Lesson Close

I have a hard time blogging during the school year, but I love to spend the summer reflecting on the past school year and thinking about my goals for the coming year. I have been watching #lessonclose and loving all of the ideas. And then I saw this one….

It all came together for me. I love the flow chart, I love the google sheets, I just love! Thank you!

I started using exit tickets more consistently in my seventh grade class this past school year. I saw was able to use the data to form flexible groups based on my plans for the day. I saw a lot of growth and could pinpoint which concepts students were struggling with. I sometimes had days that students weren’t ready for the exit ticket, and I had to quickly change my plans and save it for another time. I want to see some self-reflection about group work and so I created the rubric below.

I also wanted to find a better way to quickly assess different skills and I’ve been using formative.com so I created this…

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I did all this before I read @rawsonmath‘s post. Now, I’m seeing things in a new light. I think I can still use some of the tools I have created, but I’m seeing the organization of everything a little differently.

Thank you!

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Are stations the answer?

My time as a math coach taught me that stations are the bomb! I observed masterful first grade teachers regularly manage many different math levels without breaking a sweat. I experienced fourth grade teachers manage a room full of wiggly students during flex blocks and everyone was “getting what they needed.” Somewhere along the way we begin to believe that our students can sit for longer, focus for longer, and we don’t need to use stations to reach all learners.

A few years ago my district purchased the Connected Mathematics curriculum. I had used previous versions of the curriculum in the past and many of the problems were interesting and rich. The new version is clunky, disjointed, and difficult to use. Many of the problems are long, requiring several class sessions to complete with very little conceptual understanding. My students lose interest and are unmotivated by the time we finish a problem. The math they may have gleaned from the problem is lost in the euphoria they feel to be done.

As the year came to a close and I reflected on what went well and what didn’t, I was reminded of the times my students were engaged, challenged, and motivated to learn. The times this happened the most this year was when I was using stations in my classroom. They felt as though the tasks were interesting and at their level.

I began to think about my first unit in terms of stations using the math workshop model thinking about how I could use the best parts of the CMP curriculum. I came up with four stations including one where I will meet with students in small groups. These small group meetings will force both remediation and enrichment to happen within the station rotation.

Then I ran across this tweet….

After I read a little about responsive stations it seems like this is exactly what I need to add to make my stations even more productive. By first spending time to teach the necessary skills before starting a new unit I can really meet my students where they are. Looking at what students know and how to build off of that I can make all students feel successful.

So, my first unit is no longer my first unit. I need some station work before we start the first unit. The skills they really need to have solid are their multiplication and division relationships. I started planning my stations here. I think this will also be a great time to teach some of the classroom routines that need to get done at the beginning of the year so I’m only going to use three stations. More to come…

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The Past Year

This past school year was one of my toughest. There were a lot of reasons for this, I won’t go into all of them, but one of them was having access to technology. It was a lot to have constant access to technology. I love having iPads in my classroom, but I struggled to use them to transform my teaching without completely changing the way I teach. I need to rethink how my classroom runs and what I do.  Some thoughts….

  1. I quickly realized that I have the ability to run several different activities inside my classroom simultaneously. IPads make running stations or differentiated lessons much easier. I can distribute and collect work in a different way. We can keep unfinished card sorts or puzzles using the camera or explain everything. The paper everywhere problem is significantly streamlined. This class flow is very different.
  2. My students can and will collaborate to complete activities in different ways on the iPad, there is a different dynamic. Students are more willing to share ideas and engage in group work.
  3. Organization! Sixth graders struggle with organization. It just hard and the iPads are a game-changer. Things that used to get lost are easily stored in google drive. The sheet we use for estimation 180 was easily found and started every week, rather than handing out a new one every week. Students were able to see how they became better estimators as the year went on.
  4. Formative assessments! The world of technology has opened up my ability to quickly assess what my students are understanding. Formative and Pear Deck make it quick and easy to assess students without a lot of paper or correcting. I can bring students together and still have everyone participating and asking questions.

Now that I have seen the way the iPads effect my classroom I want to change the way I teach to match the new ways I have to reach my students.

My Day at Google

I found myself at Google last Friday. A wonderful organization, Ed Tech Teacher, along with Google organized a Jamboree for about 200 educators. We had the opportunity to heGoogle Manar from Googlers (Google employees) as well as amazing technology educators (including Jenny Mageria…check out her blog!).

The last hour of our day was spent listening to a panel of Googlers answer questions. The questions were mostly about the working culture at Google. While some of my colleagues felt as like they were bragging, I heard some really easy things that make an exciting working and learning environment.

1. Everyone’s ideas are heard.

A young software engineer talked extensively about her early weeks on the job. She initially felt intimidated and learned quickly that this was a place where her questions would be heard.  When she asked a question everyone turned to listen to her. This made her realize her opinions mattered.

After Google’s recent decision about Blogger, Google held town meeting style forums for Googlers to ask questions about the decision. The forums lasted for hours and allowed everyone to feel heard.

This takes no money. This is part of a culture where people want to come to work because they feel like they are part of something larger than themselves.

2. You are asked to step outside your comfort zone on a regular basis. You never feel like you know exactly what you are doing.

Several of the Googler talked about being kept on their toes. They are asked to do things that require them to solve problems. Their job descriptions change occasionally and they are constantly learning and growing. In a company setting where you are trying to get the most from your employees it is clear you will get more if they are kept on the verge of comfort. At first this sounds like an awful situation, but after teaching sixth grade math for so many years it is easy to see how this would be a positive. Many teachers teach the same topic and grade level for year after year. There is always a greater learning curve when something is new. The same is true with our students. If we can keep them challenged then we will see more from them.

3. The best way to deal with change is cause it.

The world of technology changes so fast and all the Googlers must keep up with it. They have found that the best way to deal with it is to be on the leading edge. What would this look like outside the walls of a company? It would be children doing great things like this. How do we inspire our students to create and make something better for themselves? How do we get students to stand on our shoulders, use what we know as their teachers, and put it together into something great?

Overall, I had a great day at Google. There are many other takeaways that could be applicable to a education setting. The culture we create in our schools is the culture our students emulate. If we have a culture of collaboration and creation our students begin to mimic it.


Technology and Formative Assessment

Now that I’m back in the classroom I have access to some great technology. My district is piloting 1:1 iPads in one cluster and the rest of the clusters have an iPad cart. I’m in a cluster with the cart so we have to share our with three other teachers. Luckily, this hasn’t been too difficult. We setup a shared google calendar and whoever gets there first gets the cart.

Our students all have access to a google email and apps account so we have a lot of options. When I started out the year I tested out a few different formative assessment options. Using the cart in math class it is easy to just have students log in and practice. I love to use the iPads for formative assessment or as a combination formative assessment/connection builder.

Before we had technology for each student I used Mastery Connect. I used bubble sheets for each student and scored with an Ipevo document camera. I never gave more than 5 questions and used them to gauge how students were doing with new concepts. This gave me a snapshot of what each student understood within each standard. If my district bought into this system I think it would be amazing for assessing and keeping data. Alas, they didn’t.

When I started working with the iPads Mastery Connect was the first place I went. I knew that they bought Socrative and was excited to see how they would be integrated. Unfortunately, they didn’t really integrate the best part. I loved seeing the standards covered as we moved through the curriculum on Mastery Connect. There is no way to link Socrative questions to the standards, so I decided to keep looking. Socrative and Mastery Connect were a little clunky on the iPads and didn’t really give me an easy way to track student understanding.

Next, I tried Exit Ticket. If my students traveled with their iPads I think this would be the system for me. Students have access to their results from previous exit tickets. The teacher view can be switched to projector view so a whole group discussion can happen. Love it! Students can use the same account for multiple classes and store everything together in one place.

Then came Pear Deck

Pear Deck takes formative assessment to the next level. I was intrigued when I realized it was integrated into google. My students wouldn’t need another login. (They can barely remember one password.) Pear Deck takes power points to the next level. I have a projector view, teacher view, and student view. There are different slide types for students to interact with: free response-draw, free response-write, free response-number, draggable, and multiple choice. I have the ability to insert images into the slides for students to graph or write on. I can switch the answers on so others can see answers anonymously. We can have a conversation about incorrect answers. I can see in teacher view how each student answered each question. At the end of class I can save every student’s answer to look at later. The possibilities are endless.

Pear Deck has changed the way I teach. I can quickly see who understands and who is still confused.

I’m sharing the Pear Decks I’ve made so far. Feel free to try them out.

Pear Deck Folder

 I did pay for a premium subscription which does give me more access, but try it out anyway. You’ll love it!

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My colleagues and I decided to enrich our CMP 3 curriculum with one of Cathy Fosnot’s Math in Context Units, Best Buys, Ratios and Rates. It has been a rewarding experience and changed the way that I think about teaching.

One thing I have regained is the benefit of “struggle.” Students that are willing to struggle are able to gain more from a problem than students that insist on having an answer first. It is sometimes tempting to teach what students need to know before they have had this experience.

I have always enjoyed teaching this way, but time constraints and the need to finish the standards in a timely way often scare me into a different teaching style. I gave my students some extra time today. I wanted to finish the problem and share out by the end of the class period today, but students were engaged and learning. I let them go on with the problem for the whole period. One student looked at me so excited and said, “I’m so excited, it feels so good to struggle and then get it.” She had just discovered what I was trying to teach. I didn’t do any of the talking, she did all of it and she learned!

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Goal Setting

I’m really excited about mathematics education. I think the Common Core Standards came at the right time and the perfect storm is upon us. Jo Boaler is creating exciting content for teachers, parents and students at Youcubed.org, Carol Dweck is putting in to words what we know is necessary to succeed, and at the same time there was enough of a shift in standards that teachers are now focusing on what students need to understand, not what they need to learn.

There are two goals I have for the upcoming school year based on all of this excitement. The first is to change my classroom culture to make mistakes more valuable. I am constantly telling students that mistakes are valuable, and they should be learning from them, but this is not evident in my classroom. I don’t show students how to learn from mistakes, and I don’t value mistakes in my grading practices.

The second goal is to come up with a more consistent classroom routine for number sense routines. There is so much good content right now that I think I could fill 180 days with number sense routines. I love Building Powerful Numeracy for Middle and High School Students by Pamela Weber Harris, Jessica Shumway’s Number Sense Routines, Number Talks by Sherry Parrish and Classroom Discussions by Chapin, O’Connor & Anderson. In addition there is so much good web content coming out of the math twitterblogosphere it’s hard to know where to start. I want to use Fawn’s math talks and visual patterns, Andrew’s Estimation 180, and Sadie’s Counting Circles.

A few months ago I attended a conference where all three authors of Classroom Discussions presented in separate workshops. Something I tool away from Nancy Anderson’s presentation really stuck with me. She said, “Math class is like a cooking show.” The more I think about this the more I love it. We should constantly be looking for the mistakes that students are making we should be bringing those to the surface and presenting them in an organized way. Don’t just hope that students choose to participate the way you want them to, have it all ready to go. While students are discussing a problem listen to the discussion and ask that student to share once you bring the class back together. Whether it is a common mistake, or a great idea the point is to make every minute in class count.

I’m not sure how to attain these goals, but I know I need to focus in on the important points. I have used Building Powerful Numeracy for Middle and High School Students and Classroom Discussions in my classroom before. I want to add in some of the other great content out there. I think I may have to rotate the number sense routines that I’m using in my classroom either weekly or daily based on what we’re doing? I’m open to suggestions.

I’m hoping that I can show the value of mistakes through some of these number sense routines and my new “cooking show” technique. One thing I’m still struggling with is how do you value mistakes while grading. If I’m encouraging students to make mistakes I need to have some way to record what mistakes they are making and what they are learning from them. Ideas?

I’m excited about a new school year. I think I’m going to grow a lot as a teacher.

First Day

September will mark my tenth year teaching in my current school district and my fourteenth year teaching. It is overwhelming to look back at all of the different ways I have started the year. I don’t feel like any of my first days were spectacular. This year things will be different!

I have been doing a lot of reading about the growth mindset. I recently purchased Carol Dweck’s book Mindset:The New Psychology of Success and I think I have the gist. It is all starting to make sense now. I have been trying for years to convince students that making mistakes is the only way to learn and if you aren’t making mistakes you aren’t learning. If you haven’t been reading about the growth mindset and fixed mindset, the premise is that once you believe that your intelligence can’t grow, it can’t (fixed mindset). You need to believe that learning comes from challenges and learn from the mistakes you make along the way (growth mindset). Great! Now that I had some research for these ideas I want a way to start off the year teaching them.

Two years ago I attended the Building Learning Communities Education Conference, while I was there I attended a session where the presenters were doing The Marshmallow Challenge. In the Marshmallow Challenge teams of four are given tape, 20 pieces of spaghetti, string, and a marshmallow. The task is to build the tallest structure that will support the marshmallow in 18 minutes. There is a great TED talk  by Tom Wujec that is also on the website. Tom stresses the importance of just trying something as soon as you have the idea, making a mistake and learning from it.

I’m really excited to start my year this way. I know there’s not a lot of math, but I want to set a tone. I want my students to be ready to accept a challenge, to make mistakes, and to learn.

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Where have I been?

It has been a long time since my last post.  I left the classroom last June. I walked out and didn’t look back. It was an extremely difficult year. I became a K-5 math coach. I thought a change would be good. I have spent that last 7 months learning about the acquisition of numbers in elementary school. I have seen the development of number sense from kindergarten up. I have had the opportunity to teach everything from 1st grade to 5th grade. It has been an amazing experience and I have met some extremely dedicated teachers.

Unfortunately, I knew right away. As soon as September came and I didn’t have my own classes with my own students I knew I had made a mistake. I missed having my students to call my own. I tried to hold it in and give this new role time to sink in. It was new for me and it was new for the teachers I was working with. I knew there would be growing pains, but I never experienced the same joy that I had in my own classroom. I have really enjoyed changing how math is taught in so many classrooms, but I knew.

One of the most interesting things I have learned about number concepts in the lower grades, unitizing five and ten are the building blocks for addition and subtraction. Students should be held back from working with larger numbers until they are comfortable with the combinations to ten.

Being able to spend the year working on the development of number concepts K-5 has given me a new appreciation for mathematics. Everything is interconnected and when students are given the ability to make these connections we can watch them do amazing things.



Egyptian Fractions

I discovered Egyptian Fractions while studying number theory at PROMYS. It was one of the long term projects that teachers could research, but didn’t really interest me at the time. When I saw a group of teachers present their research at the end of the summer I saw the implications for teaching fraction operations.

Egyptians used only unit fractions. To represent \frac{3}{8} the Egyptians would have used the fraction \frac{1}{4} and \frac{1}{8}. Together these fractions are equivalent to the original total, but use only unit fractions to express the sum. Once students have some knowledge of fraction addition they can begin to attack these problems. My students had also covered multiplication of fractions which made the process easier. Here is the activity they did:

Before introducing this activity in class students watched a five minute video about Egyptian Fractions. If you have access to United Streaming from Discovery Education, this video was a great way to start students thinking about how the Egyptians work. Our students study Ancient Egypt this time of year in history as well so this is a great activity.

One process introduced in the video is the “loaf of bread method.” Many of my students understood this method and stuck with it through the activity. If an Egyptian wants to share 5 loaves of bread with eight people he will start by splitting 4 loaves into halves. Then the leftover loaf will get split into eighths. Each person will then get half a loaf and an eighth of a loaf.  \frac{5}{8}=\frac{1}{2}+\frac{1}{8}

In this activity students were forced to work together to discuss methods. One single method will not work for all of the fractions.  This is one of those problems that students cannot divide and conquer.

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