Category Archives: Learning Labs

100 Hungry Ants: Math and Literature

This week the Kindergarten and 1st grade teachers planned with Erin, the reading specialist, and I for an activity around a children’s book. This planning was a continuation of our previous meeting about mathematizing. We jumped right into our planning by sharing books everyone brought, discussing the mathematical and language arts ideas that could arise in each. I made a list of the books the teachers shared here.

We chose the book One Hundred Hungry Ants and planned the activity for a Kindergarten class. We decided the teacher would read the story and do a notice/wonder the day before the activity. We thought doing two consecutive readings may cause some students to lose focus and we would lose their attention. Based on Allison Hintz’s advice, we wanted the students to listen and enjoy the story for the first read-through. Here is an example from one classroom:

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So many great problem and solutions, cause and effects, illustration and mathematical ideas were noticed by the students.

The following day, the teacher revisited the things students noticed and focused the students’ attention on all of the noticings about the ants. She told the students she was going to read the story one more time but this time she wanted them to focus on what was happening with the ants throughout the story. We had decided to give each student a clipboard and blank sheet of paper to record their thoughts.

We noticed a few great things during this time..

Some students like to write a lot!

After trying to draw the first 100 ants, students came up with other clear ways to show their thinking. I love the relative size of each of the lines in these!

A lot of students had unique ways of recording with numbers. Here is one that especially jumped out at me because of the blanks:

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Students shared their recordings at the end of the reading and it was great to hear so many students say they started the story by trying to draw all of the ants, but changed to something faster because 10o was a lot!

After sharing, we asked students, “What could have happened if they had 12 or 24 ants?” We put out manipulatives and let them go! So much great stuff!

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Next time I do this activity, I would like to see them choose their own number of ants.

Just as I was telling Erin that I could see this book being used in upper elementary grades when looking at generalizations about multiplication, I found some great posts by Marilyn Burns on this book for upper elementary and middle school:

Excited to do this in a 1st grade classroom today!

Mathematizing Learning Lab

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Each month, teachers choose their Learning Lab content focus for our work together. Most months, 1/2 of the grade level teachers choose to have a Math Learning Lab while the other 1/2 work with Erin, the reading specialist in an ELA Learning Lab. This month, however, we decided to mesh our ELA and Math Labs to do some mathematizing around children’s literature in Kindergarten and 1st grade! This idea was inspired by a session at NCTM last year, led by Allison Hintz, that left me thinking more about how we use read-alouds in our classrooms and the lenses by which students listen as we read.

In The Reading Teacher, Hintz and Smith describe mathematizing as, “…a process of inquiring about, organizing, and constructing meaning with a mathematical lens (Fosnot & Dolk, 2001). By mathematizing books commonly available in classroom collections and reading them aloud, teachers provide students with opportunities to explore ideas, discuss mathematical concepts, and make connections to their own lives.” Hintz, A. & Smith, T. (2013). Mathematizing Read Alouds in Three Easy Steps. The Reading Teacher, 67(2), 103-108.

Erin and I have literally been talking about this idea all year long based on Allison’s work. We discussed the ways we typically see read-alouds used, such as having a focus on a particular text structure or as a counting book in math.

As Erin was reading Kylene Beers & Robert Probst’s book, Reading Nonfiction she pointed me to a piece of the book on disciplinary literacy which automatically had me thinking about mathematizing.

Beers refers to McConachie’s book Content Matters (2010), in which she defines disciplinary literacy as, “the use of reading, reasoning, investigating, speaking, and writing required to learn and form complex content knowledge appropriate to a particular discipline.” (p.15) She continues to say, “…disciplinary literacy “emphasizes the unique tools that experts in a discipline use to engage in that discipline” (Shanahan and Shanahan 2012, p.8).

As I read this section of the book, my question became this…(almost rhetorical for me at this point)

Does a student’s lens by which they listen and/or read differ based on the content area class they are sitting in?

For example, when reading or listening to a story in Language Arts class, do students hear or look for the mathematical ideas that may emerge based on the storyline of the book or illustrations on the page? or Do students think about a storyline of a problem in math class or are they simply reading through the lens of “how am I solving this?” because they are sitting in math class?

Mathematizing gets at just this. To think about this more together, Erin and I decided to jump right into the children’s book The Doorbell Rang by Pat Hutchins. Erin talked about the ideas she had for using this in an ELA class, I talking through the mathematical ideas that could emerge in math class, and then we began planning for our K/1 Learning Lab where we wanted teachers to think more about this idea with us! We were so fortunate to have the opportunity to chat through some of our thoughts and questions with Allison the day before we were meeting with the teachers. (She is just so wonderful;)

The first part of our Learning Lab rolled out like this…

We opened with this talking point on the board:

“When you change the way you look at things, the things you look at change.”

Everyone had a couple of minutes to think about whether they agreed, disagreed, or were unsure about the statement. As with all Talking Points activities, each teacher shared as the rest of us simply listened without commenting. The range of thoughts on this was so interesting. Some teachers based it on a particular content focus, some on personal connections, while I thought there is a slight difference between the words “look” and “see.”

After the Talking Point, Erin read The Doorbell Rang to the teachers and we asked them to discuss what the story was about with a partner. This was something Allison brought up that Erin and I had not thought about in our planning. I don’t remember her exact wording here, but the loose translation was, “Read for enjoyment. We want students to read for the simple joy of reading.” While Erin and I were so focused on the activity of exploring the text through a Math or ELA lens, we realized that the teachers first just needed to enjoy the story without a purpose.

For the second reading of the book, we gave each partner a specific lens. This time, one person was listening with an ELA lens while, the other, a Math lens. We asked them to jot down notes about what ideas could emerge through these lenses with their classes. You may want to go back and watch the video again to try this out for yourself before reading ahead!

Here are some of their responses:

Together we shared these ideas and discussed how the ELA and Math lenses impacted one another. A question we asked, inspired by Allison, was “Could a student attend to the math ideas without having a deep understanding of the story?”

Many questions came up:

Could we focus on text structures and the math in the same lesson?
Could we start with an activity before reading the book, like a probable passage?
Would an open notice/wonder after the first reading allow the lens to emerge from the students? Do they then choose their own focus or do we focus on one?
How could focusing on the problem and solution get at both the ELA and Math in the book?
How could we use the pictures to think about other problems that arise in the book?
How do we work the materials part of it? Do manipulatives and white boards work for K/1 while a story is being read or is it too much distraction?
What follow-up activities, maybe writing, could we think about after the book is read?

Unfortunately, our time together ended there. On Tuesday, we meet again and the teachers are going to bring some new books for us to plan a lesson around! So excited!

Fraction & Decimal Number Lines

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Recently, our 3rd, 4th, and 5th grade teachers had the opportunity to chat math for 2 hours during a Learning Lab held on a professional development day. It was the first time we had done a vertical lab and it felt like perfect timing as 3rd and 4th grade would soon be starting their fraction unit and 5th would be entering their decimal unit. Prior to the meeting, we read the NCTM article, “Identify Fractions and Decimals on a Number Line” by Meghan Shaughnessy, so we started the meeting discussing ideas in the article. We then jumped into playing around with clothesline number lines and double number lines, discussing what they could look like at each grade level based on where students are in the fractional thinking.

I have co-taught number line lessons in both 5th grade and Kindergarten this year, but both were a bit different in not only number, but organization. In 5th grade we used one clothesline with the whole class, while in Kindergarten we used tape on the floor and students worked in small groups. Leigh, 5th grade teacher, was interested in trying the small group number lines on the floor. As we planned the lesson, the one thing we thought would be difficult about having small groups is getting around to each group to hear their conversations, especially when we were planning cards purposefully to address misconceptions and misunderstandings. However, knowing we would have the two of us circulating, as well as two 3rd grade teachers who wanted to see the lesson (yeah!), we knew we had plenty of eyes and ears around the room to hear the math conversations.

During the lesson, in groups of three, students placed 24 cards on their number line. There were two sets of cards, so after placing all of their cards, each group visited a number line with a different set of cards to discuss. Instead of boring you with all of the number choices we made, here are a few of the choices in cards and the reason(s) we chose them:

1/3 and .3: Students often think these two are equivalent so before the decimal unit we were curious to see how they were thinking around that idea and how they used what they knew about fractions or percents to reason about it.

0.3, 0.33, 0.333, 1/3: The 1/3 and .333 were there to think about equivalency, while the others were there to think about what is the same in each and how much more each decimal has to make it larger. Which you can see caused some confusion here:

2.01 and 2.08: We were curious about the distance they put between these two cards.

1 6/9 and 1.6: We wanted to see how students compared fractions and decimals when they can’t easily convert 6/9 into a decimal. Then, if they began thinking 6/9 and 6/10, how would they decide on the larger fraction and then how much distance do they put between them?

The group below practically had them on top of one another:

While this group had a bit of a space between them:

2.8 and 2.80: Tenths and hundredths equivalency. They all seemed to handle this with ease.

.005 and 1/100: Curious to see the placement in relation to the other numbers. This 1/100 is close to 0 but I wonder about it in relation to the .2. Definitely a conversation worth having!

2.8 and 2 7/8: To see how they compared the 7/8 to the 8/10.

After they visited other number lines, they had a chance to meet with that group and discuss card placements they agreed with and placements they did not. Groups then made adjustments accordingly…

Here was a group’s completed number line and my first stab at panoramic on my phone!

The journal entry we left them with was, “Which cards were the most difficult to place on the number line? Why?” Many were just as we suspected.

The conversation as I walked back over to the other building with the 3rd grade teachers was, what does this look like in 3rd grade? Could we use array images to place on the line instead of the fractions? Could the pictures include over 1 whole? What whole numbers would we use? Do we play with equivalent pictures with different partitioning? Being mindful of the students’ second grade fraction exposure, below, we are planning on trying out something very soon! I am thinking the cards like these on Illustrative, with the pictures but no fraction names at this point.

CCSS.MATH.CONTENT.2.G.A.2
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

CCSS.MATH.CONTENT.2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

…and then could the journal could be, “Can you name any of the fractions on your number line? How do you know?”…or something like that!

Establishing a Culture of Learning …The First Hour

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Every year, we as teachers work so hard to establish a safe, open place for our students to learn. My goal in moving out of the classroom year and into a math specialist role is to also establish this same culture among our staff. A culture where teachers talk about instruction, math problems, and student ideas, feel ownership in their lessons and the lessons of others, and can comfortably visit one another’s classrooms. It becomes a norm. It is not easy and definitely cannot be done alone. I am SO incredibly fortunate to have a wonderful principal, Jenny (@PrincipalNauman) and district supervisor (@EducatorKola) who support the vision and are always open to new ideas, a great ELA counterpart Erin (@EGannon5) who helps me focus and thinks about the important details I miss in my excitement about things, incredibly caring, motivated colleagues who always want to grow and learn, and all of the amazing educators in my face-to-face and online (#MTBoS) networks who I mention throughout this post.

Yesterday was Erin and my first opportunity to talk with teachers. We only had one hour to work with the full staff, so we had to truly prioritize and make the most of every minute! We decided it was most important to set the tone for the year and our work together with the teachers. We wanted to begin establishing a culture of learning. The best part was, we were not starting from scratch! Our staff is so wonderfully open to new ideas and really took Number Talks and ran with them over the past few years, however there is always room to grow and improve upon what we were already doing. PLCs are part of that room to grow. While they participated and did everything asked of them, teachers were not feeling that time was based on their individual needs as much as it should be. Being one of those teachers last year, I put myself in that group.

Instead of telling them what a learning culture could/should look and feel like, we wanted them to experience and reflect on it. What better way to do that than Talking Points? (shout out to Elizabeth @cheesemonkeysf) We designed the Talking Points to give teachers a range of ideas of how they could be used, whether around content specific statement or ones around mindset.

I have never been in a PD where Talking Points are not a hit during the activity itself, but the reflection afterward is twice as valuable! We asked them how this activity would promote a culture of learning in a classroom. We tried to quickly list ideas as they responded so the list doesn’t truly capture the appreciation teachers had for students talking and listening to one another!

When talking to my colleague Faith (@Foizym) about our plan for the hour, I really stressed how I wanted to make my work with teachers valuable this year. I wanted them to want to talk math with me and want me in the classroom and not see me in any type of evaluative role, I wanted our work together to be about their needs in order to best meet the needs of their students. She suggested having them write goals for themselves and their students. So, we asked them to complete these questions to know what each of their goals were…

We got amazing answers that really spoke to the thoughtfulness of our staff. I would love to post a few but I have to ask for some permissions first:)

Now we moved into how we were visualizing this culture permeating through our work together. Knowing we were introducing Learning Labs and Teacher Time Outs to them soon, we wanted to have them brainstorm words they associated with the word “Lab” and “Time Out” to set the stage. These slides did not have the words/ideas around it when they saw it, we put those up after they brainstormed.

Now we described our shift from PLCs to “Learning Labs” and the use of Teacher Time Outs. If you have not heard of Math Lab or Teacher Time Outs, I will point you to Elham Kazemi (@ekazemi) and her University of Washington peeps who are doing AMAZING work with this. Here is her ShadowCon speech that gives a wonderful description. Elham has been so generous in thinking this through with me and has given me wonderful advice, much of which I will continue to need I am sure!

I hope we captured it as she intended, but sadly at this point we were running out of time. There were many questions about the timely structure (that we honestly are still trying to hammer out) but overall everyone was really excited about this work! We received so many positive comments and offers to be the first to try out whatever we wanted to do!

I left completely excited about this work…even more excited than I was to start, if that is even possible! Once Erin and I work through the time constraints and the crazy schedules we know everyone keeps as teachers, I cannot wait to see the work that awaits all of us!

-Kristin

PLC Brainstorming

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As I move back into the math specialist position at my school this upcoming year, I have really been thinking a lot about the way in which our district PLCs are structured and, as a whole, how we treat each subject area as separate professional development entities. As an elementary classroom teacher, we either participate in a math PLC or a language arts PLC twice every week during our planning time. While it feels like it would work content-wise for the teachers who are K-3 and teach everything, it becomes a bit trickier when teachers are departmentalized in 4th and 5th grade. Not that there isn’t a need for everyone to be involved with both content areas due to everyone teaching RTI groups, however it still feels like there is a disconnect and sadly can lead to the “waste of my time” mantra because it doesn’t feel applicable to what they are doing in their core classroom work.

So, the question I am working through, is how can we do this better?

The more I engage in math conversations around the book Connecting Arithmetic to Algebra, the more I begin to see the structure of future PLCs evolve. (To catch up on those convos, @Simon_Gregg did a nice recap here: http://followinglearning.blogspot.fr/2015/06/mathematical-reasoning.html) It may seem odd to pull other content area ideas from here because the book is about amazing math reasoning and thinking, but I really see huge potential in this idea of “Making Claims” across all content areas. Thinking about this, I dug into the ELA CCSS, found these standards and started thinking about how this process sounded similar to our book discussions:

Upon further reading I came upon this ELA unit on Making Evidence Based claims: https://www.engageny.org/resource/making-evidence-based-claims-units-ccss-ela-literacy-grades-6-12

Then I moved into the Next Generation Science Standards and in a quick search I found this…

I just see so many potential connections here to have everyone engaged and leaving feeling like the PLCs were worth the time invested.

There is much more learning to be done on my part in the content areas, but I am seeing a way to structure our PLCs so they are not so much “by subject area” each time, but more “by ideas and reasoning process.” Questions I am thinking about….

– Could we center PLCs around ideas such as “Making Claims?” Talk about what students do during this process, how we foster the environment and share with each other content-focused work to look for similarities/differences?

– Could we center PLCs around various purposes for writing, or my favorite “Journals”? Discuss how and why we use them and share student work to discuss?

– Could I use the PLC time for this “Idea work” and have content knowledge come out more during coaching and hopefully some type of Math Lab as Elham has talked about?

As usual, not many answers and many more questions! Would love thoughts around this so I can work on making it useful and applicable for everyone next year!

-Kristin

Lesson Study: Teaching “Take 2”

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Every week, I read so many wonderfully open and honest math blogs from my tweeps, the majority of them found on this list. The blogs span across grade levels, mathematical content, teacher experience, and more impressively, the world. Whether it is a good, bad or ugly lesson, after reading the blogger’s reflections and colleagues’ comments, I am always left with the feeling that if, given the chance to do that same lesson just one more time, there would be significant improvement. Whether it be the organization of the lesson, management of the materials, questioning of the students, sharing out of responses, the task itself, or any of the other countless components of just one math class period, sometimes we all just need someone to say “Cut” on Take 1 and allow us the opportunity for a Take 2. With multiple math classes a day, we often get the chance to adjust a lesson between class periods, however there is not a second chance on that same exact lesson until the following year, nor a significant amount of time to make dramatic changes. I am not saying that we don’t revisit, learn and improve from that point on, however, how amazing would it be to erase a lesson that didn’t go “quite as planned” from a student’s memory and make it even more meaningful for them on our second take? Wouldn’t it be great to answer all of our “What ifs”?

When selected to participate in the project I blogged about here, I had the idea that it could work as a type of lesson study. Since Alicia and I were both 5th grade teachers working on fractions at the beginning of the year and planning a common task, I thought it would be interesting to see how our work together could go above just collaborating around the lesson development to actually creating a “perfect lesson”…or as close as we could possibly get to it. This lesson study would be unique in the sense that all of our work and observations would have to be virtual due to the distance between us. After all of our planning around the 5 practices, our team of Jody, Chepina, Alicia and her math coach, Jennie, decided that I would teach the lesson first, they would all observe the video (through Teaching Channel Teams), we would look at my student work and from there make adjustments for Alicia’s lesson. Being super critical of my own practice in general, it was fairly simple for me to make suggestions for improvement.:)

THE TASK: Part 1: The 5th graders want to raise money for their overnight camping trip by selling cornbread during the school district Chili Cook-Off contest. All of the cornbread pans are square. The first customer, Mrs. Farmer, wants to buy 1/4 of a pan of cornbread that is 1/3 full. What fraction of the whole pan does she want to buy? Part 2: The next customer is the elementary school principal. He wants to buy 5/6 of a pan of cornbread that is 1/2 full. What fraction of the whole pan does he want to buy? Each part also had a part b asking if the pan costs $12, how much would they pay for their piece.

MATHEMATICAL GOAL: Students will develop mathematical generalizations connecting previous understandings of whole number multiplication to multiplication with fractions. (Relational understandings)

Just some of my 5 Practices planning for the task:

With that little bit of background, here is a look into the lesson and the adjustments we made to improve…

My Class: I opened the lesson with a multiplication Number Talk. It was our hope that through the progression of problems, the area model would arise to allow for connections to our task, however in a classic case of anticipating gone bad, there was no area model to be found that day. Great thinking around the multiplication, so I wasn’t disappointed in that, but no array.

Alicia’s Class: After collaborating around the video and my reflection, we decided to start with a number talk on fraction of a whole number. Both of our classes have been working on that and thought it may put students in more of a “fraction mindset” of taking a part of something before beginning the task. We designed the progression: 1/2 of 16, 1/4 of 16, 1/8 of 16, 3/8 of 16 in hopes of pulling out thoughts such as: dividing by 2 is the same as taking half (and 4 for the fourth), a half of a half is a fourth (and the same reasoning for the 1/4 and 1/8), as well as big ideas around equivalence and decomposition. Perfect change.The students shared all of the ideas we wanted to bring out, even as far as pushing the decomposition of 3/8 from 1/8+1/8+1/8 to 3 x 1/8. Not in that exact notation but as 1/8 of 16 = 2, so 3 x 2 = 6.The only thing I wish I had seen (simply because I love when students make connections to previous problems in a NT progression) is 1/4+1/8= 3/8, so 4+2= 6.

Timing was great and the lesson was improving already…..

My Class: As I read the problem aloud and used some listening techniques I learned from @maxmathforum, students had individual think time and moved into working in a group. The first thing I noticed in my students who struggled with entry into the problem was the wording of the problem itself, “1/4 of a pan 1/3 full” muddled the whole and was confusing for them. Also, and I have mixed feelings about this, but the first part allowed for students to get the correct answer by subtracting 1/3 – 1/4 to arrive at 1/12. This is not something we had even thought about. I love the conversation that arises from this, especially because it will not work in the second part, however I thought maybe it did lead us astray from our goal for the lesson.

Alicia’s Class: Alicia launched the lesson with an actual pan of cornbread to show the class, most impressively homemade:) It gave the students a nice visual for their models/representations and I think offered access to those without entry. We changed the wording of the task so her task read, “Mrs. Farmer, walks up to buy cornbread and the pan is 1/4 full. She wants to buy 1/3 of the remaining cornbread. What fraction of the whole pan does she want to buy?” and the same type of wording changes for the second part. We also changed the order of the fractions in the first part so subtraction would not happen them upon the correct answer and in this case be an unreasonable answer of – 1/12. Having not anticipated subtraction, which seems SO obvious now…duh, it was nice to be aware that it may show up in her class and adjust accordingly. Again, I love that conversation of why it is not subtraction and will definitely revisit, but for the sake of our goal, this was much improved.

After part 1, we planned to do a quick share of strategies.

My Class: During the share, I selected and sequenced three papers. My initial thought was to share two correct representations and one with a sticking point I noticed showing up on numerous papers. I chose two students to share who had the array correct, but cut a bit differently and then a subtraction student with two separate pans drawn (one with 1/3 and one with 1/4). My hope was to draw out, from the class, that we were just dealing with one pan and get them thinking about if that made sense. However, the share went longer than anticipated so I decided to leave that out there for them to think about and move around to my few who were sticking with subtraction individually with some strategic questions about the whole.

Alicia’s Class: After seeing the lengthy share in my video, we decided to have Alicia choose three students,with correct representations and different labeling/cutting, with the third being a student who is having some numeric notation around where he/she is seeing multiplication. Alicia’s final sharer ended with his representation and numeric notation showing that he multiplied the numerators and denominators to get the answer. He ended his share wonderfully by saying you not taking 1/3 of the whole you are only taking 1/3 of the 1/4. After talking to Alicia and Jennie afterwards, this student has had some outside experience with multiplying fractions in terms of the algorithm, however struggled a bit to connect it to the why. It was nice to have him share and explain his representation.

Now both classes ventured into part 2 of the task.

My Class: I actually enjoyed this part of my lesson, and was excited to see many of my students up and using the fraction bars to create proofs for their tablemates. The biggest obstacle in my class seemed to be naming the piece. I found that after working through the first part and seeing the share, students were more comfortable with what was happening in the problem and could shade the piece the principal was getting. Many were saying the answer was 5/6, 10/12 or 5 pieces. All correct answers, but that fraction of what whole or 5 pieces the size of what? They had great discussion (even a bit of a heated argument between friends) about whether the answer was 5 or 5/6. I love that they left for lunch still arguing about it…nerdy fabulousness. I did my share with students whose representations were a progression of a student who cut the whole pan into twelfths, another who was just half cut but visualized the other twelve and one who solved it backwards at first, 1/2 of 5/6 and their partner explained it to them and redid it. I thought it was a beautiful picture of the commutative property, that even though the order doesn’t matter in the solution, the picture changes.

Alicia’s Class: I felt this part was very similar between the two classes. Her share was nice (and I wish I had done it) because she brought up one of her students who had it wrong to start and was brave enough to get up and say what she tried that didn’t work and then what worked for her the second time after talking with her group. It was beautiful and connected a lot of learners who tried it the same way the first time. She opened it up to the class for a few comments/questions after each sharer. The students were very nice in giving positive feedback as to how easy to understand the representation was and stressed that the labeling made a big difference.

I am thinking it would help in share outs to focus the students more on what we want them to be noticing, as my buddy @maxmathforum says often. For example, since our goal was to bring out the connection to multiplication, tell students that as others are sharing, be looking at their representation and for the operations they used and why they are using them to get their answer. I would love for it to explicitly come out WHY the numerators and denominators are multiplying and the connection between dividing into 6 parts is the same as multiplying by 1/6. Students did say those things but more in a vague-only-the-teacher-picks-up-on-it kind of way, but I think if we focused their thinking, it may come out more.

The ending (If you are still reading at this point, that is dedication)….

My Class: Through our group planning, we decided to end with a journal entry/exit ticket asking students to think about where they saw multiplication in the work they did. We thought bringing their attention back to their work, having multiplication in mind, would push students to think about many ideas such as taking a part of a part results in a smaller answer, the order of the fractions resulted in the same answer and the denominators multiply because you have to think in terms of the whole. So…I did not really get the results we were looking for. Don’t get me wrong, I had some wonderful responses I used to guide my instruction, however many left me with no idea of what they were thinking about the fraction of a fraction work. This was mainly because of part b in each question asking students about cost. They ALL saw multiplying there…you have 5 pieces, each is $1 so 5 x $1 = $5. That really didn’t help me as a piece of formative assessment work. Here are some of the ones more along the line of matching our goal that we used in adjusting for Alicia’s lesson: (sorry about the lightness, my copier at school obviously has some issues)

Alicia’s Class: After reviewing my student work, we decided for Alicia to use a ticket that had a new problem, 3/5 of a pan 1/2 full, followed by the question about multiplication noticings based only on the first parts of each question and the ticket. MUCH better read of what the students understood. Even if they could not see multiplication, students were able to represent the problem and come to a solution. It was more informative in terms of where to start building with that students and where they were in terms of our mathematical goal. It was interesting to find, in reviewing her tickets, that students she and Jennie thought “had it” during the lesson could not do it independently on the exit pass. We went back to their work for the day and they did seem to have the correct work and responses, however how much of that was table work?

That got me thinking how it would be nice to know what student writing was done during individual think time before the group work started. I think next group task, I will have different-colored colored pencils on the table…one color for individual time and then switch colors for group work. Then I may be able to better see a student’s thinking.

My Reflection on the Process: Throughout this entire process, I found myself saying “we did…” and “our lesson…” A LOT. It became not just my lesson that I was planning for my students, or a lesson I was observing to give feedback, but instead a wonderful collaboration in which the entire goal was to make it the best possible learning experience for the students. In planning the initial lesson, there were things that didn’t go as we thought, things we hadn’t anticipated would happen, and connections that we thought would clearly come about, that didn’t. The fantastic part is, we got a Take 2. We had the chance to talk through why things didn’t work and how we can improve for the next take. After a lesson, I am typically left wondering, “What if I had done…,” and although it was not taught again with my students, I got to see that “What ifs” play out…and it was so much better!

I am a HUGE fan of coaching to improve teacher practice and this type of lesson study took it to a whole new level for me. How wonderful would it be to see the lesson I am going to teach play out before I really have to teach it? I am really thinking hard about how this could work in a school or district. The platform of Teaching Channel Teams was invaluable in this process and I think would be an integral component in making this work….

The End….well, of just this piece….MUCH more to come,

Kristin

Collaborating and Learning Coast-to-Coast

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At the end of August, I was fortunate to be selected to participate in a project through Illustrative Math, Smarter Balanced, and the Teaching Channel focusing on the fraction learning progression of students in grades 3 – 5. We are working on creating,piloting, and revising both instructional and assessment tasks that will live on the both the Illustrative and SB digital libraries. Video of this work in action will also be captured by, and live on, the Teaching Channel website. Our team is a unique mix of educators from coast to coast. Jody (IM Project Lead & Orange County Math Supervisor), Chepina (Math methods professor from KSU), Alicia (5th grade teacher from Washington state), Jennie (Alicia’s math coach) and me…5th grade teacher on the opposite side of the country! Aside from this immediate group, we have many others at both Illustrative and SB offering guidance and feedback along our way.

The first phase of this work was using a multiplication of fraction task as the center of a professional development for Orange County educators as well as the filmed lesson for the Teaching Channel. Due to the distance between us, Google immediately became our best friend! We shared documents and created our presentation in the Drive, shared thoughts and ideas through Gmail, and had many Google Hang Outs to collaborate and meet each other virtually! It was so exciting to be working together on something we all feel so passionate about…student learning around mathematics. We worked through the task together, thought about the 5 Practices in planning the lesson and designed a type of lesson study around our work.

After the PD planning was almost complete, I did the instructional task with my students, filmed the lesson, and uploaded it to Teaching Channel Teams (if you haven’t checked this resource out, I think it is an amazing opportunity for groups to collaborate around video). All of the team members viewed the lesson, made comments, and offered suggestions to improve the lesson when Alicia teaches it in the upcoming week. As an aside, the channel allows for time stamping on the video comments so you can jump right to the point of the comment, great stuff. We planned the afternoon of our PD day around this task and used work samples and video of my students to help build deeper teacher understandings around how students reason about fractions.

Planning complete, and I am off to Orange County after my half day last Friday! After a long 6 hour flight and a nearly missed connection, I arrived at the John Wayne Airport 3 hours earlier than the time my body was saying it was! That evening I got to “meet” Jody and Chepina for the first time….but not really! Google had made it feel like I already knew them! I met up with Alicia and Jennie the following day and we had such an amazing PD day. Who doesn’t love teachers who come to a professional development on a Saturday?!? We had such an interesting group of college professors, CGI reps, public and charter school teachers, and a Smarter Balanced representative. We looked at coherence of the standards along the grade levels, read the fraction progression document, did some math as learners, and reflected on that same math as educators. The math conversations were amazing and the personal ah-has in terms of fraction work, happened at every turn! I even met a new math tweep (@edtechbydarin – 5th grade math teacher) and coerced Jody to hop back on to check out Twitter (@jody_guarino)! Follow them both, they are great!

Next week, I will be heading out to Seattle to see Alicia teach the same lesson I taught and that we revised together. Jennie will be in the room coaching during the lesson and then we all film for the Teaching Channel on our collaboration and reflections on student work. I cannot wait to see how Alicia’s students do with the new and improved lesson. We changed up the number talk and adjusted the wording of the task. I will post pics and update with the task and some sample student work soon! Here is just a glimpse at some of my student work that guided our conversations about the lesson…