Category Archives: Professional Development

Explicit Planning vs Explicit Teaching

Planning is like…..

How would you finish that sentence?

As a facilitator, I use this sentence starter to open Illustrative Mathematics’ 5 Practices Professional Learning. To be completely honest, when I designed the PD I was a little hesitant of using it because I was nervous it was opening a can of worms within the first 5 minutes of the day.  I am, however, always surprised with all of the beautiful analogies participants share and feel challenged each time to come up with something new and better than the one I used in previous sessions. When I first delivered this PD, I started with analogies like a marathon or really hard workout – something that is exhausting, a lot of work, but ends with something I take pride in. While these analogies were accurate representations of how hard I think lesson planning truly is, I was continually unhappy with where students’ ideas fit into my analogy.

My most recent sentence was this…

Planning is like putting together a puzzle. 

When sharing my reasoning with participants for the first time, I included a lot of beautiful words around mathematical connections but in the middle somewhere I used the phrase “making connections explicit” in relation to the puzzle pieces and saw an immediate reaction from a few people in the room. Of course, I had to pause and ask, “Was it the word explicit?” – answered by many nods in the room.

For a long time, the word explicit in relation to teaching held a negative, cringe-worthy connotation for me as well. If ever asked to paint a picture of what explicit teaching looks like in the math classroom, I would describe scenarios in which a teacher is either at the board telling students how to solve a problem or showing a struggling student how to solve a problem because they are stuck or “taking the long way there.” To me, being explicit meant telling students a way to do something in math class – typically in the form of a procedure.

Through teaching a problem-based curriculum [Investigations], designing and implementing math routines such as number talks, and reading Principles to Actions5 Practices and Intentional Talk , I realized that I was guilty of making mathematical ideas explicit every day in my classroom, but not in the way that made me cringe.

I was explicitly planning, not explicitly teaching.

To me, those two phrases indicate a big difference in how I think about structuring a lesson. I have found when teaching a problem-based curriculum, it is easy for ideas to be left hanging and important connections missed, forcing me to explicitly teach an idea to ensure students “get it” before they leave the class period without any understanding of the mathematical goal for the day. Many days, I would find myself frustrated because students would completely miss the point of the lesson, however now I realize this was because I was expecting them to read my mind of what I wanted them to take away from the problem. On the flip side of that coin, however, not teaching a problem-based curriculum and explicitly teaching students how to do the math in each lesson is not an option (and is a topic that could be its own blogpost).

This is exactly why I find the 5 Practices framework invaluable in planning. The framework forces me to continuously think about the mathematical goal, choose an activity that supports that goal, plan questions for students toward the goal, and sequence student work in a way that creates a productive, purposeful discussion toward an explicit mathematical idea. I have learned so much using this framework over and over again in planning for my 5th grade class, collaborating with other teachers and coaching teachers across different grade levels.

Explicit planning is how I would describe the new, open education resource (OER) by Illustrative Mathematics. As a part of the writing team, I explicitly planned warm-ups such as number talks and notice and wonder activities to elicit specific mathematical ideas that play a purposeful role in the coherent plan of the lesson and unit. But not only are the warm-ups explicitly planned, but each lesson and unit tells a mathematical story in which students arrive at a specific mathematical landing point. While they may not all arrive at that landing in the same way, the problems and discussions are structured to ensure students do not leave the work of the day without any idea of what they were working toward.

While I would love to think my blog posts paint a clear picture of explicit planning, I am not that naive. So, what does explicit planning look like in a 5 Practices Framework?

This lesson from Grade 7, Unit 2, Lesson 2 from Illustrative Mathematics’ Middle School Curriculum is one of many in the curriculum. (All images are screenshots from the online curriculum that is linked at the bottom of the post)

Practice 0: Choosing a Mathematical Goal and Appropriate Task

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Lesson Learning Goals

With the goals in mind, the lesson begins with a notice and wonder warm-up that engages students in thinking about tables, followed by two activities that build on those ideas and support the mathematical goals. While both activities demonstrate explicit planning, I am focusing on one for the sake of space.

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Task Statement


Practice 1 and 2: Anticipating & Monitoring

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Activity Narrative


Practice 3 & 4: Selecting & Sequencing

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Activity Synthesis


Practice 5: Connecting

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Activity Synthesis


So..Planning is like putting together a puzzle. It is hard, takes time, and is sometimes difficult to figure out where to start. We know all of the pieces connect in the end, but making a plan for all of those pieces to connect takes an understanding of the final picture – the goal. There will be missteps along the way and some parts will take longer than others, but we know it is important to carefully connect each piece to another as one missing piece will leave unconnected ideas and the final picture unfinished. As you work alone, the way the pieces connect to form the final picture may not always be obvious, but as others help us see the pieces in different ways during the process, connections become explicitly clear and the final picture is something in which you can take a lot of pride.

The ‘others’ in my teaching journey have helped me see a difference between explicit teaching and explicit planning. Through explicit planning I have seen the importance in understanding the mathematical goal in a way that enables me to structure activities and lessons that enable students to make important mathematical connections through their own work and discussions. It is so exciting to see IM’s curriculum be a model for how I think about explicit planning in such a coherent, purposeful progression.

Link to Illustrative Mathematics 6-8 Math Curriculum.

Link to the 7th Grade lesson featured in this post.

Asking Better Questions

I am sure we have all seen it at one time or another – those math questions that make us cringe, furrow our brow, or just plain confuse us because we can’t figure out what is even being asked. Sadly, these questions are in math programs more often than they should be and even though they may completely suck, they do give us, as educators, the opportunity to have conversations about ways we could adapt them to better learn what students truly know. These conversations happen all of the time on Twitter and I really appreciate talking through why the questions are so bad because it pushes me to have a more critical lens of the questions I ask students. Through all of these conversations, I try to lead my thinking with three questions:

  • What is the purpose of the question?
  • What does the question tell students about the math?
  • What would I learn about student thinking if they answered correctly? Incorrectly?

Andrew posted this question from a math program the other day on Twitter….

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I tried to answer my three questions…

  • What is the purpose of the question? I am not sure. Are they defining “name” as an expression? Are they defining “name” as the word? What is considered a correct answer here?
  • What does the question tell students about the math? Math is about trying to interpret what a question is asking and/or trick me because “name” could mean many things and depending on what it means, some of these answers look right. 
  • What would I learn about student thinking if they answered correctly? Incorrectly? Correctly? I am not sure I even know what that is because I don’t know what “name” means in this case. Is it a particular way the program has defined it?

On Twitter, this is the conversation that ensued, including this picture from, what I assume to be, the same math program:
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When a program gives problems like this, we not only miss out on learning what students know because they get lost trying to navigate the wording, but we also miss out on all of the great things we may not learn about their thinking. For example, even if they got the problem correct, what else might they know that we never heard?

The great thing is, when problems like this are in our math program, we don’t have to give them to students as is. We have control of the problems we put in front of students and can adapt them in ways that can be SO much better. These adaptations can open up what we learn about student thinking and change the way students view mathematics.

For example, if I want to know what students know about 12, I would just ask them. I would have them write in their journal for a few minutes individually so I had a picture of what each student knew and then would share as a class to give them the opportunity to ask one another questions.

After I saw those the problem posted on Twitter, I emailed the 2nd grade teachers in my building and asked them to give their students the following prompt:

Tell me everything you know about 12. 

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Ms. Thompson’s Class

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Mrs. Leach’s Class


Mrs. Levin’s Class

Look at all of the things we miss out on when we give worksheets from math programs like the one Andrew posted. I do believe having a program helps with coherence, but also believe it is up to us to use good professional judgement when we give worksheets like that to students. While it doesn’t help us learn much about their thinking it also sends a sad message of what learning mathematics is.

I encourage and appreciate conversations around problems like the one Andrew posted. I think, wonder, and reflect a lot about these problems. To me, adapting them is fun…I mean who doesn’t want to make learning experiences better for students?

Looking for more like this? I did this similar lesson with a Kindergarten teacher a few years ago. Every time I learn so much and they are so excited to share what they know!

Number Talk Karaoke

It is always so fun when I have the chance to hang out with my #MTBoS friends in person! This summer Max was in town, so I not only got to have lunch with him but also meet his amazing wife and puppy!  Of course, during lunch, we chatted a lot about the math work we are doing with teachers and some of the routines we are finding really valuable in their classrooms. From these two topics of conversation, Number Talk Karaoke emerged.

We both agreed that while Number Talks are invaluable in a classroom, it can be challenging to teach teachers how to use them in the classrooms. As much as we could model Number Talks during PD and show videos of them in action, it is still not the same as a teacher experiencing it for themselves in their classroom with their students. There is so much to be said for practicing all of the components that are so important during the facilitation with your own students.

That conversation then turned into two questions:  What are these important components? and How do we support teachers in these areas?  We discussed the fact that there are many books on mathematical talk in the classroom to support the work of Number Talk implementation, however the recording of student explanations during a Number Talk is often left to chance. What an important thing to leave to chance when students often write mathematics based on what they see modeled. We brainstormed ways teachers could practice this recording piece together, in a professional development setting, where students were not available.

Enter Number Talk Karaoke.

During Number Talk Karaoke, the facilitator:

  • Plays an audio recording of students during a Number Talk.
  • Asks teachers to record students’ reasoning based solely on what they hear students saying.
  • Pair up teachers to compare their recordings.
  • Ask teacher to discuss important choices they made in their recording during the Number Talk.

Max and I decided to get a recording and try it out for ourselves. So, the next week, I found two of the 3rd grade teachers in my building who were willing to give it a go!

They wanted to try out the recording piece themselves, so they asked me to facilitate the Number Talk. They sat in the back of the room, with their backs to the students and SMARTBoard so they could not see what was happening. All they had in front of them was a paper with the string of problems on it.

Before seeing our recording sheets below, try it out for yourself. In this audio clip of the Number Talk, you will hear two students explain how they solved the first problem, 35+35. The first student explains how he got 70 and the second student explains how he got 80.

Think about:

  • What do you think was really important in your recording?
  • What choices did you have to make?
  • What question(s) would you ask the second student based on what you heard?

The talk went on with three more problems that led to many more recording decisions than the ones made in just those two students, but I imagine you get the point. I have to say, when I was facilitating, I tried to be really clear in my questioning knowing that two others were trying to capture what was being said. That makes me wonder how this activity could be branched out into questioning as well!

Here was my recording on the SMARTBoard with the students:

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Here are the recordings from the two teachers in the back of the room:



We sat and chatted about the choices we made, what to record and how to record certain things. We also began to wonder how much our school/district-based Number Talk PD impacted the way we record in similar ways.

Doesn’t this seem like a lot of fun?!? It can be done in person like mine was, or take the audio and try it with a room of teachers, like Max did! <– I am waiting on his blog for this:) Keep us posted, we would love to hear what people do with this!


Establishing a Culture of Learning …The First Hour

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.

Establishing a Culture of Learning

Establishing a Culture of Learning (2)

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.

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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…

Establishing a Culture of Learning (5)

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.

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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!

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Establishing a Culture of Learning (10)

Establishing a Culture of Learning (9)

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!


My Questions Around Professional Development w/Video

When I read this blog post by Grace, and the comments that followed, I noticed some things…

1 -The wonderfully open, honest way in which Grace put herself out there and responded to each of the comments.

2 – The amount of incredibly thoughtful and thought-provoking comments.

3 – The community desire to have more of these videos for us to have discussions around.

4 – I reflect and learn so much through these interactions.

*At this point of reading, If you do not already follow Grace’s blog, you must do that ASAP*

My noticings led me to these questions around the types of video we, as a math community, would like to have available for either individual or group professional learning experience:

1 – What time range do you prefer when watching an classroom video clip? Is it different in a professional developmet setting vs at home?

2 – Do you like an open Notice/Wonder format when watching/discussing a video or prefer having a “focus question” when watching/discussing?

3 – What focus questions would be most helpful for you to either think about or discuss after watching a video?

4 – What makes you want to comment on a video or blog after watching/reading?

5 – What makes you NOT comment on a video or blog after watching/reading?

If you have any thoughts, answers, or suggestions to any of these questions, I would love your thoughts here: Google Form

Thanks so much!


#ISTE2014 Reflection

This was my first ISTE conference so I was first completely impressed with the sheer number of attendees and organization of such a massive conference. Throw in the number of passionate educators present and it makes for an unbelievable and somewhat overwhelming experience. I wanted to jot down some of my overall impressions, takeaways, and random thoughts before summer work kicks in and I forget everything by the time school starts! I looked at the conference from two perspectives, first as a classroom teacher and then as a person responsible for the math professional development in our district.

As a teacher…

1 – I loved, loved, loved the number of educators on Twitter. The #ISTE2014 hashtag was blowing my phone up every minute of every day during the conference.  The amount of multitasking going on everywhere was amazing! I have never seen so many people engaging in technology, learning, spreading the word to others, and walking at the same time 🙂 I felt connected to the many sessions I could not attend or that closed before it even started due to capacity (that was a bit frustrating at times). It truly demonstrated the need to be a connected educator and the value of networking with colleagues around the world.

2 – I was excited to see the focus of my sessions more about the student learning than the technology in and of itself. The tweets reflected the same emotion and I loved that!

3 – I got SOO many exciting ideas to use for Open House, management, and  parent communication ( Thanks to Erin Klein:)  however I do find I struggled just a bit to relate some of my tech learnings into my math classroom. I am not one to use technology for the sake of using it and my classroom thrives on student discourse. I LOVE to hear the students talking about the math with each other and I am not a “flipping” fan. Don’t get me wrong I love to use Educreations, Minecraft, Aurasma,  Nearpod, and Padlet on the ipads, but even then, I need to improve upon using them to make the math more authentic for the students. The presenters at ISTE definitely provided the inspiration and wealth of tools I can look into when doing my planning. Teachers are doing AMAZING work out there and it was so inspiring to see that during the Sessions.

4 – As a presenter as well, I loved all of the support in the room! From sound to video, to ISTE representatives, to Apple Distinguished Educators, there were tons of people on hand to make sure it was perfect! Well Done!

5 – The Expo was packed with exhibitors. I was excited to chat with @Schoology as a new LMS for my classroom and for my K-2 teachers, I found a great new product from a company called Osmo ( Check them out! There were many more interesting ones I chatted with,  however after being in heels all day, my feet could not make the trek around to everyone 🙂 One thing I find intriguing at every conference I attend, is I always have to ask myself, do the vendors here convey the mission/vision of the conference organization itself. For example, at NCTM, I find vendors selling programs/products that, in my humble opinion, do not support the Mathematical Practices and vision of what best practice is in the classroom. In the case of ISTE, I saw a vendor with bubble sheet reading software that worked with any document camera (and of course his example was a math sheet…ugh) . Don’t get me wrong, it was amazing how fast it could read the bubbles and plop a grade into their accompanying grading system, but is that truly what we see as a vendor who should be at an educational conference? Just like at NCTM, do we want a timed test program to be supported by an organization who’s vision is to “…ensure equitable mathematics learning of the highest quality for all students…” I always just find that interesting.

6 – I had the opportunity to participate in a live #satchat. It was such an amazing opportunity to meet face to face with all of the avatars I chat with on many Saturday mornings! Definitely a highlight!!

From a professional development standpoint….

I was absolutely blown away by the organization and setup of ISTE. There was something for everyone and more! There were workshops, IGNITE sessions, lecture sessions (with some recorded so attendees could watch from the tv in the hallway in case of overflow), Playgrounds where teachers were encouraged to play with the technology and experience what it was like to be a student, and Poster Sessions which I can best describe as an overwhelmingly exciting “science fair” with tables set up and manned by teachers and students describing the exciting work being done in classrooms around the world!

The format of each element was genius and definitely something I want to bring back and use in my school/district. I think starting our opening district meeting with and IGNITE session showcasing district happenings would be an amazing, invigorating way to launch the school year. I also love the feel of a Playground in which teachers just play with the math and can choose the topic that best fits their needs. A district/school hashtag where we can easily share resources and ask questions would be amazing…now to just get everyone on Twitter:).

Overall it was a great experience and I still continue to learn on the #ISTE2014 hashtag! It is full of passionate educators focusing on learning, not simply the technology. Thank you all for a wonderful conference! Looking forward to Philly 2015!

To PD or Not PD..That Is the Question

The past two years as Math Specialist, I was in a position in which I was continually planning and attending Professional Development on a regular basis. I am a learner, so I frequently got frustrated and a bit upset when teachers complained about attending the PD. I would hear such things as, “I need time to grade my papers” or “Sub plans are such a pain to write.” How could they not love these learning experiences as much as me?

Fast forward to this year, I am back into the classroom, and I completely feel their frustrations. I have papers that need to be graded, I despise sub plans, and most importantly, l have lesson plans that I need time to think about & dig deeper into. Time, as always, is a high commodity. So, as I was in my classroom Thursday evening, writing sub plans (or more accurately procrastinating by finding anything in my classroom that needed to be done BESIDES writing the plans) I found myself thinking that it would be so much easier to not attend the PD (it was by choice I was going) and just stay in the classroom on Friday. No sub plans, and I would have my planning time to get the paper grading and lesson planning done.

This was it, this is the point where teachers (me included) need to step out of their immediate surroundings, look at the bigger picture, and ask themselves the following questions….

1. How can I continue to improve student learning in my classroom if I don’t dig deeper into my content area(s)?

2. How can I grow as an educator alone?

3. How can reflecting on my own teaching with others improve my classroom experiences?

4. How can what I know about teaching help others in my network?

5. There is always SO much more to learn. Not a question, I know, but it is my driving force as an educator.

And….How great is it to have breakfast and lunch made for me and I can use the bathroom anytime I want 🙂

Needless to say, I always try to attend professional development when offered the opportunity and after leaving my PD on Friday I just found myself smiling. I love talking to others with the same passion for mathematics and teaching as myself. I learn so much and just flat out have fun while talking about impactful issues in education. We all want what is best for our students and staff and work together to make great things happen.

Don’t get me wrong, I am picky when choosing my PD. It must be relevant. I have sat in a mandatory PD or two (hundred) that have not been what I needed, but I try to find at least one thing I can take away. Even through the bad experiences, I grow. If a presenter is not engaging, I think about what I can do when I facilitate to be engaging. If the content is confusing, I think about how I can clarify things when I facilitate a professional development. I don’t let one bad experience kill all professional development opportunities for me. They are independent variables, like a die. One roll does not impact the next. One bad professional development does not impact the next one.

In the end, I owe it to my students to go. If I am learning more, they will be learning more.

Happy Saturday,