Category Archives: Professional Development Feedback

#NCTMLive #T3Learns Webinar: Establish Mathematics Goals to Focus Learning, and Elicit and Use Evidence of Student Thinking.

On Wednesday, March 28, 2018, Jennifer Wilson (@jwilson828) and I co-facilitated the first webinar in a four-part series on the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All.
Establish Mathematics Goals to Focus Learning, and
Elicit and Use Evidence of Student Thinking.

Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

  • How might we communicate with clarity to ensure that learners are focused on high quality mathematical goals?
  • What types of tasks provide opportunities for learners to notice, note, wonder, and take action as agents of their own learning?
Our slide deck:
7:00 Opening remarks

  • Share your name and grade level(s) or course(s).
  • Norm setting and Purpose
7:05 Establish mathematics goals to focus learning #LL2LU

7:10 Let’s Do Some Math:  Illustrative Math – Fruit Salad?

7:25 Quotes from Taking Action
7:30 Elicit and use evidence of student thinking #LL2LU

7:35 Let’s Do Some Math

7:45 Elicit and use student thinking – Social-Emotional
Talking Points – Elizabeth Statmore

7:55 Close and preview next webinar in the series.

Implement tasks that promote reasoning and problem solving, and use and connect mathematical representations.

Some reflections from the chat window:
  • I learned to pay attention to how my students may first solve the problem or think about it prior to me teaching it to try and see connections that are made or how I can meet them. ~C Heikkila
  • I learned how to pay attention to how I introduce tasks to students. Sometimes I place limits on their responses by telling them what I expect to see in their responses as it relates to content topics. I will be more mindful about task introduction. ~M Roland
  • I learned to pay more attention to mathematical operations, and to look for more solutions that can satisfy the given problem. ~B Hakmi
  •  I also learned the importance of productive struggle and to be patient with my students. ~M James
  • I’m thinking about how to encourage my teachers to intentionally teach the mathematical practices. ~M Hite
  • I learned to pay attention to the learning progressions so I can think of the work as a process and journey. ~B Holden
  • A new mathematical connection for me was the idea of graphing values for the product example. ~A Warden
  • I learned to pay attention to peer discussions to discover how well students are learning the concepts. ~M Grech
  • Am I anticipating the roadblocks to learning? ~L Hendry

An audio recording of the webinar and the chat transcript can be viewed at NCTM’s Partnership Series page.

Cross posted at Easing the Hurry Syndrome

#T3IC: Using technology alongside #SlowMath to promote productive struggle

At the 2018 International T³ Conference in San Antonio, Jennifer Wilson (@jwilson828) and I presented the following two hour power session.

Using technology alongside #SlowMath
to promote productive struggle

How might we shift classroom culture so that productive struggle is part of the norm? What if this same culture defines and embraces mistakes as opportunities to learn? One of the Mathematics Teaching Practices from the National Council of Teachers of Mathematics’ (NCTM) “Principles to Actions” is to support productive struggle in learning mathematics. We want all learners to make sense of tasks and persevere in solving them. The tasks we select and facilitate must offer opportunities for each learner to develop connections and deepen their conceptual understanding.

Join us to learn more about #SlowMath opportunities that encourage students to persevere through challenging tasks instead of allowing their struggle become destructive. This session will address:

  • How might we provide #SlowMath opportunities for all students to notice and question?
  • How do activities that provide for visualization and conceptual development of mathematics help students think deeply about mathematical ideas and relationships?

Here’s the agenda:

8:30 Introductions
8:40 Intent and Purpose

  • Principles to Actions
  • #SlowMath
  • Norms (SMPs)
8:45 3-2-1 Bridge Visible Thinking Routine
8:50 Using Structure to Solve a Task – Circle-Square Task

9:55 3-2-1 Bridge Visible Thinking Routine

  • 2 questions around Productive Struggle (share one with partner and listen to one of partner)
10:00 Construct a Viable Argument to make your thinking visible:
Does (x+1)²=x²+1?

10:25 3-2-1 Bridge Visible Thinking Routine

  • In the chat, 1 analogy/metaphor/simile for Productive Struggle
10:30 Close

Here’s my sketch note of our plan:

Dave Johnston (@Johnston_MSMath) recorded his thinking and learning and shared it with us via Twitter.

And, a little more feedback from Twitter:

Cross posted on The Slow Math Movement

#T3IC Leading Learners to Level Up: Deepening Understanding of Mathematical Practices

At the 2018 International T³ Conference in San Antonio, Jennifer Wilson (@jwilson828) and I presented the following 90-minute session. 

Leading Learners to Level Up:
Deepening Understanding of Mathematical Practices

We say: Persevere! Express regularity in repeated reasoning! Be precise! Show your work!… But what if I can’t yet? How might we make our thinking visible to empower our young learners to become self-correcting, self-reliant and independent? How do we coach – what strategies do we use – to help learners to embrace the Common Core State Standards for Mathematical Practice? At the end of this session, participants should be able to say I can provide my learners leveled support on the Standards for Mathematical Practice on their journey towards mathematical proficiency. I can make my thinking visible to motivate learners to ask high quality questions. I can focus on the art of questioning and formative assessment tools to lead learners to level up.

Here’s the plan:

  1. Opening remarks
  2. Council (30 seconds each): Share your name, school and grade level(s) or course(s) with your table; How are you feeling this morning?
8:40 Make Sense of Tasks and Persevere Solving Them (SMP 1)

9:05 Look for & Make Use of Structure (SMP 7)

9:35 Look for & Express Regularity in Repeated Reasoning (SMP 8)

9:55 Goal setting: Back with my learners … Next steps

Here’s my sketch note of the plan for our session.

Dave Johnston (@Johnston_MSMath) recorded his thinking and learning and shared it with us via Twitter.

#MVIFI Collider session Sketchnoting: Show what you know more than one way

At the February 16th MVIFI Collider event for professional learning, I facilitated the following 50-minute session on sketch noting twice.

Show what you know more than one way

Up your note taking skills by being visual. Learn this invaluable method for recording, showcasing understanding, and deepening comprehension.

We will meet and greet, norm, touch on research, play with words and word art, discuss tools, practice, participate in a feedback look, and close by setting a micro-goal.

Here’s my sketch note of the plan:

We watched Simon Sinek’s TED talk to practice live sketch noting.

Here are artifacts of learning from Twitter:

Committed to learning #EmboldenYourInnerMathematician

The alarm clock goes off. It is only 15 minutes earlier than usual, but still.  Could there be enough coffee to get going this early? From my warm, quiet bed, I wonder if it was a good decision to enroll in a math class that runs from 7:15 to 9:30 am every Wednesday. After wrangling all members of my family through breakfast and our morning routine – because 15 minutes early for me means 15 minutes for everyone at my house – I enjoy the drive to Trinity with slightly less traffic.

Arriving at school, ready to learn at 7:15, a small and dedicated cohort of 14 faculty-learners gathered every Wednesday morning to deeply study, learn, and implement NCTM’s Mathematics Teaching Practices. These eight teaching practices provide a framework for strengthening the teaching and learning of mathematics.

Sounds a little boring, huh? Was it worth it?

“Yes! This class has helped me deepen my learning in math, and then in turn, deepen the way I teach math for my students. I loved being able to take the math we did and applying it in my classroom through number talks, number strings, children’s literature, and mathematical practices. I always was thinking deeply about math as soon as I entered the class at 7:15 because of engaging tasks and conversation with colleagues.” Caroline Tritschler, Kindergarten Teacher

“I enjoyed the opportunity to work on math that was applicable to my grade level, but we also had the chance to see where our students have been and where they are going. I also felt as if this class pushed us to strengthen our own number sense, perseverance, and use of strategies – all of which are qualities we strive to empower in our own learners.” Casey Leonard, 2nd Grade Teacher

“This course was a huge asset in recognizing the connections throughout grade levels. I loved seeing how our calculus work could be translated into finding patterns and connections the same way we do with our most fundamental skills in Pre-K.” Katherine Anderson, Pre-K Teacher

What is worth it? What was learned?

“I learned new ways of solving problems and showing my work, different ways of thinking about a problem, and validation for insisting that students have a full understanding of the “why” behind concepts.” Vicki Eyles, 5th Grade Teacher

“I feel like I really understand the importance of showing your work in more than one way and being able to explain your thinking to others. I better understand the importance of laying a foundation for using manipulatives and drawings that will carry far past an early elementary level.” Mary Catherine Gober, 1st Grade Teacher

“I am more thoughtful about the questions I ask students and I feel like I can give parents more detail about our approach to math instruction. Additionally, I have a deeper understanding of the benefit of talking to others while “doing” math, as well as the importance of showing one’s thinking in more than one way and making connections to others’ work.” Hilary Daigre, 1st Grade Teacher

What was learned? How has it helped Trinity students?

“My students seem surprised that I am in a class, learning more math. I like to share my struggles and successes with them, modeling growth through perseverance and sharing of ideas with other teachers. I have been able to share my experiences with them, using them to encourage their growth as students. Learning with others who have different backgrounds, strengths, and perspective has been powerful.” Vicki Eyles, 5th Grade Teacher

“I have seen tremendous growth in our class as they begin to take a risk in showing their work in multiple ways. Even those that “struggle” are at least willing to take a risk in trying to solve a problem. I believe the work we did in writing learning progressions for a specific topic has really helped the students want to reach for a higher level or at least work towards asking questions to better understand the problem before they go off and try to work through the problem.” Mary Catherine Gober, 1st Grade Teacher

“Our work with multiplication and division was mind-blowing! I LOVED learning the various ways to approach multiplication/division, including using manipulatives and drawing models. It made more sense to me than anything I had learned in the past. I have shared stories about this experience with my class, including how I had to make sense of problems and really think about how I could solve them. I may not have had the most efficient method for a particular problem, but by talking with others and connecting to what they did, I was able to persevere and feel successful.” Hilary Daigre, 1st Grade Teacher

“I have a greater appreciation for the number line, the modeling, and the ability to make connections. I think the work we did impacted my students weekly. The activities we did I was able to either take back to my students or reminded me of other activities that I then used with the 6th graders. The visual patterns and connecting representations (work from Fawn Nguyen) was the most recent example. The 6th graders loved it. I also really enjoyed the math in literature as did the students!” Kristi Story, 6th Grade Teacher

But… was it boring? Would you recommend this experience to your colleagues?

“It was so much fun to be able to work with colleagues across EED and UED. I think my favorite part was mathematizing children’s literature.” Caroline Tritschler, Kindergarten Teacher

“It’s not only a great place to learn and grow in your understanding, but it’s also a great place to get to know your colleagues in a smaller setting. I’ve really enjoyed getting to know teachers that I wouldn’t have otherwise gotten to know. I genuinely looked forward to Wednesdays because of this class.” Chandler Balentine, 4th Grade Teacher

“I think it is both valuable and fun to spend time struggling with math problems which help us understand our students’ perspectives.” Jon Frank, 5th Grade Teacher

“I think the whole faculty (those that teach any grade level math) should embolden their inner mathematician. I think it was good to have a broad range of “comfort levels” in these sessions. We all learned from each other.” Kristi Story, 6th Grade Teacher

Without fail, at 9:30 after all was said and done, the time that was spent learning pedagogy and math, in fun, creative ways advanced teaching and learning at Trinity. Each Wednesday was a long day, and it was an important day for learners individually and collectively.  


PD Planning: #Mathematizing Read Alouds part 2

Time. We need more of it.

How might we gain time without adding minutes to our schedule?

What if we mathematize our read-aloud books to use them in math as well as reading and writing workshop? Could it be that we gain minutes of reading if we use children’s literature to offer context for the mathematics we are learning? Could we add minutes of math if we pause and ask mathematical questions during our literacy block?

Becky Holden and I planned the following professional learning session to build common understanding and language as we expand our knowledge of teaching numeracy through literature.  Every Kindergarten, 1st Grade, 2nd Grade, and 3rd Grade math teacher participated in 3.5-hours of professional learning over the course of two days.

Have you read How Many Seeds in a Pumpkin? by Margaret McNamara, G. Brian Karas?

Learning Targets:

Mathematical Practice:

  • I can make sense of tasks and persevere in solving them.

2nd Grade

  • I can work with equal groups of objects to gain foundations for multiplication.
  • I can skip-count by 2s, 5, 10s, and 100s within 1000 to strengthen my understanding of place value.

3rd Grade

  • I can represent and solve problems involving multiplication and division.
  • I can use place value understanding and properties of operations to perform multi-digit arithmetic.

Learning Progressions:

I can apply mathematical flexibility.
#ShowYourWork Algebra

Here’s what it looked like:

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Here’s some of what the teacher-learners said:

I learned to look at books with a new critical eye for both literacy and mathematical lessons. I learned that I can read the same book more than once to delve deeper into different skills. This is what we are learning in Workshop as well. Using a mentor text for different skills is such a great way to integrate learning.

I learned how to better integrate math with other subjects as well as push pass the on answer and look for more than one way to answer the question as well as show in more than one way how I got that answer and to take that to the classroom for my students.

I learned how to integrate literacy practice and math practice at once. In addition, I also learned how to deepen learning and ask higher thinking questions, as well as how to let students answer their own questions and have productive struggle.

I learned that there are many different ways to notice mathematical concepts throughout books. It took a second read through for me to see the richness in the math concepts that could be taught.

I learned that there are many children’s literature that writes about multiple mathematical skills and in a very interesting way!

How might we notice and note opportunities to pause, wonder, and question? What is to be gained by blending learning?

2015 in review

Learning needs feedback and reflection.

The stats helper monkeys have been busy putting together a personalized report detailing how Experiments in Learning by Doing did in 2015. Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 37,000 times in 2015. If it were a concert at Sydney Opera House, it would take about 14 sold-out performances for that many people to see it.

The busiest day of the year was November 17th with 1,508 views. The most popular post that day was Fluency: comprehension, accuracy, flexibility, and efficiency.

Click here to see the complete report.

How might we learn and grow from feedback, data, and patterns?

Enhancing Growth Mindset in Math – Learning together

We asked:

How might we, as a community of learners, grow in our knowledge and understanding to enhance the growth mindset of each of our young learners?

As a team, we have completed Jo Boaler’s How to Learn Math: For Students and have shared our thinking, understanding, and learning.

Blending online and face-to-face learning, we worked through the Stanford units outside of school so that we could explore and learn more when together.

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Here are some of the reflections shared by our team.

As a teacher my goal is to help children approach math and all subject areas with a growth mindset. It is of utmost importance that my students truly know that I believe in them and their ability to succeed!

Everyone my age should know that you should never equate being good at math with speed. Just because someone is a slower problem solver does not mean that they are a weak math student. Rather, sometimes the slower math thinkers are the strongest math thinkers because they are thinking about the problem on a deeper level. Being good at math is about being able to think deeply about the problem and making connections with it.

When talking to yourself about your work and learning new things, reminding yourself that you can try harder and improve is critical to potential success.  People are more willing to persevere through difficult tasks (and moments in life) when they engage in positive self talk.  

Mistakes and struggling, in life and in math, are the keys to learning, brain growth, and success.

Thinking slowly and deeply about math and new ideas is good and advantageous to your learning and growth.

Taking the time to think deeply about math problems is much more important than solving problems quickly.  The best mathematicians are the ones who embrace challenges and maintain a determined attitude when they do not arrive at quick and easy solutions.  

Number flexibility is so powerful for [students]. I love discussing how different students can arrive at the same answer but with multiple strategies. 

Working with others, hearing different strategies, and working strategically through problems with a group helps to look at problems in many different ways.

“I am giving you this feedback because I believe in you.”  As teachers, we always try to convey implicitly that we believe in our students, and that they are valued and loved in our class.  However, that explicit message is extraordinary.  It changes the entire perception of corrections or modifications to an essay–from “This is wrong, you need to make it right” to “I want to help you make this the best it can be,” a message we always intended to convey, but may not have been perceived.  

Good math thinkers think deeply and ask questions rather than speeding through for an answer.

Math is a topic that is filled with connections between big ideas.  Numbers are meant to be manipulated, and answers can be obtained through numerous pathways.  People who practice reasoning, discuss ideas with others, have a growth-mindset, and use positive mathematical strategies (as opposed to memorization) are the most successful.

We learn and share.


Lesson and Assessment Design – #T3Learns

What are we intentional about in our planning, process, and implementation?

  • Are the learning targets clear and explicit?
  • What are important check points and questions to guide the community to know if learning is occurring?
  • Is there a plan for actions needed when we learn we must pivot?

On Saturday, a small cadre of T3 Instructors gathered to learn together, to explore learning progressions, and to dive deeper in understanding of the Standards for Mathematical Practice.

The pitch:

Screen Shot 2014-10-19 at 11.59.57 AM

Jennifer and I fleshed out the essential learning in more detail:

  • I can design lessons anchored in CCSS or NGSS.
    • I can design a lesson incorporating national standards, an interactive TI-Nspire document, a learning progression, and a formative assessment plan.
    • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can design a learning progression for a skill, competency, or process.
    • I can use student-friendly language when writing “I can…” statements.
    • I can design a leveled assessment for students based on a learning progression.
  • I can collaborate with colleagues to design and refine lessons and assessments.
    • I can calibrate learning progressions with CCSS and/or NGSS.
    • I can calibrate learning progressions with colleagues by giving and receiving growth mindset oriented feedback, i.e. I can offer actionable feedback to colleagues using I like… I wonder… what if…
    • I can refine my learning progressions and assessments using feedback from colleagues.

The first morning session offered our friends and colleagues an opportunity to experience a low-floor-high-ceiling task from Jo Boaler combined with a SMP learning progression.  After the break, we transitioned to explore the Standards for Mathematical Practice in community. The afternoon session’s challenge was to redesign a lesson to incorporate the design components experienced in the morning session.

Don’t miss the tweets from this session.

Here are snippets of the feedback:

I came expecting…

  • To learn about good pedagogy and experience in real time examples of the same. To improve my own skills with lesson design and good pedagogy.
  • Actually, I came expecting a great workshop. I was not disappointed. I came expecting that there would be more focus using the TI-Nspire technology (directly). However, the structure and design was like none other…challenging at first…but then stimulating!
  • to learn how to be more deliberate in creating lessons. Both for the students I mentor and for T3 workshops.
  • I came expecting to deepen my knowledge of lesson design and assessment and to be challenged to incorporate more of this type of teaching into my classes.

I have gotten…

  • so much more than I anticipated. I learned how to begin writing clear “I can” statements. I also have been enriched by those around me. Picking the brains of others has always been a win!
  • More than I bargained. The PD was more of an institute. It seemed to have break-out sessions where I could learn through collaboration, participation, and then challenging direct instruction, … and more!
  • a clear mind map of the process involved in designing lessons. A clarification of what learning progressions are. Modeling skills for when I present trainings. Strengthening my understanding of the 8 math practices.
  • a better idea of a learning progression within a single goal. I think I had not really thought about progressions within a single lesson before. Thanks for opening my eyes to applying it to individual lesson goals.

I still need (or want)…

  • To keep practicing to gain a higher level of expertise and comfort with good lesson design. Seeing how seamlessly these high quality practices can be integrated into lessons inspires me to delve into the resources provided and learn more about them. I appreciate the opportunity to stay connected as I continue to learn.
  • days like this where I can collaborate and get feedback on activities that will improve my teaching and delivery of professional development
  • I want to get better at writing the “I can” statements that are specific to a lesson.
  • I want to keep learning about the use of the five practices and formative assessment.

We want to see more collaborative productive struggle, pathways for success, opportunities for self- and formative assessment, productive conversation to learn, and more.

As Jennifer always says … and so the journey continues…

[Cross-posted at Easing the Hurry Syndrome]


Deep Dive into Standards of Mathematical Practice

As a team, we commit to make learning pathways visible. We are working on both horizontal and vertical alignment.  We seek to calibrate our practices with national standards.

On Friday afternoon, we met to take a deep dive into the Standards of Mathematical Practice. Jennifer Wilson joined us to coach, facilitate, and learn. We are grateful for her collaboration, inspiration, and guidance.

The pitch:

Screen Shot 2014-10-19 at 8.25.45 PM

The plan:


  • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can begin to design lessons incorporating national standards, a learning progression, and a formative assessment plan.


  • Safe space
    • I can talk about what I know, and I can talk about what I don’t know.
    • I can be brave, vulnerable, kind, and considerate to myself and others while learning.
  • Celebrate opportunities to learn
    • I can learn from mistakes, and I can celebrate what I thought before and now know.


Learning Plan:

Screen Shot 2014-10-19 at 8.38.36 PM

The learning progressions:

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The slide deck:

As a community of learners, we

Screen Shot 2014-10-19 at 8.50.05 PM Screen Shot 2014-10-19 at 8.50.16 PM