the students feel welcome with the things that they will see when they come in the room.

In addition this year, I decided focus on  teaching my students the difference between a fixed and a growth mindset.  This seems to be quite a popular  bulletin board this year. I am encouraged because today two students referred to it and we really have not spent any time on it.

Looking forward to adding  pictures and  the Prud’homme Planets learn and grow together.

The Never Ending Resources on the Web

What an amazing time we live in. So much  information and resources just a click away.   I  am going to incorporate Estimation 180 into my daily math block. This will be a great way to get students having conversations and supporting their answers. In addition, students will see that  estimation is all around them in the world and is not limited to a math problem. Finally, often students will make estimations that are not reasonable. I think using this site will get them thinking more realistically about their estimations.

Discovering a whole new world through Twitter

When  I signed up for Math Rocks , I figured I would have the opportunity to  connect with a variety of people who all had an interest in teaching math. I had no idea that my  connections would reach beyond the  people I would  sit with in a  room in Round Rock . Until a couple of weeks ago, I had no need or desire to be a part of the twitter world. That all changed after day one of our  first Math Rocks meeting. To be honest , I thought well  I will make this but that is as far as I will go. Over the past week,   I am starting to see why this can be such a valuable tool.  I have had to opportunity to read a variety of blogs  from all over the world and gain some insight on how different people view and teach math. I really enjoyed one article about ” How to turn  every child into a “math person”  .   I hope that as I continue to use  Twitter that I will become more efficient at finding tweets that I want to read and follower without getting side tracked on occasion. So glad I had a gentle shove to get involved with twitter.

Goals and obstacles to a great math classroom – Math Rocks Mission # 3

So excited about this upcoming year and all I will get to learn and try through my participation in Math Rocks. Thanks for  great 2 days of learning . As  I think about this next year and what I would like to see happen in my room the first goal  I have for math is for intentional talk. Though I have my students talk and discuss about their math, I really want my students to have purposeful and meaningful conversations.  Secondly, I  would like to incorporate daily the use of the  images, what does not belong and the number sense activities into my routine. Just the few that we did, I was able to see just how much information that can be covered in a short time. Though I have used these at different times in my room, I want o commit to being consistent with them.

For my students I want to them to find  joy and excitement in their math learning. I want them to be empowered to explore math in all  subjects and connect their math to their daily lives. Secondly, I want my students to write on a regular basis about their math understandings.

The main obstacle I believe I will face is time . Often times it seems that it is a challenge to  cover all of the material in a timely manner in all subjects. To address, the issue of time, I  that I will  incorporate some of my journal writing to be  about math.

Math Rock Mission 1

One thing that I do in my classroom to make it mine is to  make and create  songs that go with   our learning. In math we begin the year by chanting  I am a mathematician and as we learn things we add to the song  so at one point it will have this :

I ‘m a mathematician I can do addition, I can multiply and I can divide. As we learn more things, we have add to the song and each day at the end of the day we  sing this song.